Finite Group Databasebeta

← #11884113

Subgroups — #11884113

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5550C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592710C211yesmaximal, characteristic, complemented
6#10591188C211yesmaximal, characteristic, complemented
7#10591185C211yesmaximal, characteristic, complemented
8#10591180C211yesmaximal, characteristic, complemented
9#10591171C211yesmaximal, characteristic, complemented
10#10591170C211yesmaximal, characteristic, complemented
11#10591169C211yesmaximal, characteristic, complemented
12#10590376C211yesmaximal, characteristic, complemented
13#10590363C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#83506—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C2×#3748C2211yescharacteristic, complemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#937—21no—
26C3×D4×Dic3—21no—
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C3×#894—21no—
32C3×#888—21no—
33C3×#884—21no—
34C3×D3×C22⋊C4—21no—
35C3×#878—21no—
36C3×#878—21no—
37C3×#875C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×#869C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3718C2211yescharacteristic, complemented
43C2×#3718C2211yescharacteristic, complemented
44#63827—24no—
45C2×#3715—24no—
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3715C2211yescharacteristic
52#63657C2211yescharacteristic
53#63657C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic
63C3×D4×Q8—31no—
64C3×#546—31no—
65C2×#951—31no—
66C2×#942—31no—
67C22×#215—31no—
68C22×#214—31no—
69#5550D311yescharacteristic
70D4×Dic6D311yescharacteristic, complemented
71#5239—31no—
72#5228—31no—
73#5227—31no—
74#5218—31no—
75#5086—31no—
76#5083—31no—
77#5060—31no—
78#5054—31no—
79#5051—31no—
80#5051—31no—
81#5050—31no—
82#5049—31no—
83#5047—31no—
84#5046—31no—
85#5042—31no—
86#5040—31no—
87#5028—31no—
88#5026—31no—
89#5019—31no—
90#5018—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—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×Dic6—22no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—21no—
114C2×C3×Dic6—21no—
115C2×C3×Dic6—41no—
116C2×C3×Dic6—41no—
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×C4⋊C4D411yescharacteristic
122C32×C22⋊C4D411yescharacteristic
123C32×C22⋊C4D411yescharacteristic
124C32×C42C2311yescharacteristic
125#3748—22no—
126C2×C3⋊(C3⋊C8)—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×C4×Dic3—21no—
147#3718—22no—
148#3718—22no—
149#3718—41no—
150#3715—22no—
151#3715—22no—
152#3715—22no—
153#3715—22no—
154#3715—41no—
155#3715D414yescomplemented
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C2×#235C2×D311yescharacteristic
162C22×D12C2×D311yescharacteristic
163C22×Dic6C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic, complemented
165C3×C4⋊Q8—31no—
166C3×C4⋊Q8—61no—
167C3×#124—31no—
168C3×#123—61no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8—61no—
174C3×#121—31no—
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#951—64no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191#942—64no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—31no—
197C2×#215—31no—
198C2×#215—64no—
199#937—21no—
200D4×Dic3—21no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—31no—
205C2×#214—31no—
206C2×#214—31no—
207C2×#214—64no—
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—
219#888—21no—
220#884—21no—
221D3×C22⋊C4—21no—
222#878—21no—
223#878—21no—
224#875C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic
226#869C2×D311yescharacteristic, complemented
227C4×Dic6C2×D311yescharacteristic, complemented
228#835—31no—
229#835—31no—
230#835—31no—
231#835—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#810—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—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C32×D4—22no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C3×#67—42no—
272C3×#67—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3—42no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—42no—
287C3×C4×D3—81no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—31no—
305#546—31no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8—61no—
328C2×C3×Q8—61no—
329C2×C3×Q8—121no—
330C2×C3×Q8—121no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—62no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—121no—
339C2×C3×D4#6711yescharacteristic
340C2×C3×D4#6711yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—21no—
352C2×#67—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355#235—22no—
356#235—41no—
357C2×D12—22no—
358C2×D12—21no—
359C2×D12—41no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×Dic6—22no—
365C2×Dic6—22no—
366C2×Dic6—21no—
367C2×Dic6—21no—
368C2×Dic6—41no—
369C2×Dic6—41no—
370C2×Dic6C22×D311yescharacteristic
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4#6711yescharacteristic
384C3×C4⋊C4#6711yescharacteristic
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4#6711yescharacteristic
395C3×C22⋊C4#6711yescharacteristic
396C3×C22⋊C4#6711yescharacteristic
397C3×C22⋊C4#6711yescharacteristic
398C3×C42—21no—
399C3×C42—61no—
400C3×C42C22×D311yescharacteristic
401C3×C42C22×D311yescharacteristic
402#217—21no—
403#217—21no—
404#217—21no—
405#216—62no—
406#216—62no—
407#216—62no—
408#216—62no—
409#216—121no—
410#216—121no—
411#215—34no—
412#215—62no—
413#215—62no—
414#215—62no—
415#215—62no—
416#215—121no—
417#214—34no—
418#214—62no—
419#214—62no—
420#214—62no—
421#214—62no—
422#214—121no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427C4⋊Dic3—21no—
428C4⋊Dic3—21no—
429C4⋊Dic3C22×D311yescharacteristic
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434Dic3⋊C4—21no—
435C4×Dic3—21no—
436#208—62no—
437#208—62no—
438#208—122no—
439C2×C3⋊C8—31no—
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—61no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—62no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8—122no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32#13712yescomplemented
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—22no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4—21no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—31no—
482C22×Q8—31no—
483C22×D4—31no—
484#137—184no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—91no—
497C4⋊Q8—31no—
498C4⋊Q8—61no—
499#124—31no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—31no—
504C22⋊Q8—61no—
505C22⋊Q8—61no—
506#121—31no—
507#121—61no—
508#120—61no—
509C4×Q8—31no—
510C4×D4—31no—
511C4×D4—61no—
512C4×D4D3211yescharacteristic
513C2×C22⋊C4—61no—
514#107—91no—
515C4⋊C8—91no—
516#103—91no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—91no—
521#102—91no—
522C22⋊C8—91no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—241no—
532C23×C3C2×#6711yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C23×C3C2×#6711yescharacteristic
535C23×C3C2×#6711yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—81no—
541C3×Q8—32no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×Q8—122no—
551C3×D4—22no—
552C3×D4—22no—
553C3×D4—32no—
554C3×D4—42no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—122no—
559C3×D4—122no—
560C3×D4—241no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
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—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—122no—
585C2×C3×C4—122no—
586C2×C3×C4—122no—
587C2×C3×C4—241no—
588C2×C3×C4C2×#6711yescharacteristic
589C2×C3×C4C2×#6711yescharacteristic
590C2×C3×C4C2×#6711yescharacteristic
591C2×C3×C4C2×#6711yescharacteristic
592C2×C3×C4C2×#6711yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C2×#6711yescharacteristic
595C2×C3×C4C2×#6711yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598#67—42no—
599#67—81no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—42no—
607C2×Dic3—42no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—42no—
612D12D3×D412yes—
613C4×D3—42no—
614C4×D3—81no—
615Dic6—21no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—42no—
623Dic6—42no—
624Dic6D3×D412yes—
625C3⋊C8—32no—
626C3⋊C8—32no—
627C3⋊C8—62no—
628C3⋊C8—61no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—61no—
634C3⋊C8—121no—
635C3⋊C8—121no—
636C3⋊C8—121no—
637C2×C32—22no—
638C2×C32—41no—
639C2×C32D4211yescharacteristic
640C2×C32C2×#13711yescharacteristic
641C2×C32#57711yescharacteristic
642C3×D3—42no—
643C3×D3—81no—
644C24—61no—
645#41—62no—
646#41—121no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—31no—
651C2×Q8—62no—
652C2×Q8—62no—
653C2×Q8—61no—
654C2×Q8—61no—
655C2×Q8—121no—
656C2×Q8—121no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—121no—
664C2×D4#62511yescharacteristic
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4C2×D3211yescharacteristic
670C22×C4C2×D3211yescharacteristic
671Q16—182no—
672Q16—182no—
673Q16—361no—
674SD16—94no—
675SD16—182no—
676SD16—182no—
677SD16—182no—
678SD16—182no—
679SD16—361no—
680M16—182no—
681C2×C8—91no—
682C2×C8—91no—
683C2×C8—91no—
684C2×C8—91no—
685C2×C8—182no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4#62511yescharacteristic
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4#62511yescharacteristic
703C22⋊C4#62511yescharacteristic
704C42—61no—
705C42C2×D3211yescharacteristic
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—22no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—62no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—244no—
730C22×C3#94212yescomplemented
731C22×C3#95112yescomplemented
732C22×C3C22×#6711yescharacteristic
733C22×C3C22×#6711yescharacteristic
734C2×D3—22no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—84no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—62no—
756C3×C4—121no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4#100411yescharacteristic
764C3×C4#100411yescharacteristic
765Dic3—22no—
766Dic3—41no—
767Dic3—41no—
768Dic3—41no—
769Dic3—41no—
770Dic3—41no—
771C32#326611yescharacteristic, complemented, Sylow
772C23—61no—
773C23—61no—
774C23—122no—
775C23—122no—
776C23—241no—
777C23C2×#62511yescharacteristic
778C23C2×#62511yescharacteristic
779Q8—32no—
780Q8—61no—
781Q8—61no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—61no—
787Q8—122no—
788Q8—122no—
789D4—22no—
790D4—32no—
791D4—61no—
792D4—61no—
793D4—61no—
794D4—122no—
795D4—122no—
796D4—241no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—122no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—241no—
811C2×C4C2×#62511yescharacteristic
812C2×C4C2×#62511yescharacteristic
813C2×C4C2×#62511yescharacteristic
814C2×C4C2×#62511yescharacteristic
815C2×C4C22×D3211yescharacteristic
816C8—92no—
817C8—181no—
818C8—181no—
819C8—181no—
820C2×C3—22no—
821C2×C3—22no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—42no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—81no—
829C2×C3—122no—
830C2×C3—241no—
831C2×C3D4×#6711yescharacteristic
832C2×C3D4×#6711yescharacteristic
833C2×C3C2×#94211yescharacteristic
834C2×C3C2×#95111yescharacteristic
835C2×C3#583611yescharacteristic
836C2×C3#583711yescharacteristic
837D3—42no—
838D3—81no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—62no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—244no—
851C22#6382712yescomplemented
852C22C22×#62511yescharacteristic
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—62no—
858C4—121no—
859C4—121no—
860C4—121no—
861C4—121no—
862C4—121no—
863C4D32×D411yescharacteristic
864C4#6431311yescharacteristic
865C3—21no—
866C3#8350611yescharacteristic, complemented
867C3#8355911yescharacteristic, complemented
868C2—22no—
869C2—41no—
870C2—122no—
871C2—241no—
872C2C2×#6382711yescharacteristic
873C2D4×#62511yescharacteristic
874C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5550C2
hypercenterC4×D4D32
hypocenterC32#3266
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
2. C3×D4×Dic6C2semidirect
3. C2×#63827C2semidirect
4. C22×#3715C2semidirect
5. #10592710C2semidirect
6. #10591188C2semidirect
7. #10591185C2semidirect
8. #10591180C2semidirect
9. #10591171C2semidirect
10. #10591170C2semidirect
11. #10591169C2semidirect
12. #10590376C2semidirect
13. #10590363C2semidirect
14. #10590358C2semidirect
15. #10590267C2semidirect
21. C22×C3×Dic6C22semidirect
23. C2×#3748C22semidirect
30. C3×#924C22semidirect
39. C3×#869C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3718C22semidirect
42. C2×#3718C22semidirect
43. C2×#3718C22semidirect
53. #63657C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. #63630C22semidirect
56. #63576C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
70. D4×Dic6D3semidirect
155. #3715D4semidirect
164. C22×Dic6C2×D3semidirect
211. #924C2×D3semidirect
226. #869C2×D3semidirect
227. C4×Dic6C2×D3semidirect
459. C22×C32#137semidirect
730. C22×C3#942semidirect
731. C22×C3#951semidirect
771. C32#3266semidirect
851. C22#63827semidirect
866. C3#83506semidirect
867. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C3×#55502
C3×D4×Dic62
C2×#638272
C22×#37152
#105927102
#105911882
#105911852
#105911802
#105911712
#105911702
#105911692
#105903762
#105903632
#105903582
#105902672
#835593
#835063