Finite Group Databasebeta

← #11857976

Subgroups — #11857976

Order 1152.

1619 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3D3×#892C211yesmaximal, characteristic, complemented
4#10592501C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6C3×#4803C211yesmaximal, characteristic, complemented
7#10591562C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10590954C211yesmaximal, characteristic, complemented
11#10590941C211yesmaximal, characteristic, complemented
12#10590670C211yesmaximal, characteristic, complemented
13#10590608C211yesmaximal, characteristic, complemented
14#10590607C211yesmaximal, characteristic, complemented
15#10590594C211yesmaximal, characteristic, complemented
16#78881—31nomaximal
17#78830—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21#64319—24no—
22#64319C418yescomplemented
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3795—21no—
28C2×#3795—21no—
29C2×#3795C2211yescharacteristic
30C2×#3795C2211yescharacteristic
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×#103C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63643C2211yescharacteristic, complemented
51#63637C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, 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#4804D311yescharacteristic, complemented
80#4803—31no—
81#4803D311yescharacteristic, complemented
82#4802—31no—
83#4802—31no—
84#4802—31no—
85#4802—31no—
86#4802—61no—
87#4772—31no—
88#4772—31no—
89#4771—31no—
90#4771—31no—
91#4770—31no—
92#4770—31no—
93#4770—31no—
94#4770—31no—
95C22×D32—21no—
96C22×D32D411yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98Q8×C3⋊D3—22no—
99Q8×C3⋊D3C2×C414yescomplemented
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634—21no—
103C2×#634C2311yescharacteristic
104C3×#239—22no—
105C3×#239—22no—
106C3×#239C2×C414yes—
107C3×#239C2×C414yescomplemented
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×#625—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×#624D411yescharacteristic
121C2×D3×Dic3—21no—
122C2×D3×Dic3—21no—
123C2×D3×Dic3—21no—
124C2×D3×Dic3D411yescharacteristic
125C2×D3×Dic3D411yescharacteristic
126#3802—28no—
127#3802—22no—
128#3802C2×C414yescomplemented
129C4×D32—28no—
130C4×D32C2×C414yes—
131C4×D32D414yes—
132#3795—22no—
133#3795—22no—
134#3795—28no—
135#3795—28no—
136#3795C2×C414yes—
137#3795C2×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×#239C2×D311yescharacteristic
170C2×#239C2×D311yescharacteristic
171C2×D3×Q8—31no—
172C2×D3×Q8—31no—
173C2×D3×Q8—61no—
174C2×#237—31no—
175C2×#237—31no—
176C2×#237—61no—
177C2×#237—61no—
178C2×D3×D4—31no—
179C2×D3×D4—31no—
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—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103C2×D311yescharacteristic, complemented
230C3×#103C2×D311yescharacteristic, complemented
231C3×#102—31no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102—31no—
235#835—31no—
236#835—31no—
237#835—61no—
238#835C2×D311yescharacteristic, complemented
239#835C2×D311yescharacteristic, complemented
240#832—31no—
241#832—31no—
242#832—31no—
243#832—31no—
244#821—31no—
245#821—31no—
246#821C2×D311yescharacteristic, complemented
247#821C2×D311yescharacteristic, complemented
248#816—31no—
249#816—31no—
250#816—31no—
251#816—31no—
252#816—61no—
253#810—31no—
254#810—31no—
255#810—31no—
256#810—31no—
257#810—61no—
258#809—31no—
259#809—31no—
260#809C2×D311yescharacteristic, complemented
261#809C2×D311yescharacteristic, complemented
262C22×C3⋊D3C2×D411yescharacteristic
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C2×D32—24no—
268C2×D32—41no—
269C2×D32—41no—
270C2×D32—42no—
271C2×D32—42no—
272C2×D32C22⋊C414yes—
273C32×Q8—21no—
274C32×Q8C22×C412yes—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2411yescharacteristic
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3C2×D411yescharacteristic
281C4×C3⋊D3—24no—
282C4×C3⋊D3C22×C412yes—
283C4×C3⋊D3C2×D412yes—
284#634—21no—
285#634—24no—
286#634C22×C412yes—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—24no—
292C3×D12—24no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12C22×C412yes—
296C3×D12C22×C412yes—
297C3×C4×D3—24no—
298C3×C4×D3—24no—
299C3×C4×D3—42no—
300C3×C4×D3C22×C412yes—
301C3×C4×D3C22×C412yes—
302C3×C4×D3C2×D412yes—
303C3×C4×D3C2×D412yes—
304#625—24no—
305#625—24no—
306#625—24no—
307#624C22⋊C414yes—
308D3×Dic3—24no—
309D3×Dic3—24no—
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—
336C3×#41—34no—
337C3×#41—34no—
338C3×#41—62no—
339C3×#41—62no—
340C2×C3×Q8—21no—
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363#239—22no—
364#239—22no—
365#239C4×D314yes—
366#239C4×D314yescomplemented
367D3×Q8—34no—
368D3×Q8—34no—
369D3×Q8—64no—
370D3×Q8—62no—
371D3×Q8—62no—
372D3×Q8—122no—
373#237—34no—
374#237—34no—
375#237—68no—
376#237—68no—
377#237—62no—
378#237—62no—
379D3×D4—34no—
380D3×D4—34no—
381D3×D4—62no—
382D3×D4—62no—
383D3×D4—68no—
384D3×D4—68no—
385#235—34no—
386#235—34no—
387#235—68no—
388#235—68no—
389#235—62no—
390#235—62no—
391C2×D12—21no—
392C2×D12—21no—
393C2×D12C22×D311yescharacteristic
394C2×D12C22×D311yescharacteristic
395C2×C4×D3—21no—
396C2×C4×D3—21no—
397C2×C4×D3—21no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—34no—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—61no—
409C2×C4×D3—68no—
410C2×C4×D3—68no—
411C2×C4×D3—61no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3—61no—
416C2×C4×D3—121no—
417C2×C4×D3C22×D311yescharacteristic
418C2×C4×D3C22×D311yescharacteristic
419C2×Dic6—31no—
420C2×Dic6—31no—
421C2×Dic6—61no—
422C2×Dic6—61no—
423C2×Dic6—61no—
424C2×Dic6—121no—
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×C32C22×D411yescharacteristic
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3C2×C22⋊C412yes—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3C2×C22⋊C412yes—
495C2×C3×D3C2×C22⋊C412yes—
496D32—44no—
497D32—48no—
498C32×C4—22no—
499C32×C4—41no—
500C32×C4C23×C411yescharacteristic
501C32×C4C22×D411yescharacteristic
502C3⋊Dic3—22no—
503C3⋊Dic3—41no—
504C3⋊Dic3C2×C22⋊C412yes—
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—91no—
542#103—91no—
543#103—91no—
544#103—91no—
545#103—91no—
546#103D3211yescharacteristic, complemented
547#102—31no—
548#102—31no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102—91no—
555C23×C3—31no—
556C23×C3—31no—
557C23×C3—61no—
558C23×C3—61no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—31no—
562C22×D3—31no—
563C22×D3—34no—
564C22×D3—34no—
565C22×D3—61no—
566C22×D3—64no—
567C22×D3—64no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—122no—
573C22×D3—122no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3D3×D411yescharacteristic
577C22×D3D3×D411yescharacteristic
578C3×Q8—21no—
579C3×Q8—21no—
580C3×Q8—22no—
581C3×Q8—41no—
582C3×Q8C2×C4×D312yes—
583C3×Q8C2×C4×D312yes—
584C3×D4—32no—
585C3×D4—32no—
586C3×D4—64no—
587C3×D4—64no—
588C3×D4—61no—
589C3×D4—61no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—32no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—64no—
604C2×C3×C4—64no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—122no—
608C2×C3×C4C23×D311yescharacteristic
609C2×C3×C4C23×D311yescharacteristic
610#67—64no—
611#67—64no—
612#67—64no—
613#67—64no—
614#67—64no—
615#67—64no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—34no—
621C2×Dic3—34no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—64no—
626C2×Dic3—64no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—122no—
632C2×Dic3D3×D411yescharacteristic
633C2×Dic3D3×D411yescharacteristic
634D12—24no—
635D12—24no—
636D12—21no—
637D12—21no—
638D12C2×C4×D312yes—
639D12C2×C4×D312yes—
640C4×D3—24no—
641C4×D3—24no—
642C4×D3—34no—
643C4×D3—34no—
644C4×D3—32no—
645C4×D3—32no—
646C4×D3—32no—
647C4×D3—32no—
648C4×D3—34no—
649C4×D3—34no—
650C4×D3—42no—
651C4×D3—62no—
652C4×D3—62no—
653C4×D3—64no—
654C4×D3—64no—
655C4×D3—64no—
656C4×D3—64no—
657C4×D3—124no—
658C4×D3—122no—
659C4×D3C2×C4×D312yes—
660C4×D3C2×C4×D312yes—
661C4×D3D3×D412yes—
662C4×D3D3×D412yes—
663Dic6—32no—
664Dic6—32no—
665Dic6—62no—
666Dic6—64no—
667Dic6—64no—
668Dic6—61no—
669Dic6—61no—
670Dic6—124no—
671Dic6—121no—
672C3×C8—21no—
673C3×C8—21no—
674C3×C8—41no—
675C3×C8—61no—
676C3×C8—61no—
677C3⋊C8—21no—
678C3⋊C8—21no—
679C3⋊C8—61no—
680C3⋊C8—61no—
681C3⋊C8—121no—
682C2×C32C22×C22⋊C411yescharacteristic
683C2×C32#57511yescharacteristic
684C2×C32#57511yescharacteristic
685C3⋊D3—22no—
686C3×D3—22no—
687C3×D3—22no—
688C3×D3—42no—
689C3×D3—42no—
690C24—91no—
691C24—181no—
692#41—34no—
693#41—34no—
694#41—62no—
695#41—62no—
696#41—94no—
697#41—94no—
698#41—182no—
699#41—182no—
700#41—188no—
701#41—188no—
702C2×Q8—94no—
703C2×Q8—91no—
704C2×Q8—181no—
705C2×Q8—182no—
706C2×Q8C2×D3211yescharacteristic
707C2×D4—31no—
708C2×D4—31no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—94no—
712C2×D4—182no—
713C2×D4—181no—
714C2×D4—188no—
715C2×D4—181no—
716C2×D4—181no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—91no—
723C22×C4—94no—
724C22×C4—94no—
725C22×C4—91no—
726C22×C4—91no—
727C22×C4—91no—
728C22×C4—181no—
729C22×C4—181no—
730C22×C4—181no—
731C22×C4—188no—
732C22×C4—181no—
733M16—62no—
734M16—182no—
735M16—182no—
736M16—182no—
737C2×C8—31no—
738C2×C8—31no—
739C2×C8—62no—
740C2×C8—91no—
741C2×C8—182no—
742C2×C8C2×D3211yescharacteristic
743C4⋊C4—31no—
744C4⋊C4—31no—
745C4⋊C4—61no—
746C4⋊C4—91no—
747C4⋊C4—181no—
748C4⋊C4C2×D3211yescharacteristic
749C22⋊C4—61no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C42—61no—
754C42—181no—
755C42—181no—
756C42—181no—
757C22×C3—21no—
758C22×C3—32no—
759C22×C3—32no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3C2×D3×D411yescharacteristic
771C22×C3C2×D3×D411yescharacteristic
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—21no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—32no—
779C2×D3—32no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—62no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—61no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—124no—
792C2×D3—124no—
793C2×D3—128no—
794C2×D3—128no—
795C2×D3D3×C22⋊C412yes—
796C2×D3D3×C22⋊C412yes—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—32no—
802C3×C4—32no—
803C3×C4—42no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—81no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4C22×C4×D311yescharacteristic
810C3×C4C22×C4×D311yescharacteristic
811C3×C4C2×D3×D411yescharacteristic
812C3×C4C2×D3×D411yescharacteristic
813Dic3—32no—
814Dic3—32no—
815Dic3—41no—
816Dic3—41no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—122no—
821Dic3—121no—
822Dic3—121no—
823Dic3—241no—
824Dic3D3×C22⋊C412yes—
825Dic3D3×C22⋊C412yes—
826C32#289611yescharacteristic, complemented, Sylow
827C23—31no—
828C23—31no—
829C23—61no—
830C23—61no—
831C23—94no—
832C23—91no—
833C23—184no—
834C23—361no—
835C23—361no—
836C23—362no—
837C23—362no—
838Q8—21no—
839Q8—92no—
840Q8—184no—
841Q8—181no—
842Q8C4×D3212yes—
843D4—32no—
844D4—32no—
845D4—64no—
846D4—64no—
847D4—61no—
848D4—61no—
849D4—184no—
850D4—184no—
851D4—184no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—64no—
861C2×C4—64no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—94no—
865C2×C4—94no—
866C2×C4—94no—
867C2×C4—91no—
868C2×C4—92no—
869C2×C4—92no—
870C2×C4—122no—
871C2×C4—184no—
872C2×C4—184no—
873C2×C4—184no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—362no—
877C2×C4C22×D3211yescharacteristic
878C8—21no—
879C8—61no—
880C8—61no—
881C8—181no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—62no—
886C2×C3—62no—
887C2×C3—122no—
888C2×C3—122no—
889C2×C3C2×D3×C22⋊C411yescharacteristic
890C2×C3C2×D3×C22⋊C411yescharacteristic
891C2×C3#576811yescharacteristic
892C2×C3#576811yescharacteristic
893C2×C3#577311yescharacteristic
894C2×C3#577711yescharacteristic
895D3—22no—
896D3—22no—
897D3—42no—
898D3—42no—
899D3—62no—
900D3—62no—
901D3—122no—
902C22—32no—
903C22—32no—
904C22—61no—
905C22—61no—
906C22—61no—
907C22—61no—
908C22—62no—
909C22—62no—
910C22—92no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—181no—
916C22—181no—
917C22—364no—
918C22—368no—
919C22D32×D411yescharacteristic
920C4—22no—
921C4—32no—
922C4—32no—
923C4—41no—
924C4—92no—
925C4—121no—
926C4—121no—
927C4—182no—
928C4—361no—
929C4C2×C4×D3211yescharacteristic
930C4D32×D411yescharacteristic
931C3—21no—
932C3#7883011yescharacteristic, complemented
933C3#7888111yescharacteristic, complemented
934C2—62no—
935C2—62no—
936C2—122no—
937C2—122no—
938C2—182no—
939C2D32×C22⋊C411yescharacteristic
940C2#1059474511yescharacteristic
941C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#64319C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

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. #10592501C2semidirect
5. C3×#4804C2semidirect
6. C3×#4803C2semidirect
7. #10591562C2semidirect
8. #10591556C2semidirect
9. #10591550C2semidirect
10. #10590954C2semidirect
11. #10590941C2semidirect
12. #10590670C2semidirect
13. #10590608C2semidirect
14. #10590607C2semidirect
15. #10590594C2semidirect
22. #64319C4semidirect
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×#103C22semidirect
49. #63662C22semidirect
50. #63643C22semidirect
51. #63637C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#821C22semidirect
55. C3×#821C22semidirect
56. C3×#809C22semidirect
57. C3×#809C22semidirect
58. #63567C22semidirect
59. #63567C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63562C22semidirect
79. #4804D3semidirect
81. #4803D3semidirect
99. Q8×C3⋊D3C2×C4semidirect
107. C3×#239C2×C4semidirect
128. #3802C2×C4semidirect
137. #3795C2×C4semidirect
208. C2×ΓL(1,𝔽25)C2×D3semidirect
210. C2×D3×C8C2×D3semidirect
219. #892C2×D3semidirect
221. D3×C4⋊C4C2×D3semidirect
229. C3×#103C2×D3semidirect
230. C3×#103C2×D3semidirect
238. #835C2×D3semidirect
239. #835C2×D3semidirect
246. #821C2×D3semidirect
247. #821C2×D3semidirect
260. #809C2×D3semidirect
261. #809C2×D3semidirect
366. #239C4×D3semidirect
546. #103D32semidirect
826. C32#2896semidirect
932. C3#78830semidirect
933. C3#78881semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×D3×ΓL(1,𝔽25)2
D3×#8922
#105925012
C3×#48042
C3×#48032
#105915622
#105915562
#105915502
#105909542
#105909412
#105906702
#105906082
#105906072
#105905942
#788813
#788303