Finite Group Databasebeta

← #11867153

Subgroups — #11867153

Order 1152.

1163 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
1C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
2D3×#930C211yesmaximal, characteristic, complemented
3#10595005C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592814C211yesmaximal, characteristic, complemented
6C3×#5114C211yesmaximal, characteristic, complemented
7#10591177C211yesmaximal, characteristic, complemented
8#10591164C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590850C211yesmaximal, characteristic, complemented
11#10590835C211yesmaximal, characteristic, complemented
12#10590833C211yesmaximal, characteristic, complemented
13#10590827C211yesmaximal, characteristic, complemented
14#10590681C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#83772—31nomaximal
17#80657—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24#64139C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C2×C3×ΓL(1,𝔽25)—24no—
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
35#63978—21no—
36#63977—21no—
37#63952—21no—
38D3×(C2×D3)⋊C4—21no—
39#63909C2211yescharacteristic
40#63909C2211yescharacteristic, complemented
41#63908C2211yescharacteristic
42#63906—21no—
43#63904—21no—
44D3×C4⋊Dic3C2211yescharacteristic
45#63856C2211yescharacteristic, complemented
46#63850—21no—
47#63841C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50#63794—24no—
51#63648C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63645C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#817C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C22×C3×M16—31no—
64#5791—31no—
65C2×#930—31no—
66C2×#914—31no—
67C2×#908—31no—
68C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
69#5627—31no—
70D3×#121—31no—
71C3×#465—31no—
72#5174—31no—
73#5135—31no—
74#5135—31no—
75#5134—31no—
76#5134—31no—
77#5133—31no—
78#5131—31no—
79#5121—31no—
80#5115—31no—
81#5115—31no—
82#5115—31no—
83#5115—61no—
84#5114—31no—
85#5114D311yescharacteristic, complemented
86#5048—31no—
87#5038—31no—
88#4865—31no—
89#4861—31no—
90#4812—31no—
91#4803—31no—
92#4782—31no—
93#4770—31no—
94C23×C3×D3D411yescharacteristic
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111D3×#67—44no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—22no—
121#3799—22no—
122#3799—22no—
123C2×C32×C8—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126#3752—21no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3745—22no—
131C3×#217—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C2×C3×C3⋊C8—22no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×ΓL(1,𝔽25)—22no—
141C3×ΓL(1,𝔽25)—22no—
142C3×ΓL(1,𝔽25)—22no—
143C3×ΓL(1,𝔽25)D414yescomplemented
144#3724—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3717—22no—
153#3714—22no—
154#3055—91noSylow
155C23×C3×C4—31no—
156C22×#67—61no—
157C2×#239—31no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C2×#235—31no—
161C22×D12—31no—
162C22×C4×D3C2×D311yescharacteristic
163C2×C3×SD16—31no—
164C2×C3×M16—31no—
165C2×C3×M16—31no—
166C2×C3×M16—31no—
167C2×C3×M16—31no—
168C2×C3×M16—64no—
169C22×C3×C8—21no—
170C22×C3×C8—31no—
171C22×C3×C8C2×D311yescharacteristic, complemented
172C22×C3×C8C2×D311yescharacteristic, complemented
173C3×C22⋊Q8—31no—
174C3×#121—31no—
175#953—61no—
176#946—31no—
177C2×#215—31no—
178#939—61no—
179#938—31no—
180C2×#213—31no—
181#930—31no—
182#930—31no—
183#930—31no—
184#930—31no—
185#930—31no—
186#930—31no—
187#930—31no—
188#930—61no—
189#930—61no—
190#930—61no—
191#930—61no—
192#930C2×D311yescharacteristic
193#929—61no—
194C4×#67—61no—
195C4×#67—61no—
196C2×(C2×D3)⋊C4—61no—
197#926—31no—
198C2×C4⋊Dic3—31no—
199#924—31no—
200#924C2×D311yescharacteristic, complemented
201C22×C3⋊C8C2×D311yescharacteristic, complemented
202#914—64no—
203#908—64no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—61no—
208C2×#204—31no—
209C2×#204C2×D311yescharacteristic, complemented
210C2×ΓL(1,𝔽25)—24no—
211C2×ΓL(1,𝔽25)C2×D311yescharacteristic
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic
213C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
214C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
215#895—31no—
216#895—31no—
217#894—61no—
218#893—61no—
219#892—31no—
220D3×C4⋊C4—31no—
221#884—61no—
222#882—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225C3×#106—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#832—31no—
230#821—31no—
231#821—31no—
232#821—31no—
233#821—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—61no—
238#821—61no—
239#821C2×D311yescharacteristic, complemented
240#818—31no—
241#818—31no—
242#818—31no—
243#818—61no—
244#817—31no—
245#817C2×D311yescharacteristic, complemented
246#816—31no—
247#816C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250#808—31no—
251#807—31no—
252C23×C32C2×D411yescharacteristic
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3×D3—22no—
256C22×C3×D3—22no—
257C22×C3×D3—21no—
258C22×C3×D3—41no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269#638—42no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C3×#67—42no—
277C2×C3×Dic3—22no—
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—22no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—22no—
289C3×C4×D3C2×D412yes—
290C3×C4×D3#4112yes—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#626—42no—
294#626—42no—
295#626—42no—
296#626—42no—
297#625—42no—
298#624—42no—
299D3×Dic3—42no—
300C32×C8—21no—
301C32×C8C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—31no—
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—91no—
318#417—91no—
319C24×C3—31no—
320C23×D3—61no—
321C23×D3—61no—
322C23×D3D1211yescharacteristic
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—61no—
338C2×#67—61no—
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—121no—
348C2×#67—121no—
349C2×#67—124no—
350C22×Dic3—61no—
351C22×Dic3D1211yescharacteristic
352#239—62no—
353#239—62no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—124no—
357#235—62no—
358#235—62no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12C22×D311yescharacteristic
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3D1211yescharacteristic
378C2×C4×D3D1211yescharacteristic
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×SD16—62no—
383C3×M16—34no—
384C3×M16—62no—
385C3×M16—62no—
386C3×M16—62no—
387C2×C3×C8—22no—
388C2×C3×C8—22no—
389C2×C3×C8—21no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—42no—
394C2×C3×C8—62no—
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404#217—21no—
405#217—61no—
406#217—61no—
407#217—61no—
408#215—62no—
409#213—62no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
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—121no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3C22×D311yescharacteristic
432C4⋊Dic3C22×D311yescharacteristic
433Dic3⋊C4—21no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437C4×Dic3—61no—
438C4×Dic3—61no—
439C2×C3⋊C8—22no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—62no—
443D24—62no—
444D24—62no—
445D24—122no—
446#204—22no—
447#204—62no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)—22no—
450ΓL(1,𝔽25)—22no—
451ΓL(1,𝔽25)#6714yescomplemented
452C22×C32—21no—
453C22×C32—21no—
454C22×C32AGL(1,ℤ/8)12yescomplemented
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
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—21no—
467C2×C3×D3—44no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3#12112yes—
472D32—84no—
473C32×C4—21no—
474C32×C4C22×D411yescharacteristic
475C32×C4C2×#4111yescharacteristic
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—91no—
484C22×D4—91no—
485C22×D4—181no—
486C23×C4—31no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—31no—
495C2×M16—31no—
496C2×M16—64no—
497C22×C8—31no—
498C22×C8D3211yescharacteristic, complemented
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—91no—
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—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3—61no—
534C23×C3—121no—
535C23×C3C2×D1211yescharacteristic
536C23×C3D3×D411yescharacteristic
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—21no—
540C22×D3—41no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
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×D3C2×D1211yescharacteristic
554C22×D3C2×D1211yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—31no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4C2×D1211yescharacteristic
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
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—122no—
593#67—122no—
594#67—122no—
595#67—242no—
596#67—242no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—122no—
608C2×Dic3C2×D1211yescharacteristic
609C2×Dic3C2×D1211yescharacteristic
610D12—21no—
611D12—21no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—121no—
621D12—121no—
622D12—121no—
623D12—121no—
624D12—122no—
625D12—122no—
626D12—122no—
627D12—122no—
628C4×D3—22no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—22no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3#23512yes—
636C4×D3C2×#6712yes—
637Dic6—21no—
638Dic6—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—22no—
642C3×C8—32no—
643C3×C8—41no—
644C3×C8—61no—
645C3×C8D3×D412yescomplemented
646C3×C8C2×#6712yescomplemented
647C3⋊C8—21no—
648C3⋊C8C2×#6712yescomplemented
649C2×C32—22no—
650C2×C32C2×#12111yescharacteristic
651C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
652C2×C32#57511yescharacteristic
653C3⋊D3—81no—
654C3⋊D3—81no—
655C3×D3—22no—
656C3×D3—41no—
657C3×D3—81no—
658C24—31no—
659C24—181no—
660#41—182no—
661#41—182no—
662C2×Q8—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4—182no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4—364no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—181no—
685C22×C4—181no—
686C22×C4C2×D3211yescharacteristic
687SD16—62no—
688SD16—182no—
689D8—182no—
690D8—182no—
691M16—34no—
692M16—62no—
693M16—62no—
694M16—62no—
695C2×C8—22no—
696C2×C8—31no—
697C2×C8—31no—
698C2×C8—62no—
699C2×C8C2×D3211yescharacteristic
700C2×C8C2×D3211yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—91no—
705C4⋊C4—91no—
706C4⋊C4—181no—
707C4⋊C4—181no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—181no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—22no—
724C22×C3—32no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—124no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3#90812yescomplemented
737C22×C3#91412yescomplemented
738C22×C3C22×D1211yescharacteristic
739C22×C3C2×D3×D411yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—44no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—241no—
762C2×D3—241no—
763C2×D3—241no—
764C2×D3—241no—
765C2×D3—241no—
766C2×D3—241no—
767C2×D3—244no—
768C2×D3—244no—
769C2×D3#93012yes—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—32no—
775C3×C4—41no—
776C3×C4—61no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C2×#23511yescharacteristic
781C3×C4C2×D3×D411yescharacteristic
782C3×C4D3×#4111yescharacteristic
783C3×C4C22×#6711yescharacteristic
784Dic3—21no—
785Dic3—41no—
786Dic3—41no—
787Dic3—41no—
788Dic3—121no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—241no—
793Dic3—241no—
794Dic3#93012yes—
795C32#305511yescharacteristic, complemented, Sylow
796C23—31no—
797C23—31no—
798C23—62no—
799C23—62no—
800C23—61no—
801C23—121no—
802C23—181no—
803C23—181no—
804C23—362no—
805C23—362no—
806C23—362no—
807C23D3×D1211yescharacteristic
808Q8—61no—
809Q8—61no—
810D4—61no—
811D4—61no—
812D4—122no—
813D4—181no—
814D4—181no—
815D4—181no—
816D4—181no—
817D4—362no—
818D4—362no—
819D4—362no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—31no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—362no—
841C2×C4—362no—
842C2×C4D3×D1211yescharacteristic
843C2×C4C22×D3211yescharacteristic
844C8—21no—
845C8—32no—
846C8—61no—
847C8D3×#6712yescomplemented
848C2×C3—22no—
849C2×C3—22no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—42no—
854C2×C3—62no—
855C2×C3—121no—
856C2×C3—241no—
857C2×C3D3×#12111yescharacteristic
858C2×C3C2×#90811yescharacteristic
859C2×C3#574811yescharacteristic
860C2×C3C2×#91411yescharacteristic
861C2×C3#576811yescharacteristic
862C2×C3C2×#93011yescharacteristic
863D3—22no—
864D3—41no—
865D3—81no—
866D3—241no—
867D3—241no—
868D3—241no—
869D3—241no—
870D3—481no—
871D3—481no—
872C22—21no—
873C22—21no—
874C22—32no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—61no—
880C22—124no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22—361no—
888C22—361no—
889C22—361no—
890C22—724no—
891C22#6379412yescomplemented
892C22C2×D3×D1211yescharacteristic
893C4—21no—
894C4—32no—
895C4—61no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—361no—
900C4—361no—
901C4D3×#23511yescharacteristic
902C4C2×D3×#6711yescharacteristic
903C3—21no—
904C3#8065711yescharacteristic, complemented
905C3#8377211yescharacteristic, complemented
906C2—22no—
907C2—62no—
908C2—121no—
909C2—241no—
910C2—721no—
911C2—721no—
912C2C2×#6379411yescharacteristic
913C2#1059467611yescharacteristic
914C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×ΓL(1,𝔽25)C2semidirect
2. D3×#930C2semidirect
3. #10595005C2semidirect
4. C2×#63794C2semidirect
5. #10592814C2semidirect
6. C3×#5114C2semidirect
7. #10591177C2semidirect
8. #10591164C2semidirect
9. #10590939C2semidirect
10. #10590850C2semidirect
11. #10590835C2semidirect
12. #10590833C2semidirect
13. #10590827C2semidirect
14. #10590681C2semidirect
15. #10590671C2semidirect
22. C22×C32×C8C22semidirect
24. #64139C22semidirect
25. C2×#3745C22semidirect
27. C3×#924C22semidirect
28. C22×C3×C3⋊C8C22semidirect
29. C2×C3×#204C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
34. C2×C3×ΓL(1,𝔽25)C22semidirect
40. #63909C22semidirect
45. #63856C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
51. #63648C22semidirect
52. #63648C22semidirect
53. #63645C22semidirect
54. C3×#821C22semidirect
55. C3×#817C22semidirect
56. C3×#816C22semidirect
57. #63575C22semidirect
58. #63573C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
68. C22×ΓL(1,𝔽25)D3semidirect
85. #5114D3semidirect
143. C3×ΓL(1,𝔽25)D4semidirect
171. C22×C3×C8C2×D3semidirect
172. C22×C3×C8C2×D3semidirect
200. #924C2×D3semidirect
201. C22×C3⋊C8C2×D3semidirect
209. C2×#204C2×D3semidirect
213. C2×ΓL(1,𝔽25)C2×D3semidirect
214. C2×ΓL(1,𝔽25)C2×D3semidirect
239. #821C2×D3semidirect
245. #817C2×D3semidirect
247. #816C2×D3semidirect
301. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
451. ΓL(1,𝔽25)#67semidirect
454. C22×C32AGL(1,ℤ/8)semidirect
498. C22×C8D32semidirect
645. C3×C8D3×D4semidirect
646. C3×C8C2×#67semidirect
648. C3⋊C8C2×#67semidirect
736. C22×C3#908semidirect
737. C22×C3#914semidirect
795. C32#3055semidirect
847. C8D3×#67semidirect
891. C22#63794semidirect
904. C3#80657semidirect
905. C3#83772semidirect

Maximal subgroups

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

subgroupindex
C22×C3×ΓL(1,𝔽25)2
D3×#9302
#105950052
C2×#637942
#105928142
C3×#51142
#105911772
#105911642
#105909392
#105908502
#105908352
#105908332
#105908272
#105906812
#105906712
#837723
#806573