Finite Group Databasebeta

← #11909340

Subgroups — #11909340

Order 1152.

2461 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C3×#5511C212yesmaximal, complemented
3#10595035C214yesmaximal, complemented
4#10595033C211yesmaximal, characteristic, complemented
5#10595018C212yesmaximal, complemented
6#10595016C212yesmaximal, complemented
7#10594925C212yesmaximal, complemented
8#10594810C211yesmaximal, characteristic, complemented
9#10594574C214yesmaximal, complemented
10#10594530C211yesmaximal, characteristic, complemented
11#10594521C212yesmaximal, complemented
12#10594512C211yesmaximal, characteristic, complemented
13#10594476C212yesmaximal, complemented
14#10594379C211yesmaximal, characteristic, complemented
15#10594350C211yesmaximal, characteristic, complemented
16#10594343C212yesmaximal, complemented
17#10594327C212yesmaximal, complemented
18#86934—32nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2212yes—
21C2×#3799C2212yes—
22C2×#3798C2212yescomplemented
23C2×#3797C2212yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×#3752C2212yes—
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64102C2212yes—
28#64102C2211yescharacteristic
29#64102C2211yescharacteristic
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64102C2212yes—
33C3×C4×#67C2214yes—
34C3×C4×#67C2212yes—
35C3×#924C2214yes—
36C3×#924C2212yes—
37C3×#897C2212yescomplemented
38C3×#896C2214yescomplemented
39C3×D3×C4⋊C4C2212yescomplemented
40C3×#889C2214yescomplemented
41C3×#888C2212yescomplemented
42C3×#887C2212yescomplemented
43#63982C2211yescharacteristic
44#63982C2212yes—
45#63981C2214yes—
46#63980C2211yescharacteristic
47#63974C2214yes—
48#63962C2212yes—
49#63957C2212yes—
50#63919C2211yescharacteristic, complemented
51C4×#627C2211yescharacteristic, complemented
52#63915C2211yescharacteristic, complemented
53#63912C2212yescomplemented
54#63910C2214yes—
55#63909C2212yes—
56#63907C2214yescomplemented
57#63904C2214yescomplemented
58C4×#626C2214yescomplemented
59C4×#625C2211yescharacteristic, complemented
60#63900C2212yescomplemented
61#63897C2214yes—
62#63894C2212yes—
63#63888C2214yescomplemented
64#63883C2214yescomplemented
65#63874C2212yescomplemented
66#63873C2211yescharacteristic, complemented
67#63871C2214yescomplemented
68#63870C2212yescomplemented
69#63870C2211yescharacteristic, complemented
70#63868C2214yescomplemented
71#63865C2212yescomplemented
72#63865C2212yescomplemented
73#63865C2212yescomplemented
74#63864C2212yes—
75#63862C2212yescomplemented
76#63855C2212yescomplemented
77#63854C2214yescomplemented
78#63853C2214yescomplemented
79#63850C2214yescomplemented
80#63848C2214yescomplemented
81#63843C2212yescomplemented
82#63838C2212yescomplemented
83#63836C2214yescomplemented
84C3×#554—32no—
85#5733—32no—
86#5727—32no—
87#5693—34no—
88#5692—34no—
89#5643—32no—
90#5638—34no—
91#5637—34no—
92#5633—34no—
93#5631—32no—
94#5630—32no—
95D3×C22⋊Q8—34no—
96#5622—32no—
97#5574—32no—
98#5568—32no—
99#5556—34no—
100#5550—32no—
101#5547—34no—
102#5538—32no—
103#5511D312yescomplemented
104#5507—32no—
105#5504—32no—
106C2×#893—32no—
107C2×#893—61no—
108C23×C3⋊D3C2312yes—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2312yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×C4⋊(C3⋊D3)—24no—
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C2×C4⋊(C3⋊D3)C2312yes—
116C2×C4⋊(C3⋊D3)C2311yescharacteristic
117C2×C4×C3⋊D3—44no—
118C2×C4×C3⋊D3C2312yes—
119C2×C4×C3⋊D3C2312yes—
120C2×C4×C3⋊D3C2312yes—
121C2×C4×C3⋊D3C2312yes—
122C2×C3×#67C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×C4×D3C2314yes—
125C2×C3×Dic6C2312yes—
126C2×C3×Dic6C2314yes—
127C2×#627C2311yescharacteristic
128C2×#627C2312yes—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#625C2311yescharacteristic
132C2×#624C2314yes—
133C2×#624C2314yes—
134#3799—28no—
135#3798—44no—
136#3797—44no—
137C32×C4⋊C4C2311yescharacteristic
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2312yes—
140#3752C2312yes—
141#3752C2312yes—
142#3752C2312yes—
143#3752C2312yes—
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2311yescharacteristic
148C3×#217C2314yes—
149C3×#217C2312yes—
150C3×(C2×D3)⋊C4C2312yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×C4⋊Dic3C2312yes—
153C3×C4⋊Dic3C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2312yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2312yes—
160C3×C4×Dic3C2314yes—
161#3724C2312yes—
162#3724C2312yes—
163#3724C2312yes—
164#3724C2311yescharacteristic
165#3724C2311yescharacteristic
166Dic3⋊Dic3C2312yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2312yes—
169Dic3⋊Dic3C2312yes—
170#3722C2314yes—
171#3722C2314yes—
172#3722C2314yes—
173#3722C2314yes—
174(C2×D3)⋊Dic3C2312yes—
175(C2×D3)⋊Dic3C2312yes—
176(C2×D3)⋊Dic3C2312yes—
177Dic32C2314yes—
178#3520—91noSylow
179C2×#239—32no—
180C2×D3×Q8—34no—
181C2×#235—34no—
182C2×#235—32no—
183C22×D12—32no—
184C22×D12—61no—
185C22×C4×D3—34no—
186C22×C4×D3—62no—
187C3×C4⋊Q8—32no—
188C3×#125—34no—
189C3×C22⋊Q8—34no—
190C3×C22⋊Q8—32no—
191C3×C22⋊Q8—34no—
192C3×C22⋊Q8—32no—
193C3×C4×Q8—32no—
194C3×C4×D4—32no—
195C3×C4×D4—34no—
196C2×C3×C4⋊C4—21no—
197C2×C3×C4⋊C4—32no—
198C2×C3×C4⋊C4C2×D312yes—
199#947—34no—
200#947—32no—
201#946—34no—
202#946—34no—
203Q8×Dic3—32no—
204#944—32no—
205#939—32no—
206#937—34no—
207#935—32no—
208#930—32no—
209#929—34no—
210C4×#67—32no—
211C4×#67—34no—
212C4×#67—34no—
213C4×#67C2×D314yes—
214C4×#67C2×D312yes—
215C2×(C2×D3)⋊C4—34no—
216C2×(C2×D3)⋊C4—62no—
217#926—32no—
218#924C2×D312yes—
219#924C2×D314yes—
220C2×C4×Dic3—32no—
221C2×C4×Dic3—61no—
222#898—32no—
223#898—34no—
224#898—34no—
225#898—34no—
226#897—34no—
227#897C2×D312yescomplemented
228#896—34no—
229#896—34no—
230#896—34no—
231#896—34no—
232#896C2×D314yescomplemented
233#895—32no—
234#895—34no—
235#894—34no—
236#894—34no—
237#894—34no—
238#894—34no—
239#894—34no—
240#893—34no—
241#893—34no—
242#893—34no—
243#893—32no—
244#893—32no—
245#893—32no—
246#893—32no—
247#893—32no—
248#893—61no—
249#893—62no—
250#893—61no—
251#893—61no—
252#893—61no—
253#893—62no—
254#892—34no—
255D3×C4⋊C4—34no—
256D3×C4⋊C4—34no—
257D3×C4⋊C4—34no—
258D3×C4⋊C4C2×D312yescomplemented
259#889—34no—
260#889—32no—
261#889C2×D314yescomplemented
262#888—32no—
263#888C2×D312yescomplemented
264#887—32no—
265#887—34no—
266#887C2×D312yescomplemented
267#886—32no—
268#885—34no—
269#885—32no—
270#884—34no—
271#884—34no—
272#883—34no—
273#883—34no—
274#882—34no—
275D3×C22⋊C4—34no—
276D3×C22⋊C4—34no—
277#879—32no—
278#878—32no—
279#878—34no—
280#877—34no—
281#876—34no—
282#875—32no—
283C4×D12—34no—
284C4×D12—32no—
285#872—32no—
286#872—34no—
287#872—34no—
288C4×Dic6—32no—
289C23×C32C2411yescharacteristic
290C22×C3⋊D3—24no—
291C22×C3⋊D3—24no—
292C22×C3⋊D3—42no—
293C22×C3⋊D3C2412yes—
294C22×C3⋊D3C2412yes—
295C22×C3×D3C2412yes—
296C2×C32×C4—22no—
297C2×C32×C4—42no—
298C2×C32×C4C2412yes—
299C2×C32×C4C2411yescharacteristic
300C2×C32×C4C2412yes—
301C2×C32×C4C2411yescharacteristic
302C2×C3⋊Dic3—22no—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3C2411yescharacteristic
305C2×C3⋊Dic3C2411yescharacteristic
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2411yescharacteristic
308C4⋊(C3⋊D3)—24no—
309C4⋊(C3⋊D3)—22no—
310C4⋊(C3⋊D3)#4114yescomplemented
311C4×C3⋊D3—24no—
312C4×C3⋊D3—24no—
313C4×C3⋊D3—42no—
314C4×C3⋊D3—42no—
315C3×#67—24no—
316C2×C3×Dic3C2414yes—
317C2×C3×Dic3C2414yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×C4×D3—24no—
322C3×C4×D3—44no—
323C3×Dic6—24no—
324C3×Dic6—44no—
325#627—22no—
326#627—24no—
327#626—28no—
328#626—44no—
329#625—22no—
330#624—28no—
331#624—44no—
332#556—91no—
333#554—32no—
334#552—92no—
335#551—94no—
336D4×Q8—91no—
337#548—92no—
338#547—91no—
339#547—91no—
340#546—92no—
341#542—92no—
342#539—94no—
343#533—91no—
344#529—91no—
345#525—92no—
346C2×C22⋊Q8—92no—
347#520—92no—
348C2×C4×D4—91no—
349C23×D3—34no—
350C23×D3—62no—
351C2×C3×Q8—32no—
352C2×C3×Q8—34no—
353C2×C3×D4—32no—
354C22×C3×C4—21no—
355C22×C3×C4—22no—
356C22×C3×C4—32no—
357C22×C3×C4—34no—
358C22×C3×C4C22×D312yes—
359C22×C3×C4C22×D314yes—
360C2×#67—32no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67C22×D312yes—
364C22×Dic3—32no—
365C22×Dic3—32no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368#239—68no—
369D3×Q8—128no—
370#235—68no—
371#235—128no—
372C2×D12—32no—
373C2×D12—34no—
374C2×D12—32no—
375C2×D12—34no—
376C2×D12—34no—
377C2×D12—61no—
378C2×D12—62no—
379C2×D12—61no—
380C2×D12—68no—
381C2×D12—68no—
382C2×C4×D3—34no—
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—34no—
386C2×C4×D3—34no—
387C2×C4×D3—34no—
388C2×C4×D3—34no—
389C2×C4×D3—34no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—128no—
395C2×C4×D3—128no—
396C2×C4×D3C22×D312yes—
397C2×C4×D3C22×D314yes—
398C2×Dic6—32no—
399C2×Dic6—34no—
400C2×Dic6C22×D312yes—
401C2×Dic6C22×D314yes—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—22no—
404C3×C4⋊C4—21no—
405C3×C4⋊C4—32no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—32no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4C22×D312yes—
413C3×C4⋊C4C22×D312yes—
414C3×C4⋊C4C22×D314yes—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—32no—
417C3×C22⋊C4—32no—
418C3×C22⋊C4—34no—
419C3×C42—32no—
420C3×C42—34no—
421#217—32no—
422#217—32no—
423#217—32no—
424#217C22×D314yes—
425#217C22×D312yes—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—32no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4C22×D314yes—
446(C2×D3)⋊C4C22×D312yes—
447C4⋊Dic3—32no—
448C4⋊Dic3—34no—
449C4⋊Dic3—32no—
450C4⋊Dic3—32no—
451C4⋊Dic3C22×D312yes—
452C4⋊Dic3C22×D314yes—
453Dic3⋊C4—32no—
454Dic3⋊C4—32no—
455Dic3⋊C4—32no—
456Dic3⋊C4—32no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—32no—
462Dic3⋊C4C22×D314yes—
463Dic3⋊C4C22×D314yes—
464Dic3⋊C4C22×D312yes—
465Dic3⋊C4C22×D314yes—
466Dic3⋊C4C22×D314yes—
467C4×Dic3—32no—
468C4×Dic3—32no—
469C4×Dic3—32no—
470C4×Dic3—32no—
471C4×Dic3—34no—
472C4×Dic3—34no—
473C4×Dic3—61no—
474C4×Dic3—61no—
475C4×Dic3—61no—
476C4×Dic3—61no—
477C4×Dic3C22×D312yes—
478C4×Dic3C22×D314yes—
479C22×C32—21no—
480C22×C32—21no—
481C22×C322−1+412yes—
482C22×C32C2511yescharacteristic
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3—48no—
489C2×C3⋊D3C2×#4114yes—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C32×C4—21no—
494C32×C4—22no—
495C32×C4—22no—
496C32×C4C2×#4112yes—
497C3⋊Dic3—21no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3⋊Dic3H(5,𝔽2)12yes—
501C3×Dic3—22no—
502C3×Dic3—24no—
503C3×Dic3—22no—
504C3×Dic3—24no—
505C3×Dic3—22no—
506C2×#41—92no—
507C2×#41—92no—
508C22×Q8—92no—
509C22×D4—91no—
510C23×C4—92no—
511C4⋊Q8—32no—
512C4⋊Q8—91no—
513C4⋊Q8—91no—
514#126—94no—
515#126—92no—
516#126—94no—
517#125—34no—
518#125—91no—
519#125—92no—
520#124—92no—
521#124—91no—
522#124—94no—
523#123—94no—
524#123—94no—
525#123—92no—
526#123—94no—
527#123—94no—
528C22⋊Q8—34no—
529C22⋊Q8—32no—
530C22⋊Q8—34no—
531C22⋊Q8—32no—
532C22⋊Q8—91no—
533C22⋊Q8—92no—
534C22⋊Q8—92no—
535C22⋊Q8—92no—
536C22⋊Q8—92no—
537C22⋊Q8—94no—
538C22⋊Q8—94no—
539#121—92no—
540#121—94no—
541#121—92no—
542#121—91no—
543#120—94no—
544C4×Q8—32no—
545C4×Q8—91no—
546C4×Q8—92no—
547C4×Q8—92no—
548C4×D4—34no—
549C4×D4—32no—
550C4×D4—92no—
551C4×D4—94no—
552C4×D4—94no—
553C4×D4—91no—
554C4×D4—91no—
555C4×D4—92no—
556C4×D4—91no—
557C4×D4—91no—
558C4×D4—91no—
559C4×D4—92no—
560#117—92no—
561#117—94no—
562#117—92no—
563#117—92no—
564C2×C4⋊C4—32no—
565C2×C4⋊C4—94no—
566C2×C4⋊C4—92no—
567C2×C4⋊C4D3211yescharacteristic
568C2×C22⋊C4—94no—
569C2×C22⋊C4—92no—
570C2×C42—91no—
571C23×C3—21no—
572C23×C3—32no—
573C23×C3C23×D312yes—
574C22×D3—34no—
575C22×D3—34no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3—68no—
579C22×D3—68no—
580C22×D3—68no—
581C22×D3—124no—
582C22×D3—124no—
583C22×D3—124no—
584C22×D3C23×D312yes—
585C3×Q8—64no—
586C3×Q8—124no—
587C3×D4—64no—
588C2×C3×C4—24no—
589C2×C3×C4—24no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—34no—
595C2×C3×C4—34no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—44no—
600C2×C3×C4—44no—
601C2×C3×C4—64no—
602C2×C3×C4—124no—
603C2×C3×C4C23×D312yes—
604C2×C3×C4C23×D314yes—
605C2×C3×C4C23×D314yes—
606C2×C3×C4C23×D312yes—
607#67—24no—
608#67—68no—
609#67—64no—
610#67—124no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—64no—
620C2×Dic3—64no—
621C2×Dic3—64no—
622C2×Dic3—122no—
623C2×Dic3C23×D314yes—
624C2×Dic3C23×D314yes—
625C2×Dic3C23×D312yes—
626C2×Dic3C23×D312yes—
627C2×Dic3C23×D312yes—
628D12—38no—
629D12—64no—
630D12—68no—
631D12—68no—
632D12—64no—
633D12—68no—
634D12—64no—
635D12—124no—
636C4×D3—24no—
637C4×D3—44no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—68no—
642C4×D3—124no—
643C4×D3—124no—
644C4×D3—124no—
645C4×D3—124no—
646C4×D3—124no—
647C4×D3—124no—
648C4×D3—124no—
649C4×D3—124no—
650Dic6—24no—
651Dic6—44no—
652Dic6—68no—
653Dic6—64no—
654C2×C32—22no—
655C2×C32C22×#4111yescharacteristic
656C2×C32C2×H(5,𝔽2)11yescharacteristic
657C2×C32C2×2−1+411yescharacteristic
658C3⋊D3—24no—
659C3⋊D3—42no—
660C3×D3—42no—
661C24—92no—
662#41—188no—
663#41—364no—
664C2×Q8—32no—
665C2×Q8—34no—
666C2×Q8—91no—
667C2×Q8—92no—
668C2×Q8—364no—
669C2×D4—32no—
670C2×D4—94no—
671C2×D4—94no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—92no—
675C2×D4—91no—
676C2×D4—184no—
677C22×C4—32no—
678C22×C4—34no—
679C22×C4—94no—
680C22×C4—94no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—92no—
684C22×C4—92no—
685C22×C4—92no—
686C22×C4—92no—
687C22×C4—364no—
688C22×C4C2×D3211yescharacteristic
689C22×C4C2×D3212yes—
690C4⋊C4—34no—
691C4⋊C4—32no—
692C4⋊C4—34no—
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—32no—
696C4⋊C4—34no—
697C4⋊C4—92no—
698C4⋊C4—91no—
699C4⋊C4—92no—
700C4⋊C4—94no—
701C4⋊C4—92no—
702C4⋊C4—91no—
703C4⋊C4—92no—
704C4⋊C4—92no—
705C4⋊C4—92no—
706C4⋊C4C2×D3211yescharacteristic
707C4⋊C4C2×D3212yes—
708C4⋊C4C2×D3211yescharacteristic
709C22⋊C4—32no—
710C22⋊C4—34no—
711C22⋊C4—32no—
712C22⋊C4—34no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—92no—
718C22⋊C4—92no—
719C22⋊C4—92no—
720C22⋊C4—92no—
721C22⋊C4—92no—
722C22⋊C4—92no—
723C22⋊C4—92no—
724C42—34no—
725C42—32no—
726C42—94no—
727C42—91no—
728C42—91no—
729C42—91no—
730C42—91no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3#100714yes—
741C22×C3C24×D312yes—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—38no—
746C2×D3—64no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—64no—
751C2×D3—64no—
752C2×D3—64no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—1216no—
758C2×D3—1216no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—24no—
762C3×C4—24no—
763C3×C4—22no—
764C3×C4—42no—
765C3×C4—42no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—64no—
769C3×C4—62no—
770C3×C4—64no—
771C3×C4D3×#4114yes—
772Dic3—22no—
773Dic3—24no—
774Dic3—22no—
775Dic3—22no—
776Dic3—24no—
777Dic3—34no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—62no—
783Dic3—121no—
784Dic3—121no—
785C32#352011yescharacteristic, complemented, Sylow
786C23—32no—
787C23—92no—
788C23—92no—
789C23—184no—
790C23—184no—
791C23—362no—
792C23C22×D3211yescharacteristic
793Q8—64no—
794Q8—124no—
795Q8—182no—
796Q8—184no—
797D4—64no—
798D4—94no—
799D4—184no—
800D4—188no—
801D4—182no—
802D4—182no—
803D4—364no—
804C2×C4—22no—
805C2×C4—32no—
806C2×C4—34no—
807C2×C4—32no—
808C2×C4—34no—
809C2×C4—32no—
810C2×C4—42no—
811C2×C4—64no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—124no—
817C2×C4—184no—
818C2×C4—184no—
819C2×C4—188no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—364no—
825C2×C4C22×D3212yes—
826C2×C4C22×D3211yescharacteristic
827C2×C4C22×D3212yes—
828C2×C4C22×D3211yescharacteristic
829C2×C3—24no—
830C2×C3—24no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—122no—
835C2×C3C2×#100712yes—
836C2×C3C2×D3×#4112yes—
837C2×C3D3×H(5,𝔽2)12yes—
838D3—42no—
839D3—68no—
840D3—124no—
841D3—124no—
842D3—124no—
843C22—21no—
844C22—21no—
845C22—62no—
846C22—62no—
847C22—62no—
848C22—94no—
849C22—182no—
850C22—182no—
851C22—182no—
852C22—182no—
853C22—182no—
854C22—368no—
855C22#6431612yes—
856C22C23×D3211yescharacteristic
857C4—21no—
858C4—22no—
859C4—22no—
860C4—62no—
861C4—64no—
862C4—64no—
863C4—62no—
864C4—62no—
865C4—92no—
866C4—181no—
867C4—181no—
868C4—181no—
869C4#6430612yes—
870C3—21no—
871C3#8693412yescomplemented
872C2—22no—
873C2—122no—
874C2—184no—
875C2—362no—
876C2C2×#6430611yescharacteristic
877C2#1059667511yescharacteristic
878C2C2×#6431611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
2. C3×#5511C2semidirect
3. #10595035C2semidirect
4. #10595033C2semidirect
5. #10595018C2semidirect
6. #10595016C2semidirect
7. #10594925C2semidirect
8. #10594810C2semidirect
9. #10594574C2semidirect
10. #10594530C2semidirect
11. #10594521C2semidirect
12. #10594512C2semidirect
13. #10594476C2semidirect
14. #10594379C2semidirect
15. #10594350C2semidirect
16. #10594343C2semidirect
17. #10594327C2semidirect
22. C2×#3798C22semidirect
23. C2×#3797C22semidirect
37. C3×#897C22semidirect
38. C3×#896C22semidirect
39. C3×D3×C4⋊C4C22semidirect
40. C3×#889C22semidirect
41. C3×#888C22semidirect
42. C3×#887C22semidirect
50. #63919C22semidirect
51. C4×#627C22semidirect
52. #63915C22semidirect
53. #63912C22semidirect
56. #63907C22semidirect
57. #63904C22semidirect
58. C4×#626C22semidirect
59. C4×#625C22semidirect
60. #63900C22semidirect
63. #63888C22semidirect
64. #63883C22semidirect
65. #63874C22semidirect
66. #63873C22semidirect
67. #63871C22semidirect
68. #63870C22semidirect
69. #63870C22semidirect
70. #63868C22semidirect
71. #63865C22semidirect
72. #63865C22semidirect
73. #63865C22semidirect
75. #63862C22semidirect
76. #63855C22semidirect
77. #63854C22semidirect
78. #63853C22semidirect
79. #63850C22semidirect
80. #63848C22semidirect
81. #63843C22semidirect
82. #63838C22semidirect
83. #63836C22semidirect
103. #5511D3semidirect
227. #897C2×D3semidirect
232. #896C2×D3semidirect
258. D3×C4⋊C4C2×D3semidirect
261. #889C2×D3semidirect
263. #888C2×D3semidirect
266. #887C2×D3semidirect
310. C4⋊(C3⋊D3)#41semidirect
785. C32#3520semidirect
871. C3#86934semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C3×#55112
#105950352
#105950332
#105950182
#105950162
#105949252
#105948102
#105945742
#105945302
#105945212
#105945122
#105944762
#105943792
#105943502
#105943432
#105943272
#869343