Finite Group Databasebeta

← #11867137

Subgroups — #11867137

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×#64123C211yesmaximal, characteristic, complemented
2#10595430C211yesmaximal, characteristic, complemented
3#10595282C211yesmaximal, characteristic, complemented
4C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
5C3×#5174C211yesmaximal, characteristic, complemented
6C3×#5171C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591585C211yesmaximal, characteristic, complemented
9#10591554C211yesmaximal, characteristic, complemented
10#10591453C211yesmaximal, characteristic, complemented
11#10591449C211yesmaximal, characteristic, complemented
12#10591426C211yesmaximal, characteristic, complemented
13#10590835C211yesmaximal, characteristic, complemented
14#10590832C211yesmaximal, characteristic, complemented
15#10590688C211yesmaximal, characteristic, complemented
16#80805—31nomaximal
17#80657—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×#3811—21no—
21C2×C4×D32C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25#64123—24no—
26C2×#3745C2211yescharacteristic, complemented
27C2×#3743C2211yescharacteristic
28C3×#946C2211yescharacteristic, complemented
29C3×#946C2211yescharacteristic, complemented
30C3×#938C2211yescharacteristic
31C3×#938C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63974—21no—
35#63971—21no—
36#63971—21no—
37#63923—21no—
38#63909C2211yescharacteristic
39#63909C2211yescharacteristic
40#63909C2211yescharacteristic, complemented
41#63909C2211yescharacteristic, complemented
42#63900C2211yescharacteristic
43#63897—21no—
44#63881—21no—
45#63881—21no—
46#63849C2211yescharacteristic
47C2×#3712C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D3×ΓL(1,𝔽25)—24no—
51C3×#835C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#817C2211yescharacteristic, complemented
57#63576C2211yescharacteristic, complemented
58#63574C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#914—31no—
65C2×#914—61no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68#5627—31no—
69#5627—31no—
70D3×#121—31no—
71D3×#121—31no—
72C3×#468—31no—
73C3×#465—31no—
74#5174D311yescharacteristic, complemented
75#5171D311yescharacteristic, complemented
76#5135—31no—
77#5115—31no—
78#5049—31no—
79#5048—31no—
80#5039—31no—
81#5038—31no—
82#4883—31no—
83#4881—31no—
84#4865—31no—
85#4861—31no—
86#4812—31no—
87#4807—31no—
88#4803—31no—
89#4803—31no—
90#4782—31no—
91#4775—31no—
92#4770—31no—
93#4770—31no—
94C23×C3⋊D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99#3832—22no—
100#3832—22no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112#3811—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#624—21no—
118C2×#624D411yescharacteristic
119C2×D3×Dic3D411yescharacteristic
120C2×D3×Dic3D411yescharacteristic
121C4×D32—22no—
122C4×D32—22no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3755—22no—
126#3753—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3745—22no—
129#3743D414yescomplemented
130C3×#217—21no—
131C3×#217—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×ΓL(1,𝔽25)—22no—
143C3×D3×C8—22no—
144#3724—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150Dic32—21no—
151#3712—22no—
152#3711—22no—
153D3×C3⋊C8—22no—
154#3055—91noSylow
155C2×#239—31no—
156C2×#239—31no—
157C2×#239—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×SD16—21no—
166C2×C3×SD16C2×D311yescharacteristic, complemented
167C2×C3×SD16C2×D311yescharacteristic, complemented
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×#121—31no—
174#946C2×D311yescharacteristic, complemented
175#946C2×D311yescharacteristic, complemented
176C2×#215—31no—
177C2×#215—31no—
178C2×#215—61no—
179#939—61no—
180#939—61no—
181#938C2×D311yescharacteristic
182#938C2×D311yescharacteristic
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—61no—
186#930—31no—
187#930—31no—
188#930—31no—
189#930—31no—
190C2×#208—31no—
191C22×C3⋊C8—31no—
192#914—64no—
193#914—64no—
194#914—68no—
195D3×M16—64no—
196C2×D24—31no—
197C2×D24—31no—
198C2×D24—61no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—61no—
205C2×ΓL(1,𝔽25)—64no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
207C2×D3×C8—31no—
208C2×D3×C8C2×D311yescharacteristic, complemented
209#895—31no—
210#895—31no—
211#895—31no—
212#895—31no—
213#894—61no—
214#894—61no—
215#893—61no—
216#893—61no—
217#892—31no—
218#892—31no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4—31no—
221#884—61no—
222#884—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#67⋊C4—61no—
227D3×C22⋊C4—61no—
228D3×C22⋊C4—61no—
229C3×#107—31no—
230C3×#106—31no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#102—31no—
234C3×#102—31no—
235#835C2×D311yescharacteristic, complemented
236#835C2×D311yescharacteristic, complemented
237#832C2×D311yescharacteristic, complemented
238#832C2×D311yescharacteristic, complemented
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#818C2×D311yescharacteristic, complemented
244#817C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#808—31no—
250#808—31no—
251#807—31no—
252#807—31no—
253C23×C32—21no—
254C22×C3⋊D3—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×Q8—21no—
266C32×Q8—21no—
267C32×D4—21no—
268C32×D4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—42no—
278C4×C3⋊D3—42no—
279C4×C3⋊D3C2×D412yes—
280C4×C3⋊D3#4112yes—
281C3×#67—42no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293#626—42no—
294#626—42no—
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—91no—
310#469—91no—
311#468—31no—
312#468—91no—
313#466—91no—
314#466—91no—
315#465—31no—
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×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—121no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346#239—62no—
347#239—62no—
348#239—62no—
349#239—62no—
350#239—64no—
351#239—122no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—64no—
357D3×D4—122no—
358D3×D4—124no—
359D3×D4—124no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—121no—
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×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—121no—
389C2×C4×D3C22×D311yescharacteristic
390C2×C4×D3C22×D311yescharacteristic
391C3×SD16—24no—
392C3×SD16—22no—
393C3×SD16—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×C4⋊C4—61no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411#217—21no—
412#217—21no—
413#215—62no—
414#215—62no—
415#215—64no—
416#213—62no—
417#213—62no—
418#213—64no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
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—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431C4⋊Dic3C22×D311yescharacteristic
432C4⋊Dic3C22×D311yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
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
448D24—64no—
449D24—62no—
450D24—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×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—41no—
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#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×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4C2×#4111yescharacteristic
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×SD16D3211yescharacteristic, complemented
498C2×D8—91no—
499C2×D8—91no—
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—31no—
509C22⋊Q8—31no—
510#121—31no—
511#121—31no—
512#121—91no—
513#121—91no—
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—31no—
529#103—31no—
530#102—31no—
531#102—31no—
532#102—91no—
533#102—91no—
534#102—91no—
535#102—91no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—41no—
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—61no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—121no—
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×Q8—22no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—41no—
573C3×D4—22no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—41no—
579C3×D4—122no—
580C3×D4—122no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
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×C4—61no—
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—42no—
598#67—42no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—124no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—61no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3D3×D411yescharacteristic
616C2×Dic3D3×D411yescharacteristic
617D12—62no—
618D12—62no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—121no—
628D12—121no—
629D12—122no—
630D12—122no—
631D12—124no—
632D12—122no—
633D12—122no—
634D12—122no—
635D12—122no—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—32no—
641C4×D3—32no—
642C4×D3—32no—
643C4×D3—32no—
644C4×D3—62no—
645C4×D3—62no—
646C4×D3—62no—
647C4×D3—62no—
648C4×D3—62no—
649C4×D3—62no—
650C4×D3—122no—
651C4×D3—122no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—124no—
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×C32C2×#12111yescharacteristic
667C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
668C2×C32#57511yescharacteristic
669C3⋊D3—22no—
670C3⋊D3—81no—
671C3⋊D3—81no—
672C3×D3—22no—
673C3×D3—41no—
674C24—91no—
675C24—181no—
676#41—182no—
677#41—182no—
678C2×Q8C2×D3211yescharacteristic
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—182no—
689C2×D4—182no—
690C2×D4—181no—
691C2×D4—364no—
692C2×D4C2×D3211yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—91no—
698C22×C4—91no—
699C22×C4—181no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—181no—
703SD16—22no—
704SD16—182no—
705D8—182no—
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—61no—
722C4⋊C4—61no—
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—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C2×D3×D411yescharacteristic
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—32no—
758C2×D3—32no—
759C2×D3—62no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—124no—
767C2×D3—124no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—244no—
787C2×D3—244no—
788C2×D3—248no—
789C2×D3#91412yescomplemented
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—42no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—121no—
798C3×C4—121no—
799C3×C4—121no—
800C3×C4—121no—
801C3×C4C2×D3×D411yescharacteristic
802C3×C4C2×D3×D411yescharacteristic
803C3×C4D3×#4111yescharacteristic
804C3×C4D3×#4111yescharacteristic
805Dic3—21no—
806Dic3—21no—
807Dic3—32no—
808Dic3—32no—
809Dic3—41no—
810Dic3—41no—
811Dic3—41no—
812Dic3—41no—
813Dic3—62no—
814C32#305511yescharacteristic, complemented, Sylow
815C23—21no—
816C23—31no—
817C23—31no—
818C23—91no—
819C23—182no—
820C23—182no—
821C23—181no—
822C23—181no—
823C23—362no—
824C23—362no—
825C23—362no—
826C23—361no—
827Q8—21no—
828Q8—21no—
829D4—21no—
830D4—21no—
831D4—122no—
832D4—122no—
833D4—181no—
834D4—181no—
835D4—181no—
836D4—181no—
837D4—362no—
838D4—362no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843C2×C4—21no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—91no—
855C2×C4—92no—
856C2×C4—92no—
857C2×C4—182no—
858C2×C4—182no—
859C2×C4—182no—
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—81no—
873C2×C3—81no—
874C2×C3—121no—
875C2×C3D3×#12111yescharacteristic
876C2×C3D3×#12111yescharacteristic
877C2×C3C2×#91411yescharacteristic
878C2×C3#576811yescharacteristic
879C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
880C2×C3#577711yescharacteristic
881D3—22no—
882D3—41no—
883D3—62no—
884D3—62no—
885D3—122no—
886D3—242no—
887D3—242no—
888D3—241no—
889D3—241no—
890D3—241no—
891D3—241no—
892C22—32no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—61no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—61no—
901C22—92no—
902C22—181no—
903C22—181no—
904C22—364no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—361no—
911C22—724no—
912C22D32×D411yescharacteristic
913C4—41no—
914C4—61no—
915C4—61no—
916C4—92no—
917C4—121no—
918C4—121no—
919C4—121no—
920C4—121no—
921C4#6431211yescharacteristic
922C4C2×#381111yescharacteristic
923C3—21no—
924C3#8065711yescharacteristic, complemented
925C3#8080511yescharacteristic, complemented
926C2—62no—
927C2—81no—
928C2—121no—
929C2—182no—
930C2—721no—
931C2—721no—
932C2D3×#91411yescharacteristic
933C2#1059474611yescharacteristic
934C2#1059528211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#64123C2semidirect
2. #10595430C2semidirect
3. #10595282C2semidirect
4. C2×D3×ΓL(1,𝔽25)C2semidirect
5. C3×#5174C2semidirect
6. C3×#5171C2semidirect
7. #10591589C2semidirect
8. #10591585C2semidirect
9. #10591554C2semidirect
10. #10591453C2semidirect
11. #10591449C2semidirect
12. #10591426C2semidirect
13. #10590835C2semidirect
14. #10590832C2semidirect
15. #10590688C2semidirect
22. C2×C32×SD16C22semidirect
23. C2×#3755C22semidirect
24. C2×#3753C22semidirect
26. C2×#3745C22semidirect
28. C3×#946C22semidirect
29. C3×#946C22semidirect
32. C2×C3×ΓL(1,𝔽25)C22semidirect
33. C2×C3×D3×C8C22semidirect
40. #63909C22semidirect
41. #63909C22semidirect
48. C2×#3711C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C3×#835C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#832C22semidirect
55. C3×#818C22semidirect
56. C3×#817C22semidirect
57. #63576C22semidirect
58. #63574C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63564C22semidirect
74. #5174D3semidirect
75. #5171D3semidirect
129. #3743D4semidirect
166. C2×C3×SD16C2×D3semidirect
167. C2×C3×SD16C2×D3semidirect
174. #946C2×D3semidirect
175. #946C2×D3semidirect
206. C2×ΓL(1,𝔽25)C2×D3semidirect
208. C2×D3×C8C2×D3semidirect
235. #835C2×D3semidirect
236. #835C2×D3semidirect
237. #832C2×D3semidirect
238. #832C2×D3semidirect
243. #818C2×D3semidirect
244. #817C2×D3semidirect
301. C32×C8C2×D4semidirect
302. C3⋊(C3⋊C8)C2×D4semidirect
479. C2×C3×D3AGL(1,ℤ/8)semidirect
497. C2×SD16D32semidirect
658. C3×C8D3×D4semidirect
659. C3×C8D3×D4semidirect
789. C2×D3#914semidirect
814. C32#3055semidirect
866. C8#3811semidirect
924. C3#80657semidirect
925. C3#80805semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
#105954302
#105952822
C2×D3×ΓL(1,𝔽25)2
C3×#51742
C3×#51712
#105915892
#105915852
#105915542
#105914532
#105914492
#105914262
#105908352
#105908322
#105906882
#808053
#806573