Finite Group Databasebeta

← #11857954

Subgroups — #11857954

Order 1152.

1639 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3D3×#892C211yesmaximal, characteristic, complemented
4#10592469C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6C3×#4771C211yesmaximal, characteristic, complemented
7#10591426C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9#10591414C211yesmaximal, characteristic, complemented
10#10590691C211yesmaximal, characteristic, complemented
11#10590690C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590610C211yesmaximal, characteristic, complemented
14#10590609C211yesmaximal, characteristic, complemented
15#10590602C211yesmaximal, characteristic, complemented
16#78881—31nomaximal
17#78830—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×#3811—21no—
22C22×#624—21no—
23C2×#3804—21no—
24C2×#3804—21no—
25#64312—24no—
26#64312C418yescomplemented
27C2×C4×D32C2211yescharacteristic
28C2×#3799C2211yescharacteristic
29C2×#3799C2211yescharacteristic
30C2×#3797C2211yescharacteristic
31C2×#3743C2211yescharacteristic
32#64101C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34C2×C3×D3×C8C2211yescharacteristic, complemented
35C3×#892C2211yescharacteristic, complemented
36C3×D3×C4⋊C4C2211yescharacteristic, complemented
37D3×(C2×D3)⋊C4—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63878—21no—
40C4×D3×Dic3—21no—
41#63849C2211yescharacteristic
42#63841C2211yescharacteristic, complemented
43#63836—21no—
44C2×#3712C2211yescharacteristic
45C2×#3711C2211yescharacteristic, complemented
46C2×D3×C3⋊C8C2211yescharacteristic, complemented
47D3×ΓL(1,𝔽25)—24no—
48C32×#102C2211yescharacteristic, complemented
49#63659C2211yescharacteristic, complemented
50#63648C2211yescharacteristic, complemented
51#63636C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63564C2211yescharacteristic, complemented
64C2×D3×#41—31no—
65C2×D3×#41—31no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68D3×#117—31no—
69C2×#892—31no—
70C3×#417—31no—
71C3×#416—31no—
72#5233—31no—
73#5232—31no—
74#5133—31no—
75#5113—31no—
76#5002—31no—
77#4966—31no—
78#4804—31no—
79#4804—31no—
80#4803—31no—
81#4803—31no—
82#4802—31no—
83#4802—31no—
84#4802—31no—
85#4802—31no—
86#4772—31no—
87#4772D311yescharacteristic, complemented
88#4771—31no—
89#4771D311yescharacteristic, complemented
90#4770—31no—
91#4770—31no—
92#4770—31no—
93#4770—31no—
94#4770—61no—
95C23×C3⋊D3—21no—
96C22×D32D411yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99D4×C3⋊D3—22no—
100D4×C3⋊D3C2×C414yescomplemented
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C3×#237—22no—
108C3×#237—22no—
109C3×#237C2×C414yes—
110C3×#237C2×C414yescomplemented
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116#3811—28no—
117C2×#627—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#624—21no—
121C2×#624—21no—
122C2×#624—21no—
123C2×#624—28no—
124C2×#624D411yescharacteristic
125#3804—28no—
126#3804—28no—
127C2×D3×Dic3—21no—
128C2×D3×Dic3D411yescharacteristic
129C2×D3×Dic3D411yescharacteristic
130C4×D32C2×C414yes—
131C4×D32D414yes—
132#3799—22no—
133#3799—22no—
134#3799C2×C414yes—
135#3799C2×C414yescomplemented
136#3797—22no—
137#3797C2×C414yescomplemented
138C2×C32×C8C2311yescharacteristic
139C32×C4⋊C4C2311yescharacteristic
140#3752—21no—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4×C3⋊Dic3—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144#3743—22no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×ΓL(1,𝔽25)—22no—
153C3×D3×C8—22no—
154Dic3⋊Dic3—21no—
155#3722—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3712—22no—
160#3711—22no—
161D3×C3⋊C8—22no—
162#2896—91noSylow
163C2×C3×#41—31no—
164C2×C3×#41—31no—
165D3×#41—38no—
166D3×#41—38no—
167D3×#41—64no—
168D3×#41—64no—
169C2×#239—31no—
170C2×#239—31no—
171C2×D3×Q8—31no—
172C2×D3×Q8—31no—
173C2×#237—61no—
174C2×#237—61no—
175C2×#237C2×D311yescharacteristic
176C2×#237C2×D311yescharacteristic
177C2×D3×D4—31no—
178C2×D3×D4—31no—
179C2×D3×D4—61no—
180C2×D3×D4—61no—
181C2×D3×D4—61no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—61no—
185C2×#235—61no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—61no—
189C22×C4×D3—61no—
190C2×C3×M16—31no—
191C22×C3×C8—31no—
192C3×#117—31no—
193C2×C3×C4⋊C4—31no—
194C2×(C2×D3)⋊C4—61no—
195#926—31no—
196C2×C4⋊Dic3—31no—
197C2×C4×Dic3—61no—
198C2×#208—31no—
199C22×C3⋊C8—31no—
200D3×M16—64no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—61no—
207C2×ΓL(1,𝔽25)—64no—
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic, complemented
211#892—31no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892—31no—
216#892—61no—
217#892—61no—
218#892—61no—
219#892C2×D311yescharacteristic, complemented
220D3×C4⋊C4—31no—
221D3×C4⋊C4C2×D311yescharacteristic, complemented
222D3×C22⋊C4—61no—
223#877—61no—
224#872—61no—
225C42×D3—61no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#102—21no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235#835—31no—
236#835—31no—
237#835—31no—
238#835—31no—
239#832—31no—
240#832—31no—
241#832—61no—
242#832C2×D311yescharacteristic, complemented
243#832C2×D311yescharacteristic, complemented
244#821—31no—
245#821—31no—
246#821—31no—
247#821—31no—
248#821—61no—
249#816—31no—
250#816—31no—
251#816C2×D311yescharacteristic, complemented
252#816C2×D311yescharacteristic, complemented
253#810—31no—
254#810—31no—
255#810C2×D311yescharacteristic, complemented
256#810C2×D311yescharacteristic, complemented
257#809—31no—
258#809—31no—
259#809—31no—
260#809—31no—
261#809—61no—
262C23×C32—21no—
263C22×C3⋊D3—21no—
264C22×C3⋊D3—24no—
265C22×C3⋊D3—42no—
266C22×C3⋊D3—42no—
267C22×C3⋊D3C2×D411yescharacteristic
268C22×C3×D3C2×D411yescharacteristic
269C22×C3×D3C2×D411yescharacteristic
270C2×D32—41no—
271C2×D32—41no—
272C2×D32C22⋊C414yes—
273C32×D4—21no—
274C32×D4C22×C412yes—
275C2×C32×C4—21no—
276C2×C32×C4C2411yescharacteristic
277#638—24no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3C2×D411yescharacteristic
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)C22×C412yes—
282C4×C3⋊D3C22×C412yes—
283C4×C3⋊D3C2×D412yes—
284C3×#67—24no—
285C3×#67—24no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—24no—
289C2×C3×Dic3—24no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C3×C4×D3—42no—
295C3×C4×D3C22×C412yes—
296C3×C4×D3C22×C412yes—
297C3×C4×D3C2×D412yes—
298C3×C4×D3C2×D412yes—
299C3×Dic6—21no—
300C3×Dic6—21no—
301C3×Dic6C22×C412yes—
302C3×Dic6C22×C412yes—
303#627—24no—
304#626—24no—
305#626—24no—
306#624—24no—
307#624—24no—
308#624—24no—
309#624C22⋊C414yes—
310D3×Dic3—42no—
311D3×Dic3C22⋊C414yes—
312D3×Dic3C22⋊C414yes—
313C32×C8—21no—
314C3⋊(C3⋊C8)—21no—
315C3×C3⋊C8—21no—
316C3×C3⋊C8—21no—
317C22×#41—91no—
318C22×M16—91no—
319C2×#117—91no—
320#419—91no—
321#419—91no—
322#418—91no—
323#418—91no—
324#417—31no—
325#417—91no—
326#417—91no—
327#417—91no—
328#416—31no—
329#416—91no—
330#416—91no—
331#416—91no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—61no—
335C23×D3—61no—
336C23×D3—121no—
337C3×#41—34no—
338C3×#41—34no—
339C3×#41—62no—
340C3×#41—62no—
341C2×C3×Q8—31no—
342C2×C3×Q8—31no—
343C2×C3×D4—21no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C22×D311yescharacteristic
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—121no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—61no—
365#239—34no—
366#239—34no—
367#239—62no—
368#239—62no—
369D3×Q8—34no—
370D3×Q8—34no—
371D3×Q8—62no—
372D3×Q8—62no—
373#237—22no—
374#237—22no—
375#237—68no—
376#237—68no—
377#237C4×D314yes—
378#237C4×D314yescomplemented
379D3×D4—34no—
380D3×D4—34no—
381D3×D4—64no—
382D3×D4—62no—
383D3×D4—62no—
384D3×D4—68no—
385D3×D4—68no—
386D3×D4—122no—
387#235—34no—
388#235—34no—
389#235—62no—
390#235—62no—
391#235—68no—
392#235—68no—
393C2×D12—31no—
394C2×D12—31no—
395C2×D12—61no—
396C2×D12—61no—
397C2×D12—61no—
398C2×C4×D3—21no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—61no—
410C2×C4×D3—68no—
411C2×C4×D3—68no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3—61no—
416C2×C4×D3—61no—
417C2×C4×D3—61no—
418C2×C4×D3—61no—
419C2×C4×D3C22×D311yescharacteristic
420C2×C4×D3C22×D311yescharacteristic
421C2×Dic6—61no—
422C2×Dic6—61no—
423C2×Dic6C22×D311yescharacteristic
424C2×Dic6C22×D311yescharacteristic
425C3×M16—62no—
426C2×C3×C8—21no—
427C2×C3×C8—31no—
428C2×C3×C8—31no—
429C2×C3×C8—62no—
430C2×C3×C8C22×D311yescharacteristic
431C2×C3×C8C22×D311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—61no—
436C3×C4⋊C4C22×D311yescharacteristic
437C3×C4⋊C4C22×D311yescharacteristic
438C3×C22⋊C4—61no—
439C3×C42—61no—
440#217—61no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—121no—
448C4⋊Dic3—31no—
449C4⋊Dic3—31no—
450C4⋊Dic3—61no—
451C4⋊Dic3—61no—
452C4⋊Dic3C22×D311yescharacteristic
453C4⋊Dic3C22×D311yescharacteristic
454Dic3⋊C4—21no—
455Dic3⋊C4—61no—
456C4×Dic3—21no—
457C4×Dic3—61no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—61no—
461C4×Dic3—61no—
462C4×Dic3—61no—
463C4×Dic3—121no—
464#208—62no—
465C2×C3⋊C8—31no—
466C2×C3⋊C8—31no—
467C2×C3⋊C8—61no—
468C2×C3⋊C8—62no—
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471ΓL(1,𝔽25)—22no—
472ΓL(1,𝔽25)—62no—
473ΓL(1,𝔽25)—62no—
474ΓL(1,𝔽25)—62no—
475ΓL(1,𝔽25)—62no—
476ΓL(1,𝔽25)—62no—
477ΓL(1,𝔽25)—122no—
478D3×C8—22no—
479D3×C8—62no—
480C22×C32—22no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32C22×D411yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—48no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—41no—
490C2×C3⋊D3C2×C22⋊C412yes—
491C2×C3×D3—21no—
492C2×C3×D3—21no—
493C2×C3×D3—21no—
494C2×C3×D3—21no—
495C2×C3×D3C2×C22⋊C412yes—
496C2×C3×D3C2×C22⋊C412yes—
497D32—44no—
498C32×C4—41no—
499C32×C4C23×C411yescharacteristic
500C32×C4C22×D411yescharacteristic
501C3⋊Dic3—41no—
502C3⋊Dic3C2×C22⋊C412yes—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3C2×C22⋊C412yes—
508C3×Dic3C2×C22⋊C412yes—
509C2×#41—31no—
510C2×#41—31no—
511C2×#41—91no—
512C2×#41—91no—
513C2×#41—98no—
514C2×#41—181no—
515C2×#41—181no—
516C2×#41—184no—
517C22×Q8—91no—
518C22×D4—91no—
519C22×D4—181no—
520C23×C4—91no—
521C23×C4—181no—
522C2×M16—31no—
523C2×M16—91no—
524C2×M16—91no—
525C2×M16—91no—
526C2×M16—184no—
527C22×C8—31no—
528C22×C8—91no—
529#117—31no—
530#117—91no—
531#117—91no—
532#117—91no—
533#117—181no—
534#117—181no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—91no—
537C2×C22⋊C4—181no—
538C2×C42—181no—
539#103—31no—
540#103—31no—
541#103—31no—
542#103—31no—
543#103—91no—
544#103—91no—
545#103—91no—
546#103—91no—
547#102—31no—
548#102—31no—
549#102—91no—
550#102—91no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102D3211yescharacteristic, complemented
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—31no—
558C23×C3—31no—
559C23×C3—41no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—34no—
563C22×D3—34no—
564C22×D3—61no—
565C22×D3—64no—
566C22×D3—64no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—124no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3—242no—
580C22×D3—242no—
581C22×D3D3×D411yescharacteristic
582C22×D3D3×D411yescharacteristic
583C3×Q8—32no—
584C3×Q8—32no—
585C3×Q8—61no—
586C3×Q8—61no—
587C3×D4—21no—
588C3×D4—21no—
589C3×D4—22no—
590C3×D4—41no—
591C3×D4—64no—
592C3×D4—64no—
593C3×D4C2×C4×D312yes—
594C3×D4C2×C4×D312yes—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—41no—
605C2×C3×C4—64no—
606C2×C3×C4—64no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—122no—
612C2×C3×C4C23×D311yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614#67—24no—
615#67—24no—
616#67—64no—
617#67—64no—
618#67—64no—
619#67—64no—
620#67—124no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—24no—
624C2×Dic3—24no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—34no—
630C2×Dic3—34no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—121no—
635C2×Dic3—122no—
636C2×Dic3D3×D411yescharacteristic
637C2×Dic3D3×D411yescharacteristic
638D12—32no—
639D12—32no—
640D12—62no—
641D12—64no—
642D12—64no—
643D12—61no—
644D12—61no—
645D12—121no—
646C4×D3—34no—
647C4×D3—34no—
648C4×D3—32no—
649C4×D3—32no—
650C4×D3—32no—
651C4×D3—32no—
652C4×D3—34no—
653C4×D3—34no—
654C4×D3—42no—
655C4×D3—62no—
656C4×D3—62no—
657C4×D3—64no—
658C4×D3—64no—
659C4×D3—64no—
660C4×D3—64no—
661C4×D3—64no—
662C4×D3—64no—
663C4×D3—122no—
664C4×D3C2×C4×D312yes—
665C4×D3C2×C4×D312yes—
666C4×D3D3×D412yes—
667C4×D3D3×D412yes—
668Dic6—21no—
669Dic6—21no—
670Dic6—64no—
671Dic6—64no—
672Dic6C2×C4×D312yes—
673Dic6C2×C4×D312yes—
674C3×C8—21no—
675C3×C8—21no—
676C3×C8—41no—
677C3×C8—61no—
678C3×C8—61no—
679C3⋊C8—21no—
680C3⋊C8—21no—
681C3⋊C8—61no—
682C3⋊C8—61no—
683C3⋊C8—121no—
684C2×C32—42no—
685C2×C32C22×C22⋊C411yescharacteristic
686C2×C32#57511yescharacteristic
687C2×C32#57511yescharacteristic
688C3⋊D3—22no—
689C3⋊D3—42no—
690C3×D3—22no—
691C3×D3—22no—
692C24—91no—
693C24—181no—
694#41—34no—
695#41—34no—
696#41—62no—
697#41—62no—
698#41—94no—
699#41—94no—
700#41—182no—
701#41—182no—
702#41—188no—
703#41—188no—
704C2×Q8—31no—
705C2×Q8—31no—
706C2×Q8—94no—
707C2×Q8—181no—
708C2×Q8—182no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—94no—
712C2×D4—91no—
713C2×D4—181no—
714C2×D4—181no—
715C2×D4—182no—
716C2×D4—181no—
717C2×D4—188no—
718C2×D4C2×D3211yescharacteristic
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—91no—
725C22×C4—94no—
726C22×C4—94no—
727C22×C4—91no—
728C22×C4—91no—
729C22×C4—91no—
730C22×C4—181no—
731C22×C4—181no—
732C22×C4—188no—
733C22×C4—181no—
734C22×C4—181no—
735M16—62no—
736M16—182no—
737M16—182no—
738M16—182no—
739C2×C8—31no—
740C2×C8—31no—
741C2×C8—62no—
742C2×C8—91no—
743C2×C8—182no—
744C2×C8C2×D3211yescharacteristic
745C4⋊C4—31no—
746C4⋊C4—31no—
747C4⋊C4—61no—
748C4⋊C4—91no—
749C4⋊C4—181no—
750C4⋊C4C2×D3211yescharacteristic
751C22⋊C4—61no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C22⋊C4—181no—
755C42—61no—
756C42—181no—
757C42—181no—
758C42—181no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—21no—
762C22×C3—32no—
763C22×C3—32no—
764C22×C3—42no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—61no—
770C22×C3—61no—
771C22×C3—61no—
772C22×C3—61no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3C2×D3×D411yescharacteristic
776C22×C3C2×D3×D411yescharacteristic
777C2×D3—21no—
778C2×D3—21no—
779C2×D3—21no—
780C2×D3—21no—
781C2×D3—32no—
782C2×D3—32no—
783C2×D3—62no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—62no—
789C2×D3—62no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—122no—
793C2×D3—124no—
794C2×D3—124no—
795C2×D3—128no—
796C2×D3—128no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—248no—
802C2×D3—241no—
803C2×D3—241no—
804C2×D3D3×C22⋊C412yes—
805C2×D3D3×C22⋊C412yes—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—32no—
809C3×C4—32no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—81no—
815C3×C4—121no—
816C3×C4—121no—
817C3×C4C22×C4×D311yescharacteristic
818C3×C4C22×C4×D311yescharacteristic
819C3×C4C2×D3×D411yescharacteristic
820C3×C4C2×D3×D411yescharacteristic
821Dic3—22no—
822Dic3—22no—
823Dic3—32no—
824Dic3—32no—
825Dic3—41no—
826Dic3—41no—
827Dic3—62no—
828Dic3—121no—
829Dic3—121no—
830Dic3—241no—
831Dic3D3×C22⋊C412yes—
832Dic3D3×C22⋊C412yes—
833C32#289611yescharacteristic, complemented, Sylow
834C23—21no—
835C23—31no—
836C23—31no—
837C23—94no—
838C23—91no—
839C23—184no—
840C23—181no—
841C23—362no—
842C23—362no—
843C23—361no—
844C23—361no—
845Q8—32no—
846Q8—32no—
847Q8—61no—
848Q8—61no—
849Q8—184no—
850D4—21no—
851D4—64no—
852D4—64no—
853D4—92no—
854D4—184no—
855D4—184no—
856D4—184no—
857D4—181no—
858D4C4×D3212yes—
859C2×C4—21no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—64no—
867C2×C4—64no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—94no—
873C2×C4—94no—
874C2×C4—94no—
875C2×C4—91no—
876C2×C4—92no—
877C2×C4—92no—
878C2×C4—122no—
879C2×C4—184no—
880C2×C4—184no—
881C2×C4—184no—
882C2×C4—181no—
883C2×C4—362no—
884C2×C4C22×D3211yescharacteristic
885C8—21no—
886C8—61no—
887C8—61no—
888C8—181no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—62no—
895C2×C3—62no—
896C2×C3—82no—
897C2×C3C2×D3×C22⋊C411yescharacteristic
898C2×C3C2×D3×C22⋊C411yescharacteristic
899C2×C3#576811yescharacteristic
900C2×C3#576811yescharacteristic
901C2×C3#577311yescharacteristic
902C2×C3#577711yescharacteristic
903D3—22no—
904D3—22no—
905D3—62no—
906D3—62no—
907D3—122no—
908D3—122no—
909D3—122no—
910D3—242no—
911C22—22no—
912C22—32no—
913C22—32no—
914C22—41no—
915C22—41no—
916C22—61no—
917C22—61no—
918C22—61no—
919C22—61no—
920C22—92no—
921C22—181no—
922C22—181no—
923C22—182no—
924C22—368no—
925C22—364no—
926C22—361no—
927C22—361no—
928C22D32×D411yescharacteristic
929C4—32no—
930C4—32no—
931C4—41no—
932C4—62no—
933C4—62no—
934C4—92no—
935C4—121no—
936C4—121no—
937C4—361no—
938C4C2×C4×D3211yescharacteristic
939C4D32×D411yescharacteristic
940C3—21no—
941C3#7883011yescharacteristic, complemented
942C3#7888111yescharacteristic, complemented
943C2—42no—
944C2—62no—
945C2—62no—
946C2—182no—
947C2—362no—
948C2D32×C22⋊C411yescharacteristic
949C2#1059472911yescharacteristic
950C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#64312C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×D3×ΓL(1,𝔽25)C2semidirect
3. D3×#892C2semidirect
4. #10592469C2semidirect
5. C3×#4772C2semidirect
6. C3×#4771C2semidirect
7. #10591426C2semidirect
8. #10591420C2semidirect
9. #10591414C2semidirect
10. #10590691C2semidirect
11. #10590690C2semidirect
12. #10590671C2semidirect
13. #10590610C2semidirect
14. #10590609C2semidirect
15. #10590602C2semidirect
26. #64312C4semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
34. C2×C3×D3×C8C22semidirect
35. C3×#892C22semidirect
36. C3×D3×C4⋊C4C22semidirect
38. D3×C4⋊Dic3C22semidirect
42. #63841C22semidirect
45. C2×#3711C22semidirect
46. C2×D3×C3⋊C8C22semidirect
48. C32×#102C22semidirect
49. #63659C22semidirect
50. #63648C22semidirect
51. #63636C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#816C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
58. #63566C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
63. #63564C22semidirect
87. #4772D3semidirect
89. #4771D3semidirect
100. D4×C3⋊D3C2×C4semidirect
110. C3×#237C2×C4semidirect
135. #3799C2×C4semidirect
137. #3797C2×C4semidirect
208. C2×ΓL(1,𝔽25)C2×D3semidirect
210. C2×D3×C8C2×D3semidirect
219. #892C2×D3semidirect
221. D3×C4⋊C4C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
242. #832C2×D3semidirect
243. #832C2×D3semidirect
251. #816C2×D3semidirect
252. #816C2×D3semidirect
255. #810C2×D3semidirect
256. #810C2×D3semidirect
378. #237C4×D3semidirect
554. #102D32semidirect
833. C32#2896semidirect
941. C3#78830semidirect
942. C3#78881semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×D3×ΓL(1,𝔽25)2
D3×#8922
#105924692
C3×#47722
C3×#47712
#105914262
#105914202
#105914142
#105906912
#105906902
#105906712
#105906102
#105906092
#105906022
#788813
#788303