Finite Group Databasebeta

← #11707758

Subgroups — #11707758

Order 768.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3508C211yesmaximal, characteristic, complemented
2#87066C212yesmaximal, complemented
3#87055C212yesmaximal, complemented
4#87051C212yesmaximal, complemented
5#87050C212yesmaximal, complemented
6D3×#550C212yesmaximal, complemented
7#86780C212yesmaximal, complemented
8#86775C212yesmaximal, complemented
9#86770C212yesmaximal, complemented
10#86672C214yesmaximal, complemented
11#86665C214yesmaximal, complemented
12#86649C214yesmaximal, complemented
13#86629C214yesmaximal, complemented
14#86474C218yesmaximal, complemented
15#86336C214yesmaximal, complemented
16#86288C211yesmaximal, characteristic, complemented
17#86278C211yesmaximal, characteristic, complemented
18#86250C212yesmaximal, complemented
19#86241C212yesmaximal, complemented
20#86238C212yesmaximal, complemented
21#86228C212yesmaximal, complemented
22#86195C211yesmaximal, characteristic, complemented
23#86195C211yesmaximal, characteristic, complemented
24#85871C214yesmaximal, complemented
25#85845C211yesmaximal, characteristic, complemented
26#85843C211yesmaximal, characteristic, complemented
27#63014—31nomaximal, Sylow
28C2×#1009C2214yescomplemented
29C2×D3×#41C2214yescomplemented
30C2×#1004C2212yescomplemented
31C2×#1004C2212yescomplemented
32C3×#559C2212yescomplemented
33C3×#559C2212yescomplemented
34C3×#550C2212yescomplemented
35C3×#550C2212yescomplemented
36C3×#546C2214yescomplemented
37C3×#546C2214yescomplemented
38C3×#540C2214yescomplemented
39C3×#535C2212yescomplemented
40C3×#533C2211yescharacteristic, complemented
41C3×#532C2212yescomplemented
42C3×#532C2212yescomplemented
43C2×C3×#127C2211yescharacteristic, complemented
44C3×#518C2212yescomplemented
45C3×C4×#41C2211yescharacteristic, complemented
46#5834C2212yescomplemented
47#5834C2214yescomplemented
48#5834C2214yescomplemented
49#5833C2214yescomplemented
50#5829C2212yescomplemented
51#5829C2214yescomplemented
52#5828C2214yescomplemented
53#5824C2214yescomplemented
54#5805C2212yescomplemented
55#5805C2212yescomplemented
56D4×#67C2214yescomplemented
57D4×#67C2214yescomplemented
58D4×#67C2214yescomplemented
59D4×#67C2214yescomplemented
60#5732C2211yescharacteristic, complemented
61#5727C2211yescharacteristic, complemented
62#5726C2211yescharacteristic, complemented
63#5726C2212yescomplemented
64#5726C2212yescomplemented
65#5721C2211yescharacteristic, complemented
66#5719C2214yescomplemented
67#5718C2212yescomplemented
68#5718C2212yescomplemented
69#5718C2214yescomplemented
70#5718C2212yescomplemented
71#5718C2212yescomplemented
72#5717C2212yescomplemented
73#5717C2212yescomplemented
74#5717C2214yescomplemented
75#5717C2212yescomplemented
76#5717C2212yescomplemented
77#5716C2212yescomplemented
78#5716C2212yescomplemented
79#5715C2214yescomplemented
80#5715C2214yescomplemented
81D3×#127C2212yescomplemented
82D3×#127C2212yescomplemented
83D3×#127C2214yescomplemented
84#5700C2214yescomplemented
85#5693C2214yescomplemented
86#5682C2214yescomplemented
87#5681C2214yescomplemented
88#5680C2214yescomplemented
89#5680C2214yescomplemented
90#5677C2214yescomplemented
91#5676C2214yescomplemented
92#5676C2214yescomplemented
93#5676C2214yescomplemented
94#5676C2214yescomplemented
95#5674C2214yescomplemented
96#5674C2214yescomplemented
97#5668C2214yescomplemented
98#5666C2218yescomplemented
99#5663C2218yescomplemented
100#5662C2218yescomplemented
101#5659C2218yescomplemented
102#5656C2218yescomplemented
103#5655C2218yescomplemented
104#5654C2218yescomplemented
105#5653C2218yescomplemented
106#5641C2212yescomplemented
107#5639C2212yescomplemented
108#5633C2212yescomplemented
109#5631C2212yescomplemented
110#5629C2214yescomplemented
111#5629C2214yescomplemented
112#5621C2218yescomplemented
113#5620C2218yescomplemented
114#5615C2218yescomplemented
115#5614C2214yescomplemented
116#5613C2218yescomplemented
117#5611C2214yescomplemented
118#5610C2218yescomplemented
119#5610C2218yescomplemented
120#5609C2218yescomplemented
121#5609C2214yescomplemented
122#5608C2214yescomplemented
123#5607C2218yescomplemented
124#5607C2214yescomplemented
125#5605C2218yescomplemented
126D3×#121C2214yescomplemented
127D3×#121C2214yescomplemented
128D3×#121C2218yescomplemented
129#5599C2214yescomplemented
130#5599C2218yescomplemented
131#5597C2218yescomplemented
132#5595C2218yescomplemented
133#5592C2218yescomplemented
134#5590C2218yescomplemented
135#5589C2218yescomplemented
136#5585C2211yescharacteristic, complemented
137#5580C2212yescomplemented
138#5580C2212yescomplemented
139#5579C2211yescharacteristic, complemented
140#5579C2212yescomplemented
141#5579C2212yescomplemented
142#5578C2212yescomplemented
143#5577C2212yescomplemented
144#5577C2212yescomplemented
145#5577C2211yescharacteristic, complemented
146C4×#239C2212yescomplemented
147C4×#239C2212yescomplemented
148C4×D3×Q8C2212yescomplemented
149Q8×Dic6C2211yescharacteristic, complemented
150#5565C2212yescomplemented
151#5563C2212yescomplemented
152#5563C2211yescharacteristic, complemented
153#5562C2214yescomplemented
154#5562C2214yescomplemented
155#5560C2218yescomplemented
156#5558C2214yescomplemented
157#5558C2214yescomplemented
158#5554C2214yescomplemented
159#5553C2214yescomplemented
160#5553C2212yescomplemented
161#5553C2211yescharacteristic, complemented
162#5551C2214yescomplemented
163#5550C2212yescomplemented
164#5550C2218yescomplemented
165D4×D12C2214yescomplemented
166D4×D12C2214yescomplemented
167D4×D12C2211yescharacteristic, complemented
168#5548C2214yescomplemented
169#5548C2214yescomplemented
170#5548C2214yescomplemented
171#5548C2212yescomplemented
172#5547C2214yescomplemented
173#5547C2218yescomplemented
174#5546C2214yescomplemented
175#5545C2214yescomplemented
176C4×D3×D4C2214yescomplemented
177C4×D3×D4C2214yescomplemented
178C4×D3×D4C2212yescomplemented
179#5543C2211yescharacteristic, complemented
180#5540C2218yescomplemented
181#5539C2214yescomplemented
182#5535C2214yescomplemented
183#5532C2212yescomplemented
184#5532C2214yescomplemented
185#5530C2212yescomplemented
186#5528C2214yescomplemented
187#5527C2214yescomplemented
188#5494C2218yescomplemented
189#5490C2218yescomplemented
190#5490C2218yescomplemented
191C2×#884C2218yescomplemented
192#5479C2212yescomplemented
193#5477C2211yescharacteristic, complemented
194#5477C2211yescharacteristic, complemented
195#5477C2212yescomplemented
196C4×#235C2211yescharacteristic, complemented
197C4×#235C2211yescharacteristic, complemented
198C4×#235C2212yescomplemented
199C2×C4×D12C2212yescomplemented
200#3548—32no—
201#3548—31no—
202#3546—34no—
203#3546—32no—
204#3543—32no—
205#3543—34no—
206#3542—34no—
207#3542—38no—
208#3522—32no—
209#3519—32no—
210#3519—34no—
211#3517—32no—
212#3508—32no—
213#3508D311yescharacteristic, complemented
214#3498—32no—
215#3498—31no—
216#3498—31no—
217#3496—34no—
218#3496—32no—
219#3488—34no—
220#3483—31no—
221#3482—31no—
222#3481—32no—
223#3481—31no—
224D4×#41—32no—
225C2×#550—32no—
226C2×C3×#41C2314yes—
227C2×C3×#41C2314yes—
228C2×C3×#41C2311yescharacteristic
229C22×C3×D4C2312yes—
230C22×C3×D4C2312yes—
231C22×C3×D4C2312yes—
232C22×#67C2318yes—
233C22×#67C2318yes—
234#1009—416no—
235D3×#41—416no—
236C2×#239C2312yes—
237C2×#239C2314yes—
238C2×#239C2312yes—
239C2×#239C2314yes—
240C2×D3×Q8C2312yes—
241#1004—48no—
242#1004—48no—
243C2×#237C2314yes—
244C2×#237C2314yes—
245C2×#237C2314yes—
246C2×#237C2314yes—
247C2×#237C2318yes—
248C2×D3×D4C2314yes—
249C2×D3×D4C2314yes—
250C2×D3×D4C2314yes—
251C2×D3×D4C2314yes—
252C2×D3×D4C2314yes—
253C2×D3×D4C2314yes—
254C2×D3×D4C2314yes—
255C2×D3×D4C2314yes—
256C2×D3×D4C2318yes—
257C2×D3×D4C2318yes—
258C2×D3×D4C2318yes—
259C2×D3×D4C2312yes—
260C2×#235C2311yescharacteristic
261C2×#235C2311yescharacteristic
262C2×#235C2312yes—
263C2×#235C2318yes—
264C2×#235C2318yes—
265C2×#235C2312yes—
266C2×#235C2312yes—
267C2×#235C2314yes—
268C22×D12C2312yes—
269C22×D12C2318yes—
270C22×C4×D3C2318yes—
271C22×C4×D3C2314yes—
272C3×C4⋊Q8C2311yescharacteristic
273C3×C4⋊Q8C2311yescharacteristic
274C3×#127C2312yes—
275C3×#127C2312yes—
276C3×#127C2314yes—
277C3×#127C2312yes—
278C3×#127C2312yes—
279C3×#125C2312yes—
280C3×#124C2314yes—
281C3×#124C2314yes—
282C3×#124C2314yes—
283C3×#123C2318yes—
284C3×#123C2318yes—
285C3×C22⋊Q8C2312yes—
286C3×C22⋊Q8C2312yes—
287C3×#121C2318yes—
288C3×#121C2314yes—
289C3×#121C2318yes—
290C3×#121C2314yes—
291C3×#121C2314yes—
292C3×#121C2314yes—
293C3×#120C2318yes—
294C3×C4×Q8C2311yescharacteristic
295C3×C4×Q8C2311yescharacteristic
296C3×C4×Q8C2312yes—
297C3×C4×Q8C2312yes—
298C3×C4×D4C2314yes—
299C3×C4×D4C2314yes—
300C3×C4×D4C2314yes—
301C3×C4×D4C2314yes—
302C3×C4×D4C2314yes—
303C3×C4×D4C2311yescharacteristic
304C3×C4×D4C2311yescharacteristic
305C3×C4×D4C2312yes—
306C3×C4×D4C2314yes—
307C3×C4×D4C2312yes—
308C3×#117C2312yes—
309C3×#117C2312yes—
310C3×#117C2311yescharacteristic
311C2×C3×C22⋊C4C2318yes—
312C2×C3×C42C2312yes—
313C2×C3×C42C2311yescharacteristic
314#953C2318yes—
315#953C2318yes—
316#947C2312yes—
317#947C2312yes—
318#946C2312yes—
319#946C2312yes—
320#946C2312yes—
321#946C2314yes—
322#946C2314yes—
323Q8×Dic3C2312yes—
324Q8×Dic3C2312yes—
325Q8×Dic3C2312yes—
326#944C2312yes—
327#940C2314yes—
328#940C2314yes—
329#940C2314yes—
330#940C2314yes—
331#940C2314yes—
332#940C2314yes—
333#940C2312yes—
334#940C2318yes—
335#940C2318yes—
336#940C2314yes—
337#939C2318yes—
338#939C2318yes—
339#939C2318yes—
340#939C2318yes—
341#939C2318yes—
342#939C2318yes—
343#939C2318yes—
344#939C2318yes—
345#939C2314yes—
346#938C2314yes—
347#938C2314yes—
348#938C2314yes—
349#938C2314yes—
350#938C2314yes—
351#938C2314yes—
352#938C2314yes—
353#938C2314yes—
354#938C2312yes—
355#938C2318yes—
356#938C2318yes—
357#938C2314yes—
358#937C2318yes—
359#937C2318yes—
360#937C2318yes—
361#937C2318yes—
362#937C2318yes—
363#937C2318yes—
364#937C2314yes—
365#936C2314yes—
366#936C2314yes—
367#935C2318yes—
368#935C2318yes—
369D4×Dic3C2314yes—
370D4×Dic3C2314yes—
371D4×Dic3C2314yes—
372D4×Dic3C2314yes—
373D4×Dic3C2312yes—
374#930C2318yes—
375#930C2318yes—
376#930C2318yes—
377#930C2312yes—
378#930C2312yes—
379#930C2314yes—
380#930C2312yes—
381#930C2312yes—
382#930C2312yes—
383#930C2312yes—
384#930C2312yes—
385#929C2318yes—
386#929C2318yes—
387#929C2314yes—
388C4×#67C2312yes—
389C4×#67C2312yes—
390C4×#67C2318yes—
391C4×#67C2318yes—
392C4×#67C2318yes—
393C4×#67C2318yes—
394C4×#67C2312yes—
395C4×#67C2312yes—
396C4×#67C2314yes—
397C4×#67C2314yes—
398C4×#67C2314yes—
399C2×(C2×D3)⋊C4C2318yes—
400C2×(C2×D3)⋊C4C2314yes—
401#926C2311yescharacteristic
402#926C2311yescharacteristic
403#926C2312yes—
404C2×C4⋊Dic3C2312yes—
405#924C2318yes—
406#924C2312yes—
407C2×Dic3⋊C4C2318yes—
408#898C2314yes—
409#898C2314yes—
410#898C2314yes—
411#897C2312yes—
412#896C2314yes—
413#896C2318yes—
414#896C2314yes—
415#896C2318yes—
416#896C2314yes—
417#895C2312yes—
418#895C2314yes—
419#895C2318yes—
420#895C2318yes—
421#895C2314yes—
422#895C2314yes—
423#895C2312yes—
424#895C2312yes—
425#894C2314yes—
426#894C2314yes—
427#894C2314yes—
428#894C2314yes—
429#894C2318yes—
430#894C2318yes—
431#893C2314yes—
432#893C2314yes—
433#893C2312yes—
434#893C2312yes—
435#893C2312yes—
436#892C2314yes—
437#892C2312yes—
438#892C2314yes—
439#892C2312yes—
440D3×C4⋊C4C2312yes—
441D3×C4⋊C4C2314yes—
442D3×C4⋊C4C2314yes—
443D3×C4⋊C4C2314yes—
444D3×C4⋊C4C2312yes—
445#890C2312yes—
446#890C2312yes—
447#889C2314yes—
448#889C2314yes—
449#888C2312yes—
450#888C2314yes—
451#888C2312yes—
452#887C2312yes—
453#887C2314yes—
454#886C2318yes—
455#885C2314yes—
456#885C2318yes—
457#885C2318yes—
458#885C2314yes—
459#885C2314yes—
460#885C2314yes—
461#884C2314yes—
462#884C2318yes—
463#884C2318yes—
464#884C2318yes—
465#884C2318yes—
466#884C2318yes—
467#884C2318yes—
468#884C2318yes—
469#884C2318yes—
470#884C2314yes—
471#884C2314yes—
472#884C2318yes—
473#884C2318yes—
474#884C2314yes—
475#884C2314yes—
476#883C2314yes—
477#883C2318yes—
478#883C2318yes—
479#883C2318yes—
480#883C2318yes—
481#883C2314yes—
482#882C2318yes—
483#882C2318yes—
484#882C2318yes—
485#882C2318yes—
486#882C2318yes—
487#882C2314yes—
488#67⋊C4C2318yes—
489#67⋊C4C2318yes—
490#67⋊C4C2318yes—
491#67⋊C4C2318yes—
492#67⋊C4C2314yes—
493D3×C22⋊C4C2318yes—
494D3×C22⋊C4C2318yes—
495D3×C22⋊C4C2318yes—
496D3×C22⋊C4C2314yes—
497#879C2314yes—
498#879C2318yes—
499#879C2318yes—
500#878C2318yes—
501#878C2318yes—
502#878C2314yes—
503#877C2318yes—
504#876C2314yes—
505#875C2312yes—
506#875C2312yes—
507#875C2312yes—
508#875C2314yes—
509#874C2312yes—
510#874C2314yes—
511#874C2311yescharacteristic
512#874C2311yescharacteristic
513C4×D12C2312yes—
514C4×D12C2312yes—
515C4×D12C2312yes—
516C4×D12C2314yes—
517C4×D12C2314yes—
518C4×D12C2314yes—
519C4×D12C2314yes—
520C4×D12C2314yes—
521C4×D12C2311yescharacteristic
522C4×D12C2311yescharacteristic
523C4×D12C2311yescharacteristic
524C4×D12C2311yescharacteristic
525C4×D12C2312yes—
526C4×D12C2312yes—
527C4×D12C2312yes—
528C4×D12C2312yes—
529C4×D12C2314yes—
530#872C2314yes—
531#872C2314yes—
532#872C2312yes—
533#872C2312yes—
534#872C2314yes—
535C42×D3C2314yes—
536C42×D3C2314yes—
537C42×D3C2312yes—
538C42×D3C2312yes—
539#870C2312yes—
540#870C2314yes—
541#869C2312yes—
542#869C2311yescharacteristic
543#869C2311yescharacteristic
544C4×Dic6C2312yes—
545C4×Dic6C2314yes—
546C4×Dic6C2311yescharacteristic
547C4×Dic6C2311yescharacteristic
548C4×Dic6C2311yescharacteristic
549C4×Dic6C2311yescharacteristic
550C2×H(5,𝔽2)—34no—
551C2×H(5,𝔽2)—32no—
552C2×H(5,𝔽2)—32no—
553C22×#41—34no—
554#562—34no—
555#562—38no—
556#560—38no—
557#560—38no—
558#560—38no—
559#559—34no—
560#559—31no—
561#559C2×D312yescomplemented
562#559C2×D312yescomplemented
563Q82—31no—
564#557—31no—
565#556—31no—
566#556—32no—
567#555—31no—
568#555—32no—
569#555—32no—
570#555—34no—
571#554—31no—
572#554—32no—
573#554—32no—
574#554—31no—
575#554—34no—
576#553—34no—
577#553—34no—
578#553—34no—
579#553—32no—
580#553—38no—
581#553—32no—
582#552—34no—
583#552—32no—
584#551—38no—
585#551—34no—
586#550—34no—
587#550—32no—
588#550—34no—
589#550—32no—
590#550—34no—
591#550—32no—
592#550—32no—
593#550—32no—
594#550—34no—
595#550—38no—
596#550—32no—
597#550—31no—
598#550—32no—
599#550—31no—
600#550—34no—
601#550—32no—
602#550C2×D312yescomplemented
603#550C2×D312yescomplemented
604D4×Q8—31no—
605#548—34no—
606#548—32no—
607#547—34no—
608#547—32no—
609#547—31no—
610#547—32no—
611#547—38no—
612#547—32no—
613#547—34no—
614#547—34no—
615#546—32no—
616#546—34no—
617#546—34no—
618#546—34no—
619#546—34no—
620#546—34no—
621#546—38no—
622#546—38no—
623#546—38no—
624#546—32no—
625#546—38no—
626#546—34no—
627#546—38no—
628#546—38no—
629#546C2×D314yescomplemented
630#546C2×D314yescomplemented
631D42—34no—
632D42—34no—
633D42—34no—
634D42—34no—
635D42—32no—
636D42—32no—
637D42—32no—
638D42—32no—
639D42—34no—
640D42—34no—
641D42—38no—
642D42—38no—
643D42—31no—
644D42—34no—
645D42—34no—
646#542—34no—
647#542—38no—
648#540—34no—
649#540—38no—
650#540—38no—
651#540—34no—
652#540—34no—
653#540—34no—
654#540C2×D314yescomplemented
655#538—38no—
656#538—38no—
657#538—38no—
658#537—34no—
659#537—34no—
660#537—34no—
661#537—38no—
662#537—34no—
663#535—32no—
664#535—32no—
665#535—34no—
666#535—34no—
667#535—34no—
668#535—34no—
669#535—38no—
670#535—34no—
671#535—38no—
672#535C2×D312yescomplemented
673#534—38no—
674#534—38no—
675#534—38no—
676#533—32no—
677#533C2×D311yescharacteristic, complemented
678#532—32no—
679#532—32no—
680#532—34no—
681#532—34no—
682#532—34no—
683#532—32no—
684#532—34no—
685#532—31no—
686#532—32no—
687#532—31no—
688#532C2×D312yescomplemented
689#532C2×D312yescomplemented
690C2×#127—34no—
691C2×#127—32no—
692C2×#127—32no—
693C2×#127C2×D311yescharacteristic, complemented
694#529—34no—
695#529—34no—
696#529—32no—
697#529—32no—
698#529—34no—
699#529—32no—
700#525—34no—
701#525—38no—
702#525—38no—
703#525—34no—
704C2×#121—38no—
705C2×#121—34no—
706C2×#121—34no—
707C2×#121—38no—
708#520—34no—
709#518—34no—
710#518C2×D312yescomplemented
711C4×#41—32no—
712C4×#41—32no—
713C4×#41—32no—
714C4×#41—31no—
715C4×#41—31no—
716C4×#41C2×D311yescharacteristic, complemented
717C2×C4×Q8—32no—
718C2×C4×D4—34no—
719C2×C4×D4—32no—
720C2×C4×D4—34no—
721C2×C4×D4—32no—
722C24×C3C2414yes—
723C23×D3C2418yes—
724C23×D3C2414yes—
725C23×D3C2418yes—
726C3×#41—48no—
727C3×#41—48no—
728C3×#41—42no—
729C2×C3×Q8C2412yes—
730C2×C3×Q8C2411yescharacteristic
731C2×C3×Q8C2412yes—
732C2×C3×D4—44no—
733C2×C3×D4—44no—
734C2×C3×D4—44no—
735C2×C3×D4C2414yes—
736C2×C3×D4C2411yescharacteristic
737C2×C3×D4C2414yes—
738C2×C3×D4C2414yes—
739C2×C3×D4C2418yes—
740C2×C3×D4C2418yes—
741C2×C3×D4C2414yes—
742C2×C3×D4C2414yes—
743C2×C3×D4C2414yes—
744C2×C3×D4C2412yes—
745C22×C3×C4C2412yes—
746C22×C3×C4C2412yes—
747C22×C3×C4C2411yescharacteristic
748C22×C3×C4C2411yescharacteristic
749C22×C3×C4C2411yescharacteristic
750C22×C3×C4C2418yes—
751C22×C3×C4C2412yes—
752C22×C3×C4C2418yes—
753C2×#67—416no—
754C2×#67—416no—
755C2×#67C2418yes—
756C2×#67C2418yes—
757C2×#67C2412yes—
758C2×#67C2412yes—
759C2×#67C2414yes—
760C2×#67C2418yes—
761C2×#67C2418yes—
762C2×#67C2414yes—
763C2×#67C2418yes—
764C2×#67C2418yes—
765C2×#67C2418yes—
766C2×#67C2414yes—
767C2×#67C2418yes—
768C2×#67C2414yes—
769C2×#67C2414yes—
770C2×#67C2414yes—
771C22×Dic3C2418yes—
772C22×Dic3C2418yes—
773C22×Dic3C2414yes—
774#239—28no—
775#239—44no—
776#239—48no—
777#239—48no—
778D3×Q8—28no—
779#237—216no—
780#237—48no—
781#237—416no—
782#237—48no—
783#237—48no—
784D3×D4—216no—
785D3×D4—44no—
786D3×D4—48no—
787D3×D4—48no—
788D3×D4—48no—
789D3×D4—48no—
790D3×D4—48no—
791D3×D4—48no—
792D3×D4—416no—
793D3×D4—48no—
794D3×D4—416no—
795D3×D4—416no—
796#235—24no—
797#235—24no—
798#235—28no—
799#235—416no—
800#235—44no—
801#235—44no—
802#235—48no—
803#235—416no—
804C2×D12—28no—
805C2×D12—416no—
806C2×D12C2412yes—
807C2×D12C2412yes—
808C2×D12C2412yes—
809C2×D12C2411yescharacteristic
810C2×D12C2412yes—
811C2×D12C2414yes—
812C2×D12C2414yes—
813C2×D12C2414yes—
814C2×D12C2414yes—
815C2×D12C2412yes—
816C2×D12C2412yes—
817C2×D12C2418yes—
818C2×D12C2418yes—
819C2×D12C2411yescharacteristic
820C2×C4×D3—416no—
821C2×C4×D3—48no—
822C2×C4×D3C2412yes—
823C2×C4×D3C2412yes—
824C2×C4×D3C2412yes—
825C2×C4×D3C2414yes—
826C2×C4×D3C2412yes—
827C2×C4×D3C2412yes—
828C2×C4×D3C2414yes—
829C2×C4×D3C2412yes—
830C2×C4×D3C2414yes—
831C2×C4×D3C2414yes—
832C2×C4×D3C2414yes—
833C2×C4×D3C2414yes—
834C2×C4×D3C2414yes—
835C2×C4×D3C2414yes—
836C2×C4×D3C2418yes—
837C2×C4×D3C2418yes—
838C2×Dic6C2411yescharacteristic
839C2×Dic6C2414yes—
840C2×Dic6C2414yes—
841C2×Dic6C2412yes—
842C2×Dic6C2412yes—
843C2×Dic6C2411yescharacteristic
844C3×C4⋊C4C2412yes—
845C3×C4⋊C4C2414yes—
846C3×C4⋊C4C2411yescharacteristic
847C3×C4⋊C4C2412yes—
848C3×C4⋊C4C2412yes—
849C3×C4⋊C4C2412yes—
850C3×C4⋊C4C2414yes—
851C3×C4⋊C4C2411yescharacteristic
852C3×C4⋊C4C2412yes—
853C3×C4⋊C4C2412yes—
854C3×C22⋊C4C2418yes—
855C3×C22⋊C4C2418yes—
856C3×C22⋊C4C2412yes—
857C3×C22⋊C4C2418yes—
858C3×C22⋊C4C2418yes—
859C3×C22⋊C4C2414yes—
860C3×C22⋊C4C2412yes—
861C3×C22⋊C4C2412yes—
862C3×C42C2411yescharacteristic
863C3×C42C2411yescharacteristic
864C3×C42C2411yescharacteristic
865C3×C42C2412yes—
866C3×C42C2414yes—
867C3×C42C2412yes—
868C3×C42C2411yescharacteristic
869C3×C42C2412yes—
870#217C2418yes—
871#217C2418yes—
872#217C2418yes—
873#217C2414yes—
874#217C2412yes—
875#217C2412yes—
876#217C2418yes—
877#217C2414yes—
878(C2×D3)⋊C4C2412yes—
879(C2×D3)⋊C4C2414yes—
880(C2×D3)⋊C4C2412yes—
881(C2×D3)⋊C4C2414yes—
882(C2×D3)⋊C4C2412yes—
883(C2×D3)⋊C4C2412yes—
884(C2×D3)⋊C4C2414yes—
885(C2×D3)⋊C4C2414yes—
886(C2×D3)⋊C4C2414yes—
887(C2×D3)⋊C4C2414yes—
888(C2×D3)⋊C4C2414yes—
889(C2×D3)⋊C4C2414yes—
890(C2×D3)⋊C4C2414yes—
891(C2×D3)⋊C4C2414yes—
892(C2×D3)⋊C4C2414yes—
893(C2×D3)⋊C4C2414yes—
894(C2×D3)⋊C4C2414yes—
895(C2×D3)⋊C4C2414yes—
896(C2×D3)⋊C4C2418yes—
897(C2×D3)⋊C4C2414yes—
898(C2×D3)⋊C4C2418yes—
899(C2×D3)⋊C4C2414yes—
900C4⋊Dic3C2412yes—
901C4⋊Dic3C2411yescharacteristic
902C4⋊Dic3C2411yescharacteristic
903C4⋊Dic3C2411yescharacteristic
904C4⋊Dic3C2411yescharacteristic
905C4⋊Dic3C2414yes—
906C4⋊Dic3C2412yes—
907C4⋊Dic3C2412yes—
908C4⋊Dic3C2412yes—
909C4⋊Dic3C2414yes—
910C4⋊Dic3C2414yes—
911C4⋊Dic3C2414yes—
912Dic3⋊C4C2412yes—
913Dic3⋊C4C2412yes—
914Dic3⋊C4C2414yes—
915Dic3⋊C4C2412yes—
916Dic3⋊C4C2412yes—
917Dic3⋊C4C2414yes—
918Dic3⋊C4C2414yes—
919Dic3⋊C4C2414yes—
920Dic3⋊C4C2414yes—
921Dic3⋊C4C2418yes—
922Dic3⋊C4C2418yes—
923Dic3⋊C4C2414yes—
924Dic3⋊C4C2414yes—
925Dic3⋊C4C2414yes—
926C4×Dic3C2412yes—
927C4×Dic3C2412yes—
928C4×Dic3C2412yes—
929C4×Dic3C2412yes—
930C4×Dic3C2414yes—
931C4×Dic3C2414yes—
932C4×Dic3C2412yes—
933C4×Dic3C2412yes—
934C4×Dic3C2414yes—
935C4×Dic3C2414yes—
936H(5,𝔽2)—128no—
937H(5,𝔽2)—128no—
938H(5,𝔽2)—1216no—
939C2×#41—32no—
940C2×#41—32no—
941C2×#41—34no—
942C2×#41—34no—
943C2×#41—34no—
944C2×#41—34no—
945C2×#41—34no—
946C2×#41—34no—
947C2×#41—38no—
948C2×#41—31no—
949C2×#41—31no—
950C2×#41—32no—
951C2×#41—32no—
952C2×#41—38no—
953C2×#41—32no—
954C2×#41—34no—
955C2×#41—38no—
956C2×#41—1216no—
957C2×#41C22×D311yescharacteristic
958C2×#41C22×D314yes—
959C2×#41C22×D314yes—
960C22×Q8—32no—
961C22×D4—38no—
962C22×D4—38no—
963C22×D4—34no—
964C22×D4—32no—
965C22×D4—34no—
966C22×D4—34no—
967C22×D4—38no—
968C22×D4—34no—
969C22×D4—38no—
970C22×D4—34no—
971C22×D4—38no—
972C22×D4—34no—
973C22×D4—34no—
974C22×D4—34no—
975C22×D4—32no—
976C22×D4—38no—
977C22×D4C22×D312yes—
978C22×D4C22×D312yes—
979C22×D4C22×D312yes—
980C23×C4—38no—
981C23×C4—34no—
982C4⋊Q8—32no—
983C4⋊Q8—32no—
984C4⋊Q8—32no—
985C4⋊Q8—34no—
986C4⋊Q8—31no—
987C4⋊Q8—31no—
988C4⋊Q8—32no—
989C4⋊Q8C22×D311yescharacteristic
990C4⋊Q8C22×D311yescharacteristic
991#127—34no—
992#127—32no—
993#127—34no—
994#127—34no—
995#127—34no—
996#127—38no—
997#127—38no—
998#127—34no—
999#127—34no—
1000#127—34no—
1001#127—31no—
1002#127—31no—
1003#127—34no—
1004#127—32no—
1005#127C22×D312yes—
1006#127C22×D312yes—
1007#127C22×D314yes—
1008#127C22×D312yes—
1009#127C22×D312yes—
1010#126—34no—
1011#126—34no—
1012#126—34no—
1013#126—38no—
1014#126—34no—
1015#126—38no—
1016#126—34no—
1017#125—34no—
1018#125—32no—
1019#125—32no—
1020#125—34no—
1021#125—32no—
1022#125—34no—
1023#125C22×D312yes—
1024#124—32no—
1025#124—32no—
1026#124—34no—
1027#124—34no—
1028#124—34no—
1029#124—38no—
1030#124—34no—
1031#124—38no—
1032#124—34no—
1033#124—34no—
1034#124—32no—
1035#124—32no—
1036#124—32no—
1037#124—34no—
1038#124C22×D314yes—
1039#124C22×D314yes—
1040#124C22×D314yes—
1041#123—38no—
1042#123—38no—
1043#123—38no—
1044#123—34no—
1045#123—38no—
1046#123—38no—
1047#123—34no—
1048#123—34no—
1049#123—34no—
1050#123—34no—
1051#123—38no—
1052#123—34no—
1053#123—38no—
1054#123—34no—
1055#123—38no—
1056#123—38no—
1057#123—38no—
1058#123—38no—
1059#123C22×D318yes—
1060#123C22×D318yes—
1061C22⋊Q8—32no—
1062C22⋊Q8—34no—
1063C22⋊Q8—32no—
1064C22⋊Q8—34no—
1065C22⋊Q8—32no—
1066C22⋊Q8—32no—
1067C22⋊Q8—38no—
1068C22⋊Q8—34no—
1069C22⋊Q8—34no—
1070C22⋊Q8—38no—
1071C22⋊Q8—32no—
1072C22⋊Q8—34no—
1073C22⋊Q8—38no—
1074C22⋊Q8—34no—
1075C22⋊Q8—38no—
1076C22⋊Q8—38no—
1077C22⋊Q8C22×D312yes—
1078C22⋊Q8C22×D312yes—
1079#121—34no—
1080#121—38no—
1081#121—38no—
1082#121—38no—
1083#121—34no—
1084#121—38no—
1085#121—38no—
1086#121—34no—
1087#121—34no—
1088#121—38no—
1089#121—34no—
1090#121—34no—
1091#121—34no—
1092#121—34no—
1093#121—34no—
1094#121—34no—
1095#121—32no—
1096#121—38no—
1097#121—38no—
1098#121—38no—
1099#121—38no—
1100#121—32no—
1101#121—32no—
1102#121—38no—
1103#121—32no—
1104#121—34no—
1105#121—32no—
1106#121—32no—
1107#121—32no—
1108#121—32no—
1109#121—38no—
1110#121—38no—
1111#121—32no—
1112#121—38no—
1113#121—34no—
1114#121—32no—
1115#121—34no—
1116#121—34no—
1117#121—32no—
1118#121—38no—
1119#121—38no—
1120#121—34no—
1121#121—34no—
1122#121—34no—
1123#121—38no—
1124#121—34no—
1125#121—38no—
1126#121—38no—
1127#121—38no—
1128#121—38no—
1129#121—38no—
1130#121—38no—
1131#121—38no—
1132#121—34no—
1133#121—38no—
1134#121C22×D314yes—
1135#121C22×D318yes—
1136#121C22×D314yes—
1137#121C22×D314yes—
1138#121C22×D314yes—
1139#121C22×D318yes—
1140#120—38no—
1141#120—38no—
1142#120—34no—
1143#120—38no—
1144#120—38no—
1145#120—38no—
1146#120—38no—
1147#120—38no—
1148#120—38no—
1149#120—38no—
1150#120—38no—
1151#120—34no—
1152#120—38no—
1153#120—38no—
1154#120—38no—
1155#120C22×D318yes—
1156C4×Q8—32no—
1157C4×Q8—32no—
1158C4×Q8—32no—
1159C4×Q8—32no—
1160C4×Q8—34no—
1161C4×Q8—31no—
1162C4×Q8—34no—
1163C4×Q8—31no—
1164C4×Q8—32no—
1165C4×Q8—31no—
1166C4×Q8—31no—
1167C4×Q8C22×D312yes—
1168C4×Q8C22×D311yescharacteristic
1169C4×Q8C22×D312yes—
1170C4×Q8C22×D311yescharacteristic
1171C4×D4—34no—
1172C4×D4—34no—
1173C4×D4—32no—
1174C4×D4—34no—
1175C4×D4—34no—
1176C4×D4—38no—
1177C4×D4—34no—
1178C4×D4—38no—
1179C4×D4—32no—
1180C4×D4—32no—
1181C4×D4—32no—
1182C4×D4—32no—
1183C4×D4—34no—
1184C4×D4—34no—
1185C4×D4—38no—
1186C4×D4—38no—
1187C4×D4—32no—
1188C4×D4—32no—
1189C4×D4—32no—
1190C4×D4—34no—
1191C4×D4—34no—
1192C4×D4—38no—
1193C4×D4—38no—
1194C4×D4—34no—
1195C4×D4—38no—
1196C4×D4—38no—
1197C4×D4—32no—
1198C4×D4—31no—
1199C4×D4—34no—
1200C4×D4—34no—
1201C4×D4—32no—
1202C4×D4—32no—
1203C4×D4—32no—
1204C4×D4—34no—
1205C4×D4—31no—
1206C4×D4—34no—
1207C4×D4—31no—
1208C4×D4—31no—
1209C4×D4—32no—
1210C4×D4—32no—
1211C4×D4—34no—
1212C4×D4—32no—
1213C4×D4—34no—
1214C4×D4C22×D311yescharacteristic
1215C4×D4C22×D314yes—
1216C4×D4C22×D314yes—
1217C4×D4C22×D312yes—
1218C4×D4C22×D311yescharacteristic
1219C4×D4C22×D312yes—
1220C4×D4C22×D314yes—
1221C4×D4C22×D314yes—
1222C4×D4C22×D314yes—
1223C4×D4C22×D314yes—
1224#117—32no—
1225#117—31no—
1226#117—31no—
1227#117—32no—
1228#117—34no—
1229#117—32no—
1230#117—34no—
1231#117—38no—
1232#117—34no—
1233#117—32no—
1234#117—32no—
1235#117—34no—
1236#117—34no—
1237#117C22×D311yescharacteristic
1238#117C22×D312yes—
1239#117C22×D312yes—
1240C2×C4⋊C4—32no—
1241C2×C4⋊C4—38no—
1242C2×C4⋊C4—32no—
1243C2×C4⋊C4—34no—
1244C2×C4⋊C4—34no—
1245C2×C4⋊C4—32no—
1246C2×C4⋊C4—34no—
1247C2×C22⋊C4—34no—
1248C2×C22⋊C4—38no—
1249C2×C22⋊C4—38no—
1250C2×C22⋊C4—34no—
1251C2×C22⋊C4—38no—
1252C2×C22⋊C4—38no—
1253C2×C22⋊C4C22×D318yes—
1254C2×C42—34no—
1255C2×C42—32no—
1256C2×C42—34no—
1257C2×C42—32no—
1258C2×C42C22×D312yes—
1259C2×C42C22×D311yescharacteristic
1260C23×C3—44no—
1261C23×C3—44no—
1262C23×C3—44no—
1263C23×C3C2511yescharacteristic
1264C23×C3C2518yes—
1265C23×C3C2512yes—
1266C22×D3—28no—
1267C22×D3—216no—
1268C22×D3—48no—
1269C22×D3—44no—
1270C22×D3—48no—
1271C22×D3—44no—
1272C22×D3—48no—
1273C22×D3—48no—
1274C22×D3—48no—
1275C22×D3C2512yes—
1276C22×D3C2514yes—
1277C22×D3C2514yes—
1278C22×D3C2512yes—
1279C3×Q8—24no—
1280C3×Q8—24no—
1281C3×Q8—22no—
1282C3×D4—28no—
1283C3×D4—28no—
1284C3×D4—28no—
1285C3×D4—22no—
1286C3×D4—48no—
1287C3×D4—44no—
1288C3×D4—44no—
1289C3×D4—48no—
1290C3×D4—44no—
1291C3×D4—42no—
1292C2×C3×C4—24no—
1293C2×C3×C4—24no—
1294C2×C3×C4—22no—
1295C2×C3×C4—22no—
1296C2×C3×C4—22no—
1297C2×C3×C4—48no—
1298C2×C3×C4—48no—
1299C2×C3×C4—42no—
1300C2×C3×C4C2512yes—
1301C2×C3×C4C2512yes—
1302C2×C3×C4C2511yescharacteristic
1303C2×C3×C4C2511yescharacteristic
1304C2×C3×C4C2514yes—
1305C2×C3×C4C2514yes—
1306C2×C3×C4C2512yes—
1307C2×C3×C4C2511yescharacteristic
1308C2×C3×C4C2511yescharacteristic
1309C2×C3×C4C2511yescharacteristic
1310C2×C3×C4C2511yescharacteristic
1311#67—24no—
1312#67—216no—
1313#67—28no—
1314#67—24no—
1315#67—216no—
1316#67—44no—
1317#67—48no—
1318#67—44no—
1319#67—48no—
1320#67—44no—
1321#67—44no—
1322#67—48no—
1323#67—48no—
1324#67—48no—
1325#67—48no—
1326#67—44no—
1327C2×Dic3—216no—
1328C2×Dic3—44no—
1329C2×Dic3—48no—
1330C2×Dic3C2512yes—
1331C2×Dic3C2512yes—
1332C2×Dic3C2512yes—
1333C2×Dic3C2512yes—
1334C2×Dic3C2512yes—
1335C2×Dic3C2514yes—
1336C2×Dic3C2514yes—
1337C2×Dic3C2512yes—
1338D12—28no—
1339D12—28no—
1340D12—24no—
1341D12—22no—
1342D12—24no—
1343D12—24no—
1344D12—24no—
1345D12—44no—
1346D12—48no—
1347D12—42no—
1348D12—42no—
1349D12—48no—
1350D12—44no—
1351D12H(5,𝔽2)14yescomplemented
1352C4×D3—24no—
1353C4×D3—28no—
1354C4×D3—24no—
1355C4×D3—28no—
1356C4×D3—28no—
1357C4×D3—24no—
1358C4×D3—24no—
1359C4×D3—24no—
1360C4×D3—28no—
1361C4×D3—28no—
1362C4×D3—24no—
1363C4×D3—44no—
1364C4×D3—44no—
1365C4×D3—48no—
1366C4×D3—48no—
1367C4×D3—44no—
1368Dic6—22no—
1369Dic6—28no—
1370Dic6—44no—
1371Dic6—42no—
1372Dic6—42no—
1373Dic6H(5,𝔽2)14yescomplemented
1374C24—34no—
1375C24—38no—
1376C24—38no—
1377C24C23×D314yes—
1378#41—48no—
1379#41—48no—
1380#41—42no—
1381#41—64no—
1382#41—68no—
1383#41—64no—
1384#41—616no—
1385#41—68no—
1386#41—124no—
1387#41—124no—
1388#41—128no—
1389#41—1216no—
1390#41—1216no—
1391#41—128no—
1392#41—128no—
1393#41—128no—
1394#41—1216no—
1395#41—128no—
1396#41—128no—
1397#41—124no—
1398C2×Q8—31no—
1399C2×Q8—34no—
1400C2×Q8—31no—
1401C2×Q8—32no—
1402C2×Q8—34no—
1403C2×Q8—32no—
1404C2×Q8—68no—
1405C2×Q8C23×D311yescharacteristic
1406C2×Q8C23×D312yes—
1407C2×Q8C23×D312yes—
1408C2×D4—38no—
1409C2×D4—32no—
1410C2×D4—32no—
1411C2×D4—38no—
1412C2×D4—34no—
1413C2×D4—38no—
1414C2×D4—34no—
1415C2×D4—38no—
1416C2×D4—38no—
1417C2×D4—34no—
1418C2×D4—38no—
1419C2×D4—34no—
1420C2×D4—34no—
1421C2×D4—38no—
1422C2×D4—38no—
1423C2×D4—34no—
1424C2×D4—31no—
1425C2×D4—32no—
1426C2×D4—32no—
1427C2×D4—34no—
1428C2×D4—34no—
1429C2×D4—31no—
1430C2×D4—32no—
1431C2×D4—32no—
1432C2×D4—34no—
1433C2×D4—38no—
1434C2×D4—34no—
1435C2×D4—32no—
1436C2×D4—38no—
1437C2×D4—32no—
1438C2×D4—44no—
1439C2×D4—44no—
1440C2×D4—44no—
1441C2×D4—68no—
1442C2×D4—616no—
1443C2×D4—1216no—
1444C2×D4—128no—
1445C2×D4—128no—
1446C2×D4—128no—
1447C2×D4—128no—
1448C2×D4—124no—
1449C2×D4—128no—
1450C2×D4—1216no—
1451C2×D4—128no—
1452C2×D4—128no—
1453C2×D4—1216no—
1454C2×D4—1216no—
1455C2×D4—1216no—
1456C2×D4—1216no—
1457C2×D4C23×D314yes—
1458C2×D4C23×D311yescharacteristic
1459C2×D4C23×D314yes—
1460C2×D4C23×D314yes—
1461C2×D4C23×D314yes—
1462C2×D4C23×D312yes—
1463C2×D4C23×D318yes—
1464C2×D4C23×D314yes—
1465C2×D4C23×D314yes—
1466C2×D4C23×D318yes—
1467C22×C4—38no—
1468C22×C4—38no—
1469C22×C4—34no—
1470C22×C4—32no—
1471C22×C4—34no—
1472C22×C4—32no—
1473C22×C4—34no—
1474C22×C4—32no—
1475C22×C4—34no—
1476C22×C4—32no—
1477C22×C4—34no—
1478C22×C4—32no—
1479C22×C4—32no—
1480C22×C4—34no—
1481C22×C4—34no—
1482C22×C4—34no—
1483C22×C4—34no—
1484C22×C4—38no—
1485C22×C4—38no—
1486C22×C4—128no—
1487C22×C4—1216no—
1488C22×C4C23×D312yes—
1489C22×C4C23×D312yes—
1490C22×C4C23×D311yescharacteristic
1491C22×C4C23×D311yescharacteristic
1492C22×C4C23×D311yescharacteristic
1493C22×C4C23×D312yes—
1494C22×C4C23×D318yes—
1495C22×C4C23×D318yes—
1496C4⋊C4—32no—
1497C4⋊C4—34no—
1498C4⋊C4—34no—
1499C4⋊C4—31no—
1500C4⋊C4—32no—
1501C4⋊C4—32no—
1502C4⋊C4—31no—
1503C4⋊C4—38no—
1504C4⋊C4—34no—
1505C4⋊C4—32no—
1506C4⋊C4—34no—
1507C4⋊C4—38no—
1508C4⋊C4—34no—
1509C4⋊C4—34no—
1510C4⋊C4—34no—
1511C4⋊C4—32no—
1512C4⋊C4—31no—
1513C4⋊C4—31no—
1514C4⋊C4—34no—
1515C4⋊C4—32no—
1516C4⋊C4—34no—
1517C4⋊C4—34no—
1518C4⋊C4—32no—
1519C4⋊C4—32no—
1520C4⋊C4—34no—
1521C4⋊C4—34no—
1522C4⋊C4C23×D312yes—
1523C4⋊C4C23×D311yescharacteristic
1524C4⋊C4C23×D312yes—
1525C4⋊C4C23×D314yes—
1526C4⋊C4C23×D312yes—
1527C4⋊C4C23×D314yes—
1528C4⋊C4C23×D311yescharacteristic
1529C4⋊C4C23×D312yes—
1530C4⋊C4C23×D312yes—
1531C4⋊C4C23×D312yes—
1532C22⋊C4—38no—
1533C22⋊C4—38no—
1534C22⋊C4—38no—
1535C22⋊C4—34no—
1536C22⋊C4—32no—
1537C22⋊C4—32no—
1538C22⋊C4—38no—
1539C22⋊C4—34no—
1540C22⋊C4—34no—
1541C22⋊C4—34no—
1542C22⋊C4—34no—
1543C22⋊C4—34no—
1544C22⋊C4—32no—
1545C22⋊C4—34no—
1546C22⋊C4—34no—
1547C22⋊C4—34no—
1548C22⋊C4—34no—
1549C22⋊C4—38no—
1550C22⋊C4—34no—
1551C22⋊C4—34no—
1552C22⋊C4—38no—
1553C22⋊C4—32no—
1554C22⋊C4—34no—
1555C22⋊C4—32no—
1556C22⋊C4—32no—
1557C22⋊C4—34no—
1558C22⋊C4—34no—
1559C22⋊C4—34no—
1560C22⋊C4—34no—
1561C22⋊C4—34no—
1562C22⋊C4C23×D318yes—
1563C22⋊C4C23×D312yes—
1564C22⋊C4C23×D318yes—
1565C22⋊C4C23×D312yes—
1566C22⋊C4C23×D314yes—
1567C22⋊C4C23×D318yes—
1568C22⋊C4C23×D318yes—
1569C22⋊C4C23×D312yes—
1570C42—32no—
1571C42—32no—
1572C42—32no—
1573C42—34no—
1574C42—34no—
1575C42—34no—
1576C42—32no—
1577C42—32no—
1578C42—34no—
1579C42—32no—
1580C42C23×D312yes—
1581C42C23×D311yescharacteristic
1582C42C23×D311yescharacteristic
1583C42C23×D314yes—
1584C42C23×D311yescharacteristic
1585C42C23×D311yescharacteristic
1586C42C23×D312yes—
1587C42C23×D312yes—
1588C22×C3—28no—
1589C22×C3—22no—
1590C22×C3—28no—
1591C22×C3—21no—
1592C22×C3—21no—
1593C22×C3—22no—
1594C22×C3—22no—
1595C22×C3—28no—
1596C22×C3—21no—
1597C22×C3—164no—
1598C22×C3C2611yescharacteristic
1599C2×D3—22no—
1600C2×D3—22no—
1601C2×D3—24no—
1602C2×D3—24no—
1603C2×D3—22no—
1604C2×D3—22no—
1605C2×D3—24no—
1606C2×D3—24no—
1607C2×D3—22no—
1608C2×D3—24no—
1609C2×D3—24no—
1610C2×D3—816no—
1611C2×D3—88no—
1612C2×D3—168no—
1613C2×D3C2×H(5,𝔽2)14yes—
1614C3×C4—24no—
1615C3×C4—21no—
1616C3×C4—21no—
1617C3×C4—22no—
1618C3×C4—22no—
1619C3×C4—24no—
1620C3×C4—22no—
1621C3×C4—21no—
1622C3×C4C2×H(5,𝔽2)12yes—
1623C3×C4C2×H(5,𝔽2)12yes—
1624C3×C4#58512yes—
1625Dic3—22no—
1626Dic3—22no—
1627Dic3—22no—
1628Dic3—24no—
1629Dic3—24no—
1630Dic3—22no—
1631Dic3—22no—
1632Dic3C2×H(5,𝔽2)14yes—
1633C23—32no—
1634C23—32no—
1635C23—34no—
1636C23—34no—
1637C23—44no—
1638C23—44no—
1639C23—44no—
1640C23—68no—
1641C23—616no—
1642C23—124no—
1643C23—128no—
1644C23—124no—
1645C23—128no—
1646C23—128no—
1647C23—128no—
1648C23—128no—
1649C23C24×D311yescharacteristic
1650C23C24×D318yes—
1651C23C24×D312yes—
1652Q8—22no—
1653Q8—24no—
1654Q8—24no—
1655Q8—34no—
1656Q8—68no—
1657Q8—62no—
1658Q8—124no—
1659Q8—122no—
1660Q8—122no—
1661D4—28no—
1662D4—22no—
1663D4—28no—
1664D4—28no—
1665D4—34no—
1666D4—44no—
1667D4—44no—
1668D4—44no—
1669D4—48no—
1670D4—48no—
1671D4—42no—
1672D4—68no—
1673D4—68no—
1674D4—64no—
1675D4—616no—
1676D4—68no—
1677D4—616no—
1678D4—64no—
1679D4—64no—
1680D4—64no—
1681D4—64no—
1682D4—62no—
1683D4—64no—
1684D4—124no—
1685D4—122no—
1686D4—122no—
1687D4—128no—
1688D4—128no—
1689D4—124no—
1690D4—124no—
1691D4—128no—
1692D4—124no—
1693D4—128no—
1694D4—124no—
1695D4—124no—
1696D4—128no—
1697D4—128no—
1698D4—128no—
1699D4—124no—
1700D4—128no—
1701C2×C4—22no—
1702C2×C4—24no—
1703C2×C4—22no—
1704C2×C4—22no—
1705C2×C4—24no—
1706C2×C4—32no—
1707C2×C4—32no—
1708C2×C4—32no—
1709C2×C4—32no—
1710C2×C4—34no—
1711C2×C4—32no—
1712C2×C4—32no—
1713C2×C4—34no—
1714C2×C4—48no—
1715C2×C4—48no—
1716C2×C4—42no—
1717C2×C4—68no—
1718C2×C4—68no—
1719C2×C4—64no—
1720C2×C4—64no—
1721C2×C4—68no—
1722C2×C4—616no—
1723C2×C4—64no—
1724C2×C4—64no—
1725C2×C4—64no—
1726C2×C4—68no—
1727C2×C4—68no—
1728C2×C4—64no—
1729C2×C4—124no—
1730C2×C4—124no—
1731C2×C4—128no—
1732C2×C4—128no—
1733C2×C4—124no—
1734C2×C4—124no—
1735C2×C4—128no—
1736C2×C4C24×D312yes—
1737C2×C4C24×D312yes—
1738C2×C4C24×D311yescharacteristic
1739C2×C4C24×D311yescharacteristic
1740C2×C4C24×D314yes—
1741C2×C4C24×D314yes—
1742C2×C4C24×D311yescharacteristic
1743C2×C4C24×D312yes—
1744C2×C4C24×D311yescharacteristic
1745C2×C4C24×D311yescharacteristic
1746C2×C4C24×D311yescharacteristic
1747C2×C3—42no—
1748C2×C3—48no—
1749C2×C3—41no—
1750C2×C3C22×H(5,𝔽2)11yescharacteristic
1751C2×C3C22×H(5,𝔽2)11yescharacteristic
1752C2×C3C2×#58511yescharacteristic
1753D3—24no—
1754D3—44no—
1755D3—44no—
1756D3—42no—
1757C22—21no—
1758C22—22no—
1759C22—28no—
1760C22—22no—
1761C22—22no—
1762C22—21no—
1763C22—21no—
1764C22—28no—
1765C22—28no—
1766C22—34no—
1767C22—62no—
1768C22—62no—
1769C22—62no—
1770C22—64no—
1771C22—64no—
1772C22—64no—
1773C22—64no—
1774C22—62no—
1775C22—62no—
1776C22—64no—
1777C22—64no—
1778C22—164no—
1779C22—2416no—
1780C22—248no—
1781C22—488no—
1782C22C25×D311yescharacteristic
1783C4—21no—
1784C4—22no—
1785C4—22no—
1786C4—22no—
1787C4—21no—
1788C4—21no—
1789C4—24no—
1790C4—24no—
1791C4—34no—
1792C4—62no—
1793C4—62no—
1794C4—64no—
1795C4—62no—
1796C4—64no—
1797C4—62no—
1798C4—62no—
1799C4#596412yes—
1800C4D3×H(5,𝔽2)12yes—
1801C4D3×H(5,𝔽2)12yes—
1802C3#6301411yescharacteristic, complemented, Sylow
1803C2—41no—
1804C2—48no—
1805C2—42no—
1806C2—64no—
1807C2—124no—
1808C2—124no—
1809C2—122no—
1810C2C2×#596411yescharacteristic
1811C2C2×D3×H(5,𝔽2)11yescharacteristic
1812C2C2×D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3508C2
hypercenter#3508D3
hypocenterC3#63014
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3508

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#3508C2semidirect
2. #87066C2semidirect
3. #87055C2semidirect
4. #87051C2semidirect
5. #87050C2semidirect
6. D3×#550C2semidirect
7. #86780C2semidirect
8. #86775C2semidirect
9. #86770C2semidirect
10. #86672C2semidirect
11. #86665C2semidirect
12. #86649C2semidirect
13. #86629C2semidirect
14. #86474C2semidirect
15. #86336C2semidirect
16. #86288C2semidirect
17. #86278C2semidirect
18. #86250C2semidirect
19. #86241C2semidirect
20. #86238C2semidirect
21. #86228C2semidirect
22. #86195C2semidirect
23. #86195C2semidirect
24. #85871C2semidirect
25. #85845C2semidirect
26. #85843C2semidirect
28. C2×#1009C22semidirect
29. C2×D3×#41C22semidirect
30. C2×#1004C22semidirect
31. C2×#1004C22semidirect
32. C3×#559C22semidirect
33. C3×#559C22semidirect
34. C3×#550C22semidirect
35. C3×#550C22semidirect
36. C3×#546C22semidirect
37. C3×#546C22semidirect
38. C3×#540C22semidirect
39. C3×#535C22semidirect
40. C3×#533C22semidirect
41. C3×#532C22semidirect
42. C3×#532C22semidirect
43. C2×C3×#127C22semidirect
44. C3×#518C22semidirect
45. C3×C4×#41C22semidirect
46. #5834C22semidirect
47. #5834C22semidirect
48. #5834C22semidirect
49. #5833C22semidirect
50. #5829C22semidirect
51. #5829C22semidirect
52. #5828C22semidirect
53. #5824C22semidirect
54. #5805C22semidirect
55. #5805C22semidirect
56. D4×#67C22semidirect
57. D4×#67C22semidirect
58. D4×#67C22semidirect
59. D4×#67C22semidirect
60. #5732C22semidirect
61. #5727C22semidirect
62. #5726C22semidirect
63. #5726C22semidirect
64. #5726C22semidirect
65. #5721C22semidirect
66. #5719C22semidirect
67. #5718C22semidirect
68. #5718C22semidirect
69. #5718C22semidirect
70. #5718C22semidirect
71. #5718C22semidirect
72. #5717C22semidirect
73. #5717C22semidirect
74. #5717C22semidirect
75. #5717C22semidirect
76. #5717C22semidirect
77. #5716C22semidirect
78. #5716C22semidirect
79. #5715C22semidirect
80. #5715C22semidirect
81. D3×#127C22semidirect
82. D3×#127C22semidirect
83. D3×#127C22semidirect
84. #5700C22semidirect
85. #5693C22semidirect
86. #5682C22semidirect
87. #5681C22semidirect
88. #5680C22semidirect
89. #5680C22semidirect
90. #5677C22semidirect
91. #5676C22semidirect
92. #5676C22semidirect
93. #5676C22semidirect
94. #5676C22semidirect
95. #5674C22semidirect
96. #5674C22semidirect
97. #5668C22semidirect
98. #5666C22semidirect
99. #5663C22semidirect
100. #5662C22semidirect
101. #5659C22semidirect
102. #5656C22semidirect
103. #5655C22semidirect
104. #5654C22semidirect
105. #5653C22semidirect
106. #5641C22semidirect
107. #5639C22semidirect
108. #5633C22semidirect
109. #5631C22semidirect
110. #5629C22semidirect
111. #5629C22semidirect
112. #5621C22semidirect
113. #5620C22semidirect
114. #5615C22semidirect
115. #5614C22semidirect
116. #5613C22semidirect
117. #5611C22semidirect
118. #5610C22semidirect
119. #5610C22semidirect
120. #5609C22semidirect
121. #5609C22semidirect
122. #5608C22semidirect
123. #5607C22semidirect
124. #5607C22semidirect
125. #5605C22semidirect
126. D3×#121C22semidirect
127. D3×#121C22semidirect
128. D3×#121C22semidirect
129. #5599C22semidirect
130. #5599C22semidirect
131. #5597C22semidirect
132. #5595C22semidirect
133. #5592C22semidirect
134. #5590C22semidirect
135. #5589C22semidirect
136. #5585C22semidirect
137. #5580C22semidirect
138. #5580C22semidirect
139. #5579C22semidirect
140. #5579C22semidirect
141. #5579C22semidirect
142. #5578C22semidirect
143. #5577C22semidirect
144. #5577C22semidirect
145. #5577C22semidirect
146. C4×#239C22semidirect
147. C4×#239C22semidirect
148. C4×D3×Q8C22semidirect
149. Q8×Dic6C22semidirect
150. #5565C22semidirect
151. #5563C22semidirect
152. #5563C22semidirect
153. #5562C22semidirect
154. #5562C22semidirect
155. #5560C22semidirect
156. #5558C22semidirect
157. #5558C22semidirect
158. #5554C22semidirect
159. #5553C22semidirect
160. #5553C22semidirect
161. #5553C22semidirect
162. #5551C22semidirect
163. #5550C22semidirect
164. #5550C22semidirect
165. D4×D12C22semidirect
166. D4×D12C22semidirect
167. D4×D12C22semidirect
168. #5548C22semidirect
169. #5548C22semidirect
170. #5548C22semidirect
171. #5548C22semidirect
172. #5547C22semidirect
173. #5547C22semidirect
174. #5546C22semidirect
175. #5545C22semidirect
176. C4×D3×D4C22semidirect
177. C4×D3×D4C22semidirect
178. C4×D3×D4C22semidirect
179. #5543C22semidirect
180. #5540C22semidirect
181. #5539C22semidirect
182. #5535C22semidirect
183. #5532C22semidirect
184. #5532C22semidirect
185. #5530C22semidirect
186. #5528C22semidirect
187. #5527C22semidirect
188. #5494C22semidirect
189. #5490C22semidirect
190. #5490C22semidirect
191. C2×#884C22semidirect
192. #5479C22semidirect
193. #5477C22semidirect
194. #5477C22semidirect
195. #5477C22semidirect
196. C4×#235C22semidirect
197. C4×#235C22semidirect
198. C4×#235C22semidirect
199. C2×C4×D12C22semidirect
213. #3508D3semidirect
561. #559C2×D3semidirect
562. #559C2×D3semidirect
602. #550C2×D3semidirect
603. #550C2×D3semidirect
629. #546C2×D3semidirect
630. #546C2×D3semidirect
654. #540C2×D3semidirect
672. #535C2×D3semidirect
677. #533C2×D3semidirect
688. #532C2×D3semidirect
689. #532C2×D3semidirect
693. C2×#127C2×D3semidirect
710. #518C2×D3semidirect
716. C4×#41C2×D3semidirect
1351. D12H(5,𝔽2)semidirect
1373. Dic6H(5,𝔽2)semidirect
1802. C3#63014semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#35082
#870662
#870552
#870512
#870502
D3×#5502
#867802
#867752
#867702
#866722
#866652
#866492
#866292
#864742
#863362
#862882
#862782
#862502
#862412
#862382
#862282
#861952
#858712
#858452
#858432
#630143