Finite Group Databasebeta

← #11910734

Subgroups — #11910734

Order 1152.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596066C211yesmaximal, characteristic, complemented
2C3×#5589C211yesmaximal, characteristic, complemented
3C3×#5587C211yesmaximal, characteristic, complemented
4#10595507C212yesmaximal, complemented
5#10595493C212yesmaximal, complemented
6#10595276C211yesmaximal, characteristic, complemented
7#10595263C212yesmaximal, complemented
8#10595235C211yesmaximal, characteristic, complemented
9#10595212C211yesmaximal, characteristic, complemented
10#10595185C212yesmaximal, complemented
11D3×#935C211yesmaximal, characteristic, complemented
12#10595129C212yesmaximal, complemented
13#10595122C212yesmaximal, complemented
14#10594206C212yesmaximal, complemented
15#10594163C212yesmaximal, complemented
16#10594149C212yesmaximal, complemented
17#10594102C212yesmaximal, complemented
18#10594093C212yesmaximal, complemented
19#10594064C212yesmaximal, complemented
20#86820—31nomaximal
21#86300—31nomaximal
22C22×C3×#67C2211yescharacteristic
23C2×C3×D3×D4C2211yescharacteristic
24C2×#3804C2212yes—
25C22×D3×Dic3C2211yescharacteristic, complemented
26C2×#3799C2211yescharacteristic, complemented
27C32×#120C2211yescharacteristic
28#64162C2212yescomplemented
29#64149C2211yescharacteristic
30#64148C2212yescomplemented
31#64147C2212yescomplemented
32#64144C2211yescharacteristic
33#64093C2212yescomplemented
34#64092C2212yescomplemented
35#64088C2212yescomplemented
36C3×#953C2211yescharacteristic
37C2×C3×#217C2212yescomplemented
38C3×#938C2212yes—
39C3×#937C2212yes—
40C3×#936C2211yescharacteristic
41C3×#935C2211yescharacteristic
42C3×#935C2211yescharacteristic
43C3×#935C2212yescomplemented
44C3×D4×Dic3C2212yescomplemented
45C3×#886C2211yescharacteristic
46C3×#884C2212yes—
47C3×#883C2212yes—
48C3×D3×C22⋊C4C2211yescharacteristic
49C3×#879C2212yescomplemented
50C3×#878C2212yescomplemented
51C3×#877C2212yescomplemented
52#63982C2212yescomplemented
53#63978C2212yescomplemented
54#63978C2212yescomplemented
55#63977C2212yes—
56#63977C2212yescomplemented
57#63975C2212yescomplemented
58Dic3×#67C2212yes—
59Dic3×#67C2212yescomplemented
60#63971C2212yes—
61#63971C2212yescomplemented
62#63969C2212yes—
63#63969C2212yes—
64D3×#217C2212yes—
65D3×#217C2211yescharacteristic, complemented
66#63964C2212yescomplemented
67#63964C2212yescomplemented
68#63962C2211yescharacteristic, complemented
69#63961C2211yescharacteristic, complemented
70#63961C2212yescomplemented
71#63959C2212yescomplemented
72#63959C2212yescomplemented
73#63958C2212yes—
74#63958C2212yescomplemented
75#63958C2212yescomplemented
76#63956C2212yescomplemented
77#63956C2212yescomplemented
78#63956C2212yescomplemented
79#63953C2212yescomplemented
80#63953C2212yescomplemented
81#63952C2212yescomplemented
82#63952C2212yescomplemented
83#63952C2212yescomplemented
84#63911C2211yescharacteristic, complemented
85C4×#626C2212yescomplemented
86#63900C2212yescomplemented
87#63899C2212yescomplemented
88#63897C2212yescomplemented
89#63895C2212yescomplemented
90#63893C2212yescomplemented
91#63890C2212yescomplemented
92#63884C2212yescomplemented
93#63881C2212yescomplemented
94#63880C2212yescomplemented
95#63877C2212yescomplemented
96D3×Dic3⋊C4C2212yescomplemented
97#63869C2212yescomplemented
98#63867C2212yescomplemented
99#63863C2211yescharacteristic, complemented
100#63861C2212yescomplemented
101#63855C2211yescharacteristic, complemented
102#63853C2212yescomplemented
103#63851C2212yescomplemented
104#63850C2212yescomplemented
105#63846C2212yescomplemented
106#63841C2212yescomplemented
107#63839C2212yescomplemented
108#63838C2212yescomplemented
109C3×#551—31no—
110C3×#534—31no—
111#5806—32no—
112#5805—31no—
113C2×#935—31no—
114#5707—32no—
115#5705—32no—
116#5674—31no—
117#5672—31no—
118#5667—32no—
119#5664—31no—
120#5664—31no—
121#5660—32no—
122#5657—32no—
123#5655—32no—
124D3×#123—31no—
125#5651—31no—
126#5650—32no—
127#5640—32no—
128#5631—32no—
129#5621—32no—
130#5615—32no—
131#5614—32no—
132#5603—32no—
133#5595—31no—
134#5595—31no—
135#5595—61no—
136#5593—32no—
137#5593—32no—
138#5589D311yescharacteristic, complemented
139#5587D311yescharacteristic, complemented
140#5586—32no—
141#5558—32no—
142#5547—32no—
143#5535—32no—
144#5529—32no—
145#5495—32no—
146#5494—32no—
147#5490—32no—
148C24×C32C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2312yes—
152C2×C32×D4C2311yescharacteristic
153C2×#638C2312yes—
154C2×#638C2312yes—
155C2×#638C2312yes—
156C2×#638C2312yes—
157C22×C3⋊Dic3C2311yescharacteristic
158C2×C4⋊(C3⋊D3)C2311yescharacteristic
159C2×C4×C3⋊D3C2312yes—
160C2×C3×#67—42no—
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2311yescharacteristic
165C2×C3×#67C2311yescharacteristic
166C22×C3×Dic3C2312yes—
167C22×C3×Dic3C2312yes—
168C22×C3×Dic3C2311yescharacteristic
169C22×C3×Dic3C2311yescharacteristic
170C3×D3×D4—42no—
171C2×C3×D12C2311yescharacteristic
172C2×C3×C4×D3C2311yescharacteristic
173C2×C3×C4×D3C2312yes—
174C2×C3×Dic6C2311yescharacteristic
175C2×#627C2312yes—
176C2×#627C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#624C2312yes—
181C2×#624C2312yes—
182#3804—44no—
183C2×D3×Dic3—42no—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186C2×D3×Dic3C2312yes—
187#3799—42no—
188C32×C22⋊C4C2312yes—
189C32×C22⋊C4C2311yescharacteristic
190#3757C2312yes—
191#3757C2312yes—
192#3757C2312yes—
193#3757C2311yescharacteristic
194#3752C2312yes—
195C4⋊(C3⋊Dic3)C2312yes—
196#3750C2312yes—
197#3750C2312yes—
198C4×C3⋊Dic3C2311yescharacteristic
199C3×#217C2312yes—
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2311yescharacteristic
204C3×#217C2312yes—
205C3×#217C2312yes—
206C3×#217C2311yescharacteristic
207C3×#217C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×C4⋊Dic3C2312yes—
211C3×C4⋊Dic3C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×C4×Dic3C2311yescharacteristic
217C3×C4×Dic3C2312yes—
218#3724C2312yes—
219#3724C2312yes—
220#3724C2312yes—
221#3724C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228#3722C2312yes—
229#3722C2312yes—
230#3722C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237Dic32C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C22×C3×D4—31no—
242C22×C3×D4—31no—
243C22×#67C2×D311yescharacteristic
244C23×Dic3—31no—
245C2×#239—31no—
246C2×#237—32no—
247C2×D3×D4C2×D311yescharacteristic
248C2×#235—32no—
249C2×#235—31no—
250C22×C4×D3—31no—
251C3×#126—32no—
252C3×#124—31no—
253C3×#123—31no—
254C3×#123—31no—
255C3×#123—32no—
256C3×#123—32no—
257C3×#123—31no—
258C3×C22⋊Q8—32no—
259C3×#121—32no—
260C3×#121—32no—
261C3×#120—21no—
262C3×#120—31no—
263C3×#120—32no—
264C3×#120C2×D311yescharacteristic
265C3×#120C2×D311yescharacteristic
266C3×C4×D4—32no—
267C3×#117—32no—
268C2×C3×C22⋊C4—32no—
269C2×C3×C22⋊C4—31no—
270#953—32no—
271#953—32no—
272#953—32no—
273#953—32no—
274#953—62no—
275#953C2×D311yescharacteristic
276C2×#217—32no—
277C2×#217—31no—
278C2×#217C2×D312yescomplemented
279#947—31no—
280#944—32no—
281#940—31no—
282#940—31no—
283#940—31no—
284#940—61no—
285#939—32no—
286#939—32no—
287#939—32no—
288#939—32no—
289#939—32no—
290#939—32no—
291#939—62no—
292#938—32no—
293#938—32no—
294#938—32no—
295#938—32no—
296#938—32no—
297#938—62no—
298#938C2×D312yes—
299#937C2×D312yes—
300#936—31no—
301#936—32no—
302#936—32no—
303#936C2×D311yescharacteristic
304#935—31no—
305#935—31no—
306#935—31no—
307#935—32no—
308#935—32no—
309#935—32no—
310#935—31no—
311#935—32no—
312#935—61no—
313#935C2×D311yescharacteristic
314#935C2×D311yescharacteristic
315#935C2×D312yescomplemented
316D4×Dic3—32no—
317D4×Dic3—32no—
318D4×Dic3C2×D312yescomplemented
319#930—32no—
320#930—32no—
321#929—32no—
322#929—31no—
323#929—32no—
324C4×#67—32no—
325C4×#67—32no—
326C4×#67—32no—
327C4×#67—32no—
328C4×#67—32no—
329C4×#67—32no—
330#926—32no—
331#926—31no—
332#924—32no—
333#924—32no—
334#924—32no—
335C2×Dic3⋊C4—32no—
336#898—32no—
337#897—32no—
338#897—32no—
339#896—32no—
340#896—32no—
341#896—32no—
342#894—32no—
343#894—32no—
344#894—32no—
345#894—32no—
346#894—32no—
347#894—32no—
348#893—32no—
349#892—32no—
350D3×C4⋊C4—32no—
351D3×C4⋊C4—32no—
352D3×C4⋊C4—32no—
353#890—32no—
354#890—32no—
355#889—32no—
356#889—32no—
357#888—32no—
358#887—32no—
359#887—32no—
360#886—31no—
361#886—32no—
362#886C2×D311yescharacteristic
363#885—32no—
364#885—32no—
365#885—32no—
366#885—32no—
367#885—32no—
368#885—32no—
369#884—32no—
370#884—32no—
371#884—32no—
372#884—32no—
373#884—32no—
374#884—32no—
375#884—32no—
376#884—62no—
377#884C2×D312yes—
378#883—32no—
379#883—32no—
380#883—32no—
381#883—32no—
382#883—32no—
383#883—32no—
384#883—32no—
385#883—62no—
386#883C2×D312yes—
387#882—32no—
388#882—32no—
389#67⋊C4—32no—
390#67⋊C4—32no—
391#67⋊C4—32no—
392#67⋊C4—32no—
393#67⋊C4—32no—
394D3×C22⋊C4—31no—
395D3×C22⋊C4—32no—
396D3×C22⋊C4C2×D311yescharacteristic
397#879—32no—
398#879—32no—
399#879—32no—
400#879—32no—
401#879—32no—
402#879—32no—
403#879—32no—
404#879—32no—
405#879—32no—
406#879—62no—
407#879C2×D312yescomplemented
408#878—32no—
409#878—32no—
410#878—32no—
411#878—32no—
412#878—32no—
413#878—32no—
414#878C2×D312yescomplemented
415#877—32no—
416#877C2×D312yescomplemented
417#874—31no—
418C4×D12—32no—
419C4×D12—32no—
420#872—31no—
421#872—32no—
422#870—32no—
423#870—32no—
424C23×C32—42no—
425C23×C32—41no—
426C23×C32C2411yescharacteristic
427C23×C32C2411yescharacteristic
428C23×C32C2412yes—
429C22×C3⋊D3C2412yes—
430C22×C3×D3—22no—
431C22×C3×D3—22no—
432C22×C3×D3—42no—
433C22×C3×D3—42no—
434C22×C3×D3C2411yescharacteristic
435C22×C3×D3C2411yescharacteristic
436C22×C3×D3C2411yescharacteristic
437C32×D4—41no—
438C32×D4—42no—
439C2×C32×C4C2411yescharacteristic
440C2×C32×C4C2412yes—
441#638—42no—
442#638—42no—
443#638—42no—
444#638—42no—
445C2×C3⋊Dic3—41no—
446C2×C3⋊Dic3C2412yes—
447C2×C3⋊Dic3C2412yes—
448C2×C3⋊Dic3C2412yes—
449C4⋊(C3⋊D3)—41no—
450C4×C3⋊D3—42no—
451C3×#67—24no—
452C3×#67—41no—
453C3×#67—41no—
454C3×#67—42no—
455C3×#67—42no—
456C2×C3×Dic3—41no—
457C2×C3×Dic3—42no—
458C2×C3×Dic3—42no—
459C2×C3×Dic3—41no—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2412yes—
466C2×C3×Dic3C2411yescharacteristic
467C3×D12—41no—
468C3×C4×D3—22no—
469C3×C4×D3—42no—
470C3×Dic6—41no—
471#627—42no—
472#627—42no—
473#626—24no—
474#626—42no—
475#626—42no—
476#624—42no—
477#624—42no—
478D3×Dic3—24no—
479D3×Dic3—42no—
480D3×Dic3—42no—
481#563—91no—
482#562—92no—
483#560—91no—
484#559—91no—
485#553—92no—
486#552—92no—
487#551—31no—
488#551—92no—
489#547—92no—
490#546—92no—
491#542—92no—
492#540—92no—
493#539—92no—
494#538—92no—
495#538—92no—
496#535—91no—
497#534—31no—
498#525—92no—
499C2×#123—91no—
500C24×C3—21no—
501C24×C3—31no—
502C24×C3—31no—
503C24×C3C22×D311yescharacteristic
504C24×C3C22×D311yescharacteristic
505C23×D3C22×D311yescharacteristic
506C23×D3C22×D311yescharacteristic
507C2×C3×Q8—31no—
508C2×C3×D4—21no—
509C2×C3×D4—22no—
510C2×C3×D4—32no—
511C2×C3×D4—32no—
512C2×C3×D4—31no—
513C2×C3×D4—31no—
514C2×C3×D4—32no—
515C2×C3×D4—31no—
516C2×C3×D4—122no—
517C2×C3×D4—122no—
518C2×C3×D4C22×D312yes—
519C2×C3×D4C22×D311yescharacteristic
520C2×C3×D4C22×D311yescharacteristic
521C2×C3×D4C22×D312yes—
522C22×C3×C4—31no—
523C22×C3×C4—32no—
524C22×C3×C4—32no—
525C22×C3×C4—31no—
526C22×C3×C4—31no—
527C22×C3×C4—32no—
528C2×#67—32no—
529C2×#67—32no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—32no—
539C2×#67—42no—
540C2×#67—62no—
541C2×#67—62no—
542C2×#67—62no—
543C2×#67—62no—
544C2×#67C22×D312yes—
545C2×#67C22×D311yescharacteristic
546C2×#67C22×D311yescharacteristic
547C2×#67C22×D312yes—
548C2×#67C22×D312yes—
549C22×Dic3—31no—
550C22×Dic3—31no—
551C22×Dic3—32no—
552C22×Dic3—32no—
553C22×Dic3—32no—
554C22×Dic3—61no—
555C22×Dic3—122no—
556C22×Dic3C22×D312yes—
557C22×Dic3C22×D311yescharacteristic
558C22×Dic3C22×D312yes—
559C22×Dic3C22×D311yescharacteristic
560#239—122no—
561#237—124no—
562D3×D4—42no—
563#235—122no—
564#235—124no—
565C2×D12—32no—
566C2×D12—32no—
567C2×D12—32no—
568C2×D12—31no—
569C2×D12—31no—
570C2×D12—61no—
571C2×D12C22×D311yescharacteristic
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—32no—
581C2×C4×D3—62no—
582C2×C4×D3—122no—
583C2×C4×D3C22×D311yescharacteristic
584C2×C4×D3C22×D312yes—
585C2×Dic6—32no—
586C2×Dic6—32no—
587C2×Dic6—32no—
588C2×Dic6—32no—
589C2×Dic6C22×D311yescharacteristic
590C3×C4⋊C4—32no—
591C3×C4⋊C4—32no—
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C22⋊C4—22no—
597C3×C22⋊C4—21no—
598C3×C22⋊C4—32no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—31no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—32no—
605C3×C22⋊C4—31no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4C22×D312yes—
610C3×C22⋊C4C22×D312yes—
611C3×C22⋊C4C22×D311yescharacteristic
612C3×C22⋊C4C22×D311yescharacteristic
613C3×C42—31no—
614C3×C42—32no—
615#217—32no—
616#217—32no—
617#217—31no—
618#217—32no—
619#217—32no—
620#217—31no—
621#217—32no—
622#217—32no—
623#217—32no—
624#217—32no—
625#217—32no—
626#217—32no—
627#217—32no—
628#217—32no—
629#217—62no—
630#217—62no—
631#217—62no—
632#217—61no—
633#217C22×D312yes—
634#217C22×D312yes—
635#217C22×D312yes—
636#217C22×D312yes—
637#217C22×D311yescharacteristic
638#217C22×D312yes—
639#217C22×D312yes—
640#217C22×D312yes—
641#217C22×D311yescharacteristic
642(C2×D3)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—32no—
648(C2×D3)⋊C4—32no—
649(C2×D3)⋊C4—32no—
650(C2×D3)⋊C4—32no—
651(C2×D3)⋊C4—32no—
652(C2×D3)⋊C4—32no—
653(C2×D3)⋊C4—32no—
654(C2×D3)⋊C4—32no—
655(C2×D3)⋊C4—32no—
656(C2×D3)⋊C4—62no—
657(C2×D3)⋊C4C22×D312yes—
658(C2×D3)⋊C4C22×D312yes—
659C4⋊Dic3—32no—
660C4⋊Dic3—32no—
661C4⋊Dic3—32no—
662C4⋊Dic3—32no—
663C4⋊Dic3—32no—
664C4⋊Dic3—32no—
665C4⋊Dic3—32no—
666C4⋊Dic3—32no—
667C4⋊Dic3—62no—
668C4⋊Dic3C22×D312yes—
669C4⋊Dic3C22×D312yes—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4—32no—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—32no—
687Dic3⋊C4—32no—
688Dic3⋊C4—62no—
689Dic3⋊C4—62no—
690Dic3⋊C4C22×D312yes—
691Dic3⋊C4C22×D312yes—
692Dic3⋊C4C22×D312yes—
693Dic3⋊C4C22×D312yes—
694C4×Dic3—31no—
695C4×Dic3—31no—
696C4×Dic3—32no—
697C4×Dic3—32no—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—32no—
702C4×Dic3—61no—
703C4×Dic3C22×D312yes—
704C4×Dic3C22×D311yescharacteristic
705C22×C32—22no—
706C22×C32—21no—
707C22×C32—21no—
708C22×C32—22no—
709C22×C32—22no—
710C22×C32—22no—
711C22×C32—22no—
712C22×C32—82no—
713C22×C32C2511yescharacteristic
714C2×C3⋊D3—22no—
715C2×C3⋊D3—22no—
716C2×C3⋊D3—22no—
717C2×C3×D3—22no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—22no—
721C2×C3×D3—22no—
722C2×C3×D3—44no—
723C2×C3×D3—82no—
724C2×C3×D3H(5,𝔽2)12yes—
725C32×C4—21no—
726C32×C4—22no—
727C3⋊Dic3—22no—
728C3⋊Dic3—22no—
729C3⋊Dic3—22no—
730C3×Dic3—22no—
731C3×Dic3—21no—
732C3×Dic3—22no—
733C3×Dic3—22no—
734C3×Dic3—22no—
735C3×Dic3—22no—
736C3×Dic3—22no—
737C2×#41—92no—
738C2×#41—91no—
739C22×D4—31no—
740C22×D4—31no—
741C23×C4—91no—
742C4⋊Q8—92no—
743#127—91no—
744#127—91no—
745#126—32no—
746#126—92no—
747#126—92no—
748#126—92no—
749#126—92no—
750#126—92no—
751#125—92no—
752#125—92no—
753#125—92no—
754#124—31no—
755#124—92no—
756#124—92no—
757#124—92no—
758#124—92no—
759#124—91no—
760#123—31no—
761#123—31no—
762#123—32no—
763#123—31no—
764#123—32no—
765#123—92no—
766#123—92no—
767#123—92no—
768#123—92no—
769#123—91no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—92no—
774#123—91no—
775#123—92no—
776#123—91no—
777#123—92no—
778C22⋊Q8—32no—
779C22⋊Q8—92no—
780C22⋊Q8—92no—
781C22⋊Q8—92no—
782C22⋊Q8—92no—
783C22⋊Q8—92no—
784C22⋊Q8—92no—
785C22⋊Q8—92no—
786#121—32no—
787#121—32no—
788#121—92no—
789#121—92no—
790#121—92no—
791#121—92no—
792#121—92no—
793#121—92no—
794#121—92no—
795#121—92no—
796#121—92no—
797#121—92no—
798#120—31no—
799#120—32no—
800#120—92no—
801#120—92no—
802#120—92no—
803#120D3211yescharacteristic
804C4×Q8—92no—
805C4×D4—32no—
806C4×D4—92no—
807C4×D4—92no—
808C4×D4—92no—
809C4×D4—92no—
810C4×D4—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814#117—32no—
815#117—92no—
816#117—91no—
817#117—92no—
818C2×C4⋊C4—92no—
819C2×C4⋊C4—92no—
820C2×C22⋊C4—32no—
821C2×C22⋊C4—31no—
822C2×C22⋊C4—91no—
823C2×C22⋊C4—92no—
824C23×C3—21no—
825C23×C3—22no—
826C23×C3—21no—
827C23×C3—31no—
828C23×C3—31no—
829C23×C3—31no—
830C23×C3—41no—
831C23×C3—41no—
832C23×C3—42no—
833C23×C3—42no—
834C23×C3—62no—
835C23×C3—62no—
836C23×C3—81no—
837C23×C3—82no—
838C23×C3—122no—
839C23×C3—122no—
840C23×C3C23×D311yescharacteristic
841C23×C3C23×D312yes—
842C23×C3C23×D311yescharacteristic
843C23×C3C23×D312yes—
844C23×C3C23×D311yescharacteristic
845C23×C3C23×D311yescharacteristic
846C22×D3—22no—
847C22×D3—22no—
848C22×D3—32no—
849C22×D3—32no—
850C22×D3—42no—
851C22×D3—42no—
852C22×D3—62no—
853C22×D3C23×D311yescharacteristic
854C22×D3C23×D311yescharacteristic
855C22×D3C23×D311yescharacteristic
856C3×Q8—121no—
857C3×D4—41no—
858C3×D4—41no—
859C3×D4—42no—
860C3×D4—42no—
861C3×D4—64no—
862C3×D4—81no—
863C3×D4—82no—
864C3×D4—121no—
865C3×D4—122no—
866C3×D4—122no—
867C3×D4—121no—
868C3×D4—121no—
869C2×C3×C4—21no—
870C2×C3×C4—22no—
871C2×C3×C4—32no—
872C2×C3×C4—32no—
873C2×C3×C4—32no—
874C2×C3×C4—32no—
875C2×C3×C4—32no—
876C2×C3×C4—31no—
877C2×C3×C4—32no—
878C2×C3×C4—62no—
879C2×C3×C4—122no—
880C2×C3×C4—121no—
881C2×C3×C4—122no—
882C2×C3×C4—122no—
883C2×C3×C4—121no—
884C2×C3×C4C23×D311yescharacteristic
885C2×C3×C4C23×D311yescharacteristic
886C2×C3×C4C23×D312yes—
887C2×C3×C4C23×D312yes—
888#67—24no—
889#67—41no—
890#67—41no—
891#67—42no—
892#67—42no—
893#67—64no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—122no—
899#67—122no—
900#67—122no—
901#67—122no—
902#67—122no—
903#67—122no—
904#67—242no—
905#67—242no—
906#67—242no—
907#67—242no—
908C2×Dic3—32no—
909C2×Dic3—32no—
910C2×Dic3—32no—
911C2×Dic3—32no—
912C2×Dic3—32no—
913C2×Dic3—32no—
914C2×Dic3—42no—
915C2×Dic3—41no—
916C2×Dic3—42no—
917C2×Dic3—41no—
918C2×Dic3—62no—
919C2×Dic3—62no—
920C2×Dic3—62no—
921C2×Dic3—64no—
922C2×Dic3—122no—
923C2×Dic3—122no—
924C2×Dic3—121no—
925C2×Dic3—121no—
926C2×Dic3—241no—
927C2×Dic3C23×D312yes—
928C2×Dic3C23×D312yes—
929C2×Dic3C23×D312yes—
930C2×Dic3C23×D312yes—
931C2×Dic3C23×D312yes—
932C2×Dic3C23×D312yes—
933C2×Dic3C23×D311yescharacteristic
934D12—41no—
935D12—64no—
936D12—121no—
937D12—121no—
938D12—122no—
939D12—122no—
940D12—241no—
941C4×D3—22no—
942C4×D3—42no—
943C4×D3—64no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948C4×D3—122no—
949C4×D3—122no—
950C4×D3—122no—
951C4×D3—122no—
952C4×D3—242no—
953Dic6—41no—
954Dic6—122no—
955Dic6—122no—
956Dic6—122no—
957Dic6—122no—
958C2×C32—41no—
959C2×C32—41no—
960C2×C32—42no—
961C2×C32C2×H(5,𝔽2)11yescharacteristic
962C2×C32#58512yes—
963C3⋊D3—42no—
964C3×D3—22no—
965C3×D3—41no—
966C3×D3—41no—
967C24—31no—
968C24—31no—
969C24C2×D3211yescharacteristic
970#41—362no—
971#41—364no—
972C2×Q8—31no—
973C2×Q8—92no—
974C2×Q8—92no—
975C2×D4—32no—
976C2×D4—32no—
977C2×D4—31no—
978C2×D4—31no—
979C2×D4—32no—
980C2×D4—31no—
981C2×D4—92no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4—92no—
988C2×D4—91no—
989C2×D4—122no—
990C2×D4—122no—
991C2×D4C2×D3212yes—
992C2×D4C2×D3211yescharacteristic
993C22×C4—32no—
994C22×C4—32no—
995C22×C4—31no—
996C22×C4—31no—
997C22×C4—31no—
998C22×C4—32no—
999C22×C4—92no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—92no—
1004C22×C4—91no—
1005C22×C4—92no—
1006C22×C4—362no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—32no—
1012C4⋊C4—32no—
1013C4⋊C4—92no—
1014C4⋊C4—92no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4—92no—
1024C4⋊C4—92no—
1025C4⋊C4—92no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—31no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—31no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—32no—
1036C22⋊C4—32no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—91no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4C2×D3211yescharacteristic
1052C22⋊C4C2×D3212yes—
1053C42—31no—
1054C42—32no—
1055C42—92no—
1056C42—92no—
1057C42—92no—
1058C42—91no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—22no—
1062C22×C3—22no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—21no—
1067C22×C3—22no—
1068C22×C3—21no—
1069C22×C3—22no—
1070C22×C3—22no—
1071C22×C3—22no—
1072C22×C3—22no—
1073C22×C3—21no—
1074C22×C3—32no—
1075C22×C3—41no—
1076C22×C3—42no—
1077C22×C3—42no—
1078C22×C3—42no—
1079C22×C3—42no—
1080C22×C3—41no—
1081C22×C3—42no—
1082C22×C3—62no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—82no—
1088C22×C3—82no—
1089C22×C3—84no—
1090C22×C3—124no—
1091C22×C3—242no—
1092C22×C3C24×D311yescharacteristic
1093C22×C3C24×D311yescharacteristic
1094C2×D3—22no—
1095C2×D3—21no—
1096C2×D3—21no—
1097C2×D3—22no—
1098C2×D3—22no—
1099C2×D3—44no—
1100C2×D3—62no—
1101C2×D3—62no—
1102C2×D3—62no—
1103C2×D3—62no—
1104C2×D3—62no—
1105C2×D3—62no—
1106C2×D3—82no—
1107C2×D3—122no—
1108C2×D3—122no—
1109C2×D3—122no—
1110C2×D3#100412yes—
1111C3×C4—21no—
1112C3×C4—22no—
1113C3×C4—21no—
1114C3×C4—22no—
1115C3×C4—42no—
1116C3×C4—41no—
1117C3×C4—62no—
1118C3×C4—62no—
1119C3×C4—62no—
1120C3×C4—62no—
1121C3×C4—61no—
1122C3×C4—62no—
1123C3×C4—62no—
1124Dic3—22no—
1125Dic3—21no—
1126Dic3—22no—
1127Dic3—22no—
1128Dic3—22no—
1129Dic3—22no—
1130Dic3—22no—
1131Dic3—62no—
1132Dic3—62no—
1133Dic3—62no—
1134Dic3—62no—
1135Dic3—62no—
1136Dic3—62no—
1137Dic3—122no—
1138Dic3—122no—
1139Dic3—122no—
1140C32#353311yescharacteristic, complemented, Sylow
1141C23—31no—
1142C23—31no—
1143C23—31no—
1144C23—41no—
1145C23—42no—
1146C23—62no—
1147C23—62no—
1148C23—92no—
1149C23—122no—
1150C23—122no—
1151C23C22×D3211yescharacteristic
1152C23C22×D3211yescharacteristic
1153C23C22×D3212yes—
1154Q8—121no—
1155Q8—362no—
1156Q8—362no—
1157D4—41no—
1158D4—42no—
1159D4—64no—
1160D4—121no—
1161D4—121no—
1162D4—121no—
1163D4—122no—
1164D4—122no—
1165D4—184no—
1166D4—361no—
1167D4—362no—
1168D4—362no—
1169D4—362no—
1170D4—362no—
1171D4—362no—
1172D4—362no—
1173C2×C4—32no—
1174C2×C4—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—31no—
1180C2×C4—62no—
1181C2×C4—92no—
1182C2×C4—92no—
1183C2×C4—92no—
1184C2×C4—122no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—122no—
1188C2×C4—122no—
1189C2×C4—184no—
1190C2×C4—362no—
1191C2×C4—362no—
1192C2×C4—362no—
1193C2×C4—362no—
1194C2×C4—362no—
1195C2×C4—361no—
1196C2×C4C22×D3211yescharacteristic
1197C2×C4C22×D3212yes—
1198C2×C3—21no—
1199C2×C3—22no—
1200C2×C3—41no—
1201C2×C3—41no—
1202C2×C3—42no—
1203C2×C3—41no—
1204C2×C3—42no—
1205C2×C3—41no—
1206C2×C3—62no—
1207C2×C3—81no—
1208C2×C3—82no—
1209C2×C3—81no—
1210C2×C3—121no—
1211C2×C3—121no—
1212C2×C3C2×#100411yescharacteristic
1213C2×C3#596412yes—
1214C2×C3D3×H(5,𝔽2)11yescharacteristic
1215C2×C3#596612yes—
1216D3—22no—
1217D3—41no—
1218D3—41no—
1219D3—122no—
1220D3—122no—
1221D3—242no—
1222C22—21no—
1223C22—21no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—32no—
1230C22—62no—
1231C22—61no—
1232C22—61no—
1233C22—62no—
1234C22—62no—
1235C22—82no—
1236C22—124no—
1237C22—182no—
1238C22—182no—
1239C22—182no—
1240C22—242no—
1241C22C23×D3211yescharacteristic
1242C4—21no—
1243C4—22no—
1244C4—61no—
1245C4—62no—
1246C4—62no—
1247C4—62no—
1248C4—62no—
1249C4—62no—
1250C4—62no—
1251C4—182no—
1252C4—182no—
1253C4—182no—
1254C3—21no—
1255C3#8630011yescharacteristic, complemented
1256C3#8682011yescharacteristic, complemented
1257C2—41no—
1258C2—42no—
1259C2—41no—
1260C2—62no—
1261C2—121no—
1262C2—121no—
1263C2—362no—
1264C2D3×#100411yescharacteristic
1265C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#120C22
hypercenter#120D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #10596066C2semidirect
2. C3×#5589C2semidirect
3. C3×#5587C2semidirect
4. #10595507C2semidirect
5. #10595493C2semidirect
6. #10595276C2semidirect
7. #10595263C2semidirect
8. #10595235C2semidirect
9. #10595212C2semidirect
10. #10595185C2semidirect
11. D3×#935C2semidirect
12. #10595129C2semidirect
13. #10595122C2semidirect
14. #10594206C2semidirect
15. #10594163C2semidirect
16. #10594149C2semidirect
17. #10594102C2semidirect
18. #10594093C2semidirect
19. #10594064C2semidirect
25. C22×D3×Dic3C22semidirect
26. C2×#3799C22semidirect
28. #64162C22semidirect
30. #64148C22semidirect
31. #64147C22semidirect
33. #64093C22semidirect
34. #64092C22semidirect
35. #64088C22semidirect
37. C2×C3×#217C22semidirect
43. C3×#935C22semidirect
44. C3×D4×Dic3C22semidirect
49. C3×#879C22semidirect
50. C3×#878C22semidirect
51. C3×#877C22semidirect
52. #63982C22semidirect
53. #63978C22semidirect
54. #63978C22semidirect
56. #63977C22semidirect
57. #63975C22semidirect
59. Dic3×#67C22semidirect
61. #63971C22semidirect
65. D3×#217C22semidirect
66. #63964C22semidirect
67. #63964C22semidirect
68. #63962C22semidirect
69. #63961C22semidirect
70. #63961C22semidirect
71. #63959C22semidirect
72. #63959C22semidirect
74. #63958C22semidirect
75. #63958C22semidirect
76. #63956C22semidirect
77. #63956C22semidirect
78. #63956C22semidirect
79. #63953C22semidirect
80. #63953C22semidirect
81. #63952C22semidirect
82. #63952C22semidirect
83. #63952C22semidirect
84. #63911C22semidirect
85. C4×#626C22semidirect
86. #63900C22semidirect
87. #63899C22semidirect
88. #63897C22semidirect
89. #63895C22semidirect
90. #63893C22semidirect
91. #63890C22semidirect
92. #63884C22semidirect
93. #63881C22semidirect
94. #63880C22semidirect
95. #63877C22semidirect
96. D3×Dic3⋊C4C22semidirect
97. #63869C22semidirect
98. #63867C22semidirect
99. #63863C22semidirect
100. #63861C22semidirect
101. #63855C22semidirect
102. #63853C22semidirect
103. #63851C22semidirect
104. #63850C22semidirect
105. #63846C22semidirect
106. #63841C22semidirect
107. #63839C22semidirect
108. #63838C22semidirect
138. #5589D3semidirect
139. #5587D3semidirect
278. C2×#217C2×D3semidirect
315. #935C2×D3semidirect
318. D4×Dic3C2×D3semidirect
407. #879C2×D3semidirect
414. #878C2×D3semidirect
416. #877C2×D3semidirect
1140. C32#3533semidirect
1255. C3#86300semidirect
1256. C3#86820semidirect

Maximal subgroups

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

subgroupindex
#105960662
C3×#55892
C3×#55872
#105955072
#105954932
#105952762
#105952632
#105952352
#105952122
#105951852
D3×#9352
#105951292
#105951222
#105942062
#105941632
#105941492
#105941022
#105940932
#105940642
#868203
#863003