Finite Group Databasebeta

← #11884115

Subgroups — #11884115

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic
3#10594915C211yesmaximal, characteristic, complemented
4C2×#63801C211yesmaximal, characteristic, complemented
5C3×#5116C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591190C211yesmaximal, characteristic, complemented
8#10591183C211yesmaximal, characteristic, complemented
9#10590970C211yesmaximal, characteristic, complemented
10#10590951C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590838C211yesmaximal, characteristic, complemented
13#10590813C211yesmaximal, characteristic, complemented
14#10590773C211yesmaximal, characteristic, complemented
15#10590760C211yesmaximal, characteristic, complemented
16#80771—31nomaximal
17#79495—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C22×C32×C8C2211yescharacteristic
23C2×#3744—24no—
24C2×#3744C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27C2×#3744C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C2×C3×Dic12C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
33#63982—21no—
34#63981—21no—
35#63974—21no—
36#67⋊Dic3—21no—
37#63910—21no—
38#63909C2211yescharacteristic
39#63897—21no—
40#63896—21no—
41#63894C2211yescharacteristic
42#63866C2211yescharacteristic, complemented
43#63864C2211yescharacteristic
44#63857C2211yescharacteristic, complemented
45#63844C2211yescharacteristic, complemented
46#63840—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic
51#63801—24no—
52C3×#830C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C3×#818C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63564C2211yescharacteristic
63C2×#918—31no—
64C2×#909—31no—
65C22×#204—31no—
66C22×#204—31no—
67C22×#204—61no—
68#5632—31no—
69#5630—31no—
70#5550—31no—
71D4×Dic6—31no—
72C3×#467—31no—
73C3×#435—31no—
74#5190—31no—
75#5134—31no—
76#5116D311yescharacteristic, complemented
77#5111D311yescharacteristic, complemented
78#5050—31no—
79#5046—31no—
80#4889—31no—
81#4886—31no—
82#4845—31no—
83#4841—31no—
84#4818—31no—
85#4808—31no—
86#4806—31no—
87#4798—31no—
88#4739—31no—
89#4738—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4710—31no—
94C23×C3⋊D3—21no—
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×#634—22no—
103C2×#634—21no—
104C2×#634—41no—
105C2×#634C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×C3×#67D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3799—22no—
118#3799—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8—22no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124#3744—22no—
125#3744—22no—
126#3744—22no—
127#3744D414yescomplemented
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—22no—
141C3×ΓL(1,𝔽25)—22no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3719—22no—
153#3719—41no—
154#3717—22no—
155#3717—41no—
156#3266—91noSylow
157C2×#239—31no—
158C2×D3×Q8—31no—
159C2×#235—31no—
160C22×D12—31no—
161C22×D12—31no—
162C22×D12—61no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—31no—
166C22×Dic6—61no—
167C2×C3×Q16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—21no—
170C22×C3×C8C2×D311yescharacteristic
171C22×C3×C8C2×D311yescharacteristic
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×C4×D4—31no—
175#947—31no—
176#944—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#215—31no—
180C2×#215—31no—
181#937—61no—
182D4×Dic3—61no—
183#930—31no—
184C4×#67C2×D311yescharacteristic
185#924—31no—
186#924C2×D311yescharacteristic
187#924C2×D311yescharacteristic
188#918—64no—
189#909—64no—
190C2×Dic12—31no—
191C2×Dic12—31no—
192C2×Dic12C2×D311yescharacteristic, complemented
193C2×#204—31no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—61no—
204C2×#204—61no—
205C2×#204—61no—
206C2×#204—61no—
207C2×#204—64no—
208C2×#204—64no—
209C2×#204—68no—
210C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
211#897—31no—
212#896—61no—
213#895—31no—
214#895—61no—
215#894—61no—
216#894—61no—
217#893—31no—
218#888—61no—
219#888—61no—
220#887—31no—
221#884—61no—
222#882—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225D3×C22⋊C4—61no—
226#878—61no—
227#878—61no—
228#878—61no—
229#875—31no—
230C4×D12—31no—
231#869—31no—
232C4×Dic6—31no—
233C3×#107—31no—
234C3×C4⋊C8—31no—
235C3×#103—31no—
236C3×#103—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#830C2×D311yescharacteristic
241#821—31no—
242#821—31no—
243(C2×D3)⋊C8C2×D311yescharacteristic, complemented
244#818C2×D311yescharacteristic, complemented
245#816—31no—
246#816—31no—
247#816C2×D311yescharacteristic, complemented
248#816C2×D311yescharacteristic, complemented
249#815C2×D311yescharacteristic, complemented
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#810—31no—
252#810—31no—
253#809—31no—
254#809—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—42no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)C2×D412yes—
274#634—21no—
275#634—21no—
276#634—21no—
277#634—42no—
278#634C2×D412yes—
279C3×#67—22no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#627—42no—
294#626—42no—
295#626—81no—
296#624—42no—
297#624—81no—
298D3×Dic3—42no—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—91no—
304C22×SD16—91no—
305D4×Q8—91no—
306#546—91no—
307#497—91no—
308#468—91no—
309#467—31no—
310#464—91no—
311#461—91no—
312#452—91no—
313#451—91no—
314#450—91no—
315#448—91no—
316#440—91no—
317#435—31no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—121no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—61no—
329C2×#67—61no—
330C2×#67D1211yescharacteristic
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—121no—
335#239—62no—
336#239—121no—
337D3×Q8—62no—
338D3×Q8—121no—
339#235—62no—
340#235—121no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—64no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—121no—
355C2×D12—121no—
356C2×D12—121no—
357C2×D12—122no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—62no—
371C2×Dic6—62no—
372C2×Dic6—62no—
373C2×Dic6—64no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6—121no—
379C2×Dic6—121no—
380C2×Dic6—121no—
381C2×Dic6—121no—
382C2×Dic6—122no—
383C2×Dic6C22×D311yescharacteristic
384C2×Dic6C22×D311yescharacteristic
385C3×Q16—62no—
386C3×M16—62no—
387C2×C3×C8—24no—
388C2×C3×C8—22no—
389C2×C3×C8—22no—
390C2×C3×C8—21no—
391C2×C3×C8—21no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C3×C4⋊C4—31no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4—61no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C42—31no—
408#217—21no—
409#217—21no—
410#217—61no—
411#217D1211yescharacteristic
412#216—62no—
413#216—121no—
414#215—62no—
415#215—121no—
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—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4D1211yescharacteristic
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—21no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4D1211yescharacteristic
439C4×Dic3—61no—
440C4×Dic3—61no—
441C4×Dic3C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444Dic12—22no—
445Dic12—62no—
446Dic12—121no—
447#204—34no—
448#204—34no—
449#204—64no—
450#204—62no—
451#204—62no—
452#204—62no—
453#204—62no—
454#204—64no—
455#204—64no—
456#204—64no—
457#204—62no—
458#204—62no—
459#204—62no—
460#204—121no—
461ΓL(1,𝔽25)—22no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32#13712yescomplemented
465C22×C32C22×D411yescharacteristic
466C2×C3⋊D3—22no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—84no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C32×C4—21no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3⋊Dic3—22no—
480C3⋊Dic3—41no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—91no—
489C22×Q8—91no—
490C22×Q8—91no—
491C22×D4—91no—
492#137—184no—
493C2×Q16—31no—
494C2×Q16—91no—
495C2×Q16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—184no—
503C2×M16—31no—
504C22×C8D3211yescharacteristic
505C4⋊Q8—91no—
506C4⋊Q8—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—31no—
510C22⋊Q8—31no—
511C22⋊Q8—91no—
512C22⋊Q8—181no—
513C22⋊Q8—181no—
514#121—91no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—31no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—31no—
524#103—31no—
525#103—31no—
526#103—91no—
527#103—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—31no—
532#97—31no—
533C23×C3—21no—
534C23×C3—31no—
535C23×C3C2×D1211yescharacteristic
536C23×C3D3×D411yescharacteristic
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—124no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—242no—
549C22×D3—241no—
550C22×D3—241no—
551C22×D3—242no—
552C22×D3C2×D1211yescharacteristic
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—62no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
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—31no—
568C2×C3×C4—31no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4C2×D1211yescharacteristic
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—22no—
580#67—122no—
581#67—241no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—122no—
593C2×Dic3—122no—
594C2×Dic3—122no—
595C2×Dic3—124no—
596C2×Dic3C2×D1211yescharacteristic
597C2×Dic3C2×D1211yescharacteristic
598C2×Dic3C2×D1211yescharacteristic
599D12—32no—
600D12—32no—
601D12—62no—
602D12—62no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—121no—
610D12—121no—
611D12—122no—
612D12—122no—
613D12—124no—
614D12—122no—
615D12—241no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—241no—
622C4×D3—241no—
623Dic6—21no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—32no—
628Dic6—32no—
629Dic6—62no—
630Dic6—61no—
631Dic6—61no—
632Dic6—62no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—121no—
638Dic6—121no—
639Dic6—122no—
640Dic6—122no—
641Dic6—122no—
642Dic6—122no—
643Dic6—124no—
644C3×C8—22no—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8—22no—
648C3×C8—61no—
649C3×C8—61no—
650C3×C8D3×D412yes—
651C3×C8D3×D412yes—
652C3⋊C8—21no—
653C3⋊C8—21no—
654C2×C32—22no—
655C2×C32D4211yescharacteristic
656C2×C32C2×#13711yescharacteristic
657C2×C32#57711yescharacteristic
658C3⋊D3—42no—
659C3⋊D3—81no—
660C3×D3—41no—
661C24—181no—
662#41—182no—
663#41—361no—
664C2×Q8—31no—
665C2×Q8—31no—
666C2×Q8—91no—
667C2×Q8—91no—
668C2×Q8—182no—
669C2×Q8—181no—
670C2×Q8—182no—
671C2×Q8—181no—
672C2×Q8—361no—
673C2×Q8—361no—
674C2×D4—31no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—182no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—361no—
682C22×C4—31no—
683C22×C4—181no—
684C22×C4—181no—
685C22×C4—181no—
686C22×C4—181no—
687C22×C4C2×D3211yescharacteristic
688Q16—62no—
689Q16—182no—
690Q16—361no—
691SD16—94no—
692SD16—182no—
693SD16—182no—
694SD16—182no—
695SD16—182no—
696SD16—361no—
697M16—62no—
698C2×C8—22no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8C2×D3211yescharacteristic
702C2×C8C2×D3211yescharacteristic
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C4⋊C4—181no—
711C4⋊C4—181no—
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—31no—
722C42—181no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—22no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3#90912yescomplemented
735C22×C3#91812yescomplemented
736C22×C3C22×D1211yescharacteristic
737C22×C3C2×D3×D411yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—122no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—122no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—241no—
756C2×D3—241no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—244no—
760C2×D3—244no—
761C2×D3—248no—
762C3×C4—22no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4C2×D3×D411yescharacteristic
775C3×C4C2×D3×D411yescharacteristic
776C3×C4#100911yescharacteristic
777C3×C4#100911yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—21no—
781Dic3—41no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—62no—
786Dic3—62no—
787Dic3—122no—
788Dic3—122no—
789Dic3—121no—
790Dic3—121no—
791C32#326611yescharacteristic, complemented, Sylow
792C23—31no—
793C23—181no—
794C23—181no—
795C23—362no—
796C23—362no—
797C23—721no—
798C23D3×D1211yescharacteristic
799Q8—61no—
800Q8—61no—
801Q8—61no—
802Q8—61no—
803Q8—92no—
804Q8—181no—
805Q8—181no—
806Q8—181no—
807Q8—362no—
808Q8—362no—
809D4—62no—
810D4—92no—
811D4—181no—
812D4—181no—
813D4—181no—
814D4—362no—
815D4—362no—
816D4—721no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—181no—
829C2×C4—181no—
830C2×C4—362no—
831C2×C4—362no—
832C2×C4—362no—
833C2×C4—721no—
834C2×C4D3×D1211yescharacteristic
835C2×C4C22×D3211yescharacteristic
836C8—21no—
837C8—61no—
838C8—61no—
839C8#381112yes—
840C2×C3—24no—
841C2×C3—22no—
842C2×C3—22no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—121no—
847C2×C3D4×D1211yescharacteristic
848C2×C3#560911yescharacteristic
849C2×C3C2×#90911yescharacteristic
850C2×C3#575111yescharacteristic
851C2×C3C2×#91811yescharacteristic
852C2×C3#577011yescharacteristic
853D3—41no—
854D3—122no—
855D3—122no—
856D3—242no—
857D3—242no—
858D3—241no—
859D3—241no—
860C22—21no—
861C22—21no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—182no—
866C22—361no—
867C22—361no—
868C22—361no—
869C22—361no—
870C22—361no—
871C22—724no—
872C22#6380112yescomplemented
873C22C2×D3×D1211yescharacteristic
874C4—21no—
875C4—61no—
876C4—61no—
877C4—61no—
878C4—121no—
879C4—121no—
880C4—121no—
881C4—121no—
882C4—182no—
883C4—361no—
884C4#6430811yescharacteristic
885C4C2×#381111yescharacteristic
886C3—21no—
887C3#7949511yescharacteristic, complemented
888C3#8077111yescharacteristic, complemented
889C2—22no—
890C2—121no—
891C2—362no—
892C2—721no—
893C2#1059467911yescharacteristic
894C2C2×#6380111yescharacteristic
895C2#1059507411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC22×C8D32
hypocenterC32#3266
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×#3744C2semidirect
3. #10594915C2semidirect
4. C2×#63801C2semidirect
5. C3×#5116C2semidirect
6. C3×#5111C2semidirect
7. #10591190C2semidirect
8. #10591183C2semidirect
9. #10590970C2semidirect
10. #10590951C2semidirect
11. #10590899C2semidirect
12. #10590838C2semidirect
13. #10590813C2semidirect
14. #10590773C2semidirect
15. #10590760C2semidirect
21. C2×D3×Dic6C22semidirect
31. C2×C3×Dic12C22semidirect
32. C2×C3×ΓL(1,𝔽25)C22semidirect
42. #63866C22semidirect
44. #63857C22semidirect
45. #63844C22semidirect
47. C2×#3719C22semidirect
48. C2×#3719C22semidirect
53. C3×(C2×D3)⋊C8C22semidirect
54. C3×#818C22semidirect
55. C3×#816C22semidirect
56. C3×#816C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
76. #5116D3semidirect
77. #5111D3semidirect
127. #3744D4semidirect
192. C2×Dic12C2×D3semidirect
210. C2×ΓL(1,𝔽25)C2×D3semidirect
243. (C2×D3)⋊C8C2×D3semidirect
244. #818C2×D3semidirect
247. #816C2×D3semidirect
248. #816C2×D3semidirect
249. #815C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
464. C22×C32#137semidirect
734. C22×C3#909semidirect
735. C22×C3#918semidirect
791. C32#3266semidirect
872. C22#63801semidirect
887. C3#79495semidirect
888. C3#80771semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
#105950182
#105949152
C2×#638012
C3×#51162
C3×#51112
#105911902
#105911832
#105909702
#105909512
#105908992
#105908382
#105908132
#105907732
#105907602
#807713
#794953