Finite Group Databasebeta

← #11884286

Subgroups — #11884286

Order 1152.

1060 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595357C211yesmaximal, characteristic, complemented
3#10595244C211yesmaximal, characteristic, complemented
4C2×#63933C211yesmaximal, characteristic, complemented
5#10592861C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7#10591634C211yesmaximal, characteristic, complemented
8#10591611C211yesmaximal, characteristic, complemented
9#10591597C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591436C211yesmaximal, characteristic, complemented
12#10590962C211yesmaximal, characteristic, complemented
13#10590849C211yesmaximal, characteristic, complemented
14#10590751C211yesmaximal, characteristic, complemented
15#10590724C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#80264—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic
23#64153C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63980—21no—
34#63976—21no—
35#63961—21no—
36C2×(C2×D3)⋊Dic3—21no—
37#63933—24no—
38#63908C2211yescharacteristic
39#63905—21no—
40C4×#625C2211yescharacteristic
41#63898C2211yescharacteristic, complemented
42#63885—21no—
43#63884—21no—
44D3×Dic3⋊C4—21no—
45#63863C2211yescharacteristic
46#63857C2211yescharacteristic
47#63856C2211yescharacteristic
48C2×#3719C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5829—31no—
65#5824—31no—
66C2×#950—31no—
67#5806—31no—
68C2×#914D311yescharacteristic, complemented
69C2×#912—31no—
70#5631—31no—
71C3×#452—31no—
72#5239—31no—
73#5218—31no—
74#5190—31no—
75#5187—31no—
76#5173D311yescharacteristic, complemented
77#5171—31no—
78#5167—31no—
79#5162—31no—
80#5162—31no—
81#5162—61no—
82#5158—31no—
83#5153—31no—
84#5152—31no—
85#5137—31no—
86#5127—31no—
87#5048—31no—
88#4819—31no—
89#4816—31no—
90#4785—31no—
91#4776—31no—
92#4734—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×#239—22no—
103C3×#239—41no—
104C3×#237—22no—
105C3×#237—41no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×#625D411yescharacteristic
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120#3795—22no—
121#3795—41no—
122C32×SD16—22no—
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125#3754—22no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128#3750—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#216—41no—
132C3×#215—22no—
133C3×#213D414yescomplemented
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×ΓL(1,𝔽25)—22no—
141#3724—21no—
142#3724D411yescharacteristic
143Dic3⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151(C2×D3)⋊Dic3D411yescharacteristic
152#3719—22no—
153#3716—41no—
154#3715—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C2×#239C2×D311yescharacteristic
161C2×#237—31no—
162C2×#237C2×D311yescharacteristic
163C2×D3×D4C2×D311yescharacteristic
164C2×#235—31no—
165C3×AGL(1,ℤ/8)—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—21no—
168C2×C3×SD16—31no—
169C2×C3×SD16C2×D311yescharacteristic
170C2×C3×SD16C2×D311yescharacteristic
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C2×C3×M16—31no—
174C3×C22⋊Q8—31no—
175#953—61no—
176C2×#217—61no—
177#950—64no—
178#947—31no—
179#946—31no—
180#946C2×D311yescharacteristic, complemented
181#944—31no—
182#944—31no—
183#944—61no—
184C2×#216—31no—
185C2×#216C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215C2×D311yescharacteristic
188#939—61no—
189#939—61no—
190#939—61no—
191#938—31no—
192#937—61no—
193#936—31no—
194#935—61no—
195#935—61no—
196D4×Dic3—31no—
197D4×Dic3—31no—
198D4×Dic3—31no—
199D4×Dic3—61no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—61no—
205C2×#213C2×D311yescharacteristic
206#930—31no—
207#929—61no—
208#929—61no—
209C4×#67—31no—
210C4×#67—31no—
211C2×(C2×D3)⋊C4—61no—
212#924—31no—
213#924—31no—
214C2×Dic3⋊C4—61no—
215C22×C3⋊C8—31no—
216#914—24no—
217#912—64no—
218C2×Dic12—31no—
219C2×D24C2×D311yescharacteristic
220C2×#204—31no—
221C2×ΓL(1,𝔽25)C2×D311yescharacteristic
222C2×D3×C8—31no—
223#897—31no—
224#894—61no—
225#893—31no—
226D3×C4⋊C4—61no—
227#884—61no—
228#883—61no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#832—31no—
236#832—31no—
237#832C2×D311yescharacteristic
238#830—31no—
239#821—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8C2×D311yescharacteristic, complemented
242#817—31no—
243#816—31no—
244#816—31no—
245#816—61no—
246#816C2×D311yescharacteristic, complemented
247#815—31no—
248#815—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—61no—
252#809—31no—
253#808—31no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—81no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—42no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#625—41no—
295#625—42no—
296#625—81no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—31no—
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—91no—
316#442—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—121no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—31no—
345C2×#67—31no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C22×Dic3—21no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—121no—
356#239—22no—
357#239—41no—
358#237—22no—
359#237—41no—
360#237—62no—
361#237—121no—
362D3×D4—22no—
363D3×D4—41no—
364#235—62no—
365#235—121no—
366C2×D12—21no—
367C2×D12C22×D311yescharacteristic
368C2×D12C22×D311yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3C22×D311yescharacteristic
373C2×C4×D3C22×D311yescharacteristic
374C2×Dic6—31no—
375C2×Dic6—31no—
376C2×Dic6—61no—
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—121no—
379C3×SD16—22no—
380C3×SD16—22no—
381C3×SD16—42no—
382C3×SD16—62no—
383C3×D8—34no—
384C3×D8—62no—
385C3×M16—62no—
386C2×C3×C8—21no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C22⋊C4—61no—
394#217—31no—
395#217—31no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—121no—
405#216—41no—
406#216—62no—
407#215—22no—
408#215—62no—
409#214—62no—
410#214—62no—
411#214—62no—
412#214—122no—
413#214—121no—
414#213#6714yescomplemented
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
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—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—121no—
440Dic3⋊C4—121no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—61no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450Dic12—62no—
451D24—22no—
452#204—121no—
453ΓL(1,𝔽25)—22no—
454D3×C8—62no—
455C22×C32—22no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
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—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—91no—
486C22×D4—31no—
487AGL(1,ℤ/8)—64no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16D3211yescharacteristic
496C2×D8—31no—
497C2×D8—31no—
498C2×M16—31no—
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—91no—
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—91no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—241no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—81no—
543C22×D3D3×D411yescharacteristic
544C22×D3D3×D411yescharacteristic
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—22no—
556C3×D4—32no—
557C3×D4—41no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—122no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4D3×D412yes—
565C3×D4C2×#6712yes—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—122no—
579C2×C3×C4—122no—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—42no—
583#67—42no—
584#67—121no—
585#67—121no—
586#67—122no—
587#67—122no—
588#67—241no—
589#67—241no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—42no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—122no—
606C2×Dic3—122no—
607C2×Dic3—241no—
608C2×Dic3—241no—
609C2×Dic3—242no—
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612D12—21no—
613D12—21no—
614D12—21no—
615D12—42no—
616D12C2×#6712yes—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—42no—
622C4×D3—122no—
623C4×D3—122no—
624Dic6—21no—
625Dic6—21no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—32no—
635C3×C8—41no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8C2×#6712yes—
642C2×C32—42no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—81no—
650C24—61no—
651#41—62no—
652#41—62no—
653#41—121no—
654#41—121no—
655#41—182no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—91no—
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—62no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—121no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4C2×D3211yescharacteristic
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—121no—
679Q16—182no—
680SD16—22no—
681SD16—62no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—34no—
686D8—62no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—182no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C22⋊C4—61no—
702C22⋊C4—91no—
703C22⋊C4—91no—
704C22⋊C4—181no—
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—22no—
714C22×C3—21no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—61no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—244no—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C2×D3×D411yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—22no—
743C2×D3—21no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—84no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—81no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4C2×D3×D411yescharacteristic
760C3×C4#100411yescharacteristic
761C3×C4#100411yescharacteristic
762C3×C4C22×#6711yescharacteristic
763Dic3—21no—
764Dic3—21no—
765Dic3—41no—
766Dic3—41no—
767Dic3—62no—
768Dic3—61no—
769Dic3—61no—
770Dic3—61no—
771Dic3—61no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—241no—
778Dic3—241no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—21no—
781C23—31no—
782C23—31no—
783C23—61no—
784C23—61no—
785C23—122no—
786C23—122no—
787C23—241no—
788Q8—21no—
789Q8—21no—
790Q8—61no—
791Q8—61no—
792Q8—181no—
793Q8—181no—
794D4—21no—
795D4—32no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—122no—
800D4—122no—
801D4—122no—
802D4—361no—
803D4—362no—
804D4—721no—
805D4D3×#6712yes—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—721no—
824C2×C4C22×D3211yescharacteristic
825C8—21no—
826C8—32no—
827C8—61no—
828C8—181no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—82no—
835C2×C3—121no—
836C2×C3—122no—
837C2×C3—121no—
838C2×C3—241no—
839C2×C3#559011yescharacteristic
840C2×C3#576811yescharacteristic
841C2×C3#577311yescharacteristic
842C2×C3#577511yescharacteristic
843C2×C3#577811yescharacteristic
844C2×C3D4×#6711yescharacteristic
845D3—41no—
846D3—41no—
847D3—42no—
848D3—81no—
849C22—22no—
850C22—41no—
851C22—41no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—244no—
865C22D32×D411yescharacteristic
866C4—41no—
867C4—61no—
868C4—61no—
869C4—121no—
870C4—121no—
871C4—181no—
872C4—181no—
873C4—361no—
874C4—361no—
875C4#6431311yescharacteristic
876C4C2×D3×#6711yescharacteristic
877C3—21no—
878C3#8026411yescharacteristic, complemented
879C3#8395411yescharacteristic, complemented
880C2—42no—
881C2—121no—
882C2—121no—
883C2—122no—
884C2—241no—
885C2#1059474511yescharacteristic
886C2#1059475411yescharacteristic
887C2#1059528711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. #10595357C2semidirect
3. #10595244C2semidirect
4. C2×#63933C2semidirect
5. #10592861C2semidirect
6. C3×#5173C2semidirect
7. #10591634C2semidirect
8. #10591611C2semidirect
9. #10591597C2semidirect
10. #10591459C2semidirect
11. #10591436C2semidirect
12. #10590962C2semidirect
13. #10590849C2semidirect
14. #10590751C2semidirect
15. #10590724C2semidirect
21. C2×#3795C22semidirect
23. #64153C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#216C22semidirect
41. #63898C22semidirect
48. C2×#3719C22semidirect
50. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63643C22semidirect
54. #63641C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#816C22semidirect
58. #63573C22semidirect
59. #63563C22semidirect
62. #63555C22semidirect
68. C2×#914D3semidirect
76. #5173D3semidirect
133. C3×#213D4semidirect
180. #946C2×D3semidirect
185. C2×#216C2×D3semidirect
241. (C2×D3)⋊C8C2×D3semidirect
246. #816C2×D3semidirect
414. #213#67semidirect
779. C32#3267semidirect
878. C3#80264semidirect
879. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105953572
#105952442
C2×#639332
#105928612
C3×#51732
#105916342
#105916112
#105915972
#105914592
#105914362
#105909622
#105908492
#105907512
#105907242
#839543
#802643