Finite Group Databasebeta

← #11904626

Subgroups — #11904626

Order 1152.

3530 conjugacy classes of subgroups.

The subgroup lattice has 1697 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×#64312C211yesmaximal, characteristic, complemented
3D4×#638C211yesmaximal, characteristic, complemented
4C3×#5806C211yesmaximal, characteristic, complemented
5#10595526C212yesmaximal, complemented
6#10595513C212yesmaximal, complemented
7#10595493C212yesmaximal, complemented
8C2×#63958C212yesmaximal, complemented
9#10595291C212yesmaximal, complemented
10D3×#938C211yesmaximal, characteristic, complemented
11#10595244C211yesmaximal, characteristic, complemented
12#10595237C211yesmaximal, characteristic, complemented
13#10595236C211yesmaximal, characteristic, complemented
14#10595235C211yesmaximal, characteristic, complemented
15D4×#626C211yesmaximal, characteristic, complemented
16#10595222C211yesmaximal, characteristic, complemented
17#10595159C212yesmaximal, complemented
18#10595156C212yesmaximal, complemented
19#10595148C212yesmaximal, complemented
20#10595060C211yesmaximal, characteristic, complemented
21#10595007C211yesmaximal, characteristic, complemented
22#10594894C211yesmaximal, characteristic, complemented
23#10594830C211yesmaximal, characteristic, complemented
24#87285—31nomaximal
25#86629—31nomaximal
26C22×C32×D4C2211yescharacteristic, complemented
27C22×#638C2212yescomplemented
28C2×D4×C3⋊D3C2211yescharacteristic, complemented
29C22×C3×#67C2212yescomplemented
30C22×C3×#67C2212yescomplemented
31C3×#1004—28no—
32C2×C3×#237C2211yescharacteristic
33C2×C3×#237C2211yescharacteristic, complemented
34C2×C3×#237C2212yescomplemented
35C2×C3×#237C2211yescharacteristic, complemented
36C2×C3×D3×D4C2212yescomplemented
37C2×C3×D3×D4C2211yescharacteristic, complemented
38C2×C3×D3×D4C2211yescharacteristic, complemented
39C2×C3×#235C2211yescharacteristic, complemented
40C2×C3×#235C2211yescharacteristic, complemented
41C2×#3811C2212yescomplemented
42C2×D3×#67C2212yescomplemented
43C22×#626C2212yescomplemented
44C22×#624C2212yescomplemented
45C2×#3804C2212yescomplemented
46C2×#3804C2212yescomplemented
47#64312—28no—
48C2×C4×D32C2211yescharacteristic, complemented
49C2×#3799C2211yescharacteristic, complemented
50C2×#3799C2211yescharacteristic, complemented
51C2×#3797C2211yescharacteristic, complemented
52#64162C2212yescomplemented
53#64149C2211yescharacteristic, complemented
54#64148C2212yescomplemented
55#64147C2211yescharacteristic, complemented
56#64146C2212yescomplemented
57D4×C3⋊Dic3C2211yescharacteristic, complemented
58#64139C2211yescharacteristic, complemented
59C4×#638C2211yescharacteristic, complemented
60C3×#953C2212yescomplemented
61C2×C3×#217C2212yescomplemented
62C3×#939C2212yescomplemented
63C3×#938C2211yescharacteristic, complemented
64C3×#936C2211yescharacteristic, complemented
65C3×#935C2212yescomplemented
66C3×D4×Dic3C2211yescharacteristic, complemented
67C3×C4×#67C2211yescharacteristic, complemented
68C3×#924C2211yescharacteristic, complemented
69#63983C2211yescharacteristic, complemented
70#63981C2212yescomplemented
71#63980C2212yescomplemented
72#63979C2212yescomplemented
73#63979C2212yescomplemented
74#63978C2212yescomplemented
75#63978C2212yescomplemented
76#63977C2212yescomplemented
77#63977C2212yescomplemented
78#63977C2212yescomplemented
79#63976C2212yescomplemented
80#67⋊Dic3C2212yescomplemented
81Dic3×#67C2212yescomplemented
82#63971C2212yescomplemented
83#63970C2212yescomplemented
84#63970C2211yescharacteristic, complemented
85#63969C2211yescharacteristic, complemented
86D3×#217C2212yescomplemented
87C2×Dic3⋊Dic3C2212yescomplemented
88#63964C2212yescomplemented
89#63961C2212yescomplemented
90C2×(C2×D3)⋊Dic3C2212yescomplemented
91#63959C2212yescomplemented
92#63959C2212yescomplemented
93#63958C2212yescomplemented
94#63958C2212yescomplemented
95#63958C2212yescomplemented
96#63958C2212yescomplemented
97#63958C2212yescomplemented
98#63958C2212yescomplemented
99#63958C2211yescharacteristic, complemented
100#63958C2212yescomplemented
101#63958C2212yescomplemented
102#63955C2212yescomplemented
103#63952C2212yescomplemented
104#63952C2212yescomplemented
105#63922C2211yescharacteristic, complemented
106#63916C2211yescharacteristic, complemented
107#63911C2211yescharacteristic, complemented
108#63909C2211yescharacteristic, complemented
109#63908C2211yescharacteristic, complemented
110#63906C2212yescomplemented
111#63904C2212yescomplemented
112#63904C2212yescomplemented
113C4×#626C2211yescharacteristic, complemented
114C4×#625C2211yescharacteristic, complemented
115D3×C4⋊Dic3C2211yescharacteristic, complemented
116#63888C2212yescomplemented
117#63888C2211yescharacteristic, complemented
118#63887C2211yescharacteristic, complemented
119#63886C2212yescomplemented
120#63884C2211yescharacteristic, complemented
121#63863C2211yescharacteristic, complemented
122#63856C2211yescharacteristic, complemented
123#63855C2211yescharacteristic, complemented
124#63851C2212yescomplemented
125#63843C2211yescharacteristic, complemented
126Dic3×Dic6C2211yescharacteristic, complemented
127C2×C3×H(5,𝔽2)—31no—
128C2×D3×#41—31no—
129C2×D3×#41—31no—
130C2×#1004D311yescharacteristic, complemented
131C3×#546—31no—
132#5834—31no—
133#5834—31no—
134#5833—32no—
135#5833—31no—
136#5831—31no—
137#5831—31no—
138#5829—31no—
139#5828—32no—
140#5828—31no—
141#5827—31no—
142#5806—31no—
143#5806—32no—
144#5806—32no—
145#5806D311yescharacteristic, complemented
146#5805—32no—
147#5805—31no—
148D4×#67—31no—
149D4×#67—31no—
150D4×#67—32no—
151D4×#67—32no—
152D4×#67—31no—
153D4×#67—61no—
154C2×#938—32no—
155C2×#938—31no—
156#5677—31no—
157#5674—31no—
158#5656—32no—
159#5654—32no—
160#5633—31no—
161#5629—31no—
162#5609—32no—
163D3×#121—31no—
164#5599—31no—
165#5597—32no—
166#5592—32no—
167#5590—32no—
168#5553—31no—
169D4×D12—31no—
170#5547—31no—
171#5546—31no—
172#5490—32no—
173C2×#884—32no—
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×#638—44no—
185C2×#638C2312yes—
186C2×#638C2312yes—
187C2×#638C2311yescharacteristic
188C2×#638C2312yes—
189C2×#638C2312yes—
190C2×#638C2312yes—
191C22×C3⋊Dic3C2312yes—
192D4×C3⋊D3—24no—
193C2×C4⋊(C3⋊D3)C2311yescharacteristic
194C2×C4×C3⋊D3C2311yescharacteristic
195C2×C3×#67—28no—
196C2×C3×#67—28no—
197C2×C3×#67C2312yes—
198C2×C3×#67C2311yescharacteristic
199C2×C3×#67C2312yes—
200C2×C3×#67C2311yescharacteristic
201C2×C3×#67C2312yes—
202C2×C3×#67C2312yes—
203C2×C3×#67C2312yes—
204C2×C3×#67C2311yescharacteristic
205C2×C3×#67C2312yes—
206C2×C3×#67C2312yes—
207C22×C3×Dic3C2312yes—
208C22×C3×Dic3C2312yes—
209C22×C3×Dic3C2312yes—
210C22×C3×Dic3C2312yes—
211C3×#237—24no—
212C3×#237—28no—
213C3×#237—24no—
214C3×#237D418yescomplemented
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×C4×D3C2311yescharacteristic
223C2×C3×C4×D3C2312yes—
224C2×C3×C4×D3C2311yescharacteristic
225C2×C3×C4×D3C2311yescharacteristic
226C2×C3×Dic6C2311yescharacteristic
227C2×C3×Dic6C2311yescharacteristic
228C2×C3×Dic6C2311yescharacteristic
229#3811—28no—
230D3×#67—44no—
231C2×#627C2312yes—
232C2×#626—44no—
233C2×#626C2312yes—
234C2×#626C2312yes—
235C2×#626C2311yescharacteristic
236C2×#626C2312yes—
237C2×#626C2312yes—
238C2×#626C2312yes—
239C2×#626C2312yes—
240C2×#625C2312yes—
241C2×#625C2311yescharacteristic
242C2×#624—28no—
243C2×#624C2312yes—
244C2×#624C2312yes—
245C2×#624C2312yes—
246C2×#624C2311yescharacteristic
247#3804—28no—
248#3804—28no—
249C2×D3×Dic3C2311yescharacteristic
250C2×D3×Dic3C2311yescharacteristic
251C2×D3×Dic3C2312yes—
252C4×D32—24no—
253#3799—24no—
254#3799—24no—
255#3797—24no—
256#3757C2311yescharacteristic
257#3757C2312yes—
258#3757C2312yes—
259#3752C2311yescharacteristic
260#3752C2312yes—
261C4⋊(C3⋊Dic3)C2311yescharacteristic
262#3750C2311yescharacteristic
263C4×C3⋊Dic3C2311yescharacteristic
264C3×#217C2312yes—
265C3×#217C2311yescharacteristic
266C3×#217C2312yes—
267C3×#217C2312yes—
268C3×#217C2312yes—
269C3×#217C2312yes—
270C3×(C2×D3)⋊C4C2311yescharacteristic
271C3×C4⋊Dic3C2311yescharacteristic
272C3×Dic3⋊C4C2312yes—
273C3×Dic3⋊C4C2311yescharacteristic
274C3×C4×Dic3C2311yescharacteristic
275#3724C2312yes—
276#3724C2311yescharacteristic
277Dic3⋊Dic3C2312yes—
278Dic3⋊Dic3C2312yes—
279Dic3⋊Dic3C2311yescharacteristic
280Dic3⋊Dic3C2311yescharacteristic
281Dic3⋊Dic3C2311yescharacteristic
282Dic3⋊Dic3C2312yes—
283#3722C2311yescharacteristic
284#3722C2312yes—
285(C2×D3)⋊Dic3C2312yes—
286(C2×D3)⋊Dic3C2312yes—
287(C2×D3)⋊Dic3C2311yescharacteristic
288(C2×D3)⋊Dic3C2311yescharacteristic
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—31no—
301C2×C3×#41—32no—
302C2×C3×#41—31no—
303C2×C3×#41—31no—
304C2×C3×#41—31no—
305C22×C3×D4—21no—
306C22×C3×D4—32no—
307C22×C3×D4—32no—
308C22×C3×D4—31no—
309C22×C3×D4—32no—
310C22×C3×D4—31no—
311C22×C3×D4C2×D311yescharacteristic, complemented
312C22×C3×D4C2×D311yescharacteristic, complemented
313C22×#67—32no—
314C22×#67—32no—
315C22×#67—32no—
316C22×#67—32no—
317C22×#67—62no—
318C22×#67C2×D312yescomplemented
319C22×#67C2×D312yescomplemented
320D3×#41—68no—
321D3×#41—68no—
322C2×#239—31no—
323C2×#239—31no—
324C2×D3×Q8—31no—
325C2×D3×Q8—31no—
326#1004—28no—
327C2×#237—32no—
328C2×#237—32no—
329C2×#237C2×D311yescharacteristic
330C2×#237C2×D312yescomplemented
331C2×#237C2×D311yescharacteristic, complemented
332C2×#237C2×D311yescharacteristic, complemented
333C2×D3×D4—31no—
334C2×D3×D4—31no—
335C2×D3×D4—32no—
336C2×D3×D4—32no—
337C2×D3×D4—32no—
338C2×D3×D4—61no—
339C2×D3×D4C2×D312yescomplemented
340C2×D3×D4C2×D311yescharacteristic, complemented
341C2×D3×D4C2×D311yescharacteristic, complemented
342C2×#235—32no—
343C2×#235—32no—
344C2×#235—31no—
345C2×#235—31no—
346C2×#235C2×D311yescharacteristic, complemented
347C2×#235C2×D311yescharacteristic, complemented
348C22×D12—32no—
349C22×C4×D3—32no—
350C22×C4×D3—32no—
351C22×C4×D3—31no—
352C22×C4×D3—31no—
353C3×#124—31no—
354C3×#123—32no—
355C3×C22⋊Q8—31no—
356C3×#121—31no—
357C3×#121—32no—
358C3×#120—32no—
359C3×C4×D4—31no—
360C3×C4×D4—31no—
361C2×C3×C22⋊C4—32no—
362#953—32no—
363#953—32no—
364#953—32no—
365#953—32no—
366#953—32no—
367#953—32no—
368#953—62no—
369#953C2×D312yescomplemented
370C2×#217—32no—
371C2×#217—32no—
372C2×#217C2×D312yescomplemented
373#947—31no—
374#946—31no—
375#946—31no—
376#946—31no—
377#946—32no—
378Q8×Dic3—31no—
379Q8×Dic3—31no—
380#940—31no—
381#940—31no—
382#940—32no—
383#940—32no—
384#940—32no—
385#940—32no—
386#940—31no—
387#940—61no—
388#939—32no—
389#939—32no—
390#939—32no—
391#939—31no—
392#939—32no—
393#939—32no—
394#939—32no—
395#939—32no—
396#939—32no—
397#939—32no—
398#939—62no—
399#939C2×D312yescomplemented
400#938—31no—
401#938—31no—
402#938—32no—
403#938—31no—
404#938—31no—
405#938—32no—
406#938—31no—
407#938—32no—
408#938—32no—
409#938—32no—
410#938—32no—
411#938—32no—
412#938—32no—
413#938—32no—
414#938—31no—
415#938—61no—
416#938C2×D311yescharacteristic, complemented
417#937—32no—
418#937—32no—
419#937—32no—
420#937—31no—
421#937—31no—
422#937—32no—
423#937—31no—
424#937—62no—
425#936—31no—
426#936—32no—
427#936—32no—
428#936C2×D311yescharacteristic, complemented
429#935—32no—
430#935—31no—
431#935—31no—
432#935C2×D312yescomplemented
433D4×Dic3—31no—
434D4×Dic3—31no—
435D4×Dic3—32no—
436D4×Dic3—32no—
437D4×Dic3—61no—
438D4×Dic3C2×D311yescharacteristic, complemented
439#930—31no—
440#930—31no—
441#930—32no—
442#930—32no—
443#930—31no—
444#930—32no—
445#930—31no—
446#930—61no—
447#929—32no—
448C4×#67—31no—
449C4×#67—31no—
450C4×#67—32no—
451C4×#67—31no—
452C4×#67—31no—
453C4×#67—32no—
454C4×#67—32no—
455C4×#67—32no—
456C4×#67—32no—
457C4×#67—31no—
458C4×#67—61no—
459C4×#67C2×D311yescharacteristic, complemented
460C2×(C2×D3)⋊C4—32no—
461#926—32no—
462#926—31no—
463C2×C4⋊Dic3—32no—
464C2×C4⋊Dic3—31no—
465#924—31no—
466#924—32no—
467#924—32no—
468#924C2×D311yescharacteristic, complemented
469C2×Dic3⋊C4—32no—
470#896—32no—
471#896—31no—
472#896—32no—
473#895—31no—
474#895—32no—
475#895—31no—
476#894—31no—
477#893—32no—
478#893—32no—
479D3×C4⋊C4—31no—
480#887—31no—
481#885—32no—
482#885—32no—
483#884—32no—
484#884—32no—
485#884—32no—
486#884—32no—
487#884—32no—
488#884—32no—
489#884—31no—
490#884—32no—
491#884—32no—
492#884—32no—
493#884—32no—
494#883—31no—
495#882—32no—
496#882—32no—
497#882—32no—
498#882—32no—
499#882—31no—
500#67⋊C4—32no—
501#67⋊C4—32no—
502#67⋊C4—32no—
503D3×C22⋊C4—32no—
504#878—32no—
505#878—31no—
506#877—32no—
507#874—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⋊D3—24no—
518C22×C3⋊D3—24no—
519C22×C3⋊D3—42no—
520C22×C3⋊D3C2412yes—
521C22×C3⋊D3C2411yescharacteristic
522C22×C3×D3—24no—
523C22×C3×D3—24no—
524C22×C3×D3—42no—
525C22×C3×D3—42no—
526C22×C3×D3—42no—
527C22×C3×D3—42no—
528C22×C3×D3C2411yescharacteristic
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—22no—
542#638—24no—
543#638—24no—
544#638—42no—
545#638—42no—
546#638—42no—
547C2×C3⋊Dic3—42no—
548C2×C3⋊Dic3C2411yescharacteristic
549C2×C3⋊Dic3C2412yes—
550C2×C3⋊Dic3C2411yescharacteristic
551C2×C3⋊Dic3C2411yescharacteristic
552C4⋊(C3⋊D3)—22no—
553C4×C3⋊D3—22no—
554C3×#67—24no—
555C3×#67—24no—
556C3×#67—22no—
557C3×#67—22no—
558C3×#67—24no—
559C3×#67—24no—
560C3×#67—24no—
561C3×#67—42no—
562C3×#67—41no—
563C3×#67C2×D418yescomplemented
564C2×C3×Dic3—24no—
565C2×C3×Dic3—24no—
566C2×C3×Dic3—42no—
567C2×C3×Dic3C2×D418yescomplemented
568C2×C3×Dic3C2411yescharacteristic
569C2×C3×Dic3C2412yes—
570C2×C3×Dic3C2411yescharacteristic
571C2×C3×Dic3C2412yes—
572C2×C3×Dic3C2411yescharacteristic
573C2×C3×Dic3C2411yescharacteristic
574C2×C3×Dic3C2412yes—
575C2×C3×Dic3C2411yescharacteristic
576C3×D12—22no—
577C3×D12—22no—
578C3×C4×D3—22no—
579C3×C4×D3—22no—
580C3×C4×D3—24no—
581C3×C4×D3C2×D414yescomplemented
582C3×Dic6—22no—
583C3×Dic6—22no—
584C3×Dic6C2×D414yescomplemented
585#627—24no—
586#626—22no—
587#626—24no—
588#626—24no—
589#626—24no—
590#626—42no—
591#626—42no—
592#626—42no—
593#625—41no—
594#625—42no—
595#624—24no—
596#624—24no—
597#624—24no—
598#624—22no—
599D3×Dic3—22no—
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—31no—
609#546—92no—
610#546—92no—
611#546—91no—
612D42—91no—
613D42—92no—
614D42—92no—
615D42—91no—
616#537—92no—
617#537—91no—
618#535—92no—
619#535—91no—
620#525—91no—
621#525—92no—
622C2×#121—92no—
623C2×#121—91no—
624#520—91no—
625C24×C3—22no—
626C24×C3—32no—
627C24×C3—32no—
628C24×C3C22×D312yes—
629C24×C3C22×D312yes—
630C23×D3—32no—
631C23×D3—32no—
632C23×D3—31no—
633C23×D3—31no—
634C23×D3—62no—
635C23×D3C22×D312yes—
636C23×D3C22×D312yes—
637C3×#41—38no—
638C3×#41—64no—
639C3×#41—64no—
640C3×#41—68no—
641C3×#41—64no—
642C3×#41—64no—
643C2×C3×Q8—31no—
644C2×C3×Q8—31no—
645C2×C3×Q8—31no—
646C2×C3×D4—24no—
647C2×C3×D4—24no—
648C2×C3×D4—21no—
649C2×C3×D4—22no—
650C2×C3×D4—21no—
651C2×C3×D4—32no—
652C2×C3×D4—31no—
653C2×C3×D4—32no—
654C2×C3×D4—32no—
655C2×C3×D4—32no—
656C2×C3×D4—32no—
657C2×C3×D4—32no—
658C2×C3×D4—31no—
659C2×C3×D4—31no—
660C2×C3×D4—32no—
661C2×C3×D4—31no—
662C2×C3×D4—31no—
663C2×C3×D4—44no—
664C2×C3×D4—64no—
665C2×C3×D4—68no—
666C2×C3×D4—68no—
667C2×C3×D4—68no—
668C2×C3×D4—64no—
669C2×C3×D4C22×D312yes—
670C2×C3×D4C22×D311yescharacteristic
671C2×C3×D4C22×D312yes—
672C2×C3×D4C22×D311yescharacteristic
673C2×C3×D4C22×D311yescharacteristic
674C2×C3×D4C22×D311yescharacteristic
675C22×C3×C4—21no—
676C22×C3×C4—32no—
677C22×C3×C4—31no—
678C22×C3×C4—32no—
679C22×C3×C4—32no—
680C22×C3×C4—32no—
681C22×C3×C4—32no—
682C22×C3×C4—31no—
683C22×C3×C4—31no—
684C22×C3×C4C22×D311yescharacteristic
685C22×C3×C4C22×D311yescharacteristic
686C2×#67—28no—
687C2×#67—28no—
688C2×#67—32no—
689C2×#67—32no—
690C2×#67—31no—
691C2×#67—32no—
692C2×#67—31no—
693C2×#67—32no—
694C2×#67—32no—
695C2×#67—32no—
696C2×#67—32no—
697C2×#67—32no—
698C2×#67—32no—
699C2×#67—32no—
700C2×#67—31no—
701C2×#67—32no—
702C2×#67—31no—
703C2×#67—32no—
704C2×#67—32no—
705C2×#67—32no—
706C2×#67—31no—
707C2×#67—32no—
708C2×#67—32no—
709C2×#67—32no—
710C2×#67—32no—
711C2×#67—61no—
712C2×#67—62no—
713C2×#67—62no—
714C2×#67—62no—
715C2×#67—62no—
716C2×#67—62no—
717C2×#67—124no—
718C2×#67—124no—
719C2×#67—124no—
720C2×#67—124no—
721C2×#67—128no—
722C2×#67C22×D312yes—
723C2×#67C22×D311yescharacteristic
724C2×#67C22×D311yescharacteristic
725C2×#67C22×D312yes—
726C2×#67C22×D312yes—
727C2×#67C22×D312yes—
728C2×#67C22×D312yes—
729C2×#67C22×D311yescharacteristic
730C2×#67C22×D312yes—
731C2×#67C22×D312yes—
732C22×Dic3—32no—
733C22×Dic3—32no—
734C22×Dic3—31no—
735C22×Dic3—31no—
736C22×Dic3—32no—
737C22×Dic3—62no—
738C22×Dic3C22×D312yes—
739C22×Dic3C22×D312yes—
740C22×Dic3C22×D312yes—
741C22×Dic3C22×D312yes—
742#239—64no—
743#239—64no—
744D3×Q8—64no—
745D3×Q8—64no—
746#237—24no—
747#237—28no—
748#237—24no—
749#237—68no—
750#237—68no—
751#237#6718yescomplemented
752D3×D4—24no—
753D3×D4—28no—
754D3×D4—24no—
755D3×D4—68no—
756D3×D4—64no—
757D3×D4—64no—
758D3×D4—68no—
759D3×D4—124no—
760D3×D4—124no—
761#235—24no—
762#235—24no—
763#235—64no—
764#235—68no—
765#235—68no—
766#235—64no—
767C2×D12—31no—
768C2×D12—32no—
769C2×D12—32no—
770C2×D12—32no—
771C2×D12—31no—
772C2×D12—31no—
773C2×D12—32no—
774C2×D12—32no—
775C2×D12—32no—
776C2×D12—61no—
777C2×D12—124no—
778C2×D12C22×D311yescharacteristic
779C2×D12C22×D311yescharacteristic
780C2×C4×D3—31no—
781C2×C4×D3—31no—
782C2×C4×D3—31no—
783C2×C4×D3—31no—
784C2×C4×D3—32no—
785C2×C4×D3—32no—
786C2×C4×D3—31no—
787C2×C4×D3—32no—
788C2×C4×D3—32no—
789C2×C4×D3—32no—
790C2×C4×D3—31no—
791C2×C4×D3—32no—
792C2×C4×D3—32no—
793C2×C4×D3—61no—
794C2×C4×D3—64no—
795C2×C4×D3—68no—
796C2×C4×D3—68no—
797C2×C4×D3—64no—
798C2×C4×D3C22×D311yescharacteristic
799C2×C4×D3C22×D312yes—
800C2×C4×D3C22×D311yescharacteristic
801C2×C4×D3C22×D311yescharacteristic
802C2×Dic6—32no—
803C2×Dic6—32no—
804C2×Dic6C22×D311yescharacteristic
805C2×Dic6C22×D311yescharacteristic
806C2×Dic6C22×D311yescharacteristic
807C3×C4⋊C4—31no—
808C3×C4⋊C4—31no—
809C3×C4⋊C4—32no—
810C3×C22⋊C4—32no—
811C3×C22⋊C4—32no—
812C3×C22⋊C4—32no—
813C3×C22⋊C4—32no—
814C3×C22⋊C4—31no—
815C3×C22⋊C4—32no—
816C3×C22⋊C4—31no—
817C3×C42—31no—
818#217—32no—
819#217—32no—
820#217—31no—
821#217—32no—
822#217—32no—
823#217—31no—
824#217—31no—
825#217—32no—
826#217—32no—
827#217—32no—
828#217—31no—
829#217—31no—
830#217—32no—
831#217—31no—
832#217—31no—
833#217—32no—
834#217—61no—
835#217—62no—
836#217—62no—
837#217C22×D312yes—
838#217C22×D312yes—
839#217C22×D312yes—
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—31no—
851(C2×D3)⋊C4—32no—
852(C2×D3)⋊C4—31no—
853(C2×D3)⋊C4—31no—
854(C2×D3)⋊C4—32no—
855(C2×D3)⋊C4—31no—
856(C2×D3)⋊C4—32no—
857(C2×D3)⋊C4—31no—
858(C2×D3)⋊C4—32no—
859(C2×D3)⋊C4—31no—
860(C2×D3)⋊C4—32no—
861(C2×D3)⋊C4—61no—
862(C2×D3)⋊C4—62no—
863(C2×D3)⋊C4C22×D311yescharacteristic
864C4⋊Dic3—31no—
865C4⋊Dic3—31no—
866C4⋊Dic3—31no—
867C4⋊Dic3—32no—
868C4⋊Dic3—32no—
869C4⋊Dic3—32no—
870C4⋊Dic3—31no—
871C4⋊Dic3—31no—
872C4⋊Dic3—61no—
873C4⋊Dic3C22×D311yescharacteristic
874Dic3⋊C4—31no—
875Dic3⋊C4—31no—
876Dic3⋊C4—32no—
877Dic3⋊C4—31no—
878Dic3⋊C4—31no—
879Dic3⋊C4—32no—
880Dic3⋊C4—32no—
881Dic3⋊C4—31no—
882Dic3⋊C4—32no—
883Dic3⋊C4—31no—
884Dic3⋊C4—32no—
885Dic3⋊C4—31no—
886Dic3⋊C4—61no—
887Dic3⋊C4C22×D312yes—
888Dic3⋊C4C22×D311yescharacteristic
889C4×Dic3—31no—
890C4×Dic3—31no—
891C4×Dic3—32no—
892C4×Dic3—32no—
893C4×Dic3—32no—
894C4×Dic3—32no—
895C4×Dic3—61no—
896C4×Dic3C22×D311yescharacteristic
897C22×C32—21no—
898C22×C32—22no—
899C22×C32—22no—
900C22×C32—22no—
901C22×C32—21no—
902C22×C32—22no—
903C22×C32—21no—
904C22×C32—22no—
905C22×C32—84no—
906C22×C32C22×D414yes—
907C22×C32C2511yescharacteristic
908C2×C3⋊D3—21no—
909C2×C3⋊D3—21no—
910C2×C3⋊D3—22no—
911C2×C3⋊D3—22no—
912C2×C3⋊D3—22no—
913C2×C3⋊D3—48no—
914C2×C3⋊D3H(5,𝔽2)12yescomplemented
915C2×C3×D3—21no—
916C2×C3×D3—21no—
917C2×C3×D3—21no—
918C2×C3×D3—21no—
919C2×C3×D3—22no—
920C2×C3×D3—21no—
921C2×C3×D3—22no—
922C2×C3×D3—21no—
923C2×C3×D3—21no—
924C2×C3×D3—21no—
925C2×C3×D3—22no—
926C2×C3×D3—84no—
927C2×C3×D3—84no—
928C2×C3×D3C22×D412yes—
929D32—44no—
930C32×C4—21no—
931C32×C4C22×D412yes—
932C3⋊Dic3—21no—
933C3⋊Dic3—21no—
934C3⋊Dic3—22no—
935C3⋊Dic3—21no—
936C3×Dic3—21no—
937C3×Dic3—22no—
938C3×Dic3—21no—
939C3×Dic3—22no—
940C3×Dic3—21no—
941C3×Dic3—21no—
942C3×Dic3C22×D412yes—
943C3×Dic3C22×D414yes—
944H(5,𝔽2)—68no—
945C2×#41—31no—
946C2×#41—32no—
947C2×#41—31no—
948C2×#41—31no—
949C2×#41—31no—
950C2×#41—31no—
951C2×#41—92no—
952C2×#41—92no—
953C2×#41—91no—
954C2×#41—91no—
955C2×#41—188no—
956C22×Q8—91no—
957C22×D4—32no—
958C22×D4—32no—
959C22×D4—31no—
960C22×D4—32no—
961C22×D4—31no—
962C22×D4—92no—
963C22×D4—92no—
964C22×D4—92no—
965C22×D4—92no—
966C22×D4—91no—
967C22×D4D3211yescharacteristic, complemented
968C23×C4—92no—
969C23×C4—91no—
970#127—91no—
971#127—92no—
972#127—92no—
973#127—91no—
974#124—31no—
975#124—92no—
976#124—92no—
977#124—91no—
978#123—32no—
979#123—91no—
980#123—91no—
981#123—92no—
982C22⋊Q8—31no—
983C22⋊Q8—92no—
984C22⋊Q8—91no—
985C22⋊Q8—92no—
986C22⋊Q8—91no—
987C22⋊Q8—92no—
988C22⋊Q8—91no—
989#121—31no—
990#121—32no—
991#121—92no—
992#121—91no—
993#121—92no—
994#121—92no—
995#121—92no—
996#121—92no—
997#121—92no—
998#121—92no—
999#121—92no—
1000#121—92no—
1001#121—92no—
1002#121—91no—
1003#121—91no—
1004#121—92no—
1005#121—91no—
1006#121—92no—
1007#121—92no—
1008#121—92no—
1009#121—91no—
1010#121—92no—
1011#121—91no—
1012#121—92no—
1013#121—91no—
1014#120—32no—
1015#120—92no—
1016#120—91no—
1017#120—92no—
1018#120—92no—
1019#120—92no—
1020#120—91no—
1021#120—92no—
1022#120—92no—
1023#120—92no—
1024C4×Q8—91no—
1025C4×Q8—91no—
1026C4×D4—31no—
1027C4×D4—31no—
1028C4×D4—91no—
1029C4×D4—92no—
1030C4×D4—92no—
1031C4×D4—92no—
1032C4×D4—92no—
1033C4×D4—92no—
1034C4×D4—91no—
1035C4×D4—92no—
1036C4×D4—91no—
1037C4×D4—91no—
1038#117—91no—
1039#117—92no—
1040C2×C4⋊C4—91no—
1041C2×C4⋊C4—92no—
1042C2×C22⋊C4—32no—
1043C2×C22⋊C4—92no—
1044C2×C22⋊C4—92no—
1045C23×C3—24no—
1046C23×C3—24no—
1047C23×C3—22no—
1048C23×C3—21no—
1049C23×C3—22no—
1050C23×C3—31no—
1051C23×C3—31no—
1052C23×C3—32no—
1053C23×C3—31no—
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—82no—
1063C23×C3—122no—
1064C23×C3—122no—
1065C23×C3—122no—
1066C23×C3—122no—
1067C23×C3C23×D312yes—
1068C23×C3C23×D311yescharacteristic
1069C23×C3C23×D312yes—
1070C23×C3C23×D311yescharacteristic
1071C23×C3C23×D312yes—
1072C23×C3C23×D312yes—
1073C22×D3—24no—
1074C22×D3—24no—
1075C22×D3—31no—
1076C22×D3—31no—
1077C22×D3—32no—
1078C22×D3—32no—
1079C22×D3—42no—
1080C22×D3—42no—
1081C22×D3—42no—
1082C22×D3—42no—
1083C22×D3—61no—
1084C22×D3—62no—
1085C22×D3—62no—
1086C22×D3—62no—
1087C22×D3—62no—
1088C22×D3—64no—
1089C22×D3—64no—
1090C22×D3—64no—
1091C22×D3—64no—
1092C22×D3—62no—
1093C22×D3—124no—
1094C22×D3—124no—
1095C22×D3—121no—
1096C22×D3—121no—
1097C22×D3—122no—
1098C22×D3—122no—
1099C22×D3—242no—
1100C22×D3C23×D311yescharacteristic
1101C22×D3C23×D312yes—
1102C22×D3C23×D311yescharacteristic
1103C22×D3C23×D311yescharacteristic
1104C3×Q8—34no—
1105C3×Q8—62no—
1106C3×Q8—62no—
1107C3×D4—24no—
1108C3×D4—24no—
1109C3×D4—22no—
1110C3×D4—22no—
1111C3×D4—24no—
1112C3×D4—38no—
1113C3×D4—42no—
1114C3×D4—44no—
1115C3×D4—62no—
1116C3×D4—64no—
1117C3×D4—64no—
1118C3×D4—62no—
1119C3×D4—64no—
1120C3×D4—62no—
1121C3×D4—64no—
1122C3×D4—64no—
1123C3×D4—62no—
1124C3×D4—122no—
1125C3×D4—121no—
1126C3×D4D3×D414yescomplemented
1127C3×D4C2×#6714yescomplemented
1128C2×C3×C4—22no—
1129C2×C3×C4—22no—
1130C2×C3×C4—21no—
1131C2×C3×C4—21no—
1132C2×C3×C4—38no—
1133C2×C3×C4—32no—
1134C2×C3×C4—31no—
1135C2×C3×C4—34no—
1136C2×C3×C4—31no—
1137C2×C3×C4—32no—
1138C2×C3×C4—31no—
1139C2×C3×C4—31no—
1140C2×C3×C4—32no—
1141C2×C3×C4—31no—
1142C2×C3×C4—42no—
1143C2×C3×C4—64no—
1144C2×C3×C4—64no—
1145C2×C3×C4—64no—
1146C2×C3×C4—62no—
1147C2×C3×C4—62no—
1148C2×C3×C4—122no—
1149C2×C3×C4C23×D311yescharacteristic
1150C2×C3×C4C23×D311yescharacteristic
1151C2×C3×C4C23×D311yescharacteristic
1152C2×C3×C4C23×D311yescharacteristic
1153#67—24no—
1154#67—24no—
1155#67—22no—
1156#67—22no—
1157#67—24no—
1158#67—24no—
1159#67—24no—
1160#67—42no—
1161#67—41no—
1162#67—62no—
1163#67—64no—
1164#67—64no—
1165#67—64no—
1166#67—62no—
1167#67—62no—
1168#67—64no—
1169#67—64no—
1170#67—64no—
1171#67—64no—
1172#67—64no—
1173#67—124no—
1174#67—124no—
1175#67—122no—
1176#67—122no—
1177#67—122no—
1178#67—122no—
1179#67—121no—
1180#67—121no—
1181#67—122no—
1182#67—122no—
1183#67—122no—
1184#67—122no—
1185#67—122no—
1186#67—122no—
1187#67—122no—
1188#67—124no—
1189#67—124no—
1190#67—242no—
1191#67C2×#6718yescomplemented
1192C2×Dic3—24no—
1193C2×Dic3—24no—
1194C2×Dic3—31no—
1195C2×Dic3—31no—
1196C2×Dic3—31no—
1197C2×Dic3—32no—
1198C2×Dic3—32no—
1199C2×Dic3—31no—
1200C2×Dic3—31no—
1201C2×Dic3—31no—
1202C2×Dic3—42no—
1203C2×Dic3—61no—
1204C2×Dic3—61no—
1205C2×Dic3—61no—
1206C2×Dic3—62no—
1207C2×Dic3—62no—
1208C2×Dic3—62no—
1209C2×Dic3—122no—
1210C2×Dic3—122no—
1211C2×Dic3—122no—
1212C2×Dic3—124no—
1213C2×Dic3C2×#6718yescomplemented
1214C2×Dic3C23×D311yescharacteristic
1215C2×Dic3C23×D312yes—
1216C2×Dic3C23×D311yescharacteristic
1217C2×Dic3C23×D311yescharacteristic
1218C2×Dic3C23×D312yes—
1219C2×Dic3C23×D311yescharacteristic
1220C2×Dic3C23×D312yes—
1221C2×Dic3C23×D311yescharacteristic
1222D12—22no—
1223D12—22no—
1224D12—64no—
1225D12—62no—
1226D12—64no—
1227D12—64no—
1228D12—62no—
1229D12—62no—
1230D12—122no—
1231D12—122no—
1232D12—122no—
1233D12—122no—
1234C4×D3—22no—
1235C4×D3—22no—
1236C4×D3—24no—
1237C4×D3—62no—
1238C4×D3—64no—
1239C4×D3—64no—
1240C4×D3—64no—
1241C4×D3—62no—
1242C4×D3—62no—
1243C4×D3—62no—
1244C4×D3—62no—
1245C4×D3—62no—
1246C4×D3—64no—
1247C4×D3—64no—
1248C4×D3—64no—
1249C4×D3—122no—
1250C4×D3—122no—
1251C4×D3C2×#6714yescomplemented
1252Dic6—22no—
1253Dic6—22no—
1254Dic6—64no—
1255Dic6—64no—
1256Dic6C2×#6714yescomplemented
1257C2×C32—24no—
1258C2×C32—41no—
1259C2×C32—42no—
1260C2×C32C23×D411yescharacteristic
1261C2×C32C2×H(5,𝔽2)11yescharacteristic
1262C2×C32#58511yescharacteristic
1263C3⋊D3—22no—
1264C3⋊D3—42no—
1265C3×D3—22no—
1266C3×D3—41no—
1267C3×D3—42no—
1268C3×D3—41no—
1269C24—32no—
1270C24—32no—
1271C24—91no—
1272C24—92no—
1273C24C2×D3212yes—
1274#41—38no—
1275#41—64no—
1276#41—64no—
1277#41—68no—
1278#41—64no—
1279#41—64no—
1280#41—188no—
1281#41—184no—
1282#41—188no—
1283#41—184no—
1284C2×Q8—31no—
1285C2×Q8—31no—
1286C2×Q8—31no—
1287C2×Q8—92no—
1288C2×Q8—184no—
1289C2×D4—24no—
1290C2×D4—32no—
1291C2×D4—32no—
1292C2×D4—31no—
1293C2×D4—32no—
1294C2×D4—32no—
1295C2×D4—31no—
1296C2×D4—32no—
1297C2×D4—32no—
1298C2×D4—31no—
1299C2×D4—32no—
1300C2×D4—31no—
1301C2×D4—31no—
1302C2×D4—64no—
1303C2×D4—68no—
1304C2×D4—68no—
1305C2×D4—68no—
1306C2×D4—64no—
1307C2×D4—91no—
1308C2×D4—92no—
1309C2×D4—92no—
1310C2×D4—92no—
1311C2×D4—92no—
1312C2×D4—92no—
1313C2×D4—92no—
1314C2×D4—91no—
1315C2×D4—92no—
1316C2×D4—92no—
1317C2×D4—91no—
1318C2×D4—92no—
1319C2×D4—92no—
1320C2×D4—92no—
1321C2×D4—92no—
1322C2×D4—91no—
1323C2×D4—188no—
1324C2×D4—184no—
1325C2×D4—364no—
1326C2×D4—364no—
1327C2×D4—364no—
1328C2×D4C2×D3212yes—
1329C2×D4C2×D3211yescharacteristic
1330C2×D4C2×D3211yescharacteristic
1331C22×C4—32no—
1332C22×C4—31no—
1333C22×C4—32no—
1334C22×C4—32no—
1335C22×C4—32no—
1336C22×C4—31no—
1337C22×C4—32no—
1338C22×C4—31no—
1339C22×C4—92no—
1340C22×C4—92no—
1341C22×C4—91no—
1342C22×C4—92no—
1343C22×C4—91no—
1344C22×C4—91no—
1345C22×C4—92no—
1346C22×C4—92no—
1347C22×C4—91no—
1348C22×C4—188no—
1349C22×C4—184no—
1350C22×C4C2×D3211yescharacteristic
1351C4⋊C4—31no—
1352C4⋊C4—31no—
1353C4⋊C4—32no—
1354C4⋊C4—91no—
1355C4⋊C4—92no—
1356C4⋊C4—92no—
1357C4⋊C4—92no—
1358C4⋊C4—91no—
1359C4⋊C4—91no—
1360C4⋊C4—92no—
1361C4⋊C4—91no—
1362C4⋊C4—91no—
1363C4⋊C4—91no—
1364C22⋊C4—31no—
1365C22⋊C4—32no—
1366C22⋊C4—32no—
1367C22⋊C4—32no—
1368C22⋊C4—32no—
1369C22⋊C4—32no—
1370C22⋊C4—31no—
1371C22⋊C4—91no—
1372C22⋊C4—92no—
1373C22⋊C4—92no—
1374C22⋊C4—91no—
1375C22⋊C4—92no—
1376C22⋊C4—92no—
1377C22⋊C4—92no—
1378C22⋊C4—91no—
1379C22⋊C4—91no—
1380C22⋊C4—91no—
1381C22⋊C4—92no—
1382C22⋊C4—91no—
1383C22⋊C4—92no—
1384C22⋊C4—92no—
1385C22⋊C4—91no—
1386C22⋊C4—91no—
1387C22⋊C4—92no—
1388C42—31no—
1389C42—92no—
1390C42—92no—
1391C42—91no—
1392C22×C3—22no—
1393C22×C3—22no—
1394C22×C3—22no—
1395C22×C3—22no—
1396C22×C3—22no—
1397C22×C3—21no—
1398C22×C3—22no—
1399C22×C3—21no—
1400C22×C3—22no—
1401C22×C3—22no—
1402C22×C3—21no—
1403C22×C3—21no—
1404C22×C3—22no—
1405C22×C3—22no—
1406C22×C3—21no—
1407C22×C3—22no—
1408C22×C3—21no—
1409C22×C3—24no—
1410C22×C3—21no—
1411C22×C3—32no—
1412C22×C3—42no—
1413C22×C3—41no—
1414C22×C3—42no—
1415C22×C3—41no—
1416C22×C3—42no—
1417C22×C3—42no—
1418C22×C3—42no—
1419C22×C3—61no—
1420C22×C3—61no—
1421C22×C3—62no—
1422C22×C3—61no—
1423C22×C3—62no—
1424C22×C3—61no—
1425C22×C3—61no—
1426C22×C3—62no—
1427C22×C3—61no—
1428C22×C3—61no—
1429C22×C3—61no—
1430C22×C3—84no—
1431C22×C3—84no—
1432C22×C3—88no—
1433C22×C3—244no—
1434C22×C3—244no—
1435C22×C3C2×D3×D414yes—
1436C22×C3C22×#6714yes—
1437C22×C3C24×D311yescharacteristic
1438C22×C3C24×D311yescharacteristic
1439C2×D3—21no—
1440C2×D3—21no—
1441C2×D3—21no—
1442C2×D3—21no—
1443C2×D3—21no—
1444C2×D3—22no—
1445C2×D3—21no—
1446C2×D3—22no—
1447C2×D3—21no—
1448C2×D3—21no—
1449C2×D3—22no—
1450C2×D3—32no—
1451C2×D3—32no—
1452C2×D3—62no—
1453C2×D3—61no—
1454C2×D3—61no—
1455C2×D3—61no—
1456C2×D3—61no—
1457C2×D3—62no—
1458C2×D3—62no—
1459C2×D3—62no—
1460C2×D3—62no—
1461C2×D3—62no—
1462C2×D3—62no—
1463C2×D3—84no—
1464C2×D3—84no—
1465C2×D3—121no—
1466C2×D3—121no—
1467C2×D3—122no—
1468C2×D3—122no—
1469C2×D3—122no—
1470C2×D3—124no—
1471C2×D3—124no—
1472C2×D3—128no—
1473C2×D3—128no—
1474C2×D3—248no—
1475C2×D3C22×#6712yes—
1476C3×C4—21no—
1477C3×C4—21no—
1478C3×C4—22no—
1479C3×C4—34no—
1480C3×C4—32no—
1481C3×C4—41no—
1482C3×C4—61no—
1483C3×C4—62no—
1484C3×C4—61no—
1485C3×C4—61no—
1486C3×C4—62no—
1487C3×C4—61no—
1488C3×C4C2×D3×D412yes—
1489C3×C4C22×#6712yes—
1490Dic3—22no—
1491Dic3—21no—
1492Dic3—21no—
1493Dic3—21no—
1494Dic3—22no—
1495Dic3—21no—
1496Dic3—62no—
1497Dic3—61no—
1498Dic3—61no—
1499Dic3—62no—
1500Dic3—61no—
1501Dic3—61no—
1502Dic3—62no—
1503Dic3—61no—
1504Dic3—61no—
1505Dic3—121no—
1506Dic3—122no—
1507Dic3—121no—
1508Dic3C22×#6712yes—
1509Dic3C22×#6714yes—
1510C32#348811yescharacteristic, complemented, Sylow
1511C23—24no—
1512C23—31no—
1513C23—31no—
1514C23—32no—
1515C23—31no—
1516C23—42no—
1517C23—42no—
1518C23—64no—
1519C23—64no—
1520C23—91no—
1521C23—92no—
1522C23—122no—
1523C23—122no—
1524C23—122no—
1525C23—122no—
1526C23—184no—
1527C23—182no—
1528C23—182no—
1529C23—184no—
1530C23—362no—
1531C23—361no—
1532C23C22×D3212yes—
1533C23C22×D3211yescharacteristic
1534C23C22×D3212yes—
1535Q8—34no—
1536Q8—62no—
1537Q8—62no—
1538Q8—184no—
1539D4—24no—
1540D4—22no—
1541D4—38no—
1542D4—62no—
1543D4—62no—
1544D4—64no—
1545D4—64no—
1546D4—64no—
1547D4—62no—
1548D4—64no—
1549D4—64no—
1550D4—62no—
1551D4—122no—
1552D4—121no—
1553D4—184no—
1554D4—184no—
1555D4—182no—
1556D4—184no—
1557D4—182no—
1558D4—184no—
1559D4—184no—
1560D4—182no—
1561D4—362no—
1562D4—362no—
1563D4—362no—
1564D4—362no—
1565D4—362no—
1566D4—362no—
1567D4—362no—
1568D4—361no—
1569D4D3×#6714yescomplemented
1570C2×C4—22no—
1571C2×C4—38no—
1572C2×C4—32no—
1573C2×C4—31no—
1574C2×C4—34no—
1575C2×C4—31no—
1576C2×C4—31no—
1577C2×C4—32no—
1578C2×C4—31no—
1579C2×C4—32no—
1580C2×C4—31no—
1581C2×C4—64no—
1582C2×C4—64no—
1583C2×C4—64no—
1584C2×C4—62no—
1585C2×C4—62no—
1586C2×C4—91no—
1587C2×C4—91no—
1588C2×C4—92no—
1589C2×C4—91no—
1590C2×C4—122no—
1591C2×C4—182no—
1592C2×C4—184no—
1593C2×C4—184no—
1594C2×C4—184no—
1595C2×C4—182no—
1596C2×C4—182no—
1597C2×C4—182no—
1598C2×C4—362no—
1599C2×C4—362no—
1600C2×C4C22×D3211yescharacteristic
1601C2×C4C22×D3211yescharacteristic
1602C2×C3—24no—
1603C2×C3—24no—
1604C2×C3—21no—
1605C2×C3—21no—
1606C2×C3—21no—
1607C2×C3—44no—
1608C2×C3—42no—
1609C2×C3—41no—
1610C2×C3—42no—
1611C2×C3—42no—
1612C2×C3—41no—
1613C2×C3—62no—
1614C2×C3—82no—
1615C2×C3—121no—
1616C2×C3—122no—
1617C2×C3—121no—
1618C2×C3C22×D3×D411yescharacteristic
1619C2×C3#596411yescharacteristic
1620C2×C3D3×H(5,𝔽2)11yescharacteristic
1621C2×C3D3×H(5,𝔽2)11yescharacteristic
1622C2×C3#596611yescharacteristic
1623C2×C3C23×#6711yescharacteristic
1624D3—22no—
1625D3—41no—
1626D3—41no—
1627D3—42no—
1628D3—62no—
1629D3—62no—
1630D3—122no—
1631D3—122no—
1632D3—122no—
1633D3—242no—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—21no—
1638C22—21no—
1639C22—22no—
1640C22—21no—
1641C22—22no—
1642C22—32no—
1643C22—61no—
1644C22—61no—
1645C22—61no—
1646C22—61no—
1647C22—62no—
1648C22—61no—
1649C22—62no—
1650C22—61no—
1651C22—61no—
1652C22—62no—
1653C22—61no—
1654C22—84no—
1655C22—92no—
1656C22—181no—
1657C22—181no—
1658C22—182no—
1659C22—182no—
1660C22—182no—
1661C22—244no—
1662C22—244no—
1663C22—368no—
1664C22—364no—
1665C22C2×D3×#6714yes—
1666C22C23×D3211yescharacteristic
1667C4—21no—
1668C4—32no—
1669C4—34no—
1670C4—61no—
1671C4—62no—
1672C4—61no—
1673C4—61no—
1674C4—61no—
1675C4—62no—
1676C4—181no—
1677C4—182no—
1678C4—181no—
1679C4—181no—
1680C4C2×D3×#6712yes—
1681C3—21no—
1682C3#8662911yescharacteristic, complemented
1683C3#8728511yescharacteristic, complemented
1684C2—24no—
1685C2—41no—
1686C2—42no—
1687C2—62no—
1688C2—121no—
1689C2—122no—
1690C2—121no—
1691C2—182no—
1692C2—362no—
1693C2#1059667511yescharacteristic
1694C2#1059667811yescharacteristic
1695C2C22×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×#64312C2semidirect
3. D4×#638C2semidirect
4. C3×#5806C2semidirect
5. #10595526C2semidirect
6. #10595513C2semidirect
7. #10595493C2semidirect
8. C2×#63958C2semidirect
9. #10595291C2semidirect
10. D3×#938C2semidirect
11. #10595244C2semidirect
12. #10595237C2semidirect
13. #10595236C2semidirect
14. #10595235C2semidirect
15. D4×#626C2semidirect
16. #10595222C2semidirect
17. #10595159C2semidirect
18. #10595156C2semidirect
19. #10595148C2semidirect
20. #10595060C2semidirect
21. #10595007C2semidirect
22. #10594894C2semidirect
23. #10594830C2semidirect
26. C22×C32×D4C22semidirect
27. C22×#638C22semidirect
28. C2×D4×C3⋊D3C22semidirect
29. C22×C3×#67C22semidirect
30. C22×C3×#67C22semidirect
33. C2×C3×#237C22semidirect
34. C2×C3×#237C22semidirect
35. C2×C3×#237C22semidirect
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×#3811C22semidirect
42. C2×D3×#67C22semidirect
43. C22×#626C22semidirect
44. C22×#624C22semidirect
45. C2×#3804C22semidirect
46. C2×#3804C22semidirect
48. C2×C4×D32C22semidirect
49. C2×#3799C22semidirect
50. C2×#3799C22semidirect
51. C2×#3797C22semidirect
52. #64162C22semidirect
53. #64149C22semidirect
54. #64148C22semidirect
55. #64147C22semidirect
56. #64146C22semidirect
57. D4×C3⋊Dic3C22semidirect
58. #64139C22semidirect
59. C4×#638C22semidirect
60. C3×#953C22semidirect
61. C2×C3×#217C22semidirect
62. C3×#939C22semidirect
63. C3×#938C22semidirect
64. C3×#936C22semidirect
65. C3×#935C22semidirect
66. C3×D4×Dic3C22semidirect
67. C3×C4×#67C22semidirect
68. C3×#924C22semidirect
69. #63983C22semidirect
70. #63981C22semidirect
71. #63980C22semidirect
72. #63979C22semidirect
73. #63979C22semidirect
74. #63978C22semidirect
75. #63978C22semidirect
76. #63977C22semidirect
77. #63977C22semidirect
78. #63977C22semidirect
79. #63976C22semidirect
80. #67⋊Dic3C22semidirect
81. Dic3×#67C22semidirect
82. #63971C22semidirect
83. #63970C22semidirect
84. #63970C22semidirect
85. #63969C22semidirect
86. D3×#217C22semidirect
87. C2×Dic3⋊Dic3C22semidirect
88. #63964C22semidirect
89. #63961C22semidirect
90. C2×(C2×D3)⋊Dic3C22semidirect
91. #63959C22semidirect
92. #63959C22semidirect
93. #63958C22semidirect
94. #63958C22semidirect
95. #63958C22semidirect
96. #63958C22semidirect
97. #63958C22semidirect
98. #63958C22semidirect
99. #63958C22semidirect
100. #63958C22semidirect
101. #63958C22semidirect
102. #63955C22semidirect
103. #63952C22semidirect
104. #63952C22semidirect
105. #63922C22semidirect
106. #63916C22semidirect
107. #63911C22semidirect
108. #63909C22semidirect
109. #63908C22semidirect
110. #63906C22semidirect
111. #63904C22semidirect
112. #63904C22semidirect
113. C4×#626C22semidirect
114. C4×#625C22semidirect
115. D3×C4⋊Dic3C22semidirect
116. #63888C22semidirect
117. #63888C22semidirect
118. #63887C22semidirect
119. #63886C22semidirect
120. #63884C22semidirect
121. #63863C22semidirect
122. #63856C22semidirect
123. #63855C22semidirect
124. #63851C22semidirect
125. #63843C22semidirect
126. Dic3×Dic6C22semidirect
130. C2×#1004D3semidirect
145. #5806D3semidirect
214. C3×#237D4semidirect
311. C22×C3×D4C2×D3semidirect
312. C22×C3×D4C2×D3semidirect
318. C22×#67C2×D3semidirect
319. C22×#67C2×D3semidirect
330. C2×#237C2×D3semidirect
331. C2×#237C2×D3semidirect
332. C2×#237C2×D3semidirect
339. C2×D3×D4C2×D3semidirect
340. C2×D3×D4C2×D3semidirect
341. C2×D3×D4C2×D3semidirect
346. C2×#235C2×D3semidirect
347. C2×#235C2×D3semidirect
369. #953C2×D3semidirect
372. C2×#217C2×D3semidirect
399. #939C2×D3semidirect
416. #938C2×D3semidirect
428. #936C2×D3semidirect
432. #935C2×D3semidirect
438. D4×Dic3C2×D3semidirect
459. C4×#67C2×D3semidirect
468. #924C2×D3semidirect
537. C32×D4C2×D4semidirect
563. C3×#67C2×D4semidirect
567. C2×C3×Dic3C2×D4semidirect
581. C3×C4×D3C2×D4semidirect
584. C3×Dic6C2×D4semidirect
751. #237#67semidirect
914. C2×C3⋊D3H(5,𝔽2)semidirect
967. C22×D4D32semidirect
1126. C3×D4D3×D4semidirect
1127. C3×D4C2×#67semidirect
1191. #67C2×#67semidirect
1213. C2×Dic3C2×#67semidirect
1251. C4×D3C2×#67semidirect
1256. Dic6C2×#67semidirect
1510. C32#3488semidirect
1569. D4D3×#67semidirect
1682. C3#86629semidirect
1683. 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×#643122
D4×#6382
C3×#58062
#105955262
#105955132
#105954932
C2×#639582
#105952912
D3×#9382
#105952442
#105952372
#105952362
#105952352
D4×#6262
#105952222
#105951592
#105951562
#105951482
#105950602
#105950072
#105948942
#105948302
#872853
#866293