Finite Group Databasebeta

← #11884322

Subgroups — #11884322

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5676C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63932C211yesmaximal, characteristic, complemented
4#10593895C211yesmaximal, characteristic, complemented
5#10592759C211yesmaximal, characteristic, complemented
6C3×#5057C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591599C211yesmaximal, characteristic, complemented
9#10591598C211yesmaximal, characteristic, complemented
10#10591519C211yesmaximal, characteristic, complemented
11#10591460C211yesmaximal, characteristic, complemented
12#10591459C211yesmaximal, characteristic, complemented
13#10590365C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83503—31nomaximal
17#80567—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C32×#124C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27#64078C2211yescharacteristic, complemented
28C3×#946C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#938C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#884—21no—
33C3×#883—21no—
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic, complemented
39#63947—24no—
40#63932—24no—
41#63908—21no—
42#63891—21no—
43#63891—21no—
44D3×C4⋊Dic3—21no—
45#63857C2211yescharacteristic
46#63857C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63630C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#916—31no—
67C2×#911—31no—
68#5676D311yescharacteristic, complemented
69#5555—31no—
70#5551—31no—
71C3×#463—31no—
72#5239—31no—
73#5218—31no—
74#5173—31no—
75#5158—31no—
76#5060—31no—
77#5060—31no—
78#5060—61no—
79#5057D311yescharacteristic, complemented
80#5052—31no—
81#5047—31no—
82#5041—31no—
83#5037—31no—
84#5019—31no—
85#5014—31no—
86#5014—31no—
87#5011—31no—
88#4841—31no—
89#4836—31no—
90#4816—31no—
91#4808—31no—
92#4778—31no—
93#4776—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#239—22no—
102C3×#239—41no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12D411yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3795—22no—
119#3795—22no—
120#3795—41no—
121#3795—41no—
122C32×C22⋊C4—21no—
123C32×C22⋊C4—21no—
124C32×C42C2311yescharacteristic
125#3756—22no—
126#3756—41no—
127#3754—22no—
128#3754—41no—
129C4⋊(C3⋊Dic3)—21no—
130C4⋊(C3⋊Dic3)—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#215—22no—
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3716—22no—
152#3716—22no—
153#3713D414yescomplemented
154#3711—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239C2×D311yescharacteristic
160C2×#237—31no—
161C2×#237—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×#124—21no—
168C3×#124C2×D311yescharacteristic
169C3×#124C2×D311yescharacteristic
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#120—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C22⋊C4—61no—
179#950—64no—
180#946C2×D311yescharacteristic
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—61no—
186C2×#216—61no—
187C2×#215C2×D311yescharacteristic, complemented
188#938—61no—
189#938C2×D311yescharacteristic
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—61no—
197C2×#214—61no—
198#932—64no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213C2×D311yescharacteristic
202#930—61no—
203C2×C4⋊Dic3—61no—
204#924—31no—
205#924—31no—
206C2×#208—31no—
207C22×C3⋊C8—31no—
208#916—64no—
209#911—64no—
210C2×#204—31no—
211C2×#204—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×D3×C8—31no—
214#897—31no—
215#897—31no—
216D3×C4⋊C4—61no—
217#886—61no—
218#886—61no—
219#884—21no—
220#883—21no—
221#883—61no—
222#883—61no—
223#882—21no—
224D3×C22⋊C4—21no—
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic
227C4×D12C2×D311yescharacteristic, complemented
228#869—31no—
229#869—31no—
230#869—61no—
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#102—31no—
234#835C2×D311yescharacteristic, complemented
235#832—31no—
236#832—31no—
237#832C2×D311yescharacteristic
238#830—31no—
239#830—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242#816—31no—
243#816—31no—
244#810—31no—
245#810—31no—
246#809—31no—
247#809—31no—
248#808—31no—
249#808—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272#634—21no—
273#634—21no—
274#634—21no—
275#634—21no—
276C3×#67—42no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—41no—
285C3×D12—42no—
286C3×D12C2×D412yes—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×C4×D3—81no—
295#625—42no—
296#625—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—31no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—31no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—21no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—62no—
332C2×C3×D4—61no—
333C2×C3×D4—121no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349#239—22no—
350#239—41no—
351#237—62no—
352#237—62no—
353#237—121no—
354#237—121no—
355D3×D4—22no—
356D3×D4—41no—
357#235—62no—
358#235—62no—
359#235—121no—
360#235—121no—
361C2×D12—21no—
362C2×D12#6711yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3C22×D311yescharacteristic
371C2×C4×D3C22×D311yescharacteristic
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—31no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C3×SD16—62no—
379C3×D8—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—61no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—41no—
393C3×C22⋊C4—41no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—21no—
399C3×C42C22×D311yescharacteristic
400C3×C42C22×D311yescharacteristic
401#217—21no—
402#217—61no—
403#217—61no—
404#216—62no—
405#216—62no—
406#216—122no—
407#216—121no—
408#216—121no—
409#216—122no—
410#215—22no—
411#214—62no—
412#214—62no—
413#214—62no—
414#214—62no—
415#214—122no—
416#214—121no—
417#214—121no—
418#214—122no—
419#213—22no—
420#213—34no—
421#213—34no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4#6711yescharacteristic
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—121no—
436C4⋊Dic3—121no—
437C4⋊Dic3#6711yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439C4⋊Dic3C22×D311yescharacteristic
440Dic3⋊C4—21no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443#208—62no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—62no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453#204—62no—
454#204—62no—
455ΓL(1,𝔽25)—62no—
456D3×C8—62no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—84no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4—41no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3⋊Dic3—41no—
480C3⋊Dic3—41no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—91no—
487C2×#41—91no—
488C22×D4—31no—
489AGL(1,ℤ/8)—184no—
490#135—184no—
491C2×Q16—91no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×M16—91no—
501C22×C8—91no—
502C4⋊Q8—91no—
503#124D3211yescharacteristic
504#123—61no—
505#123—181no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—31no—
511#121—61no—
512#121—181no—
513#120—61no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—31no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—61no—
519#106—91no—
520C4⋊C8—31no—
521#103—31no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—122no—
538C23×C3—122no—
539C23×C3—241no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—81no—
545C22×D3C2×#6711yescharacteristic
546C22×D3C2×#6711yescharacteristic
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—32no—
558C3×D4—32no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—121no—
564C3×D4—122no—
565C3×D4—122no—
566C3×D4—241no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4—241no—
584C2×C3×C4D3×D411yescharacteristic
585C2×C3×C4D3×D411yescharacteristic
586C2×C3×C4C2×#6711yescharacteristic
587C2×C3×C4C2×#6711yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—42no—
591#67—81no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3—122no—
605C2×Dic3—122no—
606C2×Dic3C2×#6711yescharacteristic
607C2×Dic3C2×#6711yescharacteristic
608D12—21no—
609D12—21no—
610D12—41no—
611D12—42no—
612D12D3×D412yes—
613D12D3×D412yes—
614C4×D3—21no—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—42no—
619C4×D3—42no—
620C4×D3—81no—
621C4×D3—122no—
622C4×D3—122no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—61no—
631Dic6—121no—
632Dic6—121no—
633Dic6—121no—
634Dic6—121no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—32no—
640C3⋊C8—32no—
641C3⋊C8—62no—
642C3⋊C8—62no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C2×C32—81no—
646C2×C32D4211yescharacteristic
647C2×C32#57511yescharacteristic
648C2×C32#57711yescharacteristic
649C3×D3—41no—
650C3×D3—41no—
651C3×D3—42no—
652C3×D3—42no—
653C24—61no—
654#41—62no—
655#41—121no—
656#41—182no—
657#41—182no—
658#41—361no—
659#41—361no—
660C2×Q8—91no—
661C2×Q8—91no—
662C2×Q8C2×D3211yescharacteristic
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—31no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—62no—
669C2×D4—61no—
670C2×D4—121no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4C2×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—181no—
680C22×C4—181no—
681Q16—182no—
682Q16—361no—
683SD16—62no—
684SD16—182no—
685SD16—182no—
686SD16—182no—
687SD16—361no—
688D8—62no—
689D8—94no—
690M16—182no—
691C2×C8—31no—
692C2×C8—31no—
693C2×C8—91no—
694C2×C8—91no—
695C2×C8—182no—
696C4⋊C4—31no—
697C4⋊C4—31no—
698C4⋊C4—31no—
699C4⋊C4—61no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C4⋊C4—181no—
703C4⋊C4—181no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—31no—
707C22⋊C4—31no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C42C2×D3211yescharacteristic
715C22×C3—21no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—62no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—62no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—244no—
738C22×C3C2×D3×D411yescharacteristic
739C22×C3C22×#6711yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—22no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—84no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—81no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4C2×D3×D411yescharacteristic
769C3×C4C2×D3×D411yescharacteristic
770C3×C4#100411yescharacteristic
771C3×C4#100911yescharacteristic
772Dic3—21no—
773Dic3—21no—
774Dic3—41no—
775Dic3—41no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781Dic3—241no—
782C32#326711yescharacteristic, complemented, Sylow
783C23—21no—
784C23—31no—
785C23—31no—
786C23—61no—
787C23—61no—
788C23—122no—
789C23—122no—
790C23—241no—
791Q8—21no—
792Q8—21no—
793Q8—181no—
794Q8—181no—
795Q8—181no—
796Q8—181no—
797D4—21no—
798D4—21no—
799D4—32no—
800D4—32no—
801D4—61no—
802D4—61no—
803D4—121no—
804D4—122no—
805D4—122no—
806D4—241no—
807D4—362no—
808D4—362no—
809C2×C4—21no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—241no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4D3×#6711yescharacteristic
826C2×C4D3×#6711yescharacteristic
827C2×C4C22×D3211yescharacteristic
828C8—61no—
829C8—61no—
830C8—92no—
831C8—181no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—81no—
836C2×C3—81no—
837C2×C3—122no—
838C2×C3—121no—
839C2×C3—121no—
840C2×C3—122no—
841C2×C3—161no—
842C2×C3#560911yescharacteristic
843C2×C3#577011yescharacteristic
844C2×C3#577311yescharacteristic
845C2×C3D4×#6711yescharacteristic
846C2×C3#582211yescharacteristic
847C2×C3#583611yescharacteristic
848D3—41no—
849D3—41no—
850D3—42no—
851D3—42no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—62no—
862C22—62no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—244no—
868C22C2×D3×#6711yescharacteristic
869C4—21no—
870C4—21no—
871C4—41no—
872C4—61no—
873C4—61no—
874C4—121no—
875C4—121no—
876C4—361no—
877C4—361no—
878C4D32×D411yescharacteristic
879C4#6431411yescharacteristic
880C3—21no—
881C3#8056711yescharacteristic, complemented
882C3#8350311yescharacteristic, complemented
883C2—81no—
884C2—121no—
885C2—121no—
886C2—122no—
887C2—122no—
888C2#1059528811yescharacteristic
889C2#1059546611yescharacteristic
890C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5676C2semidirect
2. C2×#63947C2semidirect
3. C2×#63932C2semidirect
4. #10593895C2semidirect
5. #10592759C2semidirect
6. C3×#5057C2semidirect
7. #10591655C2semidirect
8. #10591599C2semidirect
9. #10591598C2semidirect
10. #10591519C2semidirect
11. #10591460C2semidirect
12. #10591459C2semidirect
13. #10590365C2semidirect
14. #10590344C2semidirect
15. #10590330C2semidirect
21. C2×#3795C22semidirect
23. C2×#3756C22semidirect
24. C2×#3756C22semidirect
27. #64078C22semidirect
29. C2×C3×#215C22semidirect
38. C3×C4×D12C22semidirect
46. #63857C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63630C22semidirect
53. C3×#835C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. #63574C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
60. #63562C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5676D3semidirect
79. #5057D3semidirect
153. #3713D4semidirect
187. C2×#215C2×D3semidirect
227. C4×D12C2×D3semidirect
234. #835C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
782. C32#3267semidirect
881. C3#80567semidirect
882. C3#83503semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
C2×#639472
C2×#639322
#105938952
#105927592
C3×#50572
#105916552
#105915992
#105915982
#105915192
#105914602
#105914592
#105903652
#105903442
#105903302
#835033
#805673