Finite Group Databasebeta

← #11867189

Subgroups — #11867189

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595306C211yesmaximal, characteristic, complemented
2C2×#63927C211yesmaximal, characteristic, complemented
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#10594612C211yesmaximal, characteristic, complemented
5#10592470C211yesmaximal, characteristic, complemented
6C3×#4782C211yesmaximal, characteristic, complemented
7C3×#4775C211yesmaximal, characteristic, complemented
8#10591498C211yesmaximal, characteristic, complemented
9#10591451C211yesmaximal, characteristic, complemented
10#10590941C211yesmaximal, characteristic, complemented
11#10590828C211yesmaximal, characteristic, complemented
12#10590825C211yesmaximal, characteristic, complemented
13#10590588C211yesmaximal, characteristic, complemented
14#10590583C211yesmaximal, characteristic, complemented
15#10590578C211yesmaximal, characteristic, complemented
16#80864—31nomaximal
17#80715—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3802—21no—
20C2×#3802C2211yescharacteristic
21C2×C4×D32C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic
24C3×#938C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic
32#63983—21no—
33#63975—21no—
34#67⋊Dic3—21no—
35#67⋊Dic3—21no—
36#63927—24no—
37#63921—21no—
38#63908C2211yescharacteristic
39#63908C2211yescharacteristic
40#63885—21no—
41#63885—21no—
42#63857C2211yescharacteristic, complemented
43#63857C2211yescharacteristic, complemented
44#63849C2211yescharacteristic
45C2×#3716C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3712C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D3×ΓL(1,𝔽25)—24no—
51C32×#102C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#911—31no—
64C2×#911—31no—
65C2×D3×M16—31no—
66C22×ΓL(1,𝔽25)—31no—
67#5606—31no—
68#5606—31no—
69D3×#121—31no—
70D3×#121—31no—
71C3×#469—31no—
72C3×#466—31no—
73#5159—31no—
74#5157—31no—
75#5134—31no—
76#5114—31no—
77#5042—31no—
78#5041—31no—
79#5039—31no—
80#5038—31no—
81#4886—31no—
82#4881—31no—
83#4864—31no—
84#4861—31no—
85#4782D311yescharacteristic, complemented
86#4780—31no—
87#4778—31no—
88#4775D311yescharacteristic, complemented
89#4771—31no—
90#4771—31no—
91#4771—61no—
92#4770—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99#3830—22no—
100#3830—22no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×#625—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#624D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118#3802—22no—
119#3802—22no—
120#3802—44no—
121C4×D32—22no—
122C4×D32—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3743—22no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#213—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×ΓL(1,𝔽25)—22no—
140C3×D3×C8—22no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3716—22no—
150#3716—22no—
151#3712D414yescomplemented
152#3711—22no—
153D3×C3⋊C8—22no—
154#3055—91noSylow
155C2×#237—31no—
156C2×#237—31no—
157C2×#237—61no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C2×C3×D8—31no—
165C2×C3×D8—31no—
166C2×C3×M16—31no—
167C22×C3×C8—31no—
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—31no—
171C3×#121—31no—
172#939—61no—
173#939—61no—
174#938—31no—
175#938—31no—
176#938C2×D311yescharacteristic, complemented
177#938C2×D311yescharacteristic, complemented
178#937—61no—
179#937—61no—
180D4×Dic3—61no—
181D4×Dic3—61no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#213C2×D311yescharacteristic, complemented
185C2×#213C2×D311yescharacteristic, complemented
186#930—31no—
187#930—31no—
188#924—31no—
189#924—31no—
190C2×#208—31no—
191C22×C3⋊C8—31no—
192#911—64no—
193#911—64no—
194D3×M16—64no—
195C2×#204—31no—
196C2×#204—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)—31no—
202C2×ΓL(1,𝔽25)—61no—
203C2×ΓL(1,𝔽25)—64no—
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
205C2×D3×C8—31no—
206C2×D3×C8C2×D311yescharacteristic, complemented
207#897—31no—
208#897—31no—
209#895C2×D311yescharacteristic
210#895C2×D311yescharacteristic
211#892—31no—
212#892—31no—
213D3×C4⋊C4—31no—
214D3×C4⋊C4—31no—
215D3×C4⋊C4—61no—
216#884—61no—
217#884—61no—
218#883—61no—
219#883—61no—
220#67⋊C4—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224C3×#107—31no—
225C3×#106—31no—
226C3×#102—21no—
227C3×#102—31no—
228C3×#102—31no—
229C3×#102C2×D311yescharacteristic, complemented
230C3×#102C2×D311yescharacteristic, complemented
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#821C2×D311yescharacteristic, complemented
237#821C2×D311yescharacteristic, complemented
238#818—31no—
239#817—31no—
240#816—31no—
241#816—31no—
242#816—61no—
243#810—31no—
244#810—31no—
245#810—61no—
246#809—31no—
247#809—31no—
248#808—31no—
249#808C2×D311yescharacteristic, complemented
250#807—31no—
251#807C2×D311yescharacteristic, complemented
252C23×C32—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—22no—
259C2×D32—22no—
260C2×D32—41no—
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—42no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4×C3⋊D3—42no—
274C4×C3⋊D3C2×D412yes—
275C4×C3⋊D3#4112yes—
276#634—21no—
277#634—21no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—42no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294#625—42no—
295#625—42no—
296#625—42no—
297#624—22no—
298D3×Dic3—22no—
299D3×Dic3—22no—
300C32×C8—21no—
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—31no—
309#469—91no—
310#468—91no—
311#468—91no—
312#466—31no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—91no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
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—61no—
344C2×#67—121no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—121no—
350#237—62no—
351#237—62no—
352#237—62no—
353#237—62no—
354#237—64no—
355#237—122no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—62no—
359D3×D4—62no—
360D3×D4—124no—
361D3×D4—124no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—61no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—121no—
380C2×C4×D3C22×D311yescharacteristic
381C2×C4×D3C22×D311yescharacteristic
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—61no—
385C3×D8—62no—
386C3×D8—62no—
387C3×M16—62no—
388C2×C3×C8—21no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—62no—
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C3×C4⋊C4—21no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403#217—21no—
404#217—21no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#214—62no—
410#214—62no—
411#213—22no—
412#213—22no—
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—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427C4⋊Dic3C22×D311yescharacteristic
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—121no—
433C4×Dic3—61no—
434C4×Dic3—61no—
435#208—62no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—61no—
439C2×C3⋊C8—62no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442#204—62no—
443#204—62no—
444ΓL(1,𝔽25)—22no—
445ΓL(1,𝔽25)—34no—
446ΓL(1,𝔽25)—34no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—122no—
451D3×C8—22no—
452D3×C8—62no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3#12112yes—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3AGL(1,ℤ/8)12yescomplemented
472D32—44no—
473D32—84no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4C2×#4111yescharacteristic
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3⋊Dic3#12112yes—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C2×#41—91no—
485C22×D4—91no—
486C22×D4—181no—
487C23×C4—91no—
488AGL(1,ℤ/8)—184no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×D8—31no—
492C2×D8—31no—
493C2×M16—31no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—91no—
497C2×M16—184no—
498C22×C8—31no—
499C22×C8—91no—
500#123—181no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503#121—31no—
504#121—31no—
505#121—31no—
506#121—31no—
507#121—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—181no—
513C4×D4—181no—
514#117—91no—
515C2×C4⋊C4—91no—
516C2×C22⋊C4—181no—
517#107—31no—
518#107—91no—
519#106—31no—
520#106—91no—
521#103—91no—
522#103—91no—
523#102—31no—
524#102—31no—
525#102—91no—
526#102—91no—
527#102—91no—
528#102D3211yescharacteristic, complemented
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—61no—
535C23×C3—61no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—31no—
539C22×D3—31no—
540C22×D3—61no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3D3×D411yescharacteristic
554C22×D3D3×D411yescharacteristic
555C3×D4—22no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—41no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—122no—
568C3×D4—122no—
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—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4C23×D311yescharacteristic
582C2×C3×C4C23×D311yescharacteristic
583#67—42no—
584#67—42no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—124no—
593#67—122no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—61no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—122no—
608C2×Dic3—122no—
609C2×Dic3—124no—
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12—42no—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—32no—
623C4×D3—32no—
624C4×D3—32no—
625C4×D3—32no—
626C4×D3—62no—
627C4×D3—62no—
628C4×D3—62no—
629C4×D3—62no—
630C4×D3—62no—
631C4×D3—62no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—242no—
635Dic6—62no—
636Dic6—61no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—121no—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—32no—
644C3×C8—32no—
645C3×C8—41no—
646C3⋊C8—61no—
647C3⋊C8—61no—
648C3⋊C8—121no—
649C3⋊C8D3×D412yescomplemented
650C3⋊C8D3×D412yescomplemented
651C2×C32—81no—
652C2×C32C2×#12111yescharacteristic
653C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
654C2×C32#57511yescharacteristic
655C3⋊D3—22no—
656C3×D3—22no—
657C3×D3—41no—
658C3×D3—81no—
659C3×D3—81no—
660C24—91no—
661C24—181no—
662#41—182no—
663#41—182no—
664C2×Q8—91no—
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—182no—
672C2×D4—182no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4—181no—
677C2×D4—364no—
678C2×D4C2×D3211yescharacteristic
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—181no—
686C22×C4—182no—
687C22×C4—182no—
688C22×C4—181no—
689SD16—182no—
690SD16—182no—
691D8—62no—
692D8—62no—
693M16—62no—
694M16—94no—
695M16—182no—
696M16—182no—
697C2×C8—31no—
698C2×C8—31no—
699C2×C8—62no—
700C2×C8—91no—
701C2×C8—182no—
702C2×C8C2×D3211yescharacteristic
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—91no—
706C4⋊C4—181no—
707C4⋊C4—181no—
708C4⋊C4—181no—
709C4⋊C4C2×D3211yescharacteristic
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—181no—
720C22×C3—21no—
721C22×C3—32no—
722C22×C3—42no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—32no—
750C2×D3—32no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—62no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—124no—
765C2×D3—124no—
766C2×D3—244no—
767C2×D3—244no—
768C2×D3#91112yescomplemented
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—81no—
776C3×C4—121no—
777C3×C4—121no—
778C3×C4C2×D3×D411yescharacteristic
779C3×C4C2×D3×D411yescharacteristic
780C3×C4D3×#4111yescharacteristic
781C3×C4D3×#4111yescharacteristic
782Dic3—21no—
783Dic3—21no—
784Dic3—32no—
785Dic3—32no—
786Dic3—41no—
787Dic3—41no—
788Dic3—62no—
789Dic3—122no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—121no—
794Dic3—241no—
795C32#305511yescharacteristic, complemented, Sylow
796C23—21no—
797C23—31no—
798C23—31no—
799C23—61no—
800C23—61no—
801C23—91no—
802C23—182no—
803C23—182no—
804C23—361no—
805C23—362no—
806C23—362no—
807C23—362no—
808Q8—181no—
809Q8—181no—
810D4—21no—
811D4—21no—
812D4—61no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—122no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—21no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—91no—
834C2×C4—92no—
835C2×C4—92no—
836C2×C4—182no—
837C2×C4—182no—
838C2×C4—182no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—362no—
842C2×C4—362no—
843C2×C4C22×D3211yescharacteristic
844C8—21no—
845C8—32no—
846C8—32no—
847C8—181no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—62no—
852C2×C3—82no—
853C2×C3—81no—
854C2×C3—81no—
855C2×C3—121no—
856C2×C3—241no—
857C2×C3—241no—
858C2×C3D3×#12111yescharacteristic
859C2×C3D3×#12111yescharacteristic
860C2×C3C2×#91111yescharacteristic
861C2×C3#576811yescharacteristic
862C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
863C2×C3#577311yescharacteristic
864D3—22no—
865D3—41no—
866D3—62no—
867D3—62no—
868D3—81no—
869D3—81no—
870D3—122no—
871C22—32no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—61no—
880C22—92no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—181no—
888C22—181no—
889C22—364no—
890C22—724no—
891C22D32×D411yescharacteristic
892C4—41no—
893C4—61no—
894C4—61no—
895C4—92no—
896C4—121no—
897C4—121no—
898C4—361no—
899C4—361no—
900C4#6430611yescharacteristic
901C4D32×D411yescharacteristic
902C3—21no—
903C3#8071511yescharacteristic, complemented
904C3#8086411yescharacteristic, complemented
905C2—62no—
906C2—81no—
907C2—121no—
908C2—182no—
909C2—241no—
910C2—241no—
911C2#1059426511yescharacteristic
912C2D3×#91111yescharacteristic
913C2#1059474511yescharacteristic
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. #10595306C2semidirect
2. C2×#63927C2semidirect
3. C2×D3×ΓL(1,𝔽25)C2semidirect
4. #10594612C2semidirect
5. #10592470C2semidirect
6. C3×#4782C2semidirect
7. C3×#4775C2semidirect
8. #10591498C2semidirect
9. #10591451C2semidirect
10. #10590941C2semidirect
11. #10590828C2semidirect
12. #10590825C2semidirect
13. #10590588C2semidirect
14. #10590583C2semidirect
15. #10590578C2semidirect
24. C3×#938C22semidirect
25. C3×#938C22semidirect
26. C2×C3×#213C22semidirect
27. C2×C3×#213C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×C3×D3×C8C22semidirect
42. #63857C22semidirect
43. #63857C22semidirect
45. C2×#3716C22semidirect
46. C2×#3716C22semidirect
48. C2×#3711C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C32×#102C22semidirect
52. #63659C22semidirect
53. #63643C22semidirect
54. #63637C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×#808C22semidirect
58. C3×#807C22semidirect
59. #63575C22semidirect
60. #63573C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
85. #4782D3semidirect
88. #4775D3semidirect
151. #3712D4semidirect
176. #938C2×D3semidirect
177. #938C2×D3semidirect
184. C2×#213C2×D3semidirect
185. C2×#213C2×D3semidirect
204. C2×ΓL(1,𝔽25)C2×D3semidirect
206. C2×D3×C8C2×D3semidirect
229. C3×#102C2×D3semidirect
230. C3×#102C2×D3semidirect
236. #821C2×D3semidirect
237. #821C2×D3semidirect
249. #808C2×D3semidirect
251. #807C2×D3semidirect
302. C3×C3⋊C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
471. C2×C3×D3AGL(1,ℤ/8)semidirect
528. #102D32semidirect
649. C3⋊C8D3×D4semidirect
650. C3⋊C8D3×D4semidirect
768. C2×D3#911semidirect
795. C32#3055semidirect
903. C3#80715semidirect
904. C3#80864semidirect

Maximal subgroups

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

subgroupindex
#105953062
C2×#639272
C2×D3×ΓL(1,𝔽25)2
#105946122
#105924702
C3×#47822
C3×#47752
#105914982
#105914512
#105909412
#105908282
#105908252
#105905882
#105905832
#105905782
#808643
#807153