Finite Group Databasebeta

← #11884423

Subgroups — #11884423

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592710C211yesmaximal, characteristic, complemented
6#10591180C211yesmaximal, characteristic, complemented
7#10591170C211yesmaximal, characteristic, complemented
8#10591166C211yesmaximal, characteristic, complemented
9#10591161C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591160C211yesmaximal, characteristic, complemented
12#10590358C211yesmaximal, characteristic, complemented
13#10590354C211yesmaximal, characteristic, complemented
14#10590347C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83577—31nomaximal
17#83507—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×#940—21no—
26C3×#937—21no—
27C3×#930C2211yescharacteristic
28C3×#930C2211yescharacteristic
29C3×#930C2211yescharacteristic, complemented
30C3×#924C2211yescharacteristic
31C3×#894—21no—
32C3×#893—21no—
33C3×#884—21no—
34C3×#884—21no—
35C3×#884—21no—
36C3×D3×C22⋊C4—21no—
37C3×#875C2211yescharacteristic
38C3×#874C2211yescharacteristic, complemented
39C3×C4×D12C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3715C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46#63823—24no—
47#63822—24no—
48C2×#3713C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3713C2211yescharacteristic
52#63657C2211yescharacteristic
53#63657C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#550—31no—
64C3×#546—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#949—31no—
68C2×#932—31no—
69#5553D311yescharacteristic, complemented
70#5550D311yescharacteristic, complemented
71#5239—31no—
72#5238—31no—
73#5238—31no—
74#5217—31no—
75#5074—31no—
76#5072—31no—
77#5058—31no—
78#5054—31no—
79#5049—31no—
80#5047—31no—
81#5042—31no—
82#5038—31no—
83#5038—31no—
84#5037—31no—
85#5037—31no—
86#5036—31no—
87#5028—31no—
88#5026—31no—
89#5018—31no—
90#5015—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—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×#235—22no—
105C3×#235—22no—
106C3×#235—22no—
107C3×#235—41no—
108C3×#235—41no—
109C3×#235—41no—
110C2×C3×D12—22no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C32×C4⋊C4D411yescharacteristic
126C32×C22⋊C4D411yescharacteristic
127C32×C22⋊C4D411yescharacteristic
128C32×C42C2311yescharacteristic
129#3748—22no—
130C2×C3⋊(C3⋊C8)—22no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#217—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×C4×Dic3—21no—
147#3718—22no—
148#3715—22no—
149#3715—22no—
150#3715—41no—
151#3715D414yescomplemented
152#3713—22no—
153#3713—22no—
154#3713—22no—
155#3713—41no—
156#3268—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×#127—31no—
166C3×#127—61no—
167C3×#124—31no—
168C3×#123—61no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171C3×#121—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#121—61no—
175C3×#121—61no—
176C3×#120—61no—
177C3×C4×Q8—31no—
178C3×C4×D4—21no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181C3×C4×D4C2×D311yescharacteristic
182C3×C4×D4C2×D311yescharacteristic
183C2×C3×C22⋊C4—61no—
184#950—64no—
185#950—64no—
186#949—64no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193#940—21no—
194#937—21no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199#932—64no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208#930C2×D311yescharacteristic
209#930C2×D311yescharacteristic
210#930C2×D311yescharacteristic, complemented
211#924C2×D311yescharacteristic
212C2×#208—31no—
213C2×#208—31no—
214C2×#208—61no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—61no—
218#894—21no—
219#893—21no—
220#884—21no—
221#884—21no—
222#884—21no—
223D3×C22⋊C4—21no—
224#875C2×D311yescharacteristic
225#874C2×D311yescharacteristic, complemented
226C4×D12C2×D311yescharacteristic
227C4×Dic6C2×D311yescharacteristic, complemented
228#835—31no—
229#835—31no—
230#832—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#809—31no—
243#809—31no—
244#809—31no—
245#809—31no—
246#807—31no—
247#807—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—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C32×D4—41no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—81no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12—42no—
292C3×D12—81no—
293C3×D12C2×D412yes—
294C3×C4×D3—42no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×C4×D3—81no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300C3×Dic6—21no—
301C3×Dic6C2×D412yes—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3⋊(C3⋊C8)—21no—
305C3⋊(C3⋊C8)C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—31no—
309#546—31no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—31no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—121no—
347C2×C3×D4#6711yescharacteristic
348C2×C3×D4#6711yescharacteristic
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365#235—22no—
366#235—22no—
367#235—22no—
368#235—41no—
369#235—41no—
370#235—41no—
371C2×D12—22no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12—21no—
375C2×D12—41no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×Dic6C22×D311yescharacteristic
385C2×Dic6C22×D311yescharacteristic
386C3×C4⋊C4—21no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4#6711yescharacteristic
392C3×C4⋊C4#6711yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4#6711yescharacteristic
403C3×C22⋊C4#6711yescharacteristic
404C3×C22⋊C4#6711yescharacteristic
405C3×C22⋊C4#6711yescharacteristic
406C3×C42—21no—
407C3×C42—61no—
408C3×C42C22×D311yescharacteristic
409C3×C42C22×D311yescharacteristic
410#217—21no—
411#216—62no—
412#216—62no—
413#215—34no—
414#215—62no—
415#215—62no—
416#215—121no—
417#214—34no—
418#214—62no—
419#214—62no—
420#214—121no—
421#213—62no—
422#213—62no—
423#213—62no—
424#213—62no—
425#213—62no—
426#213—62no—
427#213—121no—
428#213—121no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435C4⋊Dic3C22×D311yescharacteristic
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
439C4×Dic3—21no—
440#208—62no—
441#208—62no—
442#208—122no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
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⋊C8—61no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8—62no—
457C2×C3⋊C8—122no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32C22×D411yescharacteristic
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—84no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3×Dic3—22no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—31no—
491C22×D4—31no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—91no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—91no—
505#127—31no—
506#127—61no—
507#124—31no—
508#123—61no—
509C22⋊Q8—31no—
510#121—31no—
511#121—31no—
512#121—31no—
513#121—61no—
514#121—61no—
515#121—61no—
516#120—61no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—61no—
520C4×D4D3211yescharacteristic
521C2×C22⋊C4—61no—
522#107—91no—
523C4⋊C8—91no—
524#103—91no—
525#103—91no—
526#102—91no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—241no—
542C23×C3C2×#6711yescharacteristic
543C23×C3C2×#6711yescharacteristic
544C23×C3C2×#6711yescharacteristic
545C23×C3C2×#6711yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—81no—
553C3×Q8—32no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—32no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—42no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—241no—
574C3×D4—241no—
575C3×D4—241no—
576C3×D4—241no—
577C2×C3×C4—21no—
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—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—122no—
599C2×C3×C4—122no—
600C2×C3×C4—122no—
601C2×C3×C4—241no—
602C2×C3×C4C2×#6711yescharacteristic
603C2×C3×C4C2×#6711yescharacteristic
604C2×C3×C4C2×#6711yescharacteristic
605C2×C3×C4C2×#6711yescharacteristic
606C2×C3×C4C2×#6711yescharacteristic
607C2×C3×C4C2×#6711yescharacteristic
608C2×C3×C4C2×#6711yescharacteristic
609C2×C3×C4C2×#6711yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612#67—42no—
613#67—42no—
614#67—42no—
615#67—81no—
616#67—81no—
617#67—81no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12—42no—
630D12—42no—
631D12—81no—
632D12D3×D412yes—
633C4×D3—42no—
634C4×D3—42no—
635C4×D3—42no—
636C4×D3—81no—
637Dic6—21no—
638Dic6—21no—
639Dic6—21no—
640Dic6D3×D412yes—
641C3⋊C8—32no—
642C3⋊C8—32no—
643C3⋊C8—62no—
644C3⋊C8—61no—
645C3⋊C8—61no—
646C3⋊C8—61no—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—61no—
650C3⋊C8—121no—
651C3⋊C8—121no—
652C3⋊C8—121no—
653C2×C32—41no—
654C2×C32—41no—
655C2×C32D4211yescharacteristic
656C2×C32#57511yescharacteristic
657C2×C32#57611yescharacteristic
658C3×D3—42no—
659C3×D3—81no—
660C3×D3—81no—
661C3×D3—81no—
662C24—61no—
663#41—62no—
664#41—62no—
665#41—62no—
666#41—121no—
667#41—121no—
668#41—121no—
669C2×Q8—31no—
670C2×Q8—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—62no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—121no—
686C2×D4#62511yescharacteristic
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693Q16—182no—
694SD16—94no—
695SD16—182no—
696SD16—182no—
697SD16—361no—
698D8—182no—
699D8—182no—
700D8—182no—
701D8—361no—
702M16—182no—
703C2×C8—91no—
704C2×C8—91no—
705C2×C8—91no—
706C2×C8—91no—
707C2×C8—182no—
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—61no—
711C4⋊C4—61no—
712C4⋊C4#62511yescharacteristic
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4#62511yescharacteristic
721C22⋊C4#62511yescharacteristic
722C42—61no—
723C42C2×D3211yescharacteristic
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—62no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—244no—
756C22×C3C22×#6711yescharacteristic
757C22×C3C22×#6711yescharacteristic
758C2×D3—22no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—62no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100411yescharacteristic
792C3×C4#100411yescharacteristic
793Dic3—22no—
794Dic3—41no—
795Dic3—41no—
796Dic3—41no—
797C32#326811yescharacteristic, complemented, Sylow
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—122no—
803C23—122no—
804C23—241no—
805C23C2×#62511yescharacteristic
806C23C2×#62511yescharacteristic
807Q8—32no—
808Q8—61no—
809Q8—61no—
810Q8—61no—
811D4—32no—
812D4—41no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—122no—
821D4—122no—
822D4—122no—
823D4—122no—
824D4—122no—
825D4—241no—
826D4—241no—
827D4—241no—
828D4—241no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—122no—
840C2×C4—241no—
841C2×C4C2×#62511yescharacteristic
842C2×C4C2×#62511yescharacteristic
843C2×C4C2×#62511yescharacteristic
844C2×C4C2×#62511yescharacteristic
845C2×C4C22×D3211yescharacteristic
846C8—92no—
847C8—181no—
848C8—181no—
849C8—181no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—42no—
854C2×C3—41no—
855C2×C3—41no—
856C2×C3—41no—
857C2×C3—41no—
858C2×C3—81no—
859C2×C3—122no—
860C2×C3—241no—
861C2×C3—241no—
862C2×C3—241no—
863C2×C3D4×#6711yescharacteristic
864C2×C3D4×#6711yescharacteristic
865C2×C3#582211yescharacteristic
866C2×C3#582211yescharacteristic
867C2×C3#583511yescharacteristic
868C2×C3#583511yescharacteristic
869D3—42no—
870D3—81no—
871D3—81no—
872D3—81no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—62no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—244no—
892C22C22×#62511yescharacteristic
893C4—21no—
894C4—21no—
895C4—21no—
896C4—21no—
897C4—62no—
898C4—121no—
899C4—121no—
900C4—121no—
901C4D32×D411yescharacteristic
902C4#6431311yescharacteristic
903C3—21no—
904C3#8350711yescharacteristic, complemented
905C3#8357711yescharacteristic, complemented
906C2—41no—
907C2—41no—
908C2—122no—
909C2—241no—
910C2—241no—
911C2—241no—
912C2#1059478611yescharacteristic
913C2D4×#62511yescharacteristic
914C2#1059544411yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3268
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×#5553C2semidirect
2. C3×#5550C2semidirect
3. C2×#63823C2semidirect
4. C2×#63822C2semidirect
5. #10592710C2semidirect
6. #10591180C2semidirect
7. #10591170C2semidirect
8. #10591166C2semidirect
9. #10591161C2semidirect
10. #10591161C2semidirect
11. #10591160C2semidirect
12. #10590358C2semidirect
13. #10590354C2semidirect
14. #10590347C2semidirect
15. #10590267C2semidirect
20. C2×C3×#235C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
29. C3×#930C22semidirect
38. C3×#874C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3718C22semidirect
44. C2×#3715C22semidirect
45. C2×#3715C22semidirect
53. #63657C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. #63630C22semidirect
56. #63576C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
69. #5553D3semidirect
70. #5550D3semidirect
151. #3715D4semidirect
163. C2×#235C2×D3semidirect
210. #930C2×D3semidirect
225. #874C2×D3semidirect
227. C4×Dic6C2×D3semidirect
797. C32#3268semidirect
904. C3#83507semidirect
905. C3#83577semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
C3×#55502
C2×#638232
C2×#638222
#105927102
#105911802
#105911702
#105911662
#105911612
#105911602
#105903582
#105903542
#105903472
#105902672
#835773
#835073