Finite Group Databasebeta

← #11904628

Subgroups — #11904628

Order 1152.

3483 conjugacy classes of subgroups.

The subgroup lattice has 1687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×D3×#237C211yesmaximal, characteristic, complemented
3#10596277C211yesmaximal, characteristic, complemented
4C3×D4×#67C211yesmaximal, characteristic, complemented
5#672C212yesmaximal, complemented
6#10595513C212yesmaximal, complemented
7C2×#63970C212yesmaximal, complemented
8#10595494C212yesmaximal, complemented
9#10595287C212yesmaximal, complemented
10D3×#938C211yesmaximal, characteristic, complemented
11#10595246C211yesmaximal, characteristic, complemented
12#10595233C211yesmaximal, characteristic, complemented
13D4×#625C211yesmaximal, characteristic, complemented
14#10595222C211yesmaximal, characteristic, complemented
15#10595158C211yesmaximal, characteristic, complemented
16#10595157C211yesmaximal, characteristic, complemented
17#10595156C212yesmaximal, complemented
18#10595154C212yesmaximal, complemented
19#10595150C212yesmaximal, complemented
20#10595060C211yesmaximal, characteristic, complemented
21#10595006C211yesmaximal, characteristic, complemented
22#10595004C211yesmaximal, characteristic, complemented
23#10594899C211yesmaximal, characteristic, complemented
24#87285—31nomaximal
25#86607—31nomaximal
26C22×C32×D4C2211yescharacteristic, complemented
27C2×#3830C2211yescharacteristic, complemented
28C22×C3×#67C2212yescomplemented
29C22×C3×#67C2212yescomplemented
30C22×C3×#67C2212yescomplemented
31C3×#1004—28no—
32C2×C3×#237C2211yescharacteristic
33C2×C3×#237C2212yescomplemented
34C2×C3×#237C2211yescharacteristic, complemented
35C2×C3×D3×D4C2211yescharacteristic, complemented
36C2×C3×D3×D4C2212yescomplemented
37C2×C3×D3×D4C2211yescharacteristic, complemented
38C2×C3×D3×D4C2211yescharacteristic, complemented
39C2×C3×#235C2211yescharacteristic, complemented
40C2×C3×#235C2211yescharacteristic, complemented
41C2×D3×#67C2212yescomplemented
42C2×D3×#67C2212yescomplemented
43C22×#625C2212yescomplemented
44C2×#3805C2212yescomplemented
45C2×#3804C2212yescomplemented
46C22×D3×Dic3C2212yescomplemented
47D3×#237—28no—
48C2×C4×D32C2211yescharacteristic, complemented
49C2×#3796C2211yescharacteristic, complemented
50C2×#3795C2211yescharacteristic, complemented
51C2×D3×Dic6C2211yescharacteristic, complemented
52#64162C2212yescomplemented
53C2×#3757C2212yescomplemented
54#64148C2212yescomplemented
55#64147C2211yescharacteristic, complemented
56#64145C2211yescharacteristic, complemented
57#64144C2212yescomplemented
58D4×C3⋊Dic3C2211yescharacteristic, complemented
59C4×#638C2211yescharacteristic, complemented
60#64133C2211yescharacteristic, complemented
61C3×#953C2212yescomplemented
62C3×#940C2211yescharacteristic, complemented
63C3×#939C2212yescomplemented
64C3×#938C2211yescharacteristic, complemented
65C3×#937C2212yescomplemented
66C3×D4×Dic3C2211yescharacteristic, complemented
67C3×#930C2211yescharacteristic, complemented
68C3×C4×#67C2211yescharacteristic, complemented
69#63983C2211yescharacteristic, complemented
70#63980C2212yescomplemented
71#63979C2212yescomplemented
72#63979C2212yescomplemented
73#63978C2212yescomplemented
74#63978C2212yescomplemented
75#63977C2212yescomplemented
76#63976C2212yescomplemented
77#63976C2212yescomplemented
78#63976C2212yescomplemented
79#63976C2212yescomplemented
80#67⋊Dic3C2212yescomplemented
81Dic3×#67C2212yescomplemented
82Dic3×#67C2212yescomplemented
83Dic3×#67C2212yescomplemented
84#63970C2212yescomplemented
85#63970C2212yescomplemented
86#63970C2212yescomplemented
87#63970C2212yescomplemented
88#63970C2212yescomplemented
89#63970C2212yescomplemented
90#63970C2212yescomplemented
91#63970C2212yescomplemented
92#63970C2211yescharacteristic, complemented
93#63970C2212yescomplemented
94#63969C2211yescharacteristic, complemented
95D3×#217C2212yescomplemented
96C2×Dic3⋊Dic3C2212yescomplemented
97#63964C2212yescomplemented
98#63962C2212yescomplemented
99C2×(C2×D3)⋊Dic3C2212yescomplemented
100#63959C2212yescomplemented
101#63959C2212yescomplemented
102#63958C2212yescomplemented
103#63958C2211yescharacteristic, complemented
104#63955C2212yescomplemented
105#63922C2211yescharacteristic, complemented
106#63916C2211yescharacteristic, complemented
107#63914C2211yescharacteristic, complemented
108#63908C2211yescharacteristic, complemented
109#63908C2211yescharacteristic, complemented
110#63906C2212yescomplemented
111C4×#626C2211yescharacteristic, complemented
112C4×#625C2211yescharacteristic, complemented
113D3×C4⋊Dic3C2211yescharacteristic, complemented
114#63888C2211yescharacteristic, complemented
115#63887C2211yescharacteristic, complemented
116#63887C2212yescomplemented
117#63885C2212yescomplemented
118#63884C2211yescharacteristic, complemented
119#63879C2212yescomplemented
120#63879C2212yescomplemented
121#63860C2211yescharacteristic, complemented
122#63857C2211yescharacteristic, complemented
123#63855C2211yescharacteristic, complemented
124#63851C2212yescomplemented
125#63843C2211yescharacteristic, complemented
126Dic3×Dic6C2211yescharacteristic, complemented
127C2×C3×H(5,𝔽2)—31no—
128C2×D3×#41—31no—
129C2×#1004D311yescharacteristic, complemented
130C22×#237—31no—
131C3×D42—31no—
132#5834—31no—
133#5834—31no—
134#5833—32no—
135#5833—31no—
136#5831—31no—
137#5831—31no—
138#5828—32no—
139#5828—31no—
140#5827—31no—
141#5806—31no—
142#5806—31no—
143#5806—32no—
144#5806—32no—
145#5806—31no—
146#5806—61no—
147#5805—32no—
148#5805—31no—
149C2×#939—32no—
150D4×#67—32no—
151D4×#67—32no—
152D4×#67—31no—
153D4×#67—31no—
154D4×#67—32no—
155D4×#67D311yescharacteristic, complemented
156C2×#938—32no—
157C2×#938—31no—
158#5718—31no—
159#5715—31no—
160#5610—32no—
161#5608—31no—
162D3×#121—31no—
163#5599—31no—
164#5598—31no—
165#5597—32no—
166#5592—32no—
167#5591—32no—
168#5590—32no—
169#5586—32no—
170#5554—31no—
171#5552—31no—
172#5547—31no—
173#5546—31no—
174C24×C32C2312yes—
175C23×C3×D3C2312yes—
176C23×C3×D3C2312yes—
177C23×C3×D3C2312yes—
178C22×D32C2311yescharacteristic
179C2×C32×D4—24no—
180C2×C32×D4C2312yes—
181C2×C32×D4C2311yescharacteristic
182C2×C32×D4C2311yescharacteristic
183C22×C32×C4C2311yescharacteristic
184C2×#638C2312yes—
185C2×#638C2312yes—
186C2×#638C2311yescharacteristic
187C22×C3⋊Dic3C2312yes—
188C22×C3⋊Dic3C2312yes—
189#3830—24no—
190C2×C4×C3⋊D3C2311yescharacteristic
191C2×#634C2311yescharacteristic
192C2×C3×#67—28no—
193C2×C3×#67—28no—
194C2×C3×#67—44no—
195C2×C3×#67C2311yescharacteristic
196C2×C3×#67C2312yes—
197C2×C3×#67C2312yes—
198C2×C3×#67C2311yescharacteristic
199C2×C3×#67C2312yes—
200C2×C3×#67C2311yescharacteristic
201C2×C3×#67C2312yes—
202C2×C3×#67C2312yes—
203C2×C3×#67C2312yes—
204C2×C3×#67C2312yes—
205C2×C3×#67C2312yes—
206C2×C3×#67C2312yes—
207C2×C3×#67C2312yes—
208C22×C3×Dic3C2312yes—
209C22×C3×Dic3C2312yes—
210C22×C3×Dic3C2312yes—
211C3×#237—28no—
212C3×#237—24no—
213C3×#237D418yescomplemented
214C3×D3×D4—24no—
215C3×D3×D4—24no—
216C3×D3×D4—28no—
217C3×D3×D4—24no—
218C3×#235—24no—
219C3×#235—24no—
220C2×C3×D12C2311yescharacteristic
221C2×C3×D12C2311yescharacteristic
222C2×C3×D12C2311yescharacteristic
223C2×C3×C4×D3C2311yescharacteristic
224C2×C3×C4×D3C2312yes—
225C2×C3×C4×D3C2311yescharacteristic
226C2×C3×C4×D3C2311yescharacteristic
227C2×C3×Dic6C2311yescharacteristic
228C2×C3×Dic6C2311yescharacteristic
229D3×#67—28no—
230D3×#67—44no—
231C2×#627C2312yes—
232C2×#626C2312yes—
233C2×#626C2312yes—
234C2×#626C2311yescharacteristic
235C2×#625—44no—
236C2×#625C2312yes—
237C2×#625C2311yescharacteristic
238C2×#625C2312yes—
239C2×#625C2312yes—
240C2×#625C2312yes—
241C2×#625C2312yes—
242C2×#624C2311yescharacteristic
243#3805—28no—
244#3804—28no—
245C2×D3×Dic3—28no—
246C2×D3×Dic3C2312yes—
247C2×D3×Dic3C2312yes—
248C2×D3×Dic3C2312yes—
249C2×D3×Dic3C2311yescharacteristic
250C2×D3×Dic3C2311yescharacteristic
251C2×D3×Dic3C2312yes—
252C4×D32—24no—
253#3796—24no—
254#3795—24no—
255D3×Dic6—24no—
256#3757C2312yes—
257#3757C2311yescharacteristic
258#3757C2312yes—
259#3757C2312yes—
260#3757C2312yes—
261#3757C2312yes—
262#3752C2311yescharacteristic
263C4⋊(C3⋊Dic3)C2311yescharacteristic
264#3750C2312yes—
265#3750C2311yescharacteristic
266C4×C3⋊Dic3C2311yescharacteristic
267C3×#217C2311yescharacteristic
268C3×#217C2312yes—
269C3×#217C2312yes—
270C3×(C2×D3)⋊C4C2311yescharacteristic
271C3×(C2×D3)⋊C4C2312yes—
272C3×C4⋊Dic3C2311yescharacteristic
273C3×Dic3⋊C4C2311yescharacteristic
274C3×C4×Dic3C2311yescharacteristic
275#3724C2311yescharacteristic
276Dic3⋊Dic3C2312yes—
277Dic3⋊Dic3C2312yes—
278Dic3⋊Dic3C2311yescharacteristic
279Dic3⋊Dic3C2311yescharacteristic
280Dic3⋊Dic3C2312yes—
281Dic3⋊Dic3C2312yes—
282Dic3⋊Dic3C2311yescharacteristic
283#3722C2311yescharacteristic
284(C2×D3)⋊Dic3C2312yes—
285(C2×D3)⋊Dic3C2312yes—
286(C2×D3)⋊Dic3C2311yescharacteristic
287(C2×D3)⋊Dic3C2311yescharacteristic
288(C2×D3)⋊Dic3C2312yes—
289(C2×D3)⋊Dic3C2312yes—
290(C2×D3)⋊Dic3C2312yes—
291(C2×D3)⋊Dic3C2311yescharacteristic
292(C2×D3)⋊Dic3C2311yescharacteristic
293(C2×D3)⋊Dic3C2311yescharacteristic
294(C2×D3)⋊Dic3C2312yes—
295Dic32C2312yes—
296Dic32C2312yes—
297#3488—91noSylow
298C3×H(5,𝔽2)—68no—
299C2×C3×#41—31no—
300C2×C3×#41—32no—
301C2×C3×#41—31no—
302C2×C3×#41—31no—
303C2×C3×#41—31no—
304C22×C3×D4—21no—
305C22×C3×D4—32no—
306C22×C3×D4—32no—
307C22×C3×D4—32no—
308C22×C3×D4—31no—
309C22×C3×D4—31no—
310C22×C3×D4—32no—
311C22×C3×D4—31no—
312C22×C3×D4C2×D311yescharacteristic, complemented
313C22×C3×D4C2×D311yescharacteristic, complemented
314C22×#67—32no—
315C22×#67—32no—
316C22×#67—32no—
317C22×#67—32no—
318C22×#67C2×D312yescomplemented
319C22×#67C2×D312yescomplemented
320C22×#67C2×D312yescomplemented
321C23×Dic3—32no—
322D3×#41—68no—
323C2×#239—31no—
324C2×D3×Q8—31no—
325#1004—28no—
326C2×#237—31no—
327C2×#237—31no—
328C2×#237—32no—
329C2×#237—32no—
330C2×#237—32no—
331C2×#237—31no—
332C2×#237—31no—
333C2×#237—61no—
334C2×#237—68no—
335C2×#237C2×D311yescharacteristic
336C2×#237C2×D311yescharacteristic, complemented
337C2×#237C2×D312yescomplemented
338C2×D3×D4—32no—
339C2×D3×D4—32no—
340C2×D3×D4C2×D311yescharacteristic, complemented
341C2×D3×D4C2×D311yescharacteristic, complemented
342C2×D3×D4C2×D312yescomplemented
343C2×D3×D4C2×D311yescharacteristic, complemented
344C2×#235—32no—
345C2×#235—31no—
346C2×#235C2×D311yescharacteristic, complemented
347C2×#235C2×D311yescharacteristic, complemented
348C22×C4×D3—32no—
349C22×C4×D3—31no—
350C22×C4×D3—31no—
351C22×Dic6—31no—
352C3×#127—31no—
353C3×#121—31no—
354C3×#121—32no—
355C3×#121—31no—
356C3×#120—32no—
357C3×#120—32no—
358C3×C4×D4—31no—
359C3×C4×D4—31no—
360#953—32no—
361#953—32no—
362#953—32no—
363#953—32no—
364#953—32no—
365#953—32no—
366#953—32no—
367#953—62no—
368#953C2×D312yescomplemented
369C2×#217—32no—
370C2×#217—32no—
371C2×#217—32no—
372C2×#217—32no—
373C2×#217—62no—
374#946—31no—
375#946—32no—
376#946—31no—
377Q8×Dic3—31no—
378Q8×Dic3—31no—
379#940—32no—
380#940—32no—
381#940—32no—
382#940—32no—
383#940—31no—
384#940—31no—
385#940C2×D311yescharacteristic, complemented
386#939—32no—
387#939—32no—
388#939—32no—
389#939—32no—
390#939—32no—
391#939—32no—
392#939—32no—
393#939—32no—
394#939—32no—
395#939—31no—
396#939—32no—
397#939—32no—
398#939—32no—
399#939—32no—
400#939—32no—
401#939—32no—
402#939—32no—
403#939—62no—
404#939C2×D312yescomplemented
405#938—31no—
406#938—31no—
407#938—32no—
408#938—31no—
409#938—32no—
410#938—32no—
411#938—32no—
412#938—32no—
413#938—32no—
414#938—32no—
415#938—32no—
416#938—32no—
417#938—31no—
418#938—31no—
419#938—32no—
420#938—31no—
421#938—31no—
422#938—61no—
423#938C2×D311yescharacteristic, complemented
424#937—32no—
425#937—32no—
426#937—32no—
427#937—32no—
428#937—31no—
429#937—31no—
430#937—31no—
431#937C2×D312yescomplemented
432#936—31no—
433#936—31no—
434#936—32no—
435#936—32no—
436#936—31no—
437#936—61no—
438#935—32no—
439#935—32no—
440#935—32no—
441#935—31no—
442#935—31no—
443#935—62no—
444D4×Dic3—31no—
445D4×Dic3—31no—
446D4×Dic3—32no—
447D4×Dic3—32no—
448D4×Dic3—32no—
449D4×Dic3—32no—
450D4×Dic3—61no—
451D4×Dic3C2×D311yescharacteristic, complemented
452#930—32no—
453#930—32no—
454#930—31no—
455#930—31no—
456#930—32no—
457#930C2×D311yescharacteristic, complemented
458C4×#67—31no—
459C4×#67—31no—
460C4×#67—32no—
461C4×#67—32no—
462C4×#67—32no—
463C4×#67—31no—
464C4×#67—31no—
465C4×#67—32no—
466C4×#67—32no—
467C4×#67—31no—
468C4×#67—61no—
469C4×#67C2×D311yescharacteristic, complemented
470C2×(C2×D3)⋊C4—32no—
471#926—32no—
472#926—31no—
473C2×C4⋊Dic3—32no—
474C2×C4⋊Dic3—31no—
475#924—31no—
476#924—31no—
477#924—32no—
478#924—31no—
479#924—32no—
480#924—61no—
481C2×Dic3⋊C4—32no—
482#897—31no—
483#896—32no—
484#896—31no—
485#895—31no—
486#894—31no—
487D3×C4⋊C4—31no—
488#887—31no—
489#886—32no—
490#885—32no—
491#885—32no—
492#884—31no—
493#884—32no—
494#884—32no—
495#884—32no—
496#883—31no—
497#882—32no—
498#882—31no—
499#67⋊C4—32no—
500#67⋊C4—32no—
501#67⋊C4—32no—
502D3×C22⋊C4—32no—
503#878—32no—
504#878—31no—
505#878—32no—
506#877—32no—
507#875—31no—
508C4×D12—31no—
509#872—31no—
510C4×Dic6—31no—
511C23×C32—24no—
512C23×C32—42no—
513C23×C32—42no—
514C23×C32C2412yes—
515C23×C32C2411yescharacteristic
516C23×C32C2412yes—
517C22×C3⋊D3C2411yescharacteristic
518C22×C3×D3—24no—
519C22×C3×D3—24no—
520C22×C3×D3—24no—
521C22×C3×D3—24no—
522C22×C3×D3—42no—
523C22×C3×D3—42no—
524C22×C3×D3—42no—
525C22×C3×D3—42no—
526C22×C3×D3—42no—
527C22×C3×D3C2411yescharacteristic
528C22×C3×D3C2412yes—
529C22×C3×D3C2412yes—
530C22×C3×D3C2411yescharacteristic
531C22×C3×D3C2411yescharacteristic
532C2×D32—22no—
533C2×D32—22no—
534C2×D32—41no—
535C32×D4—24no—
536C32×D4—22no—
537C32×D4C2×D414yescomplemented
538C2×C32×C4—22no—
539C2×C32×C4C2411yescharacteristic
540C2×C32×C4C2411yescharacteristic
541#638—24no—
542#638—41no—
543#638—42no—
544C2×C3⋊Dic3—24no—
545C2×C3⋊Dic3—42no—
546C2×C3⋊Dic3C2411yescharacteristic
547C2×C3⋊Dic3C2412yes—
548C2×C3⋊Dic3C2411yescharacteristic
549C2×C3⋊Dic3C2412yes—
550C2×C3⋊Dic3C2411yescharacteristic
551C4×C3⋊D3—22no—
552#634—22no—
553C3×#67—24no—
554C3×#67—24no—
555C3×#67—22no—
556C3×#67—24no—
557C3×#67—22no—
558C3×#67—22no—
559C3×#67—24no—
560C3×#67—24no—
561C3×#67—24no—
562C3×#67—42no—
563C3×#67—42no—
564C3×#67—42no—
565C3×#67C2×D418yescomplemented
566C2×C3×Dic3—24no—
567C2×C3×Dic3—42no—
568C2×C3×Dic3C2×D418yescomplemented
569C2×C3×Dic3C2411yescharacteristic
570C2×C3×Dic3C2412yes—
571C2×C3×Dic3C2411yescharacteristic
572C2×C3×Dic3C2411yescharacteristic
573C2×C3×Dic3C2411yescharacteristic
574C2×C3×Dic3C2412yes—
575C2×C3×Dic3C2411yescharacteristic
576C3×D12—22no—
577C3×D12—22no—
578C3×D12—22no—
579C3×C4×D3—22no—
580C3×C4×D3—22no—
581C3×C4×D3—24no—
582C3×C4×D3C2×D414yescomplemented
583C3×Dic6—22no—
584C3×Dic6C2×D414yescomplemented
585#627—24no—
586#626—24no—
587#626—41no—
588#626—42no—
589#625—24no—
590#625—22no—
591#625—24no—
592#625—42no—
593#625—42no—
594#625—42no—
595#624—22no—
596D3×Dic3—22no—
597D3×Dic3—24no—
598D3×Dic3—24no—
599D3×Dic3—24no—
600D3×Dic3—22no—
601D3×Dic3—42no—
602C2×H(5,𝔽2)—31no—
603C22×#41—91no—
604#550—91no—
605#550—91no—
606#548—91no—
607#548—91no—
608#546—91no—
609#546—92no—
610#546—92no—
611#546—91no—
612D42—31no—
613D42—92no—
614D42—91no—
615D42—92no—
616#537—92no—
617#537—91no—
618#535—92no—
619#535—91no—
620#525—91no—
621#525—92no—
622C2×#121—91no—
623C2×#121—92no—
624#520—91no—
625C24×C3—22no—
626C24×C3—32no—
627C24×C3—32no—
628C24×C3—32no—
629C24×C3C22×D312yes—
630C24×C3C22×D312yes—
631C23×D3—31no—
632C23×D3—31no—
633C23×D3C22×D312yes—
634C23×D3C22×D312yes—
635C23×D3C22×D312yes—
636C3×#41—38no—
637C3×#41—64no—
638C3×#41—64no—
639C3×#41—68no—
640C3×#41—64no—
641C2×C3×Q8—31no—
642C2×C3×Q8—31no—
643C2×C3×D4—24no—
644C2×C3×D4—24no—
645C2×C3×D4—21no—
646C2×C3×D4—22no—
647C2×C3×D4—21no—
648C2×C3×D4—32no—
649C2×C3×D4—32no—
650C2×C3×D4—31no—
651C2×C3×D4—32no—
652C2×C3×D4—32no—
653C2×C3×D4—32no—
654C2×C3×D4—31no—
655C2×C3×D4—32no—
656C2×C3×D4—32no—
657C2×C3×D4—31no—
658C2×C3×D4—32no—
659C2×C3×D4—32no—
660C2×C3×D4—32no—
661C2×C3×D4—31no—
662C2×C3×D4—31no—
663C2×C3×D4—31no—
664C2×C3×D4—44no—
665C2×C3×D4—64no—
666C2×C3×D4—68no—
667C2×C3×D4—68no—
668C2×C3×D4—68no—
669C2×C3×D4—64no—
670C2×C3×D4—64no—
671C2×C3×D4—124no—
672C2×C3×D4C22×D312yes—
673C2×C3×D4C22×D312yes—
674C2×C3×D4C22×D311yescharacteristic
675C2×C3×D4C22×D311yescharacteristic
676C2×C3×D4C22×D311yescharacteristic
677C2×C3×D4C22×D311yescharacteristic
678C22×C3×C4—21no—
679C22×C3×C4—32no—
680C22×C3×C4—31no—
681C22×C3×C4—32no—
682C22×C3×C4—32no—
683C22×C3×C4—32no—
684C22×C3×C4—31no—
685C22×C3×C4—31no—
686C22×C3×C4C22×D311yescharacteristic
687C22×C3×C4C22×D311yescharacteristic
688C2×#67—28no—
689C2×#67—28no—
690C2×#67—32no—
691C2×#67—32no—
692C2×#67—32no—
693C2×#67—31no—
694C2×#67—32no—
695C2×#67—31no—
696C2×#67—32no—
697C2×#67—32no—
698C2×#67—31no—
699C2×#67—32no—
700C2×#67—31no—
701C2×#67—32no—
702C2×#67—32no—
703C2×#67—32no—
704C2×#67—32no—
705C2×#67—32no—
706C2×#67—32no—
707C2×#67—32no—
708C2×#67—32no—
709C2×#67—31no—
710C2×#67—32no—
711C2×#67—44no—
712C2×#67—61no—
713C2×#67—62no—
714C2×#67—62no—
715C2×#67—68no—
716C2×#67—124no—
717C2×#67—124no—
718C2×#67—124no—
719C2×#67C22×D311yescharacteristic
720C2×#67C22×D311yescharacteristic
721C2×#67C22×D312yes—
722C2×#67C22×D312yes—
723C2×#67C22×D312yes—
724C2×#67C22×D312yes—
725C2×#67C22×D312yes—
726C2×#67C22×D311yescharacteristic
727C2×#67C22×D312yes—
728C2×#67C22×D312yes—
729C2×#67C22×D312yes—
730C2×#67C22×D312yes—
731C2×#67C22×D312yes—
732C22×Dic3—32no—
733C22×Dic3—32no—
734C22×Dic3—32no—
735C22×Dic3—32no—
736C22×Dic3—31no—
737C22×Dic3—32no—
738C22×Dic3—32no—
739C22×Dic3—32no—
740C22×Dic3—31no—
741C22×Dic3—32no—
742C22×Dic3—62no—
743C22×Dic3—62no—
744C22×Dic3—68no—
745C22×Dic3C22×D312yes—
746C22×Dic3C22×D312yes—
747C22×Dic3C22×D312yes—
748#239—64no—
749D3×Q8—64no—
750#237—28no—
751#237—24no—
752#237—68no—
753#237—64no—
754#237—64no—
755#237—68no—
756#237—68no—
757#237—64no—
758#237—64no—
759#237—124no—
760#237#6718yescomplemented
761D3×D4—24no—
762D3×D4—24no—
763D3×D4—28no—
764D3×D4—24no—
765D3×D4—68no—
766D3×D4—124no—
767#235—24no—
768#235—24no—
769#235—64no—
770#235—68no—
771C2×D12—32no—
772C2×D12—31no—
773C2×D12—32no—
774C2×D12C22×D311yescharacteristic
775C2×D12C22×D311yescharacteristic
776C2×D12C22×D311yescharacteristic
777C2×C4×D3—31no—
778C2×C4×D3—32no—
779C2×C4×D3—32no—
780C2×C4×D3—31no—
781C2×C4×D3—32no—
782C2×C4×D3—31no—
783C2×C4×D3—31no—
784C2×C4×D3—31no—
785C2×C4×D3—31no—
786C2×C4×D3—32no—
787C2×C4×D3—61no—
788C2×C4×D3—64no—
789C2×C4×D3—68no—
790C2×C4×D3—64no—
791C2×C4×D3C22×D311yescharacteristic
792C2×C4×D3C22×D312yes—
793C2×C4×D3C22×D311yescharacteristic
794C2×C4×D3C22×D311yescharacteristic
795C2×Dic6—31no—
796C2×Dic6—31no—
797C2×Dic6—32no—
798C2×Dic6—32no—
799C2×Dic6—61no—
800C2×Dic6—64no—
801C2×Dic6C22×D311yescharacteristic
802C2×Dic6C22×D311yescharacteristic
803C3×C4⋊C4—31no—
804C3×C4⋊C4—31no—
805C3×C22⋊C4—32no—
806C3×C22⋊C4—32no—
807C3×C22⋊C4—31no—
808C3×C22⋊C4—31no—
809C3×C22⋊C4—32no—
810C3×C42—31no—
811#217—32no—
812#217—32no—
813#217—32no—
814#217—31no—
815#217—32no—
816#217—32no—
817#217—32no—
818#217—32no—
819#217—32no—
820#217—32no—
821#217—32no—
822#217—31no—
823#217—31no—
824#217—32no—
825#217—32no—
826#217—32no—
827#217—32no—
828#217—31no—
829#217—31no—
830#217—31no—
831#217—32no—
832#217—32no—
833#217—31no—
834#217—62no—
835#217—61no—
836#217—62no—
837#217—62no—
838#217—62no—
839#217—62no—
840#217C22×D312yes—
841#217C22×D312yes—
842#217C22×D311yescharacteristic
843(C2×D3)⋊C4—31no—
844(C2×D3)⋊C4—31no—
845(C2×D3)⋊C4—31no—
846(C2×D3)⋊C4—32no—
847(C2×D3)⋊C4—32no—
848(C2×D3)⋊C4—32no—
849(C2×D3)⋊C4—32no—
850(C2×D3)⋊C4—32no—
851(C2×D3)⋊C4—31no—
852(C2×D3)⋊C4—31no—
853(C2×D3)⋊C4—32no—
854(C2×D3)⋊C4—31no—
855(C2×D3)⋊C4—31no—
856(C2×D3)⋊C4—31no—
857(C2×D3)⋊C4—31no—
858(C2×D3)⋊C4—61no—
859(C2×D3)⋊C4C22×D311yescharacteristic
860(C2×D3)⋊C4C22×D312yes—
861C4⋊Dic3—31no—
862C4⋊Dic3—31no—
863C4⋊Dic3—31no—
864C4⋊Dic3—32no—
865C4⋊Dic3—32no—
866C4⋊Dic3—32no—
867C4⋊Dic3—32no—
868C4⋊Dic3—31no—
869C4⋊Dic3—31no—
870C4⋊Dic3—61no—
871C4⋊Dic3C22×D311yescharacteristic
872Dic3⋊C4—31no—
873Dic3⋊C4—32no—
874Dic3⋊C4—32no—
875Dic3⋊C4—31no—
876Dic3⋊C4—32no—
877Dic3⋊C4—31no—
878Dic3⋊C4—31no—
879Dic3⋊C4—32no—
880Dic3⋊C4—31no—
881Dic3⋊C4—32no—
882Dic3⋊C4—32no—
883Dic3⋊C4—31no—
884Dic3⋊C4—31no—
885Dic3⋊C4—62no—
886Dic3⋊C4—61no—
887Dic3⋊C4C22×D311yescharacteristic
888C4×Dic3—31no—
889C4×Dic3—31no—
890C4×Dic3—32no—
891C4×Dic3—32no—
892C4×Dic3—32no—
893C4×Dic3—32no—
894C4×Dic3—61no—
895C4×Dic3C22×D311yescharacteristic
896C22×C32—21no—
897C22×C32—22no—
898C22×C32—22no—
899C22×C32—22no—
900C22×C32—21no—
901C22×C32—21no—
902C22×C32—22no—
903C22×C32—22no—
904C22×C32—84no—
905C22×C32C22×D414yes—
906C22×C32C2511yescharacteristic
907C2×C3⋊D3—21no—
908C2×C3⋊D3—21no—
909C2×C3⋊D3—21no—
910C2×C3×D3—21no—
911C2×C3×D3—21no—
912C2×C3×D3—21no—
913C2×C3×D3—21no—
914C2×C3×D3—22no—
915C2×C3×D3—21no—
916C2×C3×D3—22no—
917C2×C3×D3—21no—
918C2×C3×D3—22no—
919C2×C3×D3—22no—
920C2×C3×D3—22no—
921C2×C3×D3—22no—
922C2×C3×D3—21no—
923C2×C3×D3—48no—
924C2×C3×D3—84no—
925C2×C3×D3—84no—
926C2×C3×D3C22×D412yes—
927C2×C3×D3H(5,𝔽2)12yescomplemented
928D32—44no—
929C32×C4—21no—
930C32×C4C22×D412yes—
931C3⋊Dic3—21no—
932C3⋊Dic3—22no—
933C3⋊Dic3—22no—
934C3⋊Dic3—21no—
935C3⋊Dic3—21no—
936C3×Dic3—21no—
937C3×Dic3—21no—
938C3×Dic3—22no—
939C3×Dic3—21no—
940C3×Dic3—21no—
941C3×Dic3C22×D412yes—
942C3×Dic3C22×D414yes—
943H(5,𝔽2)—68no—
944C2×#41—31no—
945C2×#41—32no—
946C2×#41—31no—
947C2×#41—31no—
948C2×#41—31no—
949C2×#41—92no—
950C2×#41—91no—
951C2×#41—92no—
952C2×#41—91no—
953C2×#41—91no—
954C2×#41—188no—
955C22×Q8—91no—
956C22×D4—32no—
957C22×D4—32no—
958C22×D4—32no—
959C22×D4—31no—
960C22×D4—31no—
961C22×D4—32no—
962C22×D4—31no—
963C22×D4—92no—
964C22×D4—92no—
965C22×D4—92no—
966C22×D4D3211yescharacteristic, complemented
967C23×C4—91no—
968C23×C4—92no—
969#127—31no—
970#127—92no—
971#127—92no—
972#127—91no—
973#124—91no—
974#124—92no—
975#124—92no—
976#124—91no—
977#123—91no—
978#123—92no—
979#123—91no—
980#123—92no—
981C22⋊Q8—92no—
982C22⋊Q8—91no—
983C22⋊Q8—92no—
984C22⋊Q8—92no—
985C22⋊Q8—91no—
986C22⋊Q8—91no—
987C22⋊Q8—91no—
988#121—31no—
989#121—32no—
990#121—31no—
991#121—92no—
992#121—92no—
993#121—91no—
994#121—92no—
995#121—91no—
996#121—91no—
997#121—92no—
998#121—91no—
999#121—92no—
1000#121—91no—
1001#121—92no—
1002#121—92no—
1003#121—92no—
1004#121—92no—
1005#121—92no—
1006#121—92no—
1007#121—92no—
1008#121—92no—
1009#121—92no—
1010#121—92no—
1011#121—91no—
1012#121—92no—
1013#120—32no—
1014#120—32no—
1015#120—91no—
1016#120—92no—
1017#120—91no—
1018#120—92no—
1019#120—92no—
1020#120—92no—
1021#120—92no—
1022#120—92no—
1023C4×Q8—91no—
1024C4×Q8—91no—
1025C4×D4—31no—
1026C4×D4—31no—
1027C4×D4—91no—
1028C4×D4—92no—
1029C4×D4—92no—
1030C4×D4—92no—
1031C4×D4—91no—
1032C4×D4—92no—
1033C4×D4—92no—
1034C4×D4—92no—
1035C4×D4—91no—
1036C4×D4—91no—
1037#117—91no—
1038#117—92no—
1039C2×C4⋊C4—91no—
1040C2×C4⋊C4—92no—
1041C2×C22⋊C4—92no—
1042C2×C22⋊C4—92no—
1043C2×C22⋊C4—92no—
1044C23×C3—24no—
1045C23×C3—24no—
1046C23×C3—21no—
1047C23×C3—22no—
1048C23×C3—22no—
1049C23×C3—31no—
1050C23×C3—31no—
1051C23×C3—32no—
1052C23×C3—31no—
1053C23×C3—32no—
1054C23×C3—44no—
1055C23×C3—42no—
1056C23×C3—42no—
1057C23×C3—42no—
1058C23×C3—42no—
1059C23×C3—44no—
1060C23×C3—64no—
1061C23×C3—64no—
1062C23×C3—64no—
1063C23×C3—64no—
1064C23×C3—82no—
1065C23×C3—122no—
1066C23×C3—122no—
1067C23×C3—122no—
1068C23×C3—122no—
1069C23×C3—122no—
1070C23×C3C23×D312yes—
1071C23×C3C23×D311yescharacteristic
1072C23×C3C23×D312yes—
1073C23×C3C23×D311yescharacteristic
1074C23×C3C23×D312yes—
1075C23×C3C23×D312yes—
1076C22×D3—24no—
1077C22×D3—24no—
1078C22×D3—24no—
1079C22×D3—24no—
1080C22×D3—31no—
1081C22×D3—31no—
1082C22×D3—42no—
1083C22×D3—42no—
1084C22×D3—42no—
1085C22×D3—42no—
1086C22×D3—42no—
1087C22×D3—61no—
1088C22×D3—62no—
1089C22×D3—62no—
1090C22×D3—62no—
1091C22×D3—62no—
1092C22×D3—121no—
1093C22×D3—121no—
1094C22×D3C23×D312yes—
1095C22×D3C23×D311yescharacteristic
1096C22×D3C23×D312yes—
1097C22×D3C23×D311yescharacteristic
1098C22×D3C23×D311yescharacteristic
1099C3×Q8—34no—
1100C3×Q8—62no—
1101C3×D4—24no—
1102C3×D4—24no—
1103C3×D4—22no—
1104C3×D4—22no—
1105C3×D4—24no—
1106C3×D4—38no—
1107C3×D4—42no—
1108C3×D4—44no—
1109C3×D4—62no—
1110C3×D4—64no—
1111C3×D4—64no—
1112C3×D4—62no—
1113C3×D4—64no—
1114C3×D4—64no—
1115C3×D4—62no—
1116C3×D4—62no—
1117C3×D4—64no—
1118C3×D4—64no—
1119C3×D4—62no—
1120C3×D4—62no—
1121C3×D4—122no—
1122C3×D4—122no—
1123C3×D4—122no—
1124C3×D4D3×D414yescomplemented
1125C3×D4C2×#6714yescomplemented
1126C2×C3×C4—22no—
1127C2×C3×C4—22no—
1128C2×C3×C4—21no—
1129C2×C3×C4—21no—
1130C2×C3×C4—38no—
1131C2×C3×C4—32no—
1132C2×C3×C4—31no—
1133C2×C3×C4—34no—
1134C2×C3×C4—31no—
1135C2×C3×C4—32no—
1136C2×C3×C4—31no—
1137C2×C3×C4—31no—
1138C2×C3×C4—31no—
1139C2×C3×C4—42no—
1140C2×C3×C4—64no—
1141C2×C3×C4—64no—
1142C2×C3×C4—62no—
1143C2×C3×C4—62no—
1144C2×C3×C4—122no—
1145C2×C3×C4C23×D311yescharacteristic
1146C2×C3×C4C23×D311yescharacteristic
1147C2×C3×C4C23×D311yescharacteristic
1148C2×C3×C4C23×D311yescharacteristic
1149#67—24no—
1150#67—24no—
1151#67—22no—
1152#67—24no—
1153#67—22no—
1154#67—22no—
1155#67—24no—
1156#67—24no—
1157#67—24no—
1158#67—42no—
1159#67—42no—
1160#67—42no—
1161#67—64no—
1162#67—64no—
1163#67—62no—
1164#67—64no—
1165#67—64no—
1166#67—62no—
1167#67—64no—
1168#67—64no—
1169#67—64no—
1170#67—124no—
1171#67—121no—
1172#67—122no—
1173#67—122no—
1174#67—122no—
1175#67—122no—
1176#67—122no—
1177#67—122no—
1178#67—122no—
1179#67—122no—
1180#67—121no—
1181#67—121no—
1182#67—122no—
1183#67—122no—
1184#67—242no—
1185#67C2×#6718yescomplemented
1186C2×Dic3—24no—
1187C2×Dic3—31no—
1188C2×Dic3—31no—
1189C2×Dic3—31no—
1190C2×Dic3—32no—
1191C2×Dic3—32no—
1192C2×Dic3—31no—
1193C2×Dic3—32no—
1194C2×Dic3—31no—
1195C2×Dic3—32no—
1196C2×Dic3—31no—
1197C2×Dic3—42no—
1198C2×Dic3—61no—
1199C2×Dic3—61no—
1200C2×Dic3—62no—
1201C2×Dic3—62no—
1202C2×Dic3—61no—
1203C2×Dic3—62no—
1204C2×Dic3—64no—
1205C2×Dic3—64no—
1206C2×Dic3—64no—
1207C2×Dic3—62no—
1208C2×Dic3—64no—
1209C2×Dic3—64no—
1210C2×Dic3—124no—
1211C2×Dic3—122no—
1212C2×Dic3—122no—
1213C2×Dic3—122no—
1214C2×Dic3—242no—
1215C2×Dic3C2×#6718yescomplemented
1216C2×Dic3C23×D311yescharacteristic
1217C2×Dic3C23×D312yes—
1218C2×Dic3C23×D311yescharacteristic
1219C2×Dic3C23×D311yescharacteristic
1220C2×Dic3C23×D311yescharacteristic
1221C2×Dic3C23×D312yes—
1222C2×Dic3C23×D311yescharacteristic
1223D12—22no—
1224D12—22no—
1225D12—22no—
1226D12—64no—
1227D12—121no—
1228D12—122no—
1229C4×D3—22no—
1230C4×D3—22no—
1231C4×D3—24no—
1232C4×D3—62no—
1233C4×D3—62no—
1234C4×D3—64no—
1235C4×D3—64no—
1236C4×D3—64no—
1237C4×D3—62no—
1238C4×D3—62no—
1239C4×D3—62no—
1240C4×D3—62no—
1241C4×D3—122no—
1242C4×D3—122no—
1243C4×D3C2×#6714yescomplemented
1244Dic6—22no—
1245Dic6—64no—
1246Dic6—62no—
1247Dic6—62no—
1248Dic6—64no—
1249Dic6—122no—
1250Dic6C2×#6714yescomplemented
1251C2×C32—24no—
1252C2×C32—41no—
1253C2×C32—42no—
1254C2×C32C23×D411yescharacteristic
1255C2×C32C2×H(5,𝔽2)11yescharacteristic
1256C2×C32#58511yescharacteristic
1257C3⋊D3—41no—
1258C3×D3—22no—
1259C3×D3—22no—
1260C3×D3—42no—
1261C3×D3—41no—
1262C3×D3—42no—
1263C24—32no—
1264C24—32no—
1265C24—32no—
1266C24—91no—
1267C24C2×D3212yes—
1268#41—38no—
1269#41—64no—
1270#41—64no—
1271#41—68no—
1272#41—64no—
1273#41—188no—
1274#41—184no—
1275#41—188no—
1276#41—184no—
1277#41—184no—
1278C2×Q8—31no—
1279C2×Q8—31no—
1280C2×Q8—92no—
1281C2×Q8—91no—
1282C2×Q8—184no—
1283C2×D4—24no—
1284C2×D4—32no—
1285C2×D4—31no—
1286C2×D4—32no—
1287C2×D4—32no—
1288C2×D4—31no—
1289C2×D4—32no—
1290C2×D4—32no—
1291C2×D4—31no—
1292C2×D4—32no—
1293C2×D4—32no—
1294C2×D4—32no—
1295C2×D4—32no—
1296C2×D4—32no—
1297C2×D4—31no—
1298C2×D4—31no—
1299C2×D4—31no—
1300C2×D4—64no—
1301C2×D4—68no—
1302C2×D4—68no—
1303C2×D4—68no—
1304C2×D4—64no—
1305C2×D4—64no—
1306C2×D4—92no—
1307C2×D4—91no—
1308C2×D4—92no—
1309C2×D4—92no—
1310C2×D4—91no—
1311C2×D4—92no—
1312C2×D4—92no—
1313C2×D4—92no—
1314C2×D4—92no—
1315C2×D4—92no—
1316C2×D4—91no—
1317C2×D4—92no—
1318C2×D4—124no—
1319C2×D4—188no—
1320C2×D4—364no—
1321C2×D4—364no—
1322C2×D4C2×D3212yes—
1323C2×D4C2×D3211yescharacteristic
1324C2×D4C2×D3211yescharacteristic
1325C22×C4—32no—
1326C22×C4—31no—
1327C22×C4—32no—
1328C22×C4—32no—
1329C22×C4—31no—
1330C22×C4—32no—
1331C22×C4—31no—
1332C22×C4—91no—
1333C22×C4—91no—
1334C22×C4—92no—
1335C22×C4—92no—
1336C22×C4—91no—
1337C22×C4—92no—
1338C22×C4—92no—
1339C22×C4—92no—
1340C22×C4—92no—
1341C22×C4—91no—
1342C22×C4—184no—
1343C22×C4—188no—
1344C22×C4C2×D3211yescharacteristic
1345C4⋊C4—31no—
1346C4⋊C4—31no—
1347C4⋊C4—91no—
1348C4⋊C4—92no—
1349C4⋊C4—92no—
1350C4⋊C4—92no—
1351C4⋊C4—91no—
1352C4⋊C4—91no—
1353C4⋊C4—91no—
1354C4⋊C4—92no—
1355C4⋊C4—91no—
1356C4⋊C4—91no—
1357C4⋊C4—92no—
1358C22⋊C4—32no—
1359C22⋊C4—32no—
1360C22⋊C4—31no—
1361C22⋊C4—31no—
1362C22⋊C4—32no—
1363C22⋊C4—91no—
1364C22⋊C4—91no—
1365C22⋊C4—92no—
1366C22⋊C4—92no—
1367C22⋊C4—92no—
1368C22⋊C4—92no—
1369C22⋊C4—91no—
1370C22⋊C4—91no—
1371C22⋊C4—91no—
1372C22⋊C4—92no—
1373C22⋊C4—91no—
1374C22⋊C4—92no—
1375C22⋊C4—92no—
1376C22⋊C4—91no—
1377C22⋊C4—92no—
1378C22⋊C4—92no—
1379C22⋊C4—92no—
1380C22⋊C4—92no—
1381C22⋊C4—91no—
1382C42—31no—
1383C42—92no—
1384C42—92no—
1385C42—91no—
1386C22×C3—22no—
1387C22×C3—22no—
1388C22×C3—22no—
1389C22×C3—22no—
1390C22×C3—22no—
1391C22×C3—21no—
1392C22×C3—22no—
1393C22×C3—21no—
1394C22×C3—22no—
1395C22×C3—22no—
1396C22×C3—21no—
1397C22×C3—22no—
1398C22×C3—21no—
1399C22×C3—21no—
1400C22×C3—22no—
1401C22×C3—22no—
1402C22×C3—21no—
1403C22×C3—24no—
1404C22×C3—21no—
1405C22×C3—32no—
1406C22×C3—32no—
1407C22×C3—42no—
1408C22×C3—41no—
1409C22×C3—42no—
1410C22×C3—41no—
1411C22×C3—42no—
1412C22×C3—42no—
1413C22×C3—42no—
1414C22×C3—61no—
1415C22×C3—61no—
1416C22×C3—61no—
1417C22×C3—61no—
1418C22×C3—62no—
1419C22×C3—61no—
1420C22×C3—62no—
1421C22×C3—61no—
1422C22×C3—62no—
1423C22×C3—62no—
1424C22×C3—61no—
1425C22×C3—62no—
1426C22×C3—62no—
1427C22×C3—84no—
1428C22×C3—84no—
1429C22×C3—88no—
1430C22×C3—128no—
1431C22×C3—244no—
1432C22×C3—244no—
1433C22×C3C2×D3×D414yes—
1434C22×C3C22×#6714yes—
1435C22×C3C24×D311yescharacteristic
1436C22×C3C24×D311yescharacteristic
1437C2×D3—21no—
1438C2×D3—21no—
1439C2×D3—21no—
1440C2×D3—21no—
1441C2×D3—22no—
1442C2×D3—22no—
1443C2×D3—22no—
1444C2×D3—21no—
1445C2×D3—21no—
1446C2×D3—22no—
1447C2×D3—22no—
1448C2×D3—21no—
1449C2×D3—22no—
1450C2×D3—48no—
1451C2×D3—61no—
1452C2×D3—61no—
1453C2×D3—61no—
1454C2×D3—61no—
1455C2×D3—61no—
1456C2×D3—61no—
1457C2×D3—84no—
1458C2×D3—84no—
1459C2×D3—121no—
1460C2×D3—121no—
1461C2×D3—121no—
1462C2×D3—124no—
1463C2×D3—124no—
1464C2×D3#100412yescomplemented
1465C2×D3C22×#6712yes—
1466C3×C4—21no—
1467C3×C4—21no—
1468C3×C4—22no—
1469C3×C4—34no—
1470C3×C4—32no—
1471C3×C4—41no—
1472C3×C4—61no—
1473C3×C4—62no—
1474C3×C4—61no—
1475C3×C4—61no—
1476C3×C4—61no—
1477C3×C4C2×D3×D412yes—
1478C3×C4C22×#6712yes—
1479Dic3—21no—
1480Dic3—21no—
1481Dic3—22no—
1482Dic3—21no—
1483Dic3—21no—
1484Dic3—62no—
1485Dic3—61no—
1486Dic3—62no—
1487Dic3—61no—
1488Dic3—62no—
1489Dic3—61no—
1490Dic3—61no—
1491Dic3—61no—
1492Dic3—62no—
1493Dic3—61no—
1494Dic3—122no—
1495Dic3—121no—
1496Dic3—121no—
1497Dic3—122no—
1498Dic3—121no—
1499Dic3C22×#6712yes—
1500Dic3C22×#6714yes—
1501C32#348811yescharacteristic, complemented, Sylow
1502C23—24no—
1503C23—31no—
1504C23—31no—
1505C23—32no—
1506C23—32no—
1507C23—31no—
1508C23—42no—
1509C23—42no—
1510C23—64no—
1511C23—64no—
1512C23—64no—
1513C23—64no—
1514C23—91no—
1515C23—122no—
1516C23—122no—
1517C23—122no—
1518C23—122no—
1519C23—122no—
1520C23—182no—
1521C23—182no—
1522C23—361no—
1523C23C22×D3212yes—
1524C23C22×D3211yescharacteristic
1525C23C22×D3212yes—
1526Q8—34no—
1527Q8—62no—
1528Q8—184no—
1529Q8—182no—
1530D4—24no—
1531D4—22no—
1532D4—38no—
1533D4—62no—
1534D4—62no—
1535D4—64no—
1536D4—64no—
1537D4—64no—
1538D4—62no—
1539D4—62no—
1540D4—64no—
1541D4—64no—
1542D4—64no—
1543D4—62no—
1544D4—62no—
1545D4—122no—
1546D4—122no—
1547D4—122no—
1548D4—184no—
1549D4—184no—
1550D4—184no—
1551D4—182no—
1552D4—184no—
1553D4—362no—
1554D4—361no—
1555D4—362no—
1556D4—361no—
1557D4—362no—
1558D4—362no—
1559D4—362no—
1560D4D3×#6714yescomplemented
1561C2×C4—22no—
1562C2×C4—38no—
1563C2×C4—32no—
1564C2×C4—31no—
1565C2×C4—34no—
1566C2×C4—31no—
1567C2×C4—31no—
1568C2×C4—32no—
1569C2×C4—31no—
1570C2×C4—31no—
1571C2×C4—64no—
1572C2×C4—64no—
1573C2×C4—62no—
1574C2×C4—62no—
1575C2×C4—91no—
1576C2×C4—92no—
1577C2×C4—91no—
1578C2×C4—91no—
1579C2×C4—92no—
1580C2×C4—122no—
1581C2×C4—182no—
1582C2×C4—182no—
1583C2×C4—184no—
1584C2×C4—184no—
1585C2×C4—184no—
1586C2×C4—182no—
1587C2×C4—184no—
1588C2×C4—182no—
1589C2×C4—362no—
1590C2×C4—362no—
1591C2×C4C22×D3211yescharacteristic
1592C2×C4C22×D3211yescharacteristic
1593C2×C3—24no—
1594C2×C3—24no—
1595C2×C3—21no—
1596C2×C3—21no—
1597C2×C3—21no—
1598C2×C3—44no—
1599C2×C3—42no—
1600C2×C3—41no—
1601C2×C3—42no—
1602C2×C3—42no—
1603C2×C3—41no—
1604C2×C3—62no—
1605C2×C3—62no—
1606C2×C3—82no—
1607C2×C3—121no—
1608C2×C3—122no—
1609C2×C3—122no—
1610C2×C3C22×D3×D411yescharacteristic
1611C2×C3C2×#100411yescharacteristic
1612C2×C3D3×H(5,𝔽2)11yescharacteristic
1613C2×C3#596611yescharacteristic
1614C2×C3#596611yescharacteristic
1615C2×C3C23×#6711yescharacteristic
1616D3—22no—
1617D3—22no—
1618D3—42no—
1619D3—42no—
1620D3—41no—
1621D3—121no—
1622D3—121no—
1623D3—241no—
1624C22—22no—
1625C22—22no—
1626C22—21no—
1627C22—22no—
1628C22—22no—
1629C22—21no—
1630C22—21no—
1631C22—22no—
1632C22—32no—
1633C22—32no—
1634C22—61no—
1635C22—61no—
1636C22—61no—
1637C22—61no—
1638C22—62no—
1639C22—62no—
1640C22—61no—
1641C22—62no—
1642C22—61no—
1643C22—62no—
1644C22—62no—
1645C22—61no—
1646C22—62no—
1647C22—84no—
1648C22—128no—
1649C22—181no—
1650C22—181no—
1651C22—181no—
1652C22—244no—
1653C22—244no—
1654C22—364no—
1655C22C2×D3×#6714yes—
1656C22C23×D3211yescharacteristic
1657C4—21no—
1658C4—32no—
1659C4—34no—
1660C4—61no—
1661C4—62no—
1662C4—61no—
1663C4—61no—
1664C4—61no—
1665C4—182no—
1666C4—181no—
1667C4—181no—
1668C4—181no—
1669C4—182no—
1670C4C2×D3×#6712yes—
1671C3—21no—
1672C3#8660711yescharacteristic, complemented
1673C3#8728511yescharacteristic, complemented
1674C2—24no—
1675C2—41no—
1676C2—42no—
1677C2—62no—
1678C2—62no—
1679C2—122no—
1680C2—121no—
1681C2—122no—
1682C2—361no—
1683C2D3×#100411yescharacteristic
1684C2#1059667911yescharacteristic
1685C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×D3×#237C2semidirect
3. #10596277C2semidirect
4. C3×D4×#67C2semidirect
5. #672C2semidirect
6. #10595513C2semidirect
7. C2×#63970C2semidirect
8. #10595494C2semidirect
9. #10595287C2semidirect
10. D3×#938C2semidirect
11. #10595246C2semidirect
12. #10595233C2semidirect
13. D4×#625C2semidirect
14. #10595222C2semidirect
15. #10595158C2semidirect
16. #10595157C2semidirect
17. #10595156C2semidirect
18. #10595154C2semidirect
19. #10595150C2semidirect
20. #10595060C2semidirect
21. #10595006C2semidirect
22. #10595004C2semidirect
23. #10594899C2semidirect
26. C22×C32×D4C22semidirect
27. C2×#3830C22semidirect
28. C22×C3×#67C22semidirect
29. C22×C3×#67C22semidirect
30. C22×C3×#67C22semidirect
33. C2×C3×#237C22semidirect
34. C2×C3×#237C22semidirect
35. C2×C3×D3×D4C22semidirect
36. C2×C3×D3×D4C22semidirect
37. C2×C3×D3×D4C22semidirect
38. C2×C3×D3×D4C22semidirect
39. C2×C3×#235C22semidirect
40. C2×C3×#235C22semidirect
41. C2×D3×#67C22semidirect
42. C2×D3×#67C22semidirect
43. C22×#625C22semidirect
44. C2×#3805C22semidirect
45. C2×#3804C22semidirect
46. C22×D3×Dic3C22semidirect
48. C2×C4×D32C22semidirect
49. C2×#3796C22semidirect
50. C2×#3795C22semidirect
51. C2×D3×Dic6C22semidirect
52. #64162C22semidirect
53. C2×#3757C22semidirect
54. #64148C22semidirect
55. #64147C22semidirect
56. #64145C22semidirect
57. #64144C22semidirect
58. D4×C3⋊Dic3C22semidirect
59. C4×#638C22semidirect
60. #64133C22semidirect
61. C3×#953C22semidirect
62. C3×#940C22semidirect
63. C3×#939C22semidirect
64. C3×#938C22semidirect
65. C3×#937C22semidirect
66. C3×D4×Dic3C22semidirect
67. C3×#930C22semidirect
68. C3×C4×#67C22semidirect
69. #63983C22semidirect
70. #63980C22semidirect
71. #63979C22semidirect
72. #63979C22semidirect
73. #63978C22semidirect
74. #63978C22semidirect
75. #63977C22semidirect
76. #63976C22semidirect
77. #63976C22semidirect
78. #63976C22semidirect
79. #63976C22semidirect
80. #67⋊Dic3C22semidirect
81. Dic3×#67C22semidirect
82. Dic3×#67C22semidirect
83. Dic3×#67C22semidirect
84. #63970C22semidirect
85. #63970C22semidirect
86. #63970C22semidirect
87. #63970C22semidirect
88. #63970C22semidirect
89. #63970C22semidirect
90. #63970C22semidirect
91. #63970C22semidirect
92. #63970C22semidirect
93. #63970C22semidirect
94. #63969C22semidirect
95. D3×#217C22semidirect
96. C2×Dic3⋊Dic3C22semidirect
97. #63964C22semidirect
98. #63962C22semidirect
99. C2×(C2×D3)⋊Dic3C22semidirect
100. #63959C22semidirect
101. #63959C22semidirect
102. #63958C22semidirect
103. #63958C22semidirect
104. #63955C22semidirect
105. #63922C22semidirect
106. #63916C22semidirect
107. #63914C22semidirect
108. #63908C22semidirect
109. #63908C22semidirect
110. #63906C22semidirect
111. C4×#626C22semidirect
112. C4×#625C22semidirect
113. D3×C4⋊Dic3C22semidirect
114. #63888C22semidirect
115. #63887C22semidirect
116. #63887C22semidirect
117. #63885C22semidirect
118. #63884C22semidirect
119. #63879C22semidirect
120. #63879C22semidirect
121. #63860C22semidirect
122. #63857C22semidirect
123. #63855C22semidirect
124. #63851C22semidirect
125. #63843C22semidirect
126. Dic3×Dic6C22semidirect
129. C2×#1004D3semidirect
155. D4×#67D3semidirect
213. C3×#237D4semidirect
312. C22×C3×D4C2×D3semidirect
313. C22×C3×D4C2×D3semidirect
318. C22×#67C2×D3semidirect
319. C22×#67C2×D3semidirect
320. C22×#67C2×D3semidirect
336. C2×#237C2×D3semidirect
337. C2×#237C2×D3semidirect
340. C2×D3×D4C2×D3semidirect
341. C2×D3×D4C2×D3semidirect
342. C2×D3×D4C2×D3semidirect
343. C2×D3×D4C2×D3semidirect
346. C2×#235C2×D3semidirect
347. C2×#235C2×D3semidirect
368. #953C2×D3semidirect
385. #940C2×D3semidirect
404. #939C2×D3semidirect
423. #938C2×D3semidirect
431. #937C2×D3semidirect
451. D4×Dic3C2×D3semidirect
457. #930C2×D3semidirect
469. C4×#67C2×D3semidirect
537. C32×D4C2×D4semidirect
565. C3×#67C2×D4semidirect
568. C2×C3×Dic3C2×D4semidirect
582. C3×C4×D3C2×D4semidirect
584. C3×Dic6C2×D4semidirect
760. #237#67semidirect
927. C2×C3×D3H(5,𝔽2)semidirect
966. C22×D4D32semidirect
1124. C3×D4D3×D4semidirect
1125. C3×D4C2×#67semidirect
1185. #67C2×#67semidirect
1215. C2×Dic3C2×#67semidirect
1243. C4×D3C2×#67semidirect
1250. Dic6C2×#67semidirect
1464. C2×D3#1004semidirect
1501. C32#3488semidirect
1560. D4D3×#67semidirect
1672. C3#86607semidirect
1673. C3#87285semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×D3×#2372
#105962772
C3×D4×#672
#6722
#105955132
C2×#639702
#105954942
#105952872
D3×#9382
#105952462
#105952332
D4×#6252
#105952222
#105951582
#105951572
#105951562
#105951542
#105951502
#105950602
#105950062
#105950042
#105948992
#872853
#866073