Finite Group Databasebeta

← #11884347

Subgroups — #11884347

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
1C2×#63809C211yesmaximal, characteristic, complemented
2C2×#63798C211yesmaximal, characteristic, complemented
3#10594005C211yesmaximal, characteristic, complemented
4#10593896C211yesmaximal, characteristic, complemented
5#10592535C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4841C211yesmaximal, characteristic, complemented
8#10590963C211yesmaximal, characteristic, complemented
9#10590961C211yesmaximal, characteristic, complemented
10#10590961C211yesmaximal, characteristic, complemented
11#10590943C211yesmaximal, characteristic, complemented
12#10590856C211yesmaximal, characteristic, complemented
13#10590841C211yesmaximal, characteristic, complemented
14#10590376C211yesmaximal, characteristic, complemented
15#10590344C211yesmaximal, characteristic, complemented
16#80567—31nomaximal
17#80445—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×#3743C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#875C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic, complemented
32C3×#869C2211yescharacteristic, complemented
33#63923—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916C2211yescharacteristic
36#63909—21no—
37#63906—21no—
38#63891—21no—
39#63890—21no—
40#63890—21no—
41D3×C4⋊Dic3—21no—
42#63871C2211yescharacteristic
43#63871C2211yescharacteristic
44#63871C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50#63809—24no—
51#63798—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63647C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60#63574C2211yescharacteristic, complemented
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic, complemented
63C2×#916—31no—
64C2×#916—31no—
65C2×#914—31no—
66C2×#911—31no—
67#5726—31no—
68#5676—31no—
69#5555—31no—
70#5554—31no—
71C3×#463—31no—
72C3×#461—31no—
73#5173—31no—
74#5173—31no—
75#5169—31no—
76#5158—31no—
77#5086—31no—
78#5060—31no—
79#5014—31no—
80#5014—31no—
81#4844D311yescharacteristic, complemented
82#4841D311yescharacteristic, complemented
83#4836—31no—
84#4836—31no—
85#4836—61no—
86#4816—31no—
87#4816—31no—
88#4810—31no—
89#4808—31no—
90#4808—31no—
91#4807—31no—
92#4778—31no—
93#4776—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116#3796—22no—
117#3796—22no—
118#3796—22no—
119#3796—41no—
120#3796—41no—
121#3796—41no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124C32×C42C2311yescharacteristic
125#3752D411yescharacteristic
126#3752D411yescharacteristic
127C4⋊(C3⋊Dic3)D411yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3743—22no—
131C8×C3⋊D3—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×D24—22no—
141C3×#204—22no—
142C3×#204—22no—
143C3×#204—22no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151#3718—22no—
152#3718—41no—
153#3715—22no—
154#3715—41no—
155#3713D414yescomplemented
156#3267—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#237—31no—
161C2×#237—31no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×C4⋊Q8—31no—
170C3×#124—31no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173#946—31no—
174#946—31no—
175#946—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#215—31no—
181C2×#215—31no—
182#938—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#213—31no—
186C2×#213—31no—
187#930—61no—
188#930—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×C4⋊Dic3—61no—
191#916—64no—
192#916—64no—
193#914—64no—
194#911—64no—
195C2×D24C2×D311yescharacteristic
196C2×#204C2×D311yescharacteristic
197C2×#204C2×D311yescharacteristic
198C2×#204C2×D311yescharacteristic, complemented
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—61no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204C2×D3×C8—61no—
205#897—31no—
206#897—31no—
207#897—31no—
208#895—31no—
209#895—61no—
210#894—61no—
211#894—61no—
212D3×C4⋊C4—61no—
213#886—61no—
214#886—61no—
215#886—61no—
216#884—61no—
217#883—61no—
218#882—61no—
219#882—61no—
220D3×C22⋊C4—61no—
221#875C2×D311yescharacteristic
222C4×D12—31no—
223C4×D12—31no—
224C4×D12—61no—
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic, complemented
227#869C2×D311yescharacteristic, complemented
228C3×C4⋊C8—21no—
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×#103—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#102—31no—
235#832—31no—
236#832—31no—
237#821C2×D311yescharacteristic
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243(C2×D3)⋊C8—61no—
244#816C2×D311yescharacteristic, complemented
245#816C2×D311yescharacteristic, complemented
246#816C2×D311yescharacteristic, complemented
247#809—31no—
248#809—31no—
249#808—31no—
250#808—31no—
251#803—31no—
252#803—31no—
253#803—61no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—41no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12C2×D412yes—
282C3×D12C2×D412yes—
283C3×C4×D3—42no—
284C3×C4×D3—81no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#626—42no—
294#626—81no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C32×C8—21no—
301C3⋊(C3⋊C8)—21no—
302C3⋊(C3⋊C8)C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—31no—
311#461—31no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337#239—62no—
338#239—62no—
339#239—62no—
340#239—121no—
341#239—121no—
342#239—121no—
343#237—62no—
344#237—62no—
345#237—62no—
346#237—121no—
347#237—121no—
348#237—121no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—121no—
352D3×D4—121no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×Dic6C22×D311yescharacteristic
375C2×Dic6C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×SD16—62no—
379C3×SD16—62no—
380C3×D8—62no—
381C2×C3×C8—21no—
382C2×C3×C8—21no—
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—21no—
396C3×C42C22×D311yescharacteristic
397C3×C42C22×D311yescharacteristic
398#217—61no—
399#216—62no—
400#216—62no—
401#216—121no—
402#216—121no—
403#215—62no—
404#215—121no—
405#214—62no—
406#214—121no—
407#213—34no—
408#213—34no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426C4⋊Dic3—21no—
427C4⋊Dic3—21no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—61no—
445D24—22no—
446#204—22no—
447#204—22no—
448#204—22no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—62no—
451ΓL(1,𝔽25)—122no—
452D3×C8—62no—
453D3×C8—62no—
454D3×C8—122no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
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—
471D32—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—91no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—31no—
501#124—31no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8D3211yescharacteristic, complemented
519#103—31no—
520#103—31no—
521#103—31no—
522#102—31no—
523#102—91no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—31no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—241no—
545C22×D3—241no—
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—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—122no—
567C2×C3×C4—241no—
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574#67—122no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—122no—
579#67—241no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—122no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—21no—
598D12—121no—
599D12—121no—
600D12—122no—
601D12—122no—
602D12—122no—
603D12—122no—
604D12—241no—
605D12D3×D412yes—
606D12D3×D412yes—
607C4×D3—42no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—61no—
611C4×D3—61no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—81no—
617C4×D3—121no—
618C4×D3—121no—
619C4×D3—121no—
620C4×D3—121no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630C3×C8—21no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—41no—
635C3×C8—41no—
636C3⋊C8—32no—
637C3⋊C8—32no—
638C3⋊C8—62no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—41no—
646C3⋊D3—41no—
647C3×D3—42no—
648C3×D3—42no—
649C3×D3—81no—
650C24—181no—
651#41—182no—
652#41—182no—
653#41—182no—
654#41—361no—
655#41—361no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—91no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—182no—
670C2×D4—361no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—182no—
679Q16—361no—
680SD16—62no—
681SD16—62no—
682SD16—62no—
683SD16—182no—
684SD16—361no—
685D8—62no—
686D8—94no—
687M16—182no—
688C2×C8—91no—
689C2×C8—91no—
690C2×C8—182no—
691C2×C8C2×D3211yescharacteristic
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—91no—
706C22⋊C4—91no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42C2×D3211yescharacteristic
712C22×C3—21no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C2×D3×D411yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—62no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—244no—
752C2×D3—244no—
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—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4C2×D3×D411yescharacteristic
767C3×C4C2×D3×D411yescharacteristic
768C3×C4#100911yescharacteristic
769C3×C4#100911yescharacteristic
770Dic3—41no—
771Dic3—41no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—121no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—61no—
783C23—61no—
784C23—61no—
785C23—91no—
786C23—91no—
787C23—362no—
788C23—362no—
789C23—721no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—32no—
797D4—32no—
798D4—61no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—361no—
803D4—362no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—721no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—122no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—241no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4#380211yescharacteristic
825C2×C4#380211yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C8—21no—
828C8—21no—
829C8—92no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—122no—
835C2×C3—122no—
836C2×C3—241no—
837C2×C3#560911yescharacteristic
838C2×C3#560911yescharacteristic
839C2×C3#576211yescharacteristic
840C2×C3#577011yescharacteristic
841C2×C3#577311yescharacteristic
842C2×C3#577711yescharacteristic
843D3—42no—
844D3—42no—
845D3—81no—
846D3—122no—
847D3—121no—
848D3—121no—
849D3—121no—
850D3—121no—
851D3—241no—
852C22—62no—
853C22—62no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—724no—
868C22C2×#380211yescharacteristic
869C4—21no—
870C4—21no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—181no—
878C4D32×D411yescharacteristic
879C4#6432011yescharacteristic
880C3—21no—
881C3#8044511yescharacteristic, complemented
882C3#8056711yescharacteristic, complemented
883C2—122no—
884C2—122no—
885C2—241no—
886C2—361no—
887C2—361no—
888C2#1059461811yescharacteristic
889C2#1059468611yescharacteristic
890C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63809C2semidirect
2. C2×#63798C2semidirect
3. #10594005C2semidirect
4. #10593896C2semidirect
5. #10592535C2semidirect
6. C3×#4844C2semidirect
7. C3×#4841C2semidirect
8. #10590963C2semidirect
9. #10590961C2semidirect
10. #10590961C2semidirect
11. #10590943C2semidirect
12. #10590856C2semidirect
13. #10590841C2semidirect
14. #10590376C2semidirect
15. #10590344C2semidirect
21. C2×#3796C22semidirect
23. C2×C8×C3⋊D3C22semidirect
28. C2×C3×#204C22semidirect
31. C3×C4×D12C22semidirect
32. C3×#869C22semidirect
44. #63871C22semidirect
45. C2×#3718C22semidirect
46. C2×#3718C22semidirect
52. C32×C4⋊C8C22semidirect
54. #63647C22semidirect
55. #63630C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. C3×#816C22semidirect
60. #63574C22semidirect
62. #63562C22semidirect
81. #4844D3semidirect
82. #4841D3semidirect
155. #3713D4semidirect
198. C2×#204C2×D3semidirect
226. C4×D12C2×D3semidirect
227. #869C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
244. #816C2×D3semidirect
245. #816C2×D3semidirect
246. #816C2×D3semidirect
518. C4⋊C8D32semidirect
781. C32#3267semidirect
881. C3#80445semidirect
882. C3#80567semidirect

Maximal subgroups

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

subgroupindex
C2×#638092
C2×#637982
#105940052
#105938962
#105925352
C3×#48442
C3×#48412
#105909632
#105909612
#105909432
#105908562
#105908412
#105903762
#105903442
#805673
#804453