Finite Group Databasebeta

← #11867143

Subgroups — #11867143

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64120C211yesmaximal, characteristic, complemented
2#10595306C211yesmaximal, characteristic, complemented
3#10595282C211yesmaximal, characteristic, complemented
4C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
5C3×#5159C211yesmaximal, characteristic, complemented
6C3×#5157C211yesmaximal, characteristic, complemented
7#10591462C211yesmaximal, characteristic, complemented
8#10591460C211yesmaximal, characteristic, complemented
9#10591453C211yesmaximal, characteristic, complemented
10#10591449C211yesmaximal, characteristic, complemented
11#10591426C211yesmaximal, characteristic, complemented
12#10591418C211yesmaximal, characteristic, complemented
13#10590838C211yesmaximal, characteristic, complemented
14#10590830C211yesmaximal, characteristic, complemented
15#10590688C211yesmaximal, characteristic, complemented
16#80864—31nomaximal
17#80715—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×#3811—21no—
21C2×C4×D32C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25#64120—24no—
26C2×#3744C2211yescharacteristic, complemented
27C2×#3743C2211yescharacteristic
28C3×#938C2211yescharacteristic
29C3×#938C2211yescharacteristic
30C3×#938C2211yescharacteristic, complemented
31C3×#938C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63983—21no—
35#63975—21no—
36#63974—21no—
37#67⋊Dic3—21no—
38#67⋊Dic3—21no—
39#63971—21no—
40#63971—21no—
41#63909C2211yescharacteristic
42#63909C2211yescharacteristic
43#63900C2211yescharacteristic
44#63857C2211yescharacteristic, complemented
45#63857C2211yescharacteristic, complemented
46#63849C2211yescharacteristic
47C2×#3712C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D3×ΓL(1,𝔽25)—24no—
51C3×#832C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#817C2211yescharacteristic, complemented
57#63576C2211yescharacteristic, complemented
58#63574C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C2×#911—31no—
64C2×#911—31no—
65C2×#911—61no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68#5606—31no—
69#5606—31no—
70D3×#121—31no—
71D3×#121—31no—
72C3×#469—31no—
73C3×#466—31no—
74#5159D311yescharacteristic, complemented
75#5157D311yescharacteristic, complemented
76#5134—31no—
77#5114—31no—
78#5042—31no—
79#5041—31no—
80#5039—31no—
81#5038—31no—
82#4886—31no—
83#4881—31no—
84#4864—31no—
85#4861—31no—
86#4782—31no—
87#4780—31no—
88#4778—31no—
89#4775—31no—
90#4771—31no—
91#4771—31no—
92#4770—31no—
93#4770—31no—
94C23×C3⋊D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C22×C3⋊Dic3—21no—
101#3830—22no—
102#3830—22no—
103D4×C3⋊D3—22no—
104D4×C3⋊D3—22no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114#3811—44no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#624—21no—
118C2×#624D411yescharacteristic
119C2×D3×Dic3D411yescharacteristic
120C2×D3×Dic3D411yescharacteristic
121C4×D32—22no—
122C4×D32—22no—
123C32×D8—22no—
124C2×C32×C8C2311yescharacteristic
125#3754—22no—
126#3753—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3744—22no—
129#3743D414yescomplemented
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×ΓL(1,𝔽25)—22no—
141C3×D3×C8—22no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3712—22no—
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—
162C2×D3×D4—61no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C2×C3×D8—21no—
166C2×C3×D8C2×D311yescharacteristic, complemented
167C2×C3×D8C2×D311yescharacteristic, complemented
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×#121—31no—
171C3×#121—31no—
172C3×#121—31no—
173C3×#121—31no—
174#939—61no—
175#939—61no—
176#938C2×D311yescharacteristic
177#938C2×D311yescharacteristic
178#938C2×D311yescharacteristic, complemented
179#938C2×D311yescharacteristic, complemented
180#937—61no—
181#937—61no—
182D4×Dic3—61no—
183D4×Dic3—61no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—61no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—61no—
190#930—31no—
191#930—31no—
192#924—31no—
193#924—31no—
194C2×#208—31no—
195C22×C3⋊C8—31no—
196#911—64no—
197#911—64no—
198#911—68no—
199D3×M16—64no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—61no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—61no—
209C2×ΓL(1,𝔽25)—64no—
210C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
211C2×D3×C8—31no—
212C2×D3×C8C2×D311yescharacteristic, complemented
213#897—31no—
214#897—31no—
215#895—31no—
216#895—31no—
217#892—31no—
218#892—31no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4—31no—
221#884—61no—
222#884—61no—
223#883—61no—
224#883—61no—
225#67⋊C4—61no—
226#67⋊C4—61no—
227D3×C22⋊C4—61no—
228D3×C22⋊C4—61no—
229C3×#107—31no—
230C3×#106—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102—31no—
235#832C2×D311yescharacteristic, complemented
236#832C2×D311yescharacteristic, complemented
237#832C2×D311yescharacteristic, complemented
238#832C2×D311yescharacteristic, complemented
239#821—31no—
240#821—31no—
241#818C2×D311yescharacteristic, complemented
242#817C2×D311yescharacteristic, complemented
243#816—31no—
244#816—31no—
245#810—31no—
246#810—31no—
247#809—31no—
248#809—31no—
249#808—31no—
250#808—31no—
251#807—31no—
252#807—31no—
253C23×C32—21no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—42no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C2×D32—22no—
263C2×D32—22no—
264C2×D32—41no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—21no—
269C2×C32×C4C2411yescharacteristic
270#638—42no—
271#638—42no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—42no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4×C3⋊D3C2×D412yes—
278C4×C3⋊D3#4112yes—
279#634—21no—
280#634—21no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—42no—
284C3×#67—42no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295#626—42no—
296#626—42no—
297#624—22no—
298#624—42no—
299D3×Dic3—22no—
300D3×Dic3—22no—
301C32×C8C2×D412yescomplemented
302C3⋊(C3⋊C8)C2×D412yescomplemented
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C2×AGL(1,ℤ/8)—91no—
306C22×M16—91no—
307#525—91no—
308C2×#121—91no—
309#469—31no—
310#469—91no—
311#468—91no—
312#468—91no—
313#466—31no—
314#466—91no—
315#465—91no—
316#465—91no—
317#428—91no—
318#418—91no—
319#417—91no—
320C23×D3—31no—
321C23×D3—31no—
322C23×D3—61no—
323C23×D3—61no—
324C23×D3—121no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C2×#67—121no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—121no—
354#237—62no—
355#237—62no—
356#237—62no—
357#237—62no—
358#237—64no—
359#237—122no—
360D3×D4—62no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—62no—
364D3×D4—64no—
365D3×D4—122no—
366D3×D4—124no—
367D3×D4—124no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×C4×D3—31no—
374C2×C4×D3—31no—
375C2×C4×D3—31no—
376C2×C4×D3—31no—
377C2×C4×D3—31no—
378C2×C4×D3—31no—
379C2×C4×D3—61no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3C22×D311yescharacteristic
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C3×D8—24no—
392C3×D8—22no—
393C3×D8—22no—
394C3×M16—62no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—62no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409#217—21no—
410#217—21no—
411#217—21no—
412#217—21no—
413#217—61no—
414#217—61no—
415#214—62no—
416#214—62no—
417#214—64no—
418#213—62no—
419#213—62no—
420#213—64no—
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—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3C22×D311yescharacteristic
432C4⋊Dic3C22×D311yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439C4×Dic3—61no—
440C4×Dic3—61no—
441#208—62no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—62no—
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448#204—64no—
449#204—62no—
450#204—62no—
451ΓL(1,𝔽25)—22no—
452ΓL(1,𝔽25)—34no—
453ΓL(1,𝔽25)—34no—
454ΓL(1,𝔽25)—64no—
455ΓL(1,𝔽25)—62no—
456ΓL(1,𝔽25)—62no—
457ΓL(1,𝔽25)—62no—
458D3×C8—22no—
459D3×C8—62no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—84no—
473C2×C3⋊D3#12112yes—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3AGL(1,ℤ/8)12yescomplemented
480D32—44no—
481C32×C4C22×D411yescharacteristic
482C32×C4C2×#4111yescharacteristic
483C3⋊Dic3—41no—
484C3⋊Dic3#12112yes—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—91no—
492C22×D4—91no—
493C22×D4—181no—
494C23×C4—91no—
495AGL(1,ℤ/8)—184no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—91no—
499C2×D8D3211yescharacteristic, complemented
500C2×M16—31no—
501C2×M16—91no—
502C2×M16—91no—
503C2×M16—91no—
504C2×M16—184no—
505C22×C8—31no—
506C22×C8—91no—
507#123—181no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—31no—
511#121—31no—
512#121—31no—
513#121—31no—
514#121—91no—
515#121—91no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×D4—181no—
520C4×D4—181no—
521#117—91no—
522C2×C4⋊C4—91no—
523C2×C22⋊C4—181no—
524#107—31no—
525#107—91no—
526#106—31no—
527#106—91no—
528#103—91no—
529#103—91no—
530#102—31no—
531#102—31no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102—91no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—41no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—61no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—124no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—242no—
564C22×D3—242no—
565C22×D3D3×D411yescharacteristic
566C22×D3D3×D411yescharacteristic
567C3×D4—22no—
568C3×D4—22no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—122no—
583C2×C3×C4—21no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—42no—
597#67—42no—
598#67—42no—
599#67—42no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—124no—
605#67—122no—
606#67—122no—
607#67—124no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—61no—
615C2×Dic3—62no—
616C2×Dic3—62no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—121no—
620C2×Dic3—122no—
621C2×Dic3—122no—
622C2×Dic3—124no—
623C2×Dic3D3×D411yescharacteristic
624C2×Dic3D3×D411yescharacteristic
625D12—62no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—121no—
631D12—122no—
632D12—122no—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—32no—
638C4×D3—32no—
639C4×D3—32no—
640C4×D3—32no—
641C4×D3—62no—
642C4×D3—62no—
643C4×D3—62no—
644C4×D3—62no—
645C4×D3—62no—
646C4×D3—62no—
647C4×D3—122no—
648C4×D3—122no—
649Dic6—62no—
650Dic6—61no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—121no—
655C3×C8—22no—
656C3×C8—61no—
657C3×C8—61no—
658C3×C8D3×D412yescomplemented
659C3×C8D3×D412yescomplemented
660C3⋊C8—21no—
661C3⋊C8—21no—
662C3⋊C8—32no—
663C3⋊C8—32no—
664C3⋊C8—62no—
665C2×C32—81no—
666C2×C32—81no—
667C2×C32C2×#12111yescharacteristic
668C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
669C2×C32#57511yescharacteristic
670C3⋊D3—22no—
671C3⋊D3—81no—
672C3×D3—22no—
673C3×D3—41no—
674C24—91no—
675C24—181no—
676#41—182no—
677#41—182no—
678C2×Q8—91no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—91no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—182no—
687C2×D4—182no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—364no—
691C2×D4C2×D3211yescharacteristic
692C2×D4C2×D3211yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—91no—
698C22×C4—91no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4—181no—
702C22×C4—181no—
703SD16—182no—
704SD16—182no—
705D8—22no—
706D8—182no—
707M16—62no—
708M16—94no—
709M16—182no—
710M16—182no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C2×C8—91no—
715C2×C8—182no—
716C2×C8C2×D3211yescharacteristic
717C4⋊C4—31no—
718C4⋊C4—31no—
719C4⋊C4—31no—
720C4⋊C4—31no—
721C4⋊C4—181no—
722C4⋊C4—181no—
723C4⋊C4—181no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—181no—
734C22×C3—21no—
735C22×C3—32no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—81no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—32no—
767C2×D3—32no—
768C2×D3—62no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—124no—
776C2×D3—124no—
777C2×D3—122no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—244no—
787C2×D3—244no—
788C2×D3—248no—
789C2×D3#91112yescomplemented
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4—121no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4—121no—
798C3×C4C2×D3×D411yescharacteristic
799C3×C4C2×D3×D411yescharacteristic
800C3×C4D3×#4111yescharacteristic
801C3×C4D3×#4111yescharacteristic
802Dic3—21no—
803Dic3—21no—
804Dic3—32no—
805Dic3—32no—
806Dic3—41no—
807Dic3—41no—
808Dic3—41no—
809Dic3—41no—
810Dic3—62no—
811Dic3—122no—
812Dic3—121no—
813Dic3—121no—
814C32#305511yescharacteristic, complemented, Sylow
815C23—21no—
816C23—21no—
817C23—31no—
818C23—31no—
819C23—91no—
820C23—182no—
821C23—182no—
822C23—181no—
823C23—362no—
824C23—362no—
825C23—362no—
826C23—361no—
827Q8—181no—
828Q8—181no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—122no—
834D4—122no—
835D4—122no—
836D4—122no—
837D4—181no—
838D4—181no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—91no—
854C2×C4—92no—
855C2×C4—92no—
856C2×C4—182no—
857C2×C4—182no—
858C2×C4—182no—
859C2×C4—181no—
860C2×C4—362no—
861C2×C4—362no—
862C2×C4C22×D3211yescharacteristic
863C8—61no—
864C8—61no—
865C8—92no—
866C8#381112yescomplemented
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—62no—
871C2×C3—82no—
872C2×C3—82no—
873C2×C3—81no—
874C2×C3—81no—
875C2×C3—81no—
876C2×C3—81no—
877C2×C3—121no—
878C2×C3D3×#12111yescharacteristic
879C2×C3D3×#12111yescharacteristic
880C2×C3C2×#91111yescharacteristic
881C2×C3#576811yescharacteristic
882C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
883C2×C3#577311yescharacteristic
884D3—22no—
885D3—41no—
886D3—62no—
887D3—62no—
888D3—122no—
889D3—242no—
890D3—241no—
891D3—241no—
892C22—32no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—61no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—92no—
905C22—181no—
906C22—181no—
907C22—364no—
908C22—361no—
909C22—361no—
910C22—361no—
911C22—724no—
912C22D32×D411yescharacteristic
913C4—61no—
914C4—61no—
915C4—92no—
916C4—121no—
917C4—121no—
918C4—121no—
919C4—121no—
920C4—361no—
921C4#6431211yescharacteristic
922C4C2×#381111yescharacteristic
923C3—21no—
924C3#8071511yescharacteristic, complemented
925C3#8086411yescharacteristic, complemented
926C2—62no—
927C2—81no—
928C2—81no—
929C2—121no—
930C2—182no—
931C2—721no—
932C2D3×#91111yescharacteristic
933C2#1059472911yescharacteristic
934C2#1059528211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64120C2semidirect
2. #10595306C2semidirect
3. #10595282C2semidirect
4. C2×D3×ΓL(1,𝔽25)C2semidirect
5. C3×#5159C2semidirect
6. C3×#5157C2semidirect
7. #10591462C2semidirect
8. #10591460C2semidirect
9. #10591453C2semidirect
10. #10591449C2semidirect
11. #10591426C2semidirect
12. #10591418C2semidirect
13. #10590838C2semidirect
14. #10590830C2semidirect
15. #10590688C2semidirect
22. C2×C32×D8C22semidirect
23. C2×#3754C22semidirect
24. C2×#3753C22semidirect
26. C2×#3744C22semidirect
30. C3×#938C22semidirect
31. C3×#938C22semidirect
32. C2×C3×ΓL(1,𝔽25)C22semidirect
33. C2×C3×D3×C8C22semidirect
44. #63857C22semidirect
45. #63857C22semidirect
48. C2×#3711C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C3×#832C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#832C22semidirect
55. C3×#818C22semidirect
56. C3×#817C22semidirect
57. #63576C22semidirect
58. #63574C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
61. #63564C22semidirect
62. #63564C22semidirect
74. #5159D3semidirect
75. #5157D3semidirect
129. #3743D4semidirect
166. C2×C3×D8C2×D3semidirect
167. C2×C3×D8C2×D3semidirect
178. #938C2×D3semidirect
179. #938C2×D3semidirect
210. C2×ΓL(1,𝔽25)C2×D3semidirect
212. C2×D3×C8C2×D3semidirect
235. #832C2×D3semidirect
236. #832C2×D3semidirect
237. #832C2×D3semidirect
238. #832C2×D3semidirect
241. #818C2×D3semidirect
242. #817C2×D3semidirect
301. C32×C8C2×D4semidirect
302. C3⋊(C3⋊C8)C2×D4semidirect
479. C2×C3×D3AGL(1,ℤ/8)semidirect
499. C2×D8D32semidirect
658. C3×C8D3×D4semidirect
659. C3×C8D3×D4semidirect
789. C2×D3#911semidirect
814. C32#3055semidirect
866. C8#3811semidirect
924. C3#80715semidirect
925. C3#80864semidirect

Maximal subgroups

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

subgroupindex
C2×#641202
#105953062
#105952822
C2×D3×ΓL(1,𝔽25)2
C3×#51592
C3×#51572
#105914622
#105914602
#105914532
#105914492
#105914262
#105914182
#105908382
#105908302
#105906882
#808643
#807153