Finite Group Databasebeta

← #11884268

Subgroups — #11884268

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×#5551C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592710C211yesmaximal, characteristic, complemented
6#10591189C211yesmaximal, characteristic, complemented
7#10591179C211yesmaximal, characteristic, complemented
8#10591170C211yesmaximal, characteristic, complemented
9#10591170C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11#10591161C211yesmaximal, characteristic, complemented
12#10590376C211yesmaximal, characteristic, complemented
13#10590363C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590344C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#83503—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C3×#938—21no—
26C3×#937—21no—
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C3×#894—21no—
32C3×D3×C4⋊C4—21no—
33C3×#884—21no—
34C3×#883—21no—
35C3×#883—21no—
36C3×D3×C22⋊C4—21no—
37C3×#875C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic, complemented
40C3×#869C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3718C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×#3715C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48#63823—24no—
49#63822—24no—
50C2×#3713C2211yescharacteristic
51C2×#3713C2211yescharacteristic
52#63657C2211yescharacteristic
53#63657C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic, complemented
63C3×#547—31no—
64C3×#546—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#949—31no—
68C2×#932—31no—
69#5551D311yescharacteristic, complemented
70#5550D311yescharacteristic, complemented
71#5239—31no—
72#5239—31no—
73#5238—31no—
74#5218—31no—
75#5086—31no—
76#5083—31no—
77#5060—31no—
78#5057—31no—
79#5052—31no—
80#5052—31no—
81#5048—31no—
82#5047—31no—
83#5047—31no—
84#5046—31no—
85#5041—31no—
86#5037—31no—
87#5019—31no—
88#5016—31no—
89#5014—31no—
90#5014—31no—
91#5011—31no—
92#5011—31no—
93#5011—61no—
94C23×C3×D3—21no—
95C2×C32×D4D411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×#235—22no—
103C3×#235—22no—
104C3×#235—22no—
105C3×#235—41no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12—22no—
109C2×C3×D12—21no—
110C2×C3×D12—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C32×C4⋊C4D411yescharacteristic
123C32×C22⋊C4D411yescharacteristic
124C32×C22⋊C4D411yescharacteristic
125C32×C42C2311yescharacteristic
126#3748—22no—
127C2×C3⋊(C3⋊C8)—22no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147#3718—22no—
148#3718—41no—
149#3715—22no—
150#3715—22no—
151#3715—22no—
152#3715—22no—
153#3715—41no—
154#3713—22no—
155#3713D414yescomplemented
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#235C2×D311yescharacteristic
162C2×#235C2×D311yescharacteristic
163C2×#235C2×D311yescharacteristic, complemented
164C22×D12C2×D311yescharacteristic
165C3×C4⋊Q8—31no—
166C3×#124—31no—
167C3×#123—61no—
168C3×#123—61no—
169C3×#123—61no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×#121—61no—
175C3×#121—61no—
176C3×#120—61no—
177C3×C4×D4—21no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C3×C4×D4C2×D311yescharacteristic
181C3×C4×D4C2×D311yescharacteristic
182C2×C3×C4⋊C4—61no—
183C2×C3×C22⋊C4—61no—
184#950—64no—
185#950—64no—
186#949—64no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196#938—21no—
197#937—21no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203#932—64no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208#930C2×D311yescharacteristic
209#924C2×D311yescharacteristic
210#924C2×D311yescharacteristic
211#924C2×D311yescharacteristic, complemented
212C2×#208—31no—
213C2×#208—31no—
214C2×#208—61no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—61no—
218#894—21no—
219D3×C4⋊C4—21no—
220#884—21no—
221#883—21no—
222#883—21no—
223D3×C22⋊C4—21no—
224#875C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic, complemented
227#869C2×D311yescharacteristic, complemented
228#835—31no—
229#835—31no—
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#830—31no—
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239#830—61no—
240#810—31no—
241#810—31no—
242#810—31no—
243#809—31no—
244#809—31no—
245#809—31no—
246#808—31no—
247#808—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—61no—
251#803—31no—
252#803—31no—
253#803—61no—
254C23×C32C2×D411yescharacteristic
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C32×D4—41no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—81no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—42no—
286C3×D12C2×D412yes—
287C3×D12C2×D412yes—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—81no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)—21no—
302C3⋊(C3⋊C8)C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—31no—
306#546—31no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
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—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—121no—
340C2×C3×D4#6711yescharacteristic
341C2×C3×D4#6711yescharacteristic
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357#235—22no—
358#235—22no—
359#235—22no—
360#235—41no—
361#235—41no—
362#235—41no—
363C2×D12—22no—
364C2×D12—21no—
365C2×D12—41no—
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×D12C22×D311yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×Dic6C22×D311yescharacteristic
375C2×Dic6C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×C4⋊C4—21no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4#6711yescharacteristic
386C3×C4⋊C4#6711yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4#6711yescharacteristic
398C3×C22⋊C4#6711yescharacteristic
399C3×C22⋊C4#6711yescharacteristic
400C3×C22⋊C4#6711yescharacteristic
401C3×C42—21no—
402C3×C42C22×D311yescharacteristic
403C3×C42C22×D311yescharacteristic
404#217—21no—
405#217—21no—
406#217—21no—
407#216—62no—
408#216—62no—
409#216—121no—
410#216—121no—
411#215—62no—
412#215—62no—
413#215—62no—
414#215—62no—
415#215—121no—
416#214—62no—
417#214—62no—
418#214—62no—
419#214—62no—
420#214—121no—
421#213—34no—
422#213—34no—
423#213—62no—
424#213—62no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430C4⋊Dic3—21no—
431C4⋊Dic3—21no—
432C4⋊Dic3C22×D311yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—21no—
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437#208—62no—
438#208—62no—
439#208—122no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
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—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8—62no—
454C2×C3⋊C8—122no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—31no—
486C22×D4—31no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—91no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—31no—
501#124—31no—
502#123—61no—
503#123—61no—
504#123—61no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507C22⋊Q8—31no—
508#121—31no—
509#121—61no—
510#121—61no—
511#120—61no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4D3211yescharacteristic
515C2×C4⋊C4—61no—
516C2×C22⋊C4—61no—
517#106—91no—
518C4⋊C8—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—241no—
536C23×C3C2×#6711yescharacteristic
537C23×C3C2×#6711yescharacteristic
538C23×C3C2×#6711yescharacteristic
539C23×C3C2×#6711yescharacteristic
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—81no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×D4—32no—
553C3×D4—32no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—42no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—122no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4—241no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4—122no—
591C2×C3×C4—122no—
592C2×C3×C4—241no—
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C2×#6711yescharacteristic
595C2×C3×C4C2×#6711yescharacteristic
596C2×C3×C4C2×#6711yescharacteristic
597C2×C3×C4C2×#6711yescharacteristic
598C2×C3×C4C2×#6711yescharacteristic
599C2×C3×C4C2×#6711yescharacteristic
600C2×C3×C4C2×#6711yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—42no—
604#67—42no—
605#67—42no—
606#67—81no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12D3×D412yes—
618D12D3×D412yes—
619C4×D3—42no—
620C4×D3—42no—
621C4×D3—42no—
622C4×D3—42no—
623C4×D3—81no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630C3⋊C8—32no—
631C3⋊C8—32no—
632C3⋊C8—62no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C3⋊C8—121no—
641C3⋊C8—121no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32D4211yescharacteristic
645C2×C32#57511yescharacteristic
646C2×C32#57711yescharacteristic
647C3×D3—42no—
648C3×D3—42no—
649C3×D3—81no—
650C24—61no—
651#41—62no—
652#41—62no—
653#41—62no—
654#41—121no—
655#41—121no—
656#41—121no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—121no—
670C2×D4#62511yescharacteristic
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4C2×D3211yescharacteristic
677C22×C4C2×D3211yescharacteristic
678Q16—182no—
679Q16—361no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—94no—
686D8—182no—
687M16—182no—
688C2×C8—91no—
689C2×C8—91no—
690C2×C8—91no—
691C2×C8—91no—
692C2×C8—182no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4#62511yescharacteristic
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4#62511yescharacteristic
710C22⋊C4#62511yescharacteristic
711C42C2×D3211yescharacteristic
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—244no—
741C22×C3C22×#6711yescharacteristic
742C22×C3C22×#6711yescharacteristic
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
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—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4C2×D3×D411yescharacteristic
773C3×C4C2×D3×D411yescharacteristic
774C3×C4#100411yescharacteristic
775C3×C4#100411yescharacteristic
776Dic3—41no—
777Dic3—41no—
778Dic3—41no—
779Dic3—41no—
780Dic3—41no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—61no—
783C23—61no—
784C23—61no—
785C23—122no—
786C23—122no—
787C23—241no—
788C23C2×#62511yescharacteristic
789C23C2×#62511yescharacteristic
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—32no—
797D4—32no—
798D4—41no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—61no—
803D4—122no—
804D4—122no—
805D4—122no—
806D4—122no—
807D4—241no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—241no—
822C2×C4C2×#62511yescharacteristic
823C2×C4C2×#62511yescharacteristic
824C2×C4C2×#62511yescharacteristic
825C2×C4C2×#62511yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C8—92no—
828C8—181no—
829C8—181no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—41no—
838C2×C3—41no—
839C2×C3—81no—
840C2×C3—122no—
841C2×C3—122no—
842C2×C3—241no—
843C2×C3D4×#6711yescharacteristic
844C2×C3D4×#6711yescharacteristic
845C2×C3#582211yescharacteristic
846C2×C3#582211yescharacteristic
847C2×C3#583611yescharacteristic
848C2×C3#583711yescharacteristic
849D3—42no—
850D3—42no—
851D3—81no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—62no—
859C22—62no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—244no—
868C22C22×#62511yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—121no—
877C4—121no—
878C4D32×D411yescharacteristic
879C4#6431311yescharacteristic
880C3—21no—
881C3#8350311yescharacteristic, complemented
882C3#8352211yescharacteristic, complemented
883C2—41no—
884C2—41no—
885C2—122no—
886C2—122no—
887C2—241no—
888C2#1059478611yescharacteristic
889C2D4×#62511yescharacteristic
890C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5551C2semidirect
2. C3×#5550C2semidirect
3. C2×#63823C2semidirect
4. C2×#63822C2semidirect
5. #10592710C2semidirect
6. #10591189C2semidirect
7. #10591179C2semidirect
8. #10591170C2semidirect
9. #10591170C2semidirect
10. #10591169C2semidirect
11. #10591161C2semidirect
12. #10590376C2semidirect
13. #10590363C2semidirect
14. #10590348C2semidirect
15. #10590344C2semidirect
20. C2×C3×#235C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
30. C3×#924C22semidirect
39. C3×C4×D12C22semidirect
40. C3×#869C22semidirect
41. C2×#3718C22semidirect
42. C2×#3718C22semidirect
47. C2×#3715C22semidirect
53. #63657C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. #63630C22semidirect
56. #63574C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. #63565C22semidirect
62. #63562C22semidirect
69. #5551D3semidirect
70. #5550D3semidirect
155. #3713D4semidirect
163. C2×#235C2×D3semidirect
211. #924C2×D3semidirect
226. C4×D12C2×D3semidirect
227. #869C2×D3semidirect
781. C32#3267semidirect
881. C3#83503semidirect
882. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C3×#55512
C3×#55502
C2×#638232
C2×#638222
#105927102
#105911892
#105911792
#105911702
#105911692
#105911612
#105903762
#105903632
#105903482
#105903442
#835223
#835033