Finite Group Databasebeta

← #11860332

Subgroups — #11860332

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic
2#10594605C211yesmaximal, characteristic, complemented
3#10594360C211yesmaximal, characteristic, complemented
4#10592560C211yesmaximal, characteristic, complemented
5C3×#4869C211yesmaximal, characteristic, complemented
6C3×#4852C211yesmaximal, characteristic, complemented
7#10590766C211yesmaximal, characteristic, complemented
8Dic3×D24C211yesmaximal, characteristic, complemented
9#10590664C211yesmaximal, characteristic, complemented
10#10590612C211yesmaximal, characteristic, complemented
11#10590594C211yesmaximal, characteristic, complemented
12#10590478C211yesmaximal, characteristic, complemented
13#10590455C211yesmaximal, characteristic, complemented
14#10590453C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#79865—31nomaximal
17C4×#914—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22#64101C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×#893C2211yescharacteristic, complemented
29C3×#887C2211yescharacteristic, complemented
30#63921—21no—
31#63904—21no—
32Dic3×D12C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34Dic3×D12C2211yescharacteristic, complemented
35C4×#624C2211yescharacteristic
36#63880—21no—
37#63879—21no—
38#63879—21no—
39#63878—21no—
40C4×D3×Dic3—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45#63798C418yescomplemented
46C32×#106C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49#63634C2211yescharacteristic, complemented
50C3×#815C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×#911—31no—
64C4×#239—31no—
65C4×D3×D4—31no—
66C4×D3×D4—31no—
67C4×#237—31no—
68C3×#442—31no—
69C3×C4×SD16—31no—
70#5164—31no—
71Dic3×D8—31no—
72C4×#215—31no—
73#5018—31no—
74#5014—31no—
75C4×#213—31no—
76#4869D311yescharacteristic, complemented
77#4861—31no—
78#4861—31no—
79#4861—61no—
80#4852D311yescharacteristic, complemented
81#4817—31no—
82#4803—31no—
83#4785—31no—
84#4771—31no—
85#4770—31no—
86#4770—31no—
87#4758—31no—
88#4756—31no—
89#4710—31no—
90#4707—31no—
91C4×D24—31no—
92C4×ΓL(1,𝔽25)—31no—
93C22×D32—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#625—21no—
105C2×#624D411yescharacteristic
106C2×#624D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3802—22no—
112#3802C2×C414yescomplemented
113C4×D32—44no—
114#3796—22no—
115#3796C2×C414yescomplemented
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C4×C3⋊Dic3—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3743C2×C414yescomplemented
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D24C2×C414yescomplemented
136C3×#204C2×C414yescomplemented
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3715C2×C414yescomplemented
145#3713C2×C414yescomplemented
146#3712—22no—
147C4×AGL(1,ℤ/8)—91noSylow
148C2×#239—31no—
149C2×#237—31no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C2×C3×SD16—31no—
155C2×C3×D8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165C2×#214—31no—
166C2×#213—31no—
167C2×#213—31no—
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—61no—
171C2×C4×Dic3—61no—
172#914—38no—
173#911—38no—
174C2×D24C2×D311yescharacteristic
175C2×#204C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—61no—
181#893—61no—
182#893C2×D311yescharacteristic
183#893C2×D311yescharacteristic
184#893C2×D311yescharacteristic, complemented
185#892—31no—
186#892—31no—
187#892—61no—
188#892—61no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—61no—
192#887C2×D311yescharacteristic, complemented
193#67⋊C4—61no—
194#67⋊C4—61no—
195#67⋊C4—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#877—61no—
199C4×D12—31no—
200C4×D12—31no—
201C4×D12—31no—
202C4×D12—61no—
203C42×D3—31no—
204C42×D3—31no—
205C42×D3—61no—
206C4×Dic6—31no—
207C3×#106—21no—
208C3×#106C2×D311yescharacteristic, complemented
209C3×#106C2×D311yescharacteristic, complemented
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#97—31no—
215C3×C4×C8—31no—
216#835—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#818—31no—
224#818—31no—
225#818—61no—
226#816—31no—
227#815—31no—
228#815C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic, complemented
231#810C2×D311yescharacteristic, complemented
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic, complemented
235#808—31no—
236#808—31no—
237#808—61no—
238#807—31no—
239#807—31no—
240#807—61no—
241#803—31no—
242C4×C3⋊C8—31no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C2×D32—24no—
248C2×D32—42no—
249C2×D32—42no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4×C3⋊D3—42no—
257C4×C3⋊D3C22×C412yes—
258C4×C3⋊D3#4112yes—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×D12C22×C412yes—
269C3×D12C22×C412yescomplemented
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×Dic6—21no—
274C3×Dic6C22×C412yescomplemented
275#626—24no—
276#625—24no—
277#624—22no—
278#624—41no—
279D3×Dic3—24no—
280D3×Dic3—42no—
281D3×Dic3—42no—
282D3×Dic3—42no—
283C32×C8C22×C412yescomplemented
284C3⋊(C3⋊C8)C22×C412yescomplemented
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C2×AGL(1,ℤ/8)—91no—
288C4×#41—91no—
289C2×C4×D4—91no—
290#442—31no—
291#442—91no—
292#440—91no—
293#440—91no—
294C4×SD16—31no—
295C4×SD16—91no—
296C4×D8—91no—
297C4×D8—91no—
298#428—91no—
299#418—91no—
300#417—91no—
301C4×M16—91no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#239—34no—
319#239—62no—
320#237—34no—
321#237—62no—
322D3×D4—34no—
323D3×D4—34no—
324D3×D4—62no—
325D3×D4—62no—
326C2×D12—61no—
327C2×D12C22×D311yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—121no—
347C2×C4×D3—124no—
348C2×C4×D3—124no—
349C2×Dic6C22×D311yescharacteristic
350C3×SD16—34no—
351C3×D8—34no—
352C2×C3×C8—21no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368C3×C42—31no—
369C3×C42—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#215—34no—
374#214—34no—
375#213—34no—
376#213—34no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—121no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—21no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—121no—
408C4×Dic3C22×D311yescharacteristic
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415D24C4×D314yescomplemented
416#204C4×D314yescomplemented
417ΓL(1,𝔽25)—34no—
418ΓL(1,𝔽25)—34no—
419ΓL(1,𝔽25)—64no—
420ΓL(1,𝔽25)—62no—
421ΓL(1,𝔽25)—62no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3C4×D412yes—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435D32—48no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4C23×C411yescharacteristic
439C32×C4C2×#4111yescharacteristic
440C3⋊Dic3—41no—
441C3⋊Dic3—41no—
442C3⋊Dic3C4×D412yes—
443C3×Dic3—22no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3AGL(1,ℤ/8)12yescomplemented
448C2×#41—91no—
449C22×D4—91no—
450C23×C4—181no—
451AGL(1,ℤ/8)—98no—
452C2×SD16—31no—
453C2×SD16—91no—
454C2×D8—31no—
455C2×D8—91no—
456C2×M16—91no—
457C2×M16—91no—
458C4×Q8—31no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4—181no—
470#117—91no—
471#117—181no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—181no—
474C2×C42—91no—
475C2×C42—181no—
476#107—91no—
477#107—91no—
478#106—91no—
479#106D3211yescharacteristic, complemented
480#103—31no—
481#103—91no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#97—31no—
489#97—91no—
490C4×C8—31no—
491C4×C8—91no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—61no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C3×Q8—32no—
508C3×Q8—61no—
509C3×D4—32no—
510C3×D4—32no—
511C3×D4—32no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—61no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—64no—
533#67—64no—
534#67—64no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—61no—
539C2×Dic3—64no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—21no—
555D12—21no—
556D12—64no—
557D12C2×C4×D312yes—
558D12C2×C4×D312yes—
559D12C2×C4×D312yescomplemented
560C4×D3—32no—
561C4×D3—32no—
562C4×D3—32no—
563C4×D3—32no—
564C4×D3—42no—
565C4×D3—42no—
566C4×D3—42no—
567C4×D3—62no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—64no—
571C4×D3—62no—
572C4×D3—121no—
573C4×D3—121no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—242no—
580Dic6—21no—
581Dic6C2×C4×D312yescomplemented
582C3×C8—22no—
583C3×C8—61no—
584C3×C8—61no—
585C3×C8C2×C4×D312yescomplemented
586C3×C8C2×C4×D312yescomplemented
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—32no—
590C3⋊C8—32no—
591C3⋊C8—62no—
592C2×C32C2×C4×D411yescharacteristic
593C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
594C2×C32#57511yescharacteristic
595C3⋊D3—22no—
596C3×D3—42no—
597C3×D3—42no—
598C3×D3—42no—
599C24—181no—
600#41—94no—
601#41—182no—
602C2×Q8—31no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—94no—
607C2×D4—181no—
608C2×D4—182no—
609C2×D4—181no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—91no—
614C22×C4—91no—
615C22×C4—91no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—364no—
622SD16—34no—
623SD16—94no—
624D8—34no—
625D8—94no—
626M16—94no—
627M16—182no—
628C2×C8—31no—
629C2×C8—31no—
630C2×C8—91no—
631C2×C8C2×D3211yescharacteristic
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4C2×D3211yescharacteristic
638C4⋊C4C2×D3211yescharacteristic
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C42—31no—
647C42—31no—
648C42—61no—
649C42—91no—
650C42—91no—
651C42—181no—
652C42—181no—
653C22×C3—21no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—32no—
669C2×D3—32no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—62no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—128no—
684C2×D3—128no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—32no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—62no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4C22×C4×D311yescharacteristic
699C3×C4C22×C4×D311yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4D3×#4111yescharacteristic
702Dic3—21no—
703Dic3—21no—
704Dic3—21no—
705Dic3—22no—
706Dic3—32no—
707Dic3—32no—
708Dic3—62no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—241no—
714Dic3—241no—
715Dic3#91412yescomplemented
716C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
717C23—61no—
718C23—61no—
719C23—61no—
720C23—91no—
721C23—184no—
722C23—362no—
723C23—362no—
724Q8—32no—
725Q8—61no—
726D4—32no—
727D4—32no—
728D4—32no—
729D4—61no—
730D4—61no—
731D4—61no—
732D4—184no—
733D4—184no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—61no—
741C2×C4—91no—
742C2×C4—92no—
743C2×C4—92no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—182no—
748C2×C4—184no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—362no—
752C2×C4—362no—
753C2×C4—362no—
754C2×C4—361no—
755C2×C4—362no—
756C2×C4C22×D3211yescharacteristic
757C8—61no—
758C8—61no—
759C8—92no—
760C8C4×D3212yescomplemented
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—122no—
765C2×C3—122no—
766C2×C3—122no—
767C2×C3C4×D3×D411yescharacteristic
768C2×C3C4×D3×D411yescharacteristic
769C2×C3C2×#91411yescharacteristic
770C2×C3#576811yescharacteristic
771C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
772C2×C3#577311yescharacteristic
773D3—42no—
774D3—42no—
775D3—42no—
776D3—62no—
777D3—62no—
778D3—122no—
779C22—62no—
780C22—62no—
781C22—62no—
782C22—92no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—181no—
790C22—181no—
791C22—368no—
792C22D32×D411yescharacteristic
793C4—32no—
794C4—41no—
795C4—41no—
796C4—62no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—92no—
801C4—361no—
802C4—361no—
803C4C2×C4×D3211yescharacteristic
804C4#6431911yescharacteristic
805C3—21no—
806C3C4×#91411yescharacteristic, complemented
807C3#7986511yescharacteristic, complemented
808C2—122no—
809C2—122no—
810C2—122no—
811C2—182no—
812C2#1059460511yescharacteristic
813C2D3×#91411yescharacteristic
814C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63798C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594605C2semidirect
3. #10594360C2semidirect
4. #10592560C2semidirect
5. C3×#4869C2semidirect
6. C3×#4852C2semidirect
7. #10590766C2semidirect
8. Dic3×D24C2semidirect
9. #10590664C2semidirect
10. #10590612C2semidirect
11. #10590594C2semidirect
12. #10590478C2semidirect
13. #10590455C2semidirect
14. #10590453C2semidirect
15. #10590452C2semidirect
28. C3×#893C22semidirect
29. C3×#887C22semidirect
34. Dic3×D12C22semidirect
41. Dic3×Dic6C22semidirect
45. #63798C4semidirect
46. C32×#106C22semidirect
47. #63645C22semidirect
48. #63635C22semidirect
49. #63634C22semidirect
50. C3×#815C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
55. C3×#809C22semidirect
56. #63566C22semidirect
59. #63563C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
76. #4869D3semidirect
80. #4852D3semidirect
112. #3802C2×C4semidirect
115. #3796C2×C4semidirect
125. #3743C2×C4semidirect
135. C3×D24C2×C4semidirect
136. C3×#204C2×C4semidirect
144. #3715C2×C4semidirect
145. #3713C2×C4semidirect
184. #893C2×D3semidirect
192. #887C2×D3semidirect
208. C3×#106C2×D3semidirect
209. C3×#106C2×D3semidirect
228. #815C2×D3semidirect
230. C8×Dic3C2×D3semidirect
231. #810C2×D3semidirect
234. #809C2×D3semidirect
269. C3×D12C22×C4semidirect
274. C3×Dic6C22×C4semidirect
283. C32×C8C22×C4semidirect
284. C3⋊(C3⋊C8)C22×C4semidirect
415. D24C4×D3semidirect
416. #204C4×D3semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
479. #106D32semidirect
559. D12C2×C4×D3semidirect
581. Dic6C2×C4×D3semidirect
585. C3×C8C2×C4×D3semidirect
586. C3×C8C2×C4×D3semidirect
715. Dic3#914semidirect
716. C32C4×AGL(1,ℤ/8)semidirect
760. C8C4×D32semidirect
806. C3C4×#914semidirect
807. C3#79865semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
#105946052
#105943602
#105925602
C3×#48692
C3×#48522
#105907662
Dic3×D242
#105906642
#105906122
#105905942
#105904782
#105904552
#105904532
#105904522
#798653
C4×#9143