Finite Group Databasebeta

← #11867152

Subgroups — #11867152

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic, complemented
2#10595081C211yesmaximal, characteristic, complemented
3#10594922C211yesmaximal, characteristic, complemented
4C2×#63798C211yesmaximal, characteristic, complemented
5C3×#5115C211yesmaximal, characteristic, complemented
6C3×#5114C211yesmaximal, characteristic, complemented
7#10591179C211yesmaximal, characteristic, complemented
8#10591166C211yesmaximal, characteristic, complemented
9#10590957C211yesmaximal, characteristic, complemented
10#10590941C211yesmaximal, characteristic, complemented
11#10590846C211yesmaximal, characteristic, complemented
12#10590845C211yesmaximal, characteristic, complemented
13#10590842C211yesmaximal, characteristic, complemented
14#10590840C211yesmaximal, characteristic, complemented
15#10590688C211yesmaximal, characteristic, complemented
16#80715—31nomaximal
17#80657—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C2×#3743—24no—
25C2×#3743C2211yescharacteristic
26C2×#3743C2211yescharacteristic
27C2×#3743C2211yescharacteristic, complemented
28C2×#3743C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×#930C2211yescharacteristic, complemented
32C3×#924C2211yescharacteristic, complemented
33C2×C3×D24C2211yescharacteristic, complemented
34C2×C3×#204C2211yescharacteristic, complemented
35#63981—21no—
36#63980—21no—
37#67⋊Dic3—21no—
38#63921—21no—
39#63916C2211yescharacteristic
40#63916C2211yescharacteristic
41#63916C2211yescharacteristic, complemented
42#63912—21no—
43#63900C2211yescharacteristic
44#63881—21no—
45#63871C2211yescharacteristic, complemented
46#63853—21no—
47#63849C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50#63798—24no—
51C3×#821C2211yescharacteristic, complemented
52C3×#821C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic, complemented
54C3×#818C2211yescharacteristic, complemented
55C3×#817C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57#63576C2211yescharacteristic, complemented
58#63574C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C22×ΓL(1,𝔽25)—31no—
66C22×ΓL(1,𝔽25)—31no—
67C22×ΓL(1,𝔽25)—61no—
68#5627—31no—
69#5606—31no—
70D3×#121—31no—
71D3×#121—31no—
72C3×#466—31no—
73C3×#465—31no—
74#5174—31no—
75#5159—31no—
76#5115D311yescharacteristic, complemented
77#5114D311yescharacteristic, complemented
78#5048—31no—
79#5041—31no—
80#5038—31no—
81#5038—31no—
82#4886—31no—
83#4881—31no—
84#4865—31no—
85#4861—31no—
86#4812—31no—
87#4803—31no—
88#4782—31no—
89#4782—31no—
90#4780—31no—
91#4771—31no—
92#4770—31no—
93#4770—31no—
94C23×C3⋊D3D411yescharacteristic
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C22×C3⋊Dic3D411yescharacteristic
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3D411yescharacteristic
101C2×C4×C3⋊D3D411yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111#3811—44no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—22no—
121#3796—22no—
122#3796—22no—
123C2×C32×C8—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126C2×C3⋊(C3⋊C8)—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3743—22no—
130#3743—22no—
131#3743—22no—
132#3743D414yescomplemented
133C3×#217—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×D24—22no—
143C3×#204—22no—
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#3715—22no—
153#3713—22no—
154#3055—91noSylow
155C2×#239—31no—
156C2×#237—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C2×D3×D4—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—61no—
164C2×C3×SD16—31no—
165C2×C3×D8—31no—
166C22×C3×C8—21no—
167C22×C3×C8C2×D311yescharacteristic, complemented
168C22×C3×C8C2×D311yescharacteristic, complemented
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171C3×#121—31no—
172C3×#121—31no—
173#946—31no—
174C2×#215—31no—
175#939—61no—
176#939—61no—
177#938—31no—
178#938—31no—
179#938—31no—
180#937—61no—
181D4×Dic3—61no—
182C2×#214—31no—
183C2×#213—31no—
184C2×#213—31no—
185#930C2×D311yescharacteristic
186#930C2×D311yescharacteristic
187#930C2×D311yescharacteristic, complemented
188#924C2×D311yescharacteristic, complemented
189C22×C3⋊C8—31no—
190C22×C3⋊C8—31no—
191C22×C3⋊C8—61no—
192#914—64no—
193#911—64no—
194C2×D24C2×D311yescharacteristic, complemented
195C2×#204C2×D311yescharacteristic, complemented
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—31no—
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)—61no—
206C2×ΓL(1,𝔽25)—61no—
207C2×ΓL(1,𝔽25)—61no—
208C2×ΓL(1,𝔽25)—64no—
209C2×ΓL(1,𝔽25)—64no—
210C2×ΓL(1,𝔽25)—68no—
211#897—31no—
212#895—31no—
213#895—31no—
214#895—31no—
215#894—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#883—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×#102—31no—
233C3×#102—31no—
234C3×#102—31no—
235#835—31no—
236#832—31no—
237#832—31no—
238#832—31no—
239#821C2×D311yescharacteristic, complemented
240#821C2×D311yescharacteristic, complemented
241#821C2×D311yescharacteristic, complemented
242#818C2×D311yescharacteristic, complemented
243#817C2×D311yescharacteristic, complemented
244#816C2×D311yescharacteristic, complemented
245#810—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#808—31no—
250#808—31no—
251#807—31no—
252#807—31no—
253C23×C32C2×D411yescharacteristic
254C22×C3⋊D3—22no—
255C22×C3⋊D3—22no—
256C22×C3⋊D3—41no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3⋊D3C2×D411yescharacteristic
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—22no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4×C3⋊D3—22no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—22no—
276C4×C3⋊D3C2×D412yes—
277C4×C3⋊D3#4112yes—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—42no—
295#626—42no—
296#626—42no—
297#626—42no—
298#625—42no—
299#624—42no—
300D3×Dic3—42no—
301C32×C8—21no—
302C32×C8C2×D412yescomplemented
303C3⋊(C3⋊C8)—21no—
304C3⋊(C3⋊C8)C2×D412yescomplemented
305C2×AGL(1,ℤ/8)—91no—
306C22×M16—91no—
307#525—91no—
308C2×#121—91no—
309#469—91no—
310#469—91no—
311#468—91no—
312#468—91no—
313#466—31no—
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—61no—
325C2×C3×Q8—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C22×C3×C4—21no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348#239—62no—
349#239—62no—
350#237—62no—
351#237—62no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—124no—
357D3×D4—124no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—64no—
382C2×C4×D3—64no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×Dic6C22×D311yescharacteristic
387C3×SD16—62no—
388C3×D8—62no—
389C2×C3×C8—24no—
390C2×C3×C8—22no—
391C2×C3×C8—22no—
392C2×C3×C8—21no—
393C2×C3×C8—21no—
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—31no—
402C3×C4⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407#217—21no—
408#217—61no—
409#217—61no—
410#217—61no—
411#215—62no—
412#214—62no—
413#213—62no—
414#213—62no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
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—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427C4⋊Dic3C22×D311yescharacteristic
428C4⋊Dic3C22×D311yescharacteristic
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434C4×Dic3—61no—
435C4×Dic3—61no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—61no—
442C2×C3⋊C8—62no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8—64no—
445D24—22no—
446#204—22no—
447ΓL(1,𝔽25)—34no—
448ΓL(1,𝔽25)—34no—
449ΓL(1,𝔽25)—64no—
450ΓL(1,𝔽25)—62no—
451ΓL(1,𝔽25)—62no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—64no—
455ΓL(1,𝔽25)—64no—
456ΓL(1,𝔽25)—64no—
457ΓL(1,𝔽25)—62no—
458ΓL(1,𝔽25)—62no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32AGL(1,ℤ/8)12yescomplemented
462C22×C32C22×D411yescharacteristic
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—44no—
469C2×C3⋊D3#12112yes—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4C2×#4111yescharacteristic
483C3⋊Dic3—21no—
484C3⋊Dic3#12112yes—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—91no—
491C22×D4—91no—
492C22×D4—181no—
493C23×C4—91no—
494AGL(1,ℤ/8)—184no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×D8—31no—
498C2×D8—91no—
499C2×M16—91no—
500C2×M16—91no—
501C2×M16—91no—
502C2×M16—91no—
503C2×M16—184no—
504C22×C8—91no—
505C22×C8D3211yescharacteristic, complemented
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509#121—31no—
510#121—31no—
511#121—31no—
512#121—91no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#120—181no—
518C4×D4—181no—
519C4×D4—181no—
520#117—91no—
521C2×C4⋊C4—91no—
522C2×C22⋊C4—181no—
523#107—31no—
524#107—91no—
525#106—31no—
526#106—91no—
527#103—31no—
528#103—91no—
529#102—31no—
530#102—31no—
531#102—31no—
532#102—91no—
533#102—91no—
534#102—91no—
535C23×C3—21no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3D3×D411yescharacteristic
540C23×C3D3×D411yescharacteristic
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—62no—
551C22×D3—62no—
552C22×D3—64no—
553C22×D3—62no—
554C22×D3—62no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—122no—
565C3×Q8—61no—
566C3×Q8—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—122no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4D3×D411yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—42no—
594#67—42no—
595#67—42no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—64no—
616C2×Dic3—122no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—122no—
624D12—122no—
625D12—122no—
626D12—122no—
627C4×D3—32no—
628C4×D3—32no—
629C4×D3—32no—
630C4×D3—32no—
631C4×D3—62no—
632C4×D3—62no—
633C4×D3—62no—
634C4×D3—62no—
635C4×D3—62no—
636C4×D3—62no—
637C4×D3—62no—
638C4×D3—64no—
639C4×D3—64no—
640C4×D3—62no—
641C4×D3—61no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—61no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648Dic6—21no—
649Dic6—21no—
650C3×C8—22no—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—22no—
654C3×C8D3×D412yescomplemented
655C3×C8D3×D412yescomplemented
656C3⋊C8—32no—
657C3⋊C8—32no—
658C3⋊C8—62no—
659C3⋊C8—62no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C2×C32—22no—
663C2×C32C2×#12111yescharacteristic
664C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
665C2×C32#57511yescharacteristic
666C3⋊D3—22no—
667C3⋊D3—41no—
668C3×D3—81no—
669C3×D3—81no—
670C3×D3—81no—
671C24—91no—
672C24—181no—
673#41—182no—
674#41—182no—
675C2×Q8—31no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—182no—
687C2×D4—182no—
688C2×D4—181no—
689C2×D4—364no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—91no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—182no—
696C22×C4—182no—
697C22×C4—181no—
698C22×C4—181no—
699C22×C4C2×D3211yescharacteristic
700SD16—62no—
701SD16—182no—
702D8—62no—
703D8—182no—
704M16—94no—
705M16—182no—
706M16—182no—
707M16—182no—
708C2×C8—22no—
709C2×C8—91no—
710C2×C8—91no—
711C2×C8—182no—
712C2×C8C2×D3211yescharacteristic
713C2×C8C2×D3211yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—31no—
717C4⋊C4—31no—
718C4⋊C4—61no—
719C4⋊C4—181no—
720C4⋊C4—181no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—181no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—22no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3#91112yescomplemented
749C22×C3#91412yescomplemented
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C2×D3×D411yescharacteristic
752C2×D3—32no—
753C2×D3—32no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—62no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—62no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—124no—
780C2×D3—124no—
781C2×D3—128no—
782C2×D3—244no—
783C2×D3—244no—
784C3×C4—22no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—121no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4—121no—
794C3×C4C2×D3×D411yescharacteristic
795C3×C4C2×D3×D411yescharacteristic
796C3×C4D3×#4111yescharacteristic
797C3×C4D3×#4111yescharacteristic
798Dic3—32no—
799Dic3—32no—
800Dic3—41no—
801Dic3—41no—
802Dic3—41no—
803Dic3—41no—
804Dic3—41no—
805Dic3—62no—
806Dic3—62no—
807Dic3—61no—
808Dic3—61no—
809C32#305511yescharacteristic, complemented, Sylow
810C23—61no—
811C23—61no—
812C23—61no—
813C23—91no—
814C23—91no—
815C23—182no—
816C23—182no—
817C23—361no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23#380211yescharacteristic
822Q8—61no—
823Q8—61no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—122no—
831D4—122no—
832D4—122no—
833D4—362no—
834D4—362no—
835D4—362no—
836D4—362no—
837D4—362no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—91no—
846C2×C4—92no—
847C2×C4—92no—
848C2×C4—91no—
849C2×C4—182no—
850C2×C4—182no—
851C2×C4—182no—
852C2×C4—181no—
853C2×C4—181no—
854C2×C4—362no—
855C2×C4—362no—
856C2×C4#380211yescharacteristic
857C2×C4C22×D3211yescharacteristic
858C8—21no—
859C8—92no—
860C8—181no—
861C8#381112yescomplemented
862C2×C3—24no—
863C2×C3—22no—
864C2×C3—22no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—241no—
869C2×C3—241no—
870C2×C3—241no—
871C2×C3D3×#12111yescharacteristic
872C2×C3D3×#12111yescharacteristic
873C2×C3C2×#91111yescharacteristic
874C2×C3C2×#91411yescharacteristic
875C2×C3#576811yescharacteristic
876C2×C3#576811yescharacteristic
877D3—62no—
878D3—62no—
879D3—81no—
880D3—81no—
881D3—81no—
882D3—122no—
883D3—122no—
884D3—121no—
885D3—121no—
886C22—21no—
887C22—21no—
888C22—92no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—181no—
899C22—181no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22—364no—
904C22—724no—
905C22#6379812yescomplemented
906C22C2×#380211yescharacteristic
907C4—21no—
908C4—92no—
909C4—121no—
910C4—121no—
911C4—121no—
912C4—121no—
913C4—121no—
914C4—181no—
915C4#6430611yescharacteristic
916C4C2×#381111yescharacteristic
917C3—21no—
918C3#8065711yescharacteristic, complemented
919C3#8071511yescharacteristic, complemented
920C2—22no—
921C2—182no—
922C2—241no—
923C2—241no—
924C2—241no—
925C2—361no—
926C2C2×#6379811yescharacteristic
927C2#1059468511yescharacteristic
928C2#1059508111yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#3743C2semidirect
2. #10595081C2semidirect
3. #10594922C2semidirect
4. C2×#63798C2semidirect
5. C3×#5115C2semidirect
6. C3×#5114C2semidirect
7. #10591179C2semidirect
8. #10591166C2semidirect
9. #10590957C2semidirect
10. #10590941C2semidirect
11. #10590846C2semidirect
12. #10590845C2semidirect
13. #10590842C2semidirect
14. #10590840C2semidirect
15. #10590688C2semidirect
22. C22×C32×C8C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
27. C2×#3743C22semidirect
28. C2×#3743C22semidirect
31. C3×#930C22semidirect
32. C3×#924C22semidirect
33. C2×C3×D24C22semidirect
34. C2×C3×#204C22semidirect
41. #63916C22semidirect
45. #63871C22semidirect
48. C2×#3715C22semidirect
49. C2×#3713C22semidirect
51. C3×#821C22semidirect
52. C3×#821C22semidirect
53. C3×#821C22semidirect
54. C3×#818C22semidirect
55. C3×#817C22semidirect
56. C3×#816C22semidirect
57. #63576C22semidirect
58. #63574C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
76. #5115D3semidirect
77. #5114D3semidirect
132. #3743D4semidirect
167. C22×C3×C8C2×D3semidirect
168. C22×C3×C8C2×D3semidirect
187. #930C2×D3semidirect
188. #924C2×D3semidirect
194. C2×D24C2×D3semidirect
195. C2×#204C2×D3semidirect
239. #821C2×D3semidirect
240. #821C2×D3semidirect
241. #821C2×D3semidirect
242. #818C2×D3semidirect
243. #817C2×D3semidirect
244. #816C2×D3semidirect
302. C32×C8C2×D4semidirect
304. C3⋊(C3⋊C8)C2×D4semidirect
461. C22×C32AGL(1,ℤ/8)semidirect
505. C22×C8D32semidirect
654. C3×C8D3×D4semidirect
655. C3×C8D3×D4semidirect
748. C22×C3#911semidirect
749. C22×C3#914semidirect
809. C32#3055semidirect
861. C8#3811semidirect
905. C22#63798semidirect
918. C3#80657semidirect
919. C3#80715semidirect

Maximal subgroups

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

subgroupindex
C22×#37432
#105950812
#105949222
C2×#637982
C3×#51152
C3×#51142
#105911792
#105911662
#105909572
#105909412
#105908462
#105908452
#105908422
#105908402
#105906882
#807153
#806573