Finite Group Databasebeta

← #11884265

Subgroups — #11884265

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
1#10595070C211yesmaximal, characteristic, complemented
2#10594890C211yesmaximal, characteristic, complemented
3C2×#63822C211yesmaximal, characteristic, complemented
4C2×#63798C211yesmaximal, characteristic, complemented
5#10592429C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4733C211yesmaximal, characteristic, complemented
8#10591179C211yesmaximal, characteristic, complemented
9#10590965C211yesmaximal, characteristic, complemented
10#10590943C211yesmaximal, characteristic, complemented
11#10590870C211yesmaximal, characteristic, complemented
12#10590856C211yesmaximal, characteristic, complemented
13#10590751C211yesmaximal, characteristic, complemented
14#10590748C211yesmaximal, characteristic, complemented
15#10590741C211yesmaximal, characteristic, complemented
16#80264—31nomaximal
17#80122—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C4×#638C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C2×#3743C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×#924C2211yescharacteristic, complemented
27C2×C3×Dic12C2211yescharacteristic, complemented
28C2×C3×D24C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31#63983—21no—
32#63971—21no—
33#63970—21no—
34#63969—21no—
35D3×(C2×D3)⋊C4—21no—
36#63905—21no—
37#63898C2211yescharacteristic
38#63898C2211yescharacteristic, complemented
39D3×Dic3⋊C4—21no—
40#63873C2211yescharacteristic, complemented
41#63871C2211yescharacteristic
42#63871C2211yescharacteristic
43#63863C2211yescharacteristic
44#63850—21no—
45C2×#3718C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49#63822—24no—
50C2×#3713C2211yescharacteristic
51#63798—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63642C2211yescharacteristic, complemented
55#63641C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60#63574C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63#5829—31no—
64#5824—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#914—31no—
68C2×#911—31no—
69#5631—31no—
70#5612—31no—
71C3×#452—31no—
72C3×#449—31no—
73#5190—31no—
74#5187—31no—
75#5169—31no—
76#5167—31no—
77#5162—31no—
78#5153—31no—
79#5048—31no—
80#5041—31no—
81#4819—31no—
82#4818—31no—
83#4816—31no—
84#4816—31no—
85#4785—31no—
86#4785—31no—
87#4783—31no—
88#4776—31no—
89#4734D311yescharacteristic, complemented
90#4733D311yescharacteristic, complemented
91#4730—31no—
92#4730—31no—
93#4730—61no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638D411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#235—22no—
102C3×#235—22no—
103C3×#235—41no—
104C3×#235—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3802—22no—
119#3802—41no—
120#3796—22no—
121#3796—41no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124#3757D411yescharacteristic
125#3752D411yescharacteristic
126#3750D411yescharacteristic
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3743—22no—
132C3×#217—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic12—41no—
138C3×D24—22no—
139C3×#204—22no—
140C3×#204—41no—
141#3724—21no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3718—22no—
152#3715—22no—
153#3715—22no—
154#3715—22no—
155#3713D414yescomplemented
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×#235C2×D311yescharacteristic
164C2×#235C2×D311yescharacteristic, complemented
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171#950—64no—
172#950—64no—
173#947—31no—
174#946—31no—
175#946—31no—
176#944—31no—
177#944—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183#939—61no—
184#939—61no—
185#938—61no—
186#937—61no—
187#937—61no—
188#936—31no—
189#935—61no—
190D4×Dic3—31no—
191D4×Dic3—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#213—31no—
196C2×#213—31no—
197#930C2×D311yescharacteristic
198#929—61no—
199#929—61no—
200C4×#67—31no—
201C4×#67—31no—
202C4×#67—61no—
203C2×(C2×D3)⋊C4—61no—
204#924C2×D311yescharacteristic, complemented
205C2×Dic3⋊C4—61no—
206C22×C3⋊C8—31no—
207C22×C3⋊C8—31no—
208C22×C3⋊C8—61no—
209#914—64no—
210#911—64no—
211C2×Dic12C2×D311yescharacteristic, complemented
212C2×D24C2×D311yescharacteristic
213C2×#204C2×D311yescharacteristic
214C2×#204C2×D311yescharacteristic
215C2×ΓL(1,𝔽25)—31no—
216C2×ΓL(1,𝔽25)—31no—
217C2×ΓL(1,𝔽25)—61no—
218#897—31no—
219#897—31no—
220#894—61no—
221#893—31no—
222#893—31no—
223D3×C4⋊C4—61no—
224#884—61no—
225#883—61no—
226#883—61no—
227D3×C22⋊C4—61no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8C2×D311yescharacteristic, complemented
234C3×C22⋊C8C2×D311yescharacteristic, complemented
235#835—31no—
236#832—31no—
237#821C2×D311yescharacteristic
238#821C2×D311yescharacteristic, complemented
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—61no—
242#816C2×D311yescharacteristic, complemented
243#816C2×D311yescharacteristic, complemented
244#815—31no—
245#815—31no—
246#815—61no—
247Dic3⋊C8—31no—
248Dic3⋊C8—31no—
249Dic3⋊C8—61no—
250#810—31no—
251#809—31no—
252#808—31no—
253#808—31no—
254C23×C32C2×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×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266#638—41no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—81no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12C2×D412yes—
285C3×D12C2×D412yes—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—42no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—81no—
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—91no—
311#461—91no—
312#452—31no—
313#452—91no—
314#450—91no—
315#449—31no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C22×C3×C4—21no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—31no—
342C2×#67—31no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350#239—62no—
351#239—121no—
352#237—62no—
353#237—121no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—121no—
357D3×D4—121no—
358#235—22no—
359#235—22no—
360#235—41no—
361#235—41no—
362C2×D12—61no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
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×Q16—121no—
378C3×SD16—62no—
379C3×SD16—121no—
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×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392#217—21no—
393#217—31no—
394#217—31no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#216—62no—
401#216—62no—
402#215—62no—
403#215—62no—
404#215—62no—
405#214—62no—
406#214—62no—
407#214—62no—
408#213—34no—
409#213—34no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
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—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3C22×D311yescharacteristic
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—21no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—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—
445C2×C3⋊C8—62no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8—122no—
448Dic12—41no—
449D24—22no—
450#204—22no—
451#204—41no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—122no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32C22×D411yescharacteristic
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×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—91no—
501#124—91no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—31no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—91no—
519#103—31no—
520#103—31no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8D3211yescharacteristic, complemented
527#97—91no—
528C23×C3—21no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3D3×D411yescharacteristic
533C23×C3D3×D411yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—31no—
538C22×D3—31no—
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—
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—41no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—122no—
575C2×C3×C4—122no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—42no—
581#67—42no—
582#67—81no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—121no—
587#67—121no—
588#67—122no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—31no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—122no—
604C2×Dic3—122no—
605C2×Dic3—241no—
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—122no—
611D12D3×D412yes—
612D12D3×D412yes—
613C4×D3—42no—
614C4×D3—42no—
615C4×D3—61no—
616C4×D3—61no—
617C4×D3—61no—
618C4×D3—61no—
619C4×D3—121no—
620C4×D3—121no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—241no—
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×C32—41no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—41no—
647C3×D3—42no—
648C3×D3—42no—
649C3×D3—81no—
650C24—181no—
651#41—62no—
652#41—62no—
653#41—121no—
654#41—121no—
655#41—182no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—182no—
670C2×D4—361no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4C2×D3211yescharacteristic
678Q16—121no—
679Q16—182no—
680SD16—62no—
681SD16—121no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
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—91no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—91no—
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—41no—
721C22×C3—41no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
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—41no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4C2×D3×D411yescharacteristic
764C3×C4C2×D3×D411yescharacteristic
765C3×C4#100411yescharacteristic
766C3×C4#100411yescharacteristic
767Dic3—41no—
768Dic3—41no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—121no—
779Dic3—121no—
780Dic3—121no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—61no—
783C23—61no—
784C23—61no—
785C23—91no—
786C23—362no—
787C23—362no—
788C23—721no—
789C23#380211yescharacteristic
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—122no—
803D4—122no—
804D4—241no—
805D4—362no—
806D4—361no—
807D4—362no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—91no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—721no—
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—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—122no—
838C2×C3—122no—
839C2×C3—241no—
840C2×C3#559011yescharacteristic
841C2×C3#559011yescharacteristic
842C2×C3#576811yescharacteristic
843C2×C3#576811yescharacteristic
844C2×C3#577511yescharacteristic
845C2×C3#577811yescharacteristic
846D3—42no—
847D3—42no—
848D3—81no—
849D3—121no—
850D3—121no—
851D3—241no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—62no—
856C22—62no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—724no—
868C22C2×#380211yescharacteristic
869C4—21no—
870C4—121no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—181no—
877C4—181no—
878C4D32×D411yescharacteristic
879C4#6431311yescharacteristic
880C3—21no—
881C3#8012211yescharacteristic, complemented
882C3#8026411yescharacteristic, complemented
883C2—41no—
884C2—122no—
885C2—122no—
886C2—241no—
887C2—361no—
888C2#1059427111yescharacteristic
889C2#1059468511yescharacteristic
890C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595070C2semidirect
2. #10594890C2semidirect
3. C2×#63822C2semidirect
4. C2×#63798C2semidirect
5. #10592429C2semidirect
6. C3×#4734C2semidirect
7. C3×#4733C2semidirect
8. #10591179C2semidirect
9. #10590965C2semidirect
10. #10590943C2semidirect
11. #10590870C2semidirect
12. #10590856C2semidirect
13. #10590751C2semidirect
14. #10590748C2semidirect
15. #10590741C2semidirect
19. C2×C3×#235C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
26. C3×#924C22semidirect
27. C2×C3×Dic12C22semidirect
38. #63898C22semidirect
40. #63873C22semidirect
45. C2×#3718C22semidirect
48. C2×#3715C22semidirect
52. C32×C22⋊C8C22semidirect
54. #63642C22semidirect
55. #63641C22semidirect
57. C3×#821C22semidirect
58. C3×#816C22semidirect
59. C3×#816C22semidirect
60. #63574C22semidirect
61. #63565C22semidirect
89. #4734D3semidirect
90. #4733D3semidirect
155. #3713D4semidirect
164. C2×#235C2×D3semidirect
204. #924C2×D3semidirect
211. C2×Dic12C2×D3semidirect
233. C3×C22⋊C8C2×D3semidirect
234. C3×C22⋊C8C2×D3semidirect
238. #821C2×D3semidirect
242. #816C2×D3semidirect
243. #816C2×D3semidirect
526. C22⋊C8D32semidirect
781. C32#3267semidirect
881. C3#80122semidirect
882. C3#80264semidirect

Maximal subgroups

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

subgroupindex
#105950702
#105948902
C2×#638222
C2×#637982
#105924292
C3×#47342
C3×#47332
#105911792
#105909652
#105909432
#105908702
#105908562
#105907512
#105907482
#105907412
#802643
#801223