Finite Group Databasebeta

← #11860343

Subgroups — #11860343

Order 1152.

1167 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic
2C4×#3802C211yesmaximal, characteristic, complemented
3C4×#3796C211yesmaximal, characteristic, complemented
4#10592406C211yesmaximal, characteristic, complemented
5C3×#4711C211yesmaximal, characteristic, complemented
6C3×#4710C211yesmaximal, characteristic, complemented
7#10590957C211yesmaximal, characteristic, complemented
8#10590941C211yesmaximal, characteristic, complemented
9#10590777C211yesmaximal, characteristic, complemented
10#10590775C211yesmaximal, characteristic, complemented
11#10590742C211yesmaximal, characteristic, complemented
12#10590740C211yesmaximal, characteristic, complemented
13#10590688C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590344C211yesmaximal, characteristic, complemented
16#79865—31nomaximal
17#79773—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23C42×C3⋊D3C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic, complemented
29C3×C4×Dic6C2211yescharacteristic, complemented
30#63921—21no—
31C4×#626—21no—
32#63902—21no—
33C4×#625—21no—
34#63900C2211yescharacteristic
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38#63881—21no—
39#63878—21no—
40C4×D3×Dic3—21no—
41#63849C2211yescharacteristic
42#63843C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45#63798C418yescomplemented
46C32×#97C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C8×C3⋊Dic3C2211yescharacteristic, complemented
49#63630C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63574C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#63562C2211yescharacteristic, 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×#440—31no—
70Dic3×SD16—31no—
71Dic3×D8—31no—
72#5026—31no—
73#5018—31no—
74#5014—31no—
75#5014—31no—
76#4881—31no—
77#4872—31no—
78#4861—31no—
79#4852—31no—
80#4803—31no—
81#4788—31no—
82#4771—31no—
83#4770—31no—
84#4770—31no—
85#4758—31no—
86#4756—31no—
87#4756—31no—
88#4711D311yescharacteristic, complemented
89#4710D311yescharacteristic, complemented
90#4707—31no—
91#4707—31no—
92#4707—61no—
93C22×D32—21no—
94C2×C4×C3⋊D3D411yescharacteristic
95C2×C4×C3⋊D3D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#625—21no—
106C2×#624—21no—
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
117C2×C32×C8C2311yescharacteristic
118C32×C42C2311yescharacteristic
119C4×C3⋊Dic3D411yescharacteristic
120C4×C3⋊Dic3D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3743—22no—
125#3743C2×C414yescomplemented
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×D24C2×C414yescomplemented
136C3×#204C2×C414yescomplemented
137#3724—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144Dic32—21no—
145#3715C2×C414yescomplemented
146#3713C2×C414yescomplemented
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—
181C2×ΓL(1,𝔽25)—61no—
182#893—31no—
183#893—31no—
184#893—31no—
185#893—61no—
186#892—31no—
187#892—31no—
188#892—61no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#887—31no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195D3×C22⋊C4—61no—
196D3×C22⋊C4—61no—
197#877—61no—
198C4×D12—61no—
199C4×D12C2×D311yescharacteristic
200C4×D12C2×D311yescharacteristic
201C4×D12C2×D311yescharacteristic, complemented
202C42×D3—31no—
203C42×D3—31no—
204C42×D3—61no—
205C42×D3—61no—
206C4×Dic6C2×D311yescharacteristic, complemented
207C3×#107—31no—
208C3×#106—31no—
209C3×#103—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#97—21no—
214C3×#97C2×D311yescharacteristic, complemented
215C3×#97C2×D311yescharacteristic, complemented
216#835—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#821C2×D311yescharacteristic
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic, complemented
223#818C2×D311yescharacteristic, complemented
224#817C2×D311yescharacteristic, complemented
225#816C2×D311yescharacteristic, complemented
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
231C8×Dic3—61no—
232#810—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#808—31no—
237#808—31no—
238#807—31no—
239#807—31no—
240#803—31no—
241#803—31no—
242#803—61no—
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×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4×C3⋊D3—22no—
257C4×C3⋊D3—41no—
258C4×C3⋊D3C22×C412yes—
259C4×C3⋊D3#4112yes—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12C22×C412yes—
269C3×D12C22×C412yes—
270C3×D12C22×C412yescomplemented
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×Dic6—21no—
275C3×Dic6C22×C412yescomplemented
276#626—24no—
277#625—24no—
278#624—42no—
279D3×Dic3—24no—
280D3×Dic3—42no—
281D3×Dic3—42no—
282D3×Dic3—42no—
283C32×C8—21no—
284C32×C8C22×C412yescomplemented
285C3⋊(C3⋊C8)—21no—
286C3⋊(C3⋊C8)C22×C412yescomplemented
287C2×AGL(1,ℤ/8)—91no—
288C4×#41—91no—
289C2×C4×D4—91no—
290#442—31no—
291#442—91no—
292#440—31no—
293#440—91no—
294C4×SD16—91no—
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—61no—
347C2×C4×D3—61no—
348C2×C4×D3—124no—
349C2×C4×D3—124no—
350C2×Dic6C22×D311yescharacteristic
351C3×SD16—34no—
352C3×D8—34no—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—21no—
368C3×C42—61no—
369C3×C42C22×D311yescharacteristic
370C3×C42C22×D311yescharacteristic
371#217—61no—
372#217—61no—
373#217—61no—
374#215—34no—
375#214—34no—
376#213—34no—
377#213—34no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—21no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—61no—
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—
422ΓL(1,𝔽25)—64no—
423C22×C32C22×D411yescharacteristic
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3C4×D412yes—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436D32—48no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4C23×C411yescharacteristic
440C32×C4C2×#4111yescharacteristic
441C3⋊Dic3—21no—
442C3⋊Dic3C4×D412yes—
443C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
444C3×Dic3—22no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C2×#41—91no—
450C22×D4—91no—
451C23×C4—181no—
452AGL(1,ℤ/8)—98no—
453C2×SD16—31no—
454C2×SD16—91no—
455C2×D8—31no—
456C2×D8—91no—
457C2×M16—91no—
458C2×M16—91no—
459C4×Q8—31no—
460C4×Q8—91no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—91no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4—181no—
470C4×D4—181no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—91no—
474C2×C22⋊C4—181no—
475C2×C42—91no—
476C2×C42—181no—
477#107—31no—
478#107—91no—
479#106—31no—
480#106—91no—
481#103—31no—
482#103—91no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102—91no—
487#102—91no—
488#102—91no—
489#97—91no—
490#97D3211yescharacteristic, complemented
491C4×C8—91no—
492C4×C8—91no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—31no—
500C22×D3—31no—
501C22×D3—61no—
502C22×D3—64no—
503C22×D3—64no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C3×Q8—32no—
509C3×Q8—61no—
510C3×D4—32no—
511C3×D4—32no—
512C3×D4—32no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—61no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—64no—
534#67—64no—
535#67—64no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—64no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—122no—
554D12—21no—
555D12—21no—
556D12—21no—
557D12—64no—
558D12C2×C4×D312yes—
559D12C2×C4×D312yes—
560D12C2×C4×D312yescomplemented
561C4×D3—32no—
562C4×D3—32no—
563C4×D3—32no—
564C4×D3—32no—
565C4×D3—42no—
566C4×D3—42no—
567C4×D3—42no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—62no—
571C4×D3—62no—
572C4×D3—64no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—121no—
580C4×D3—121no—
581C4×D3—122no—
582Dic6—21no—
583Dic6C2×C4×D312yescomplemented
584C3×C8—22no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—22no—
588C3×C8C2×C4×D312yescomplemented
589C3×C8C2×C4×D312yescomplemented
590C3⋊C8—32no—
591C3⋊C8—32no—
592C3⋊C8—62no—
593C3⋊C8—62no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C2×C32C2×C4×D411yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57511yescharacteristic
599C3⋊D3—22no—
600C3×D3—42no—
601C3×D3—42no—
602C3×D3—42no—
603C24—181no—
604#41—94no—
605#41—182no—
606C2×Q8—31no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—94no—
611C2×D4—181no—
612C2×D4—182no—
613C2×D4—181no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—91no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4—364no—
626SD16—34no—
627SD16—94no—
628D8—34no—
629D8—94no—
630M16—94no—
631M16—182no—
632C2×C8—91no—
633C2×C8—91no—
634C2×C8C2×D3211yescharacteristic
635C2×C8C2×D3211yescharacteristic
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—61no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C42—61no—
651C42—91no—
652C42—91no—
653C42—91no—
654C42—181no—
655C42—181no—
656C42C2×D3211yescharacteristic
657C22×C3—21no—
658C22×C3—62no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—32no—
673C2×D3—32no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—128no—
688C2×D3—128no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—62no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4C22×C4×D311yescharacteristic
703C3×C4C22×C4×D311yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4D3×#4111yescharacteristic
706Dic3—22no—
707Dic3—32no—
708Dic3—32no—
709Dic3—32no—
710Dic3—32no—
711Dic3—41no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—62no—
716Dic3—62no—
717Dic3—62no—
718Dic3—61no—
719Dic3—61no—
720C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
721C23—61no—
722C23—61no—
723C23—61no—
724C23—91no—
725C23—184no—
726C23—362no—
727C23—362no—
728Q8—32no—
729Q8—61no—
730D4—32no—
731D4—32no—
732D4—32no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—184no—
737D4—184no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—92no—
746C2×C4—92no—
747C2×C4—91no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—182no—
752C2×C4—184no—
753C2×C4—361no—
754C2×C4—362no—
755C2×C4—362no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4#380211yescharacteristic
759C2×C4#380211yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—21no—
762C8—92no—
763C8—181no—
764C8C4×D3212yescomplemented
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—122no—
769C2×C3—122no—
770C2×C3—122no—
771C2×C3C4×D3×D411yescharacteristic
772C2×C3C4×D3×D411yescharacteristic
773C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
774C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
775C2×C3#577311yescharacteristic
776C2×C3#577711yescharacteristic
777D3—42no—
778D3—42no—
779D3—42no—
780D3—62no—
781D3—62no—
782D3—122no—
783C22—62no—
784C22—62no—
785C22—62no—
786C22—92no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—181no—
794C22—181no—
795C22—368no—
796C22C2×#380211yescharacteristic
797C4—21no—
798C4—21no—
799C4—62no—
800C4—92no—
801C4—92no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—181no—
807C4C2×C4×D3211yescharacteristic
808C4#6430611yescharacteristic
809C3—21no—
810C3#7977311yescharacteristic, complemented
811C3#7986511yescharacteristic, complemented
812C2—122no—
813C2—122no—
814C2—122no—
815C2—182no—
816C2C4×#380211yescharacteristic
817C2#1059471611yescharacteristic
818C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63798C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C4×#3802C2semidirect
3. C4×#3796C2semidirect
4. #10592406C2semidirect
5. C3×#4711C2semidirect
6. C3×#4710C2semidirect
7. #10590957C2semidirect
8. #10590941C2semidirect
9. #10590777C2semidirect
10. #10590775C2semidirect
11. #10590742C2semidirect
12. #10590740C2semidirect
13. #10590688C2semidirect
14. #10590358C2semidirect
15. #10590344C2semidirect
28. C3×C4×D12C22semidirect
29. C3×C4×Dic6C22semidirect
37. #63898C22semidirect
42. #63843C22semidirect
45. #63798C4semidirect
46. C32×#97C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. C8×C3⋊Dic3C22semidirect
49. #63630C22semidirect
52. C3×#821C22semidirect
53. C3×#818C22semidirect
54. C3×#817C22semidirect
55. C3×#816C22semidirect
56. #63576C22semidirect
57. #63574C22semidirect
58. #63565C22semidirect
61. #63562C22semidirect
88. #4711D3semidirect
89. #4710D3semidirect
112. #3802C2×C4semidirect
115. #3796C2×C4semidirect
125. #3743C2×C4semidirect
135. C3×D24C2×C4semidirect
136. C3×#204C2×C4semidirect
145. #3715C2×C4semidirect
146. #3713C2×C4semidirect
201. C4×D12C2×D3semidirect
206. C4×Dic6C2×D3semidirect
214. C3×#97C2×D3semidirect
215. C3×#97C2×D3semidirect
222. #821C2×D3semidirect
223. #818C2×D3semidirect
224. #817C2×D3semidirect
225. #816C2×D3semidirect
270. C3×D12C22×C4semidirect
275. C3×Dic6C22×C4semidirect
284. C32×C8C22×C4semidirect
286. C3⋊(C3⋊C8)C22×C4semidirect
415. D24C4×D3semidirect
416. #204C4×D3semidirect
443. C3⋊Dic3AGL(1,ℤ/8)semidirect
490. #97D32semidirect
560. D12C2×C4×D3semidirect
583. Dic6C2×C4×D3semidirect
588. C3×C8C2×C4×D3semidirect
589. C3×C8C2×C4×D3semidirect
720. C32C4×AGL(1,ℤ/8)semidirect
764. C8C4×D32semidirect
810. C3#79773semidirect
811. C3#79865semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
C4×#38022
C4×#37962
#105924062
C3×#47112
C3×#47102
#105909572
#105909412
#105907772
#105907752
#105907422
#105907402
#105906882
#105903582
#105903442
#798653
#797733