Finite Group Databasebeta

← #11867181

Subgroups — #11867181

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#938C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#10594627C211yesmaximal, characteristic, complemented
5#10592481C211yesmaximal, characteristic, complemented
6C3×#4778C211yesmaximal, characteristic, complemented
7C3×#4770C211yesmaximal, characteristic, complemented
8#10591464C211yesmaximal, characteristic, complemented
9#10591449C211yesmaximal, characteristic, complemented
10#10590842C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590508C211yesmaximal, characteristic, complemented
14#10590501C211yesmaximal, characteristic, complemented
15#10590437C211yesmaximal, characteristic, complemented
16#80657—31nomaximal
17#78930—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×C4×D32C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22#64147C2211yescharacteristic
23C2×#3753C2211yescharacteristic, complemented
24C2×#3743C2211yescharacteristic, complemented
25#64104C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#892C2211yescharacteristic
32#63970—21no—
33D3×#217—21no—
34#63958—21no—
35#63934—24no—
36#63923—21no—
37#63916C2211yescharacteristic
38#63909C2211yescharacteristic, complemented
39#63908C2211yescharacteristic
40#63894—21no—
41#63890—21no—
42D3×C4⋊Dic3C2211yescharacteristic
43#63880—21no—
44#63871C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic, complemented
47C2×#3712C2211yescharacteristic, complemented
48C2×#3711C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D3×ΓL(1,𝔽25)—24no—
51C32×#102C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63576C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C2×#938—31no—
64C2×#932—31no—
65C2×#914—31no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68#5627—31no—
69D3×#121—31no—
70#5524—31no—
71C3×#465—31no—
72C3×#418—31no—
73#5174—31no—
74#5133—31no—
75#5115—31no—
76#5048—31no—
77#5038—31no—
78#4995—31no—
79#4865—31no—
80#4861—31no—
81#4812—31no—
82#4803—31no—
83#4782—31no—
84#4782—31no—
85#4782—31no—
86#4782—61no—
87#4780—31no—
88#4780—31no—
89#4778—31no—
90#4778D311yescharacteristic, complemented
91#4775—31no—
92#4775—31no—
93#4770D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109D3×#67—44no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#624—21no—
115C2×#624D411yescharacteristic
116C2×D3×Dic3—21no—
117C2×D3×Dic3D411yescharacteristic
118C2×D3×Dic3D411yescharacteristic
119C4×D32—22no—
120C4×D32—22no—
121#3799—22no—
122#3799—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3757—21no—
126#3753—22no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3743—22no—
131C3×#217—21no—
132C3×#214—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×ΓL(1,𝔽25)—22no—
142C3×D3×C8—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3715—22no—
150#3714—22no—
151#3712—22no—
152#3711D414yescomplemented
153D3×C3⋊C8—22no—
154#3055—91noSylow
155C22×C3×D4—31no—
156C22×#67—61no—
157C2×#239—31no—
158C2×D3×D4—61no—
159C2×D3×D4C2×D311yescharacteristic
160C2×#235—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×SD16—31no—
164C2×C3×M16—31no—
165C22×C3×C8—31no—
166C3×C22⋊Q8—31no—
167C3×#121—31no—
168C3×#117—31no—
169C2×#217—61no—
170#946—31no—
171C2×#215—31no—
172#939—61no—
173#938—31no—
174#938—31no—
175#938—31no—
176#938—31no—
177#938—61no—
178#938—61no—
179#938—61no—
180#938C2×D311yescharacteristic
181C2×#214—31no—
182C2×#214C2×D311yescharacteristic, complemented
183#932—64no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—61no—
188#930—31no—
189#930—31no—
190C2×C4⋊Dic3—31no—
191C2×#208—31no—
192C22×C3⋊C8—31no—
193#914—64no—
194D3×M16—64no—
195C2×D24—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—61no—
202C2×ΓL(1,𝔽25)—64no—
203C2×ΓL(1,𝔽25)C2×D311yescharacteristic
204C2×D3×C8—31no—
205C2×D3×C8C2×D311yescharacteristic, complemented
206#897—31no—
207#897C2×D311yescharacteristic, complemented
208#895—31no—
209#895—31no—
210#895—31no—
211#895—31no—
212#895—61no—
213#894—61no—
214#893—61no—
215#892C2×D311yescharacteristic
216D3×C4⋊C4—31no—
217#886—61no—
218#884—61no—
219#882—61no—
220#882—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223C4×D12—61no—
224C4×D12—61no—
225C3×#106—31no—
226C3×#103—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102C2×D311yescharacteristic, complemented
232C3×#102C2×D311yescharacteristic, complemented
233#835—31no—
234#832C2×D311yescharacteristic, complemented
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#821C2×D311yescharacteristic, complemented
240#818—31no—
241#816—31no—
242#816C2×D311yescharacteristic, complemented
243#809—31no—
244#809C2×D311yescharacteristic, complemented
245#808—31no—
246#808—31no—
247#808—61no—
248#808C2×D311yescharacteristic, complemented
249#807—31no—
250#807—31no—
251#807—31no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—22no—
262C2×D32—22no—
263C2×D32—41no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—21no—
276C3×#67—42no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#626—42no—
294#625—42no—
295#624—22no—
296#624—42no—
297D3×Dic3—22no—
298D3×Dic3—22no—
299D3×Dic3—42no—
300C32×C8—21no—
301C3⋊(C3⋊C8)C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—91no—
309#469—91no—
310#468—91no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—31no—
315#465—91no—
316#428—91no—
317#418—31no—
318#417—91no—
319C24×C3—61no—
320C23×D3—21no—
321C23×D3—31no—
322C23×D3—31no—
323C2×C3×Q8—31no—
324C2×C3×D4—21no—
325C2×C3×D4—31no—
326C2×C3×D4—62no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—121no—
344C2×#67—124no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—61no—
348#239—62no—
349#239—62no—
350D3×D4—22no—
351D3×D4—22no—
352D3×D4—124no—
353#235—62no—
354#235—62no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—121no—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—61no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×SD16—62no—
383C3×M16—62no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8—62no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—21no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—61no—
400#217—21no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—121no—
406#215—62no—
407#214—22no—
408#214—62no—
409#213—62no—
410#213—62no—
411#213—62no—
412#213—122no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
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—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3—21no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3C22×D311yescharacteristic
431C4⋊Dic3C22×D311yescharacteristic
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434C4×Dic3—21no—
435#208—34no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—61no—
439C2×C3⋊C8—62no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—62no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—34no—
445ΓL(1,𝔽25)—62no—
446ΓL(1,𝔽25)—62no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—122no—
450D3×C8—22no—
451D3×C8—62no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
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—84no—
470C2×C3×D3#12112yes—
471C2×C3×D3AGL(1,ℤ/8)12yescomplemented
472D32—44no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4C2×#4111yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—91no—
484C22×D4—31no—
485C22×D4—181no—
486C23×C4—91no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—91no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—184no—
497C22×C8—31no—
498C22×C8—91no—
499#123—181no—
500C22⋊Q8—31no—
501C22⋊Q8—91no—
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—181no—
512C4×D4—181no—
513#117—31no—
514C2×C4⋊C4—91no—
515C2×C22⋊C4—181no—
516#107—91no—
517#107—91no—
518#106—31no—
519#106—91no—
520#103—31no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—31no—
525#102—91no—
526#102—91no—
527#102D3211yescharacteristic, complemented
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—122no—
535C23×C3—122no—
536C23×C3—122no—
537C22×D3—21no—
538C22×D3—31no—
539C22×D3—31no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—61no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—121no—
551C22×D3—121no—
552C22×D3—121no—
553C22×D3D3×D411yescharacteristic
554C22×D3D3×D411yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—31no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—42no—
583#67—42no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—242no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—121no—
603C2×Dic3—122no—
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606D12—21no—
607D12—21no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—121no—
613D12—121no—
614D12—122no—
615D12—122no—
616D12—122no—
617D12—122no—
618D12—122no—
619D12—242no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—62no—
623C4×D3—62no—
624C4×D3—62no—
625C4×D3—61no—
626C4×D3—61no—
627C4×D3—61no—
628C4×D3—61no—
629C4×D3—62no—
630C4×D3—121no—
631C4×D3—121no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3#23512yes—
636C4×D3D3×D412yes—
637Dic6—21no—
638Dic6—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—32no—
642C3×C8—41no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—32no—
646C3⋊C8—32no—
647C3⋊C8—62no—
648C3⋊C8D3×D412yescomplemented
649C2×C32—81no—
650C2×C32C2×#12111yescharacteristic
651C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
652C2×C32#57511yescharacteristic
653C3⋊D3—41no—
654C3⋊D3—81no—
655C3×D3—22no—
656C3×D3—22no—
657C3×D3—81no—
658C24—61no—
659C24—91no—
660#41—182no—
661#41—182no—
662C2×Q8—31no—
663C2×D4—31no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—91no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—364no—
676C2×D4C2×D3211yescharacteristic
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—181no—
686C22×C4—181no—
687SD16—62no—
688SD16—182no—
689D8—182no—
690D8—182no—
691M16—62no—
692M16—94no—
693M16—182no—
694M16—182no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—62no—
698C2×C8—91no—
699C2×C8—182no—
700C2×C8C2×D3211yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—91no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C4⋊C4C2×D3211yescharacteristic
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—61no—
718C22×C3—21no—
719C22×C3—32no—
720C22×C3—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—244no—
738C22×C3C2×D3×D411yescharacteristic
739C22×C3C2×D3×D411yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—84no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—124no—
758C2×D3—124no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—241no—
766C2×D3—241no—
767C2×D3—241no—
768C2×D3#88412yes—
769C2×D3#91412yescomplemented
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—32no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—61no—
776C3×C4—81no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C2×#23511yescharacteristic
781C3×C4C2×D3×D411yescharacteristic
782C3×C4C2×D3×D411yescharacteristic
783C3×C4D3×#4111yescharacteristic
784Dic3—21no—
785Dic3—41no—
786Dic3—41no—
787Dic3—41no—
788Dic3—61no—
789Dic3—61no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—241no—
794Dic3#88412yes—
795C32#305511yescharacteristic, complemented, Sylow
796C23—21no—
797C23—31no—
798C23—31no—
799C23—61no—
800C23—91no—
801C23—122no—
802C23—122no—
803C23—122no—
804C23—182no—
805C23—182no—
806C23—181no—
807C23—361no—
808Q8—61no—
809Q8—61no—
810D4—21no—
811D4—21no—
812D4—61no—
813D4—61no—
814D4—122no—
815D4—122no—
816D4—181no—
817D4—181no—
818D4—362no—
819D4—362no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—21no—
825C2×C4—31no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—31no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—91no—
835C2×C4—182no—
836C2×C4—182no—
837C2×C4—182no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—362no—
842C2×C4—362no—
843C2×C4C22×D3211yescharacteristic
844C8—21no—
845C8—32no—
846C8—61no—
847C8—92no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—62no—
852C2×C3—62no—
853C2×C3—81no—
854C2×C3—81no—
855C2×C3—161no—
856C2×C3—241no—
857C2×C3C2×#88411yescharacteristic
858C2×C3D3×#12111yescharacteristic
859C2×C3C2×#91411yescharacteristic
860C2×C3#576811yescharacteristic
861C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
862C2×C3#577311yescharacteristic
863D3—22no—
864D3—22no—
865D3—81no—
866D3—121no—
867D3—121no—
868D3—241no—
869D3—241no—
870D3—241no—
871D3—481no—
872C22—32no—
873C22—32no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—61no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—181no—
885C22—181no—
886C22—181no—
887C22—244no—
888C22—364no—
889C22—361no—
890C22—361no—
891C22—361no—
892C22D32×D411yescharacteristic
893C4—32no—
894C4—41no—
895C4—61no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—181no—
900C4—361no—
901C4D3×#23511yescharacteristic
902C4D32×D411yescharacteristic
903C3—21no—
904C3#7893011yescharacteristic, complemented
905C3#8065711yescharacteristic, complemented
906C2—62no—
907C2—62no—
908C2—81no—
909C2—241no—
910C2—361no—
911C2—721no—
912C2D3×#88411yescharacteristic
913C2#1059472911yescharacteristic
914C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D3×#938C2semidirect
2. C2×#63934C2semidirect
3. C2×D3×ΓL(1,𝔽25)C2semidirect
4. #10594627C2semidirect
5. #10592481C2semidirect
6. C3×#4778C2semidirect
7. C3×#4770C2semidirect
8. #10591464C2semidirect
9. #10591449C2semidirect
10. #10590842C2semidirect
11. #10590826C2semidirect
12. #10590671C2semidirect
13. #10590508C2semidirect
14. #10590501C2semidirect
15. #10590437C2semidirect
23. C2×#3753C22semidirect
24. C2×#3743C22semidirect
25. #64104C22semidirect
27. C2×C3×#214C22semidirect
29. C2×C3×D3×C8C22semidirect
30. C3×#897C22semidirect
38. #63909C22semidirect
44. #63871C22semidirect
45. C2×#3715C22semidirect
46. C2×#3714C22semidirect
47. C2×#3712C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C32×#102C22semidirect
52. #63648C22semidirect
53. #63635C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×#816C22semidirect
57. C3×#809C22semidirect
58. C3×#808C22semidirect
59. #63576C22semidirect
60. #63575C22semidirect
61. #63566C22semidirect
62. #63564C22semidirect
90. #4778D3semidirect
93. #4770D3semidirect
152. #3711D4semidirect
182. C2×#214C2×D3semidirect
205. C2×D3×C8C2×D3semidirect
207. #897C2×D3semidirect
231. C3×#102C2×D3semidirect
232. C3×#102C2×D3semidirect
234. #832C2×D3semidirect
239. #821C2×D3semidirect
242. #816C2×D3semidirect
244. #809C2×D3semidirect
248. #808C2×D3semidirect
301. C3⋊(C3⋊C8)C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
471. C2×C3×D3AGL(1,ℤ/8)semidirect
527. #102D32semidirect
648. C3⋊C8D3×D4semidirect
769. C2×D3#914semidirect
795. C32#3055semidirect
904. C3#78930semidirect
905. C3#80657semidirect

Maximal subgroups

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

subgroupindex
D3×#9382
C2×#639342
C2×D3×ΓL(1,𝔽25)2
#105946272
#105924812
C3×#47782
C3×#47702
#105914642
#105914492
#105908422
#105908262
#105906712
#105905082
#105905012
#105904372
#806573
#789303