Finite Group Databasebeta

← #11860340

Subgroups — #11860340

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic
3C4×#3796C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic, complemented
6#10591445C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591426C211yesmaximal, characteristic, complemented
9#10590612C211yesmaximal, characteristic, complemented
10#10590583C211yesmaximal, characteristic, complemented
11#10590483C211yesmaximal, characteristic, complemented
12#10590459C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590247C211yesmaximal, characteristic, complemented
16#79865—31nomaximal
17#79773—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C2×#3796C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23C4×#638—21no—
24#64102C2211yescharacteristic
25C4⋊C4×C3⋊D3C2211yescharacteristic
26#64090—21no—
27C22⋊C4×C3⋊D3—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C42×C3⋊D3C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63937C418yescomplemented
35C4×#626—21no—
36#63898C2211yescharacteristic, complemented
37#63881—21no—
38#63878—21no—
39C4×D3×Dic3—21no—
40#63849C2211yescharacteristic
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#803C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×#911—31no—
64C4×#239—31no—
65C4×D3×D4—31no—
66C4×D3×D4—31no—
67C4×D3×D4—61no—
68C4×#237—31no—
69C3×#442—31no—
70C3×#440—31no—
71Dic3×SD16—31no—
72Dic3×D8—31no—
73#5026—31no—
74#5018D311yescharacteristic, complemented
75#5014—31no—
76#5014D311yescharacteristic, complemented
77#4881—31no—
78#4872—31no—
79#4861—31no—
80#4852—31no—
81#4803—31no—
82#4788—31no—
83#4771—31no—
84#4770—31no—
85#4770—31no—
86#4758—31no—
87#4756—31no—
88#4756—31no—
89#4711—31no—
90#4710—31no—
91#4707—31no—
92#4707—31no—
93C23×C3⋊D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3C2×C414yescomplemented
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3—44no—
105C2×C4×C3⋊D3D411yescharacteristic
106C2×C4×C3⋊D3D411yescharacteristic
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3796—22no—
115#3796C2×C414yescomplemented
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119#3757—21no—
120#3752—21no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C4×C3⋊Dic3D411yescharacteristic
125C4×C3⋊Dic3D411yescharacteristic
126C4×C3⋊Dic3C2311yescharacteristic
127C3×#214C2×C414yescomplemented
128C3×#213C2×C414yescomplemented
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3717C2×C414yescomplemented
144#3714C2×C414yescomplemented
145#3712—22no—
146#3712C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—91noSylow
148C2×#239—31no—
149C2×#237—31no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C22×C4×D3—61no—
154C22×C4×D3—61no—
155C22×C4×D3—62no—
156C2×C3×SD16—31no—
157C2×C3×D8—31no—
158C3×C4×Q8—31no—
159C3×C4×D4—21no—
160C3×C4×D4—31no—
161C3×C4×D4C2×D311yescharacteristic
162C3×C4×D4C2×D311yescharacteristic
163Q8×Dic3—31no—
164C2×#215—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169C2×#214C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213C2×D311yescharacteristic
172C4×#67—61no—
173C4×#67—61no—
174C4×#67—61no—
175C4×#67—62no—
176C2×C4×Dic3—61no—
177#914—38no—
178#911—38no—
179C2×D24—31no—
180C2×#204—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—31no—
185#893—31no—
186#893—31no—
187#893—31no—
188#893—61no—
189#893—61no—
190#892—31no—
191#892—31no—
192#892—61no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—61no—
196#887—31no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#67⋊C4—61no—
200#67⋊C4—62no—
201D3×C22⋊C4—61no—
202D3×C22⋊C4—61no—
203D3×C22⋊C4—62no—
204#877—61no—
205C4×D12—31no—
206C4×D12—31no—
207C4×D12—61no—
208C4×D12—61no—
209C4×D12C2×D311yescharacteristic, complemented
210C42×D3—31no—
211C42×D3—31no—
212C42×D3—61no—
213C42×D3—61no—
214C4×Dic6C2×D311yescharacteristic, complemented
215C3×#107—31no—
216C3×#106—31no—
217C3×#103—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#97—31no—
222C3×#97—31no—
223#835—31no—
224#832—31no—
225#832C2×D311yescharacteristic
226#832C2×D311yescharacteristic
227#821—31no—
228#821—31no—
229#821—31no—
230#818—31no—
231#817—31no—
232#816—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—31no—
237#810C2×D311yescharacteristic, complemented
238#809—31no—
239#809—31no—
240#809C2×D311yescharacteristic, complemented
241#808—31no—
242#808C2×D311yescharacteristic, complemented
243#807—31no—
244#807C2×D311yescharacteristic, complemented
245#803C2×D311yescharacteristic, complemented
246#803C2×D311yescharacteristic, complemented
247C23×C32—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—24no—
250C22×C3⋊D3—42no—
251C22×C3⋊D3—42no—
252C22×C3⋊D3C2×D411yescharacteristic
253C22×C3×D3—21no—
254C32×D4—21no—
255C32×D4C22×C412yes—
256C2×C32×C4—21no—
257C2×C32×C4—42no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261#638—24no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—42no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)C22×C412yes—
269C4×C3⋊D3—22no—
270C4×C3⋊D3—41no—
271C4×C3⋊D3—42no—
272C4×C3⋊D3—42no—
273C4×C3⋊D3—42no—
274C4×C3⋊D3C22×C412yes—
275C4×C3⋊D3#4112yes—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C3×D12—21no—
280C3×D12C22×C412yescomplemented
281C3×C4×D3—42no—
282C3×Dic6—21no—
283C3×Dic6C22×C412yescomplemented
284#626—24no—
285D3×Dic3—24no—
286D3×Dic3—42no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8C22×C412yescomplemented
290C3×C3⋊C8C22×C412yescomplemented
291C2×AGL(1,ℤ/8)—91no—
292C4×#41—91no—
293C2×C4×D4—91no—
294#442—31no—
295#442—91no—
296#440—31no—
297#440—91no—
298C4×SD16—91no—
299C4×SD16—91no—
300C4×D8—91no—
301C4×D8—91no—
302#428—91no—
303#418—91no—
304#417—91no—
305C4×M16—91no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—62no—
309C2×C3×Q8—31no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—22no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—62no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—62no—
327#239—34no—
328#239—62no—
329#237—34no—
330#237—62no—
331D3×D4—34no—
332D3×D4—34no—
333D3×D4—64no—
334D3×D4—62no—
335D3×D4—62no—
336D3×D4—64no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—124no—
364C2×C4×D3—124no—
365C2×C4×D3—128no—
366C2×Dic6C22×D311yescharacteristic
367C3×SD16—34no—
368C3×D8—34no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C22⋊C4—22no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—61no—
383C3×C42—21no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C22×D311yescharacteristic
387#217—61no—
388#217—61no—
389#217—61no—
390#217—62no—
391#215—34no—
392#214C4×D314yescomplemented
393#213—34no—
394#213C4×D314yescomplemented
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3C22×D311yescharacteristic
410C4⋊Dic3C22×D311yescharacteristic
411Dic3⋊C4—21no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—62no—
416C4×Dic3—21no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C2×C3⋊C8C22×D311yescharacteristic
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434D24—34no—
435#204—34no—
436ΓL(1,𝔽25)—34no—
437ΓL(1,𝔽25)—34no—
438ΓL(1,𝔽25)—62no—
439ΓL(1,𝔽25)—62no—
440C22×C32—22no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32C22×D411yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—48no—
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3C4×D412yes—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C32×C4—21no—
455C32×C4—21no—
456C32×C4—41no—
457C32×C4C23×C411yescharacteristic
458C32×C4C2×#4111yescharacteristic
459C3⋊Dic3—21no—
460C3⋊Dic3—41no—
461C3⋊Dic3C4×D412yes—
462C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
463C3×Dic3—22no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C2×#41—91no—
467C22×D4—91no—
468C23×C4—181no—
469AGL(1,ℤ/8)—98no—
470C2×SD16—31no—
471C2×SD16—91no—
472C2×D8—31no—
473C2×D8—91no—
474C2×M16—91no—
475C2×M16—91no—
476C4×Q8—31no—
477C4×Q8—91no—
478C4×D4—31no—
479C4×D4—91no—
480C4×D4—91no—
481C4×D4—91no—
482C4×D4—91no—
483C4×D4—181no—
484C4×D4—181no—
485C4×D4—181no—
486C4×D4—181no—
487C4×D4D3211yescharacteristic
488#117—91no—
489#117—181no—
490C2×C4⋊C4—91no—
491C2×C22⋊C4—181no—
492C2×C42—91no—
493C2×C42—181no—
494#107—31no—
495#107—91no—
496#106—31no—
497#106—91no—
498#103—31no—
499#103—91no—
500#102—31no—
501#102—31no—
502#102—31no—
503#102—91no—
504#102—91no—
505#102—91no—
506#97—31no—
507#97—31no—
508C4×C8—91no—
509C4×C8—91no—
510C23×C3—22no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—61no—
514C22×D3—21no—
515C22×D3—31no—
516C22×D3—31no—
517C22×D3—61no—
518C22×D3—64no—
519C22×D3—64no—
520C22×D3—62no—
521C22×D3—68no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—124no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—124no—
528C22×D3—122no—
529C22×D3—122no—
530C3×Q8—32no—
531C3×Q8—61no—
532C3×D4—22no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—22no—
536C3×D4—32no—
537C3×D4—61no—
538C3×D4C2×C4×D312yes—
539C3×D4C2×C4×D312yes—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—44no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—122no—
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—64no—
560#67—64no—
561#67—64no—
562#67—68no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—64no—
576C2×Dic3—62no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3—124no—
583D12—21no—
584D12—32no—
585D12—32no—
586D12—62no—
587D12—62no—
588D12—64no—
589D12—61no—
590D12—61no—
591D12C2×C4×D312yescomplemented
592C4×D3—32no—
593C4×D3—32no—
594C4×D3—32no—
595C4×D3—32no—
596C4×D3—42no—
597C4×D3—62no—
598C4×D3—62no—
599C4×D3—62no—
600C4×D3—62no—
601C4×D3—64no—
602C4×D3—64no—
603C4×D3—122no—
604C4×D3—122no—
605C4×D3—122no—
606C4×D3—121no—
607C4×D3—121no—
608C4×D3—124no—
609C4×D3—124no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—124no—
614C4×D3—122no—
615C4×D3—122no—
616Dic6—21no—
617Dic6C2×C4×D312yescomplemented
618C3×C8—32no—
619C3×C8—32no—
620C3×C8—61no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—21no—
624C3⋊C8C2×C4×D312yescomplemented
625C3⋊C8C2×C4×D312yescomplemented
626C2×C32—42no—
627C2×C32C2×C4×D411yescharacteristic
628C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
629C2×C32#57511yescharacteristic
630C3⋊D3—22no—
631C3⋊D3—42no—
632C3×D3—42no—
633C24—181no—
634#41—94no—
635#41—182no—
636C2×Q8—31no—
637C2×D4—31no—
638C2×D4—94no—
639C2×D4—91no—
640C2×D4—181no—
641C2×D4—182no—
642C2×D4—181no—
643C2×D4C2×D3211yescharacteristic
644C22×C4—21no—
645C22×C4—61no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—181no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4—181no—
653C22×C4—181no—
654C22×C4—181no—
655C22×C4—364no—
656SD16—34no—
657SD16—94no—
658D8—34no—
659D8—94no—
660M16—94no—
661M16—182no—
662C2×C8—31no—
663C2×C8—31no—
664C2×C8—31no—
665C2×C8—31no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—61no—
669C4⋊C4—91no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C4⋊C4C2×D3211yescharacteristic
673C22⋊C4—21no—
674C22⋊C4—61no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C42—61no—
681C42—91no—
682C42—91no—
683C42—91no—
684C42—181no—
685C42—181no—
686C42C2×D3211yescharacteristic
687C22×C3—24no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—21no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—62no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C2×D3×D411yescharacteristic
702C2×D3—22no—
703C2×D3—32no—
704C2×D3—32no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—64no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—1216no—
718C2×D3—128no—
719C2×D3—128no—
720C2×D3—122no—
721C2×D3—122no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C3×C4—22no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—41no—
734C3×C4—42no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—62no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4C22×C4×D311yescharacteristic
741C3×C4C22×C4×D311yescharacteristic
742C3×C4D3×#4111yescharacteristic
743C3×C4D3×#4111yescharacteristic
744Dic3—22no—
745Dic3—32no—
746Dic3—32no—
747Dic3—32no—
748Dic3—32no—
749Dic3—41no—
750Dic3—41no—
751Dic3—62no—
752Dic3—62no—
753Dic3—61no—
754Dic3—61no—
755Dic3—121no—
756Dic3—122no—
757Dic3—121no—
758Dic3—121no—
759C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
760C23—21no—
761C23—61no—
762C23—91no—
763C23—184no—
764C23—181no—
765C23—362no—
766C23—362no—
767Q8—32no—
768Q8—61no—
769D4—21no—
770D4—32no—
771D4—61no—
772D4—92no—
773D4—184no—
774D4—184no—
775D4—181no—
776D4C4×D3212yes—
777C2×C4—21no—
778C2×C4—42no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—92no—
785C2×C4—92no—
786C2×C4—91no—
787C2×C4—122no—
788C2×C4—182no—
789C2×C4—184no—
790C2×C4—181no—
791C2×C4—361no—
792C2×C4—362no—
793C2×C4—362no—
794C2×C4—362no—
795C2×C4—362no—
796C2×C4—362no—
797C2×C4#381111yescharacteristic
798C2×C4#381111yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—32no—
801C8—32no—
802C8—61no—
803C8—61no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—44no—
808C2×C3—42no—
809C2×C3—42no—
810C2×C3—122no—
811C2×C3C4×D3×D411yescharacteristic
812C2×C3C4×D3×D411yescharacteristic
813C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
814C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
815C2×C3#577311yescharacteristic
816C2×C3#577711yescharacteristic
817D3—42no—
818D3—64no—
819D3—62no—
820D3—62no—
821D3—124no—
822D3—122no—
823D3—122no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—62no—
828C22—92no—
829C22—121no—
830C22—121no—
831C22—181no—
832C22—181no—
833C22—182no—
834C22—368no—
835C22—361no—
836C22—361no—
837C22C2×#381111yescharacteristic
838C4—21no—
839C4—21no—
840C4—41no—
841C4—62no—
842C4—92no—
843C4—92no—
844C4—121no—
845C4—121no—
846C4—181no—
847C4—361no—
848C4C2×C4×D3211yescharacteristic
849C4#6430611yescharacteristic
850C3—21no—
851C3#7977311yescharacteristic, complemented
852C3#7986511yescharacteristic, complemented
853C2—42no—
854C2—122no—
855C2—182no—
856C2—362no—
857C2C4×#381111yescharacteristic
858C2#1059510011yescharacteristic
859C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63937C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×D4×C3⋊D3C2semidirect
3. C4×#3796C2semidirect
4. C3×#5018C2semidirect
5. C3×#5014C2semidirect
6. #10591445C2semidirect
7. #10591435C2semidirect
8. #10591426C2semidirect
9. #10590612C2semidirect
10. #10590583C2semidirect
11. #10590483C2semidirect
12. #10590459C2semidirect
13. #10590362C2semidirect
14. #10590346C2semidirect
15. #10590247C2semidirect
32. C3×C4×D12C22semidirect
33. C3×C4×Dic6C22semidirect
34. #63937C4semidirect
36. #63898C22semidirect
41. #63843C22semidirect
48. C3×#810C22semidirect
49. C3×#809C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×#803C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63566C22semidirect
59. #63563C22semidirect
60. #63553C22semidirect
61. #63553C22semidirect
74. #5018D3semidirect
76. #5014D3semidirect
99. D4×C3⋊D3C2×C4semidirect
115. #3796C2×C4semidirect
127. C3×#214C2×C4semidirect
128. C3×#213C2×C4semidirect
143. #3717C2×C4semidirect
144. #3714C2×C4semidirect
146. #3712C2×C4semidirect
209. C4×D12C2×D3semidirect
214. C4×Dic6C2×D3semidirect
237. #810C2×D3semidirect
240. #809C2×D3semidirect
242. #808C2×D3semidirect
244. #807C2×D3semidirect
245. #803C2×D3semidirect
246. #803C2×D3semidirect
280. C3×D12C22×C4semidirect
283. C3×Dic6C22×C4semidirect
289. C3×C3⋊C8C22×C4semidirect
290. C3×C3⋊C8C22×C4semidirect
392. #214C4×D3semidirect
394. #213C4×D3semidirect
462. C3⋊Dic3AGL(1,ℤ/8)semidirect
591. D12C2×C4×D3semidirect
617. Dic6C2×C4×D3semidirect
624. C3⋊C8C2×C4×D3semidirect
625. C3⋊C8C2×C4×D3semidirect
759. C32C4×AGL(1,ℤ/8)semidirect
851. C3#79773semidirect
852. C3#79865semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C2×#639372
C4×#37962
C3×#50182
C3×#50142
#105914452
#105914352
#105914262
#105906122
#105905832
#105904832
#105904592
#105903622
#105903462
#105902472
#798653
#797733