Finite Group Databasebeta

← #11884428

Subgroups — #11884428

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5599C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3#10595078C211yesmaximal, characteristic, complemented
4C2×#63829C211yesmaximal, characteristic, complemented
5#10592736C211yesmaximal, characteristic, complemented
6C3×#5038C211yesmaximal, characteristic, complemented
7#10591469C211yesmaximal, characteristic, complemented
8#10591463C211yesmaximal, characteristic, complemented
9#10591429C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591155C211yesmaximal, characteristic, complemented
12#10590595C211yesmaximal, characteristic, complemented
13#10590588C211yesmaximal, characteristic, complemented
14#10590532C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#83577—31nomaximal
17#80728—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C32×#121C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25C3×#940—21no—
26C3×#940C2211yescharacteristic, complemented
27C3×#939—21no—
28C2×C3×#213C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×C4×#67C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#887C2211yescharacteristic, complemented
34C3×#884—21no—
35C3×#67⋊C4—21no—
36#63983—21no—
37#63958—21no—
38#63925—24no—
39#63921—21no—
40#63894C2211yescharacteristic
41#63860C2211yescharacteristic
42#63857C2211yescharacteristic
43#63853—21no—
44C2×#3719C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46#63829—24no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63657C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×#832C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#550—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#911—31no—
67C2×#904—31no—
68#5612—31no—
69#5599D311yescharacteristic, complemented
70#5550—31no—
71C3×#466—31no—
72#5239—31no—
73#5238—31no—
74#5154—31no—
75#5111—31no—
76#5074—31no—
77#5072—31no—
78#5042—31no—
79#5038D311yescharacteristic, complemented
80#5037—31no—
81#5037—31no—
82#5037—31no—
83#5037—61no—
84#5036—31no—
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4889—31no—
89#4886—31no—
90#4786—31no—
91#4783—31no—
92#4773—31no—
93#4767—31no—
94C22×D32—21no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—21no—
99#3828—22no—
100#3828—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C22×C3×Dic3—21no—
111C3×#237—22no—
112C3×#237—41no—
113C3×#235—22no—
114C3×#235—41no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#626—21no—
122C2×#624—21no—
123D3×D12—22no—
124D3×D12—41no—
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127#3754—41no—
128#3753—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217D411yescharacteristic
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8—22no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3719—22no—
150#3717D414yescomplemented
151#3716—22no—
152#3715—22no—
153#3714—22no—
154#3713—41no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#237C2×D311yescharacteristic
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—61no—
164C2×#235C2×D311yescharacteristic, complemented
165C22×D12—31no—
166C2×C3×D8—31no—
167C22×C3×C8—31no—
168C3×#127—31no—
169C3×#127—61no—
170C3×#121—21no—
171C3×#121—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#121—61no—
175C3×#121C2×D311yescharacteristic, complemented
176C3×#121C2×D311yescharacteristic, complemented
177C3×C4×Q8—31no—
178C3×C4×D4—31no—
179C3×C4×D4—61no—
180#950—64no—
181#949—64no—
182C2×#216—31no—
183C2×#215—31no—
184C2×#215—31no—
185#940—21no—
186#940C2×D311yescharacteristic, complemented
187#939—21no—
188#938—61no—
189#937—61no—
190#937—61no—
191#936—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—61no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—61no—
203C2×#213C2×D311yescharacteristic
204#930C2×D311yescharacteristic
205C4×#67C2×D311yescharacteristic
206#924—31no—
207C2×#208—31no—
208C22×C3⋊C8C2×D311yescharacteristic, complemented
209#911—64no—
210C2×Dic12—31no—
211#904—64no—
212C2×D24—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×ΓL(1,𝔽25)—31no—
216#897—31no—
217#895C2×D311yescharacteristic
218#894—61no—
219#893—31no—
220#887C2×D311yescharacteristic, complemented
221#884—21no—
222#884—61no—
223#883—61no—
224#67⋊C4—21no—
225D3×C22⋊C4—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229C3×#107—31no—
230C3×#102—31no—
231C3×#102—31no—
232#835—31no—
233#832—31no—
234#832C2×D311yescharacteristic, complemented
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241Dic3⋊C8—31no—
242#810—31no—
243#810—31no—
244#810—31no—
245#810—61no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809C2×D311yescharacteristic
251#807C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—81no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—42no—
276#634—21no—
277#634—21no—
278C3×#67—41no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—81no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—81no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6C2×D412yes—
300#626—42no—
301#624—81no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—31no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—31no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—41no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—121no—
358C2×#67#6711yescharacteristic
359C22×Dic3—21no—
360#237—22no—
361#237—41no—
362D3×D4—62no—
363D3×D4—121no—
364#235—22no—
365#235—41no—
366#235—62no—
367#235—62no—
368#235—122no—
369#235—121no—
370#235—121no—
371#235—122no—
372C2×D12—21no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—61no—
376C2×D12—62no—
377C2×D12—61no—
378C2×D12—121no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—121no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C2×Dic6C22×D311yescharacteristic
392C3×D8—62no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—62no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—61no—
400C3×C4⋊C4C22×D311yescharacteristic
401C3×C4⋊C4C22×D311yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—41no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410C3×C42—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217#6711yescharacteristic
415#216—62no—
416#215—34no—
417#215—62no—
418#214—62no—
419#214—62no—
420#214—121no—
421#214—121no—
422#214—122no—
423#213—22no—
424#213—62no—
425#213—62no—
426#213—62no—
427#213—122no—
428#213—121no—
429#213—121no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4#6711yescharacteristic
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440Dic3⋊C4—21no—
441Dic3⋊C4—61no—
442Dic3⋊C4#6711yescharacteristic
443C4×Dic3—21no—
444C4×Dic3C22×D311yescharacteristic
445#208—62no—
446C2×C3⋊C8—22no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455Dic12—62no—
456D24—62no—
457#204—34no—
458#204—62no—
459ΓL(1,𝔽25)—62no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—22no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41—91no—
493C22×D4—91no—
494AGL(1,ℤ/8)—184no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—91no—
506C22×C8—31no—
507#127—31no—
508#127—61no—
509#124—91no—
510#123—181no—
511C22⋊Q8—91no—
512#121—31no—
513#121—31no—
514#121—61no—
515#121—61no—
516#121—181no—
517#121D3211yescharacteristic, complemented
518#120—181no—
519C4×Q8—31no—
520C4×D4—31no—
521C4×D4—61no—
522C4×D4—91no—
523C2×C22⋊C4—181no—
524#107—31no—
525C4⋊C8—91no—
526#103—91no—
527#103—91no—
528#102—31no—
529#102—31no—
530#102—91no—
531#102—91no—
532C22⋊C8—91no—
533C22⋊C8—91no—
534#97—91no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3D3×D411yescharacteristic
543C23×C3C2×#6711yescharacteristic
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—241no—
554C22×D3—241no—
555C22×D3C2×#6711yescharacteristic
556C3×Q8—32no—
557C3×Q8—61no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—81no—
569C3×D4—81no—
570C3×D4—82no—
571C3×D4—121no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—241no—
576C3×D4—241no—
577C3×D4—241no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4C2×#6711yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—41no—
603#67—42no—
604#67—42no—
605#67—42no—
606#67—81no—
607#67—81no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—124no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—42no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3C2×#6711yescharacteristic
619C2×Dic3C2×#6711yescharacteristic
620C2×Dic3C2×#6711yescharacteristic
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—32no—
626D12—32no—
627D12—62no—
628D12—61no—
629D12—61no—
630D12—81no—
631D12—121no—
632D12—122no—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—42no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—124no—
639C4×D3—241no—
640C4×D3—241no—
641Dic6—21no—
642Dic6—62no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6D3×D412yes—
649C3×C8—32no—
650C3×C8—61no—
651C3⋊C8—21no—
652C3⋊C8—61no—
653C3⋊C8—61no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—121no—
657C3⋊C8—121no—
658C3⋊C8D3×D412yes—
659C2×C32—41no—
660C2×C32—81no—
661C2×C32D4211yescharacteristic
662C2×C32#57511yescharacteristic
663C2×C32#57611yescharacteristic
664C3⋊D3—42no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C24—181no—
669#41—62no—
670#41—62no—
671#41—121no—
672#41—121no—
673#41—182no—
674#41—361no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×D4—21no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—182no—
690C2×D4—181no—
691C2×D4—361no—
692C2×D4C2×D3211yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4C2×D3211yescharacteristic
699Q16—182no—
700SD16—94no—
701SD16—182no—
702SD16—182no—
703SD16—361no—
704D8—62no—
705D8—182no—
706D8—182no—
707D8—361no—
708M16—182no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—62no—
712C2×C8—91no—
713C2×C8—91no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—61no—
717C4⋊C4—181no—
718C4⋊C4C2×D3211yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—31no—
721C22⋊C4—31no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C42—61no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C22×#6711yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—244no—
779C2×D3—244no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—62no—
791C3×C4—81no—
792C3×C4—121no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4C2×D3×D411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4#100911yescharacteristic
797Dic3—22no—
798Dic3—21no—
799Dic3—21no—
800Dic3—21no—
801Dic3—41no—
802Dic3—122no—
803Dic3—121no—
804Dic3—121no—
805C32#326811yescharacteristic, complemented, Sylow
806C23—21no—
807C23—31no—
808C23—61no—
809C23—61no—
810C23—181no—
811C23—362no—
812C23—362no—
813C23—721no—
814C23D3×#6711yescharacteristic
815Q8—32no—
816Q8—61no—
817Q8—181no—
818Q8—181no—
819D4—21no—
820D4—21no—
821D4—61no—
822D4—61no—
823D4—61no—
824D4—61no—
825D4—81no—
826D4—92no—
827D4—121no—
828D4—122no—
829D4—122no—
830D4—122no—
831D4—181no—
832D4—241no—
833D4—241no—
834D4—241no—
835D4—362no—
836D4—362no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—122no—
848C2×C4—122no—
849C2×C4—181no—
850C2×C4—362no—
851C2×C4—721no—
852C2×C4D3×#6711yescharacteristic
853C2×C4C22×D3211yescharacteristic
854C8—32no—
855C8—61no—
856C8—181no—
857C8—181no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—41no—
862C2×C3—41no—
863C2×C3—81no—
864C2×C3—81no—
865C2×C3—81no—
866C2×C3—121no—
867C2×C3—161no—
868C2×C3—241no—
869C2×C3—241no—
870C2×C3#560911yescharacteristic
871C2×C3#575711yescharacteristic
872C2×C3#576811yescharacteristic
873C2×C3D4×#6711yescharacteristic
874C2×C3#582211yescharacteristic
875C2×C3#583511yescharacteristic
876D3—41no—
877D3—81no—
878D3—81no—
879D3—122no—
880D3—122no—
881D3—242no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—61no—
889C22—61no—
890C22—61no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—182no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22C2×D3×#6711yescharacteristic
902C4—21no—
903C4—41no—
904C4—61no—
905C4—61no—
906C4—61no—
907C4—62no—
908C4—121no—
909C4—361no—
910C4D32×D411yescharacteristic
911C4#6431411yescharacteristic
912C3—21no—
913C3#8072811yescharacteristic, complemented
914C3#8357711yescharacteristic, complemented
915C2—41no—
916C2—81no—
917C2—121no—
918C2—241no—
919C2—241no—
920C2—362no—
921C2#1059509611yescharacteristic
922C2#1059529111yescharacteristic
923C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5599C2semidirect
2. C2×#63925C2semidirect
3. #10595078C2semidirect
4. C2×#63829C2semidirect
5. #10592736C2semidirect
6. C3×#5038C2semidirect
7. #10591469C2semidirect
8. #10591463C2semidirect
9. #10591429C2semidirect
10. #10591161C2semidirect
11. #10591155C2semidirect
12. #10590595C2semidirect
13. #10590588C2semidirect
14. #10590532C2semidirect
15. #10590457C2semidirect
20. C2×C3×#235C22semidirect
22. C32×#121C22semidirect
23. C2×#3754C22semidirect
26. C3×#940C22semidirect
31. C22×C3×C3⋊C8C22semidirect
33. C3×#887C22semidirect
44. C2×#3719C22semidirect
47. C2×#3716C22semidirect
52. #63657C22semidirect
53. #63637C22semidirect
55. C3×#832C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
62. #63554C22semidirect
69. #5599D3semidirect
79. #5038D3semidirect
150. #3717D4semidirect
164. C2×#235C2×D3semidirect
175. C3×#121C2×D3semidirect
176. C3×#121C2×D3semidirect
186. #940C2×D3semidirect
208. C22×C3⋊C8C2×D3semidirect
220. #887C2×D3semidirect
234. #832C2×D3semidirect
251. #807C2×D3semidirect
517. #121D32semidirect
805. C32#3268semidirect
913. C3#80728semidirect
914. C3#83577semidirect

Maximal subgroups

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

subgroupindex
C3×#55992
C2×#639252
#105950782
C2×#638292
#105927362
C3×#50382
#105914692
#105914632
#105914292
#105911612
#105911552
#105905952
#105905882
#105905322
#105904572
#835773
#807283