Finite Group Databasebeta

← #11884481

Subgroups — #11884481

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4#10594527C211yesmaximal, characteristic, complemented
5#10592497C211yesmaximal, characteristic, complemented
6C3×#4812C211yesmaximal, characteristic, complemented
7C3×#4810C211yesmaximal, characteristic, complemented
8#10591655C211yesmaximal, characteristic, complemented
9#10591621C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590749C211yesmaximal, characteristic, complemented
12#10590724C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590576C211yesmaximal, characteristic, complemented
15#10590461C211yesmaximal, characteristic, complemented
16#80836—31nomaximal
17#80128—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic
25#64096C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31C3×#895C2211yescharacteristic
32C3×#895C2211yescharacteristic, complemented
33#63947—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63914—21no—
37#63914C2211yescharacteristic, complemented
38#63909C2211yescharacteristic
39#63902—21no—
40C4×#625C2211yescharacteristic
41#63898C2211yescharacteristic
42#63886—21no—
43#63885—21no—
44#63885—21no—
45#63850—21no—
46C2×#3716C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63795—24no—
52C32×#103C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63#5829—31no—
64C2×#950—31no—
65C2×#916—31no—
66C2×#911—31no—
67C2×#908—31no—
68#5630—31no—
69#5599—31no—
70#5599—31no—
71C3×#468—31no—
72C3×#449—31no—
73#5176—31no—
74#5176—31no—
75#5173—31no—
76#5150—31no—
77#5127—31no—
78#5047—31no—
79#5038—31no—
80#5036—31no—
81#4889—31no—
82#4883—31no—
83#4812D311yescharacteristic, complemented
84#4810D311yescharacteristic, complemented
85#4798—31no—
86#4798—31no—
87#4798—61no—
88#4786—31no—
89#4781—31no—
90#4773—31no—
91#4757—31no—
92#4734—31no—
93#4730—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×#239—22no—
99C3×#239—41no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#625D411yescharacteristic
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3795—22no—
122#3795—22no—
123#3795—41no—
124#3795—41no—
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127#3756—22no—
128#3752—21no—
129#3752—21no—
130#3750—21no—
131C4×C3⋊Dic3—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3744—22no—
135C3×#215—22no—
136C3×#215—41no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D24—22no—
145C3×ΓL(1,𝔽25)—22no—
146#3724D411yescharacteristic
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151#3716D414yescomplemented
152#3714—22no—
153#3714—41no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239C2×D311yescharacteristic
159C2×#237—31no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C2×C3×M16—31no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171C3×#121—31no—
172#950—64no—
173#947—31no—
174#947—31no—
175#947—61no—
176#946C2×D311yescharacteristic
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—61no—
180C2×#215C2×D311yescharacteristic, complemented
181C2×#215C2×D311yescharacteristic, complemented
182#940—31no—
183#940—31no—
184#940—61no—
185#940—61no—
186#939—61no—
187#939—61no—
188#939—61no—
189#937—61no—
190D4×Dic3—31no—
191C2×#214—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196#930—31no—
197#929—61no—
198C4×#67—31no—
199C4×#67—31no—
200C2×(C2×D3)⋊C4—61no—
201C22×C3⋊C8—31no—
202#916—64no—
203#911—64no—
204#908—64no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24C2×D311yescharacteristic
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—61no—
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic
213C2×D3×C8—31no—
214#895—31no—
215#895—61no—
216#895C2×D311yescharacteristic
217#895C2×D311yescharacteristic, complemented
218#894—61no—
219#893—31no—
220#887—31no—
221#887—31no—
222#887—61no—
223#884—61no—
224#884—61no—
225#882—61no—
226#67⋊C4—61no—
227#67⋊C4—61no—
228D3×C22⋊C4—61no—
229C3×#107—31no—
230C3×#103—21no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#832—31no—
237#830—31no—
238#821C2×D311yescharacteristic, complemented
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8C2×D311yescharacteristic, complemented
241#816—31no—
242#815—31no—
243#815—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247#810—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#809C2×D311yescharacteristic
253#807C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273#634—21no—
274#634C2×D412yes—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×D12—81no—
285C3×D12—81no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292#626—42no—
293#626—81no—
294#625—41no—
295#625—42no—
296#625—42no—
297#625—42no—
298#625—81no—
299D3×Dic3—42no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—31no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—31no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C2×#67—31no—
338C2×#67—31no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352#239—22no—
353#239—41no—
354#237—62no—
355#237—62no—
356#237—121no—
357#237—121no—
358D3×D4—62no—
359D3×D4—121no—
360#235—62no—
361#235—62no—
362#235—121no—
363#235—121no—
364C2×D12—21no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—121no—
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C3×SD16—62no—
387C3×SD16—121no—
388C3×D8—62no—
389C3×M16—62no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C3×C4⋊C4—21no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403#217—31no—
404#217—31no—
405#217—61no—
406#216—62no—
407#216—62no—
408#216—122no—
409#215—22no—
410#215—41no—
411#214—34no—
412#213—62no—
413#213—62no—
414#213—62no—
415#213—121no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
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—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4—121no—
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—31no—
433Dic3⋊C4—31no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—121no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—61no—
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3—121no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449D24—22no—
450D24—62no—
451D24—121no—
452#204—34no—
453#204—62no—
454#204—62no—
455#204—122no—
456ΓL(1,𝔽25)—22no—
457D3×C8—62no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
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—
477D32—84no—
478C32×C4—41no—
479C32×C4—41no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—22no—
483C3⋊Dic3—21no—
484C3⋊Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—31no—
504C22×C8—91no—
505#127—91no—
506#127—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—31no—
510#121—31no—
511#121—31no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—91no—
524#103—91no—
525#103D3211yescharacteristic, complemented
526#102—31no—
527#102—31no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3D3×D411yescharacteristic
551C22×D3D3×D411yescharacteristic
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×D4—32no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—241no—
566C3×D4—241no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—122no—
585#67—121no—
586#67—121no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—241no—
594#67—241no—
595#67—241no—
596C2×Dic3—21no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—121no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3—241no—
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—81no—
622D12—81no—
623D12—121no—
624D12—121no—
625D12—122no—
626D12—241no—
627D12D3×D412yes—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—241no—
636Dic6—32no—
637Dic6—32no—
638Dic6—62no—
639Dic6—61no—
640Dic6—61no—
641Dic6—121no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—32no—
645C3×C8—41no—
646C3×C8—61no—
647C3⋊C8—21no—
648C3⋊C8—61no—
649C3⋊C8—61no—
650C3⋊C8—121no—
651C3⋊C8D3×D412yes—
652C2×C32D4211yescharacteristic
653C2×C32#57511yescharacteristic
654C2×C32#57611yescharacteristic
655C3⋊D3—81no—
656C3×D3—41no—
657C3×D3—42no—
658C3×D3—41no—
659C3×D3—81no—
660C3×D3—81no—
661C24—181no—
662#41—62no—
663#41—121no—
664#41—182no—
665#41—182no—
666#41—361no—
667#41—361no—
668C2×Q8—91no—
669C2×Q8C2×D3211yescharacteristic
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—91no—
677C2×D4—91no—
678C2×D4—181no—
679C2×D4—182no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—361no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—181no—
690C22×C4—181no—
691C22×C4—181no—
692Q16—182no—
693SD16—62no—
694SD16—94no—
695SD16—121no—
696SD16—182no—
697D8—62no—
698D8—182no—
699D8—182no—
700D8—361no—
701M16—62no—
702C2×C8—31no—
703C2×C8—31no—
704C2×C8—91no—
705C2×C8—182no—
706C2×C8C2×D3211yescharacteristic
707C4⋊C4—31no—
708C4⋊C4—61no—
709C4⋊C4—91no—
710C4⋊C4—181no—
711C4⋊C4C2×D3211yescharacteristic
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—91no—
716C22⋊C4—91no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—91no—
722C42—181no—
723C22×C3—21no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—62no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3C2×D3×D411yescharacteristic
740C22×C3C2×D3×D411yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—22no—
747C2×D3—21no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—241no—
763C2×D3—241no—
764C2×D3—241no—
765C2×D3—244no—
766C2×D3—244no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—81no—
776C3×C4—81no—
777C3×C4—121no—
778C3×C4C2×D3×D411yescharacteristic
779C3×C4C2×D3×D411yescharacteristic
780C3×C4#100411yescharacteristic
781C3×C4#100911yescharacteristic
782Dic3—21no—
783Dic3—21no—
784Dic3—41no—
785Dic3—61no—
786Dic3—61no—
787Dic3—61no—
788Dic3—61no—
789Dic3—62no—
790Dic3—62no—
791Dic3—122no—
792Dic3—121no—
793Dic3—121no—
794C32#326811yescharacteristic, complemented, Sylow
795C23—31no—
796C23—31no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—181no—
801C23—362no—
802C23—362no—
803C23—721no—
804Q8—21no—
805Q8—21no—
806Q8—92no—
807Q8—181no—
808D4—32no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—122no—
815D4—181no—
816D4—181no—
817D4—241no—
818D4—241no—
819D4—362no—
820D4—361no—
821D4—362no—
822D4—362no—
823D4—362no—
824D4—721no—
825D4—721no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—91no—
836C2×C4—91no—
837C2×C4—122no—
838C2×C4—181no—
839C2×C4—362no—
840C2×C4—362no—
841C2×C4—721no—
842C2×C4C22×D3211yescharacteristic
843C8—21no—
844C8—32no—
845C8—61no—
846C8—181no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—121no—
851C2×C3—122no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3#559011yescharacteristic
856C2×C3#560911yescharacteristic
857C2×C3#576811yescharacteristic
858C2×C3#577411yescharacteristic
859C2×C3#577411yescharacteristic
860C2×C3#577711yescharacteristic
861D3—41no—
862D3—42no—
863D3—41no—
864D3—81no—
865D3—81no—
866D3—241no—
867D3—241no—
868D3—481no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—62no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22—724no—
888C22D32×D411yescharacteristic
889C4—41no—
890C4—41no—
891C4—61no—
892C4—61no—
893C4—121no—
894C4—181no—
895C4—181no—
896C4—182no—
897C4#6430711yescharacteristic
898C4D32×D411yescharacteristic
899C3—21no—
900C3#8012811yescharacteristic, complemented
901C3#8083611yescharacteristic, complemented
902C2—121no—
903C2—121no—
904C2—122no—
905C2—241no—
906C2—241no—
907C2—721no—
908C2#1059427511yescharacteristic
909C2#1059475011yescharacteristic
910C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595427C2semidirect
2. C2×#63947C2semidirect
3. C2×#63795C2semidirect
4. #10594527C2semidirect
5. #10592497C2semidirect
6. C3×#4812C2semidirect
7. C3×#4810C2semidirect
8. #10591655C2semidirect
9. #10591621C2semidirect
10. #10590968C2semidirect
11. #10590749C2semidirect
12. #10590724C2semidirect
13. #10590595C2semidirect
14. #10590576C2semidirect
15. #10590461C2semidirect
21. C2×#3795C22semidirect
23. C2×#3756C22semidirect
25. #64096C22semidirect
27. C2×C3×#215C22semidirect
28. C2×C3×#215C22semidirect
32. C3×#895C22semidirect
37. #63914C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#103C22semidirect
53. #63641C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
58. C3×#807C22semidirect
59. #63567C22semidirect
60. #63562C22semidirect
62. #63555C22semidirect
83. #4812D3semidirect
84. #4810D3semidirect
151. #3716D4semidirect
180. C2×#215C2×D3semidirect
181. C2×#215C2×D3semidirect
217. #895C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
238. #821C2×D3semidirect
240. (C2×D3)⋊C8C2×D3semidirect
253. #807C2×D3semidirect
525. #103D32semidirect
794. C32#3268semidirect
900. C3#80128semidirect
901. C3#80836semidirect

Maximal subgroups

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

subgroupindex
#105954272
C2×#639472
C2×#637952
#105945272
#105924972
C3×#48122
C3×#48102
#105916552
#105916212
#105909682
#105907492
#105907242
#105905952
#105905762
#105904612
#808363
#801283