Finite Group Databasebeta

← #11859479

Subgroups — #11859479

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595017C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C2×#63804C211yesmaximal, characteristic, complemented
4#10592426C211yesmaximal, characteristic, complemented
5C3×#4729C211yesmaximal, characteristic, complemented
6C3×#67⋊C8C211yesmaximal, characteristic, complemented
7#10591156C211yesmaximal, characteristic, complemented
8C3⋊C8×#67C211yesmaximal, characteristic, complemented
9#10590958C211yesmaximal, characteristic, complemented
10#10590731C211yesmaximal, characteristic, complemented
11#10590730C211yesmaximal, characteristic, complemented
12#10590721C211yesmaximal, characteristic, complemented
13#10590720C211yesmaximal, characteristic, complemented
14#10590666C211yesmaximal, characteristic, complemented
15C8×#624C211yesmaximal, characteristic, complemented
16#79538—31nomaximal
17#79422—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63979C411yescharacteristic
29#63958C411yescharacteristic
30#63958C411yescharacteristic
31#63953C411yescharacteristic
32#63913C411yescharacteristic
33#63910C411yescharacteristic
34#63910C411yescharacteristic
35C4×#626C2211yescharacteristic
36C4×#626C2211yescharacteristic
37C4×#624C2211yescharacteristic
38#63840C411yescharacteristic
39C2×#3712C2211yescharacteristic
40C2×#3712C2211yescharacteristic
41C2×#3711C2211yescharacteristic
42#63817—24no—
43C2×#3710C2211yescharacteristic
44C2×#3710C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63804—24no—
47C32×C22⋊C8C2211yescharacteristic
48#63657C2211yescharacteristic
49#63647C2211yescharacteristic
50#63647C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62Dic3×C3⋊C8C2211yescharacteristic
63C2×#907—31no—
64C2×#907—31no—
65C2×#901—31no—
66C2×#901—31no—
67#5548—31no—
68#5548—31no—
69C3×#436—31no—
70C3×C8×D4—31no—
71#5128—31no—
72#5128—31no—
73C8×#67—31no—
74C8×#67—31no—
75#5012—31no—
76D4×C3⋊C8—31no—
77#4838—31no—
78#4837—31no—
79#4837—31no—
80#4834—31no—
81#4729—31no—
82#4729D311yescharacteristic, complemented
83#4727—31no—
84#4727—31no—
85#4727—31no—
86#4727—31no—
87#4727—61no—
88#67⋊C8—31no—
89#67⋊C8D311yescharacteristic, complemented
90#4688—31no—
91C8×D12—31no—
92C4×D3×C8—31no—
93C4×D3×C8—31no—
94C22×C32×C4C2311yescharacteristic
95C2×#638C2×C411yescharacteristic
96C2×#638C2×C411yescharacteristic
97#3828—22no—
98#3828—22no—
99C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2×C411yescharacteristic
103C2×C3×#67C2×C411yescharacteristic
104C2×C3×#67C2×C411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#627C2×C411yescharacteristic
108C2×#626C2×C411yescharacteristic
109C2×#626C2×C411yescharacteristic
110C2×#626C2×C411yescharacteristic
111C2×#626C2×C411yescharacteristic
112C2×#625C2×C411yescharacteristic
113C2×#624C2×C411yescharacteristic
114C2×#624C2×C411yescharacteristic
115#3798—22no—
116#3798—22no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3743—22no—
122C8×C3⋊D3—22no—
123C3×#217C2×C411yescharacteristic
124C3×#217C2×C411yescharacteristic
125C3×(C2×D3)⋊C4C2×C411yescharacteristic
126C3×(C2×D3)⋊C4C2×C411yescharacteristic
127C3×Dic3⋊C4C2×C411yescharacteristic
128C3×Dic3⋊C4C2×C411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C3×#208—22no—
132C2×C3×C3⋊C8—22no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139Dic3⋊Dic3C2×C411yescharacteristic
140Dic3⋊Dic3C2×C411yescharacteristic
141#3722C2×C411yescharacteristic
142#3722C2×C411yescharacteristic
143(C2×D3)⋊Dic3C2×C411yescharacteristic
144(C2×D3)⋊Dic3C2×C411yescharacteristic
145Dic32C2×C411yescharacteristic
146Dic32C2×C411yescharacteristic
147#3712—22no—
148#3712—22no—
149#3711—22no—
150#3710—22no—
151#3710D414yescomplemented
152D3×C3⋊C8—22no—
153#2931—91noSylow
154C2×#235—31no—
155C2×#235—31no—
156C2×#235—31no—
157C2×#235—31no—
158C2×#235—61no—
159C2×C3×M16—31no—
160C2×C3×M16—31no—
161C22×C3×C8—31no—
162C22×C3×C8—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165#940—31no—
166#940—31no—
167#938—31no—
168#938—31no—
169C4×#67—31no—
170C4×#67—31no—
171C4×#67C2×D311yescharacteristic
172C4×#67C2×D311yescharacteristic
173C2×#208—31no—
174C2×#208C2×D311yescharacteristic
175C22×C3⋊C8—31no—
176C22×C3⋊C8C2×D311yescharacteristic
177#907—64no—
178#907—64no—
179#901—64no—
180#901—64no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)—31no—
187C2×ΓL(1,𝔽25)—31no—
188C2×ΓL(1,𝔽25)—61no—
189C2×ΓL(1,𝔽25)C2×D311yescharacteristic
190C2×D3×C8—31no—
191C2×D3×C8—31no—
192C2×D3×C8—31no—
193C2×D3×C8—31no—
194C2×D3×C8—31no—
195C2×D3×C8—31no—
196C2×D3×C8—31no—
197C2×D3×C8—61no—
198C2×D3×C8C2×D311yescharacteristic
199#895—31no—
200#895—31no—
201#888—31no—
202#888—31no—
203#885—31no—
204#885—31no—
205#885—31no—
206#885—31no—
207#884—31no—
208#884—31no—
209#884—31no—
210#884—31no—
211C4×D12—31no—
212C4×D12—31no—
213C42×D3—31no—
214C42×D3—31no—
215C3×C4⋊C8—31no—
216C3×C4⋊C8—31no—
217C3×C22⋊C8—21no—
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×C22⋊C8C2×D311yescharacteristic
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C4×C8—31no—
223C3×C4×C8—31no—
224#830—31no—
225#830—31no—
226#830—31no—
227#830—31no—
228#830—61no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235(C2×D3)⋊C8—61no—
236(C2×D3)⋊C8—61no—
237(C2×D3)⋊C8C2×D311yescharacteristic
238(C2×D3)⋊C8C2×D311yescharacteristic
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8C2×D311yescharacteristic
242Dic3⋊C8C2×D311yescharacteristic
243C8×Dic3—31no—
244C8×Dic3—31no—
245C8×Dic3C2×D311yescharacteristic
246C8×Dic3C2×D311yescharacteristic
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4×C3⋊C8—31no—
250C4×C3⋊C8—31no—
251C23×C32C22×C411yescharacteristic
252C22×C3⋊D3C22×C411yescharacteristic
253C22×C3⋊D3C22×C411yescharacteristic
254C22×C3×D3C22×C411yescharacteristic
255C22×C3×D3C22×C411yescharacteristic
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C22×C411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260#638—22no—
261#638—22no—
262C2×C3⋊Dic3C22×C411yescharacteristic
263C2×C3⋊Dic3C22×C411yescharacteristic
264C4⋊(C3⋊D3)—22no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3C2×D412yes—
268C4×C3⋊D3#4112yes—
269#634—22no—
270C3×#67—22no—
271C3×#67—22no—
272C2×C3×Dic3C22×C411yescharacteristic
273C2×C3×Dic3C22×C411yescharacteristic
274C2×C3×Dic3C22×C411yescharacteristic
275C2×C3×Dic3C22×C411yescharacteristic
276C2×C3×Dic3C22×C411yescharacteristic
277C2×C3×Dic3C22×C411yescharacteristic
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282#627—22no—
283#626—22no—
284#626—22no—
285#626—22no—
286#626—22no—
287#625—22no—
288#624—22no—
289#624—22no—
290C32×C8—21no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8C2×D412yes—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C2×#131—91no—
300#532—91no—
301#436—31no—
302#436—91no—
303#436—91no—
304#436—91no—
305C8×D4—31no—
306C8×D4—91no—
307C8×D4—91no—
308C8×D4—91no—
309#423—91no—
310#408—91no—
311#408—91no—
312C2×C4×C8—91no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—31no—
321C2×#67—31no—
322C2×#67—31no—
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67C4×D311yescharacteristic
333C2×#67C4×D311yescharacteristic
334#235—62no—
335#235—62no—
336#235—62no—
337#235—62no—
338#235—62no—
339#235—62no—
340#235—62no—
341#235—62no—
342#235—122no—
343#235—122no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—61no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3C22×D311yescharacteristic
362C2×C4×D3C22×D311yescharacteristic
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—61no—
368C3×M16—62no—
369C3×M16—62no—
370C2×C3×C8—21no—
371C2×C3×C8—21no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
375C2×C3×C8—31no—
376C2×C3×C8—62no—
377C2×C3×C8—62no—
378C2×C3×C8C22×D311yescharacteristic
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C42—31no—
389C3×C42—31no—
390#217—31no—
391#217—31no—
392#217C4×D311yescharacteristic
393#217C4×D311yescharacteristic
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4C4×D311yescharacteristic
401(C2×D3)⋊C4C4×D311yescharacteristic
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4C4×D311yescharacteristic
407Dic3⋊C4C4×D311yescharacteristic
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3C22×D311yescharacteristic
413C4×Dic3C22×D311yescharacteristic
414#208—22no—
415#208—62no—
416C2×C3⋊C8—22no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—61no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8—62no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428ΓL(1,𝔽25)—22no—
429ΓL(1,𝔽25)—62no—
430ΓL(1,𝔽25)—62no—
431ΓL(1,𝔽25)—62no—
432ΓL(1,𝔽25)—62no—
433ΓL(1,𝔽25)—62no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)—62no—
436ΓL(1,𝔽25)—122no—
437D3×C8—22no—
438D3×C8—34no—
439D3×C8—34no—
440D3×C8—62no—
441D3×C8—62no—
442D3×C8—62no—
443D3×C8—62no—
444D3×C8—62no—
445D3×C8—122no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32C23×C411yescharacteristic
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3C4×D412yes—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C32×C4—21no—
463C32×C4C22×D411yescharacteristic
464C32×C4C2×#4111yescharacteristic
465C3⋊Dic3—21no—
466C3⋊Dic3C4×D412yes—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3#13112yescomplemented
472C3×Dic3#13112yescomplemented
473C2×#41—91no—
474C2×#41—91no—
475#131—184no—
476#131—184no—
477C2×M16—31no—
478C2×M16—31no—
479C2×M16—91no—
480C2×M16—91no—
481C2×M16—91no—
482C2×M16—91no—
483C22×C8—31no—
484C22×C8—31no—
485C22×C8—91no—
486C22×C8—91no—
487C22×C8—91no—
488C22×C8—91no—
489C4⋊Q8—91no—
490#127—91no—
491#124—91no—
492#124—91no—
493#121—91no—
494#121—91no—
495#121—91no—
496#121—91no—
497C4×D4—31no—
498C4×D4—31no—
499C4×D4—91no—
500C4×D4—91no—
501C2×C42—91no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8—91no—
505C4⋊C8—91no—
506C22⋊C8—31no—
507C22⋊C8—31no—
508C22⋊C8—91no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512C22⋊C8—91no—
513C22⋊C8D3211yescharacteristic
514C4×C8—31no—
515C4×C8—31no—
516C4×C8—91no—
517C4×C8—91no—
518C23×C3—21no—
519C23×C3—31no—
520C23×C3—31no—
521C23×C3C2×C4×D311yescharacteristic
522C23×C3C2×C4×D311yescharacteristic
523C22×D3—31no—
524C22×D3—31no—
525C22×D3—31no—
526C22×D3—31no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3C2×C4×D311yescharacteristic
530C22×D3C2×C4×D311yescharacteristic
531C3×D4—62no—
532C3×D4—62no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4C2×C4×D311yescharacteristic
552C2×C3×C4C2×C4×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—22no—
556#67—22no—
557#67—62no—
558#67—62no—
559#67—62no—
560#67—62no—
561#67—62no—
562#67—62no—
563#67—62no—
564#67—62no—
565#67—62no—
566#67—62no—
567#67—122no—
568#67—122no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3C2×C4×D311yescharacteristic
576C2×Dic3C2×C4×D311yescharacteristic
577C2×Dic3C2×C4×D311yescharacteristic
578C2×Dic3C2×C4×D311yescharacteristic
579C2×Dic3C2×C4×D311yescharacteristic
580C2×Dic3C2×C4×D311yescharacteristic
581D12—62no—
582D12—62no—
583D12—62no—
584D12—62no—
585D12—62no—
586D12—62no—
587D12—122no—
588C4×D3—21no—
589C4×D3—21no—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—32no—
593C4×D3—32no—
594C4×D3—32no—
595C4×D3—32no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—62no—
599C4×D3—62no—
600C4×D3—61no—
601C4×D3—61no—
602C4×D3—61no—
603C4×D3—61no—
604C4×D3—62no—
605C4×D3—62no—
606C4×D3—121no—
607C4×D3—121no—
608Dic6—62no—
609Dic6—62no—
610Dic6—62no—
611Dic6—62no—
612Dic6—122no—
613C3×C8—21no—
614C3×C8—21no—
615C3×C8—21no—
616C3×C8—21no—
617C3×C8—32no—
618C3×C8—32no—
619C3×C8—41no—
620C3×C8—41no—
621C3×C8—61no—
622C3×C8—61no—
623C3⋊C8—21no—
624C3⋊C8—21no—
625C3⋊C8—61no—
626C3⋊C8—61no—
627C3⋊C8—61no—
628C3⋊C8—61no—
629C3⋊C8—121no—
630C3⋊C8—121no—
631C3⋊C8D3×D412yes—
632C3⋊C8D3×D412yes—
633C2×C32—41no—
634C2×C32C2×C4×D411yescharacteristic
635C2×C32C2×#13111yescharacteristic
636C2×C32C2×#13111yescharacteristic
637C3⋊D3—22no—
638C3⋊D3—41no—
639C3×D3—41no—
640C3×D3—41no—
641#41—182no—
642#41—182no—
643#41—182no—
644#41—182no—
645C2×Q8—91no—
646C2×Q8—91no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—91no—
650C2×D4—91no—
651C2×D4—91no—
652C2×D4—91no—
653C2×D4—91no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—91no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—91no—
662C22×C4—91no—
663C22×C4C2×D3211yescharacteristic
664M16—62no—
665M16—62no—
666M16—182no—
667M16—182no—
668M16—182no—
669M16—182no—
670C2×C8—31no—
671C2×C8—31no—
672C2×C8—31no—
673C2×C8—31no—
674C2×C8—62no—
675C2×C8—62no—
676C2×C8—94no—
677C2×C8—91no—
678C2×C8—91no—
679C2×C8—182no—
680C2×C8—182no—
681C2×C8—182no—
682C2×C8C2×D3211yescharacteristic
683C2×C8C2×D3211yescharacteristic
684C4⋊C4—31no—
685C4⋊C4—31no—
686C4⋊C4—91no—
687C4⋊C4—91no—
688C22⋊C4—31no—
689C22⋊C4—31no—
690C22⋊C4—31no—
691C22⋊C4—31no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C42—31no—
697C42—31no—
698C42—91no—
699C42—91no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3C22×C4×D311yescharacteristic
717C22×C3C22×C4×D311yescharacteristic
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—32no—
725C2×D3—32no—
726C2×D3—62no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—32no—
747C3×C4—32no—
748C3×C4—41no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D411yescharacteristic
755C3×C4D3×#4111yescharacteristic
756C3×C4D3×#4111yescharacteristic
757Dic3—21no—
758Dic3—21no—
759Dic3—21no—
760Dic3—21no—
761Dic3—32no—
762Dic3—32no—
763Dic3—62no—
764Dic3—61no—
765Dic3—61no—
766Dic3—121no—
767Dic3#90112yescomplemented
768Dic3#90712yescomplemented
769C32#293111yescharacteristic, complemented, Sylow
770C23—31no—
771C23—31no—
772C23—91no—
773C23—91no—
774C23C4×D3211yescharacteristic
775Q8—182no—
776Q8—182no—
777D4—62no—
778D4—62no—
779D4—182no—
780D4—182no—
781D4—182no—
782D4—182no—
783D4—182no—
784D4—182no—
785D4—182no—
786D4—182no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—31no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—91no—
800C2×C4—92no—
801C2×C4—92no—
802C2×C4—91no—
803C2×C4—182no—
804C2×C4—182no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4C4×D3211yescharacteristic
808C2×C4C22×D3211yescharacteristic
809C8—21no—
810C8—21no—
811C8—32no—
812C8—32no—
813C8—61no—
814C8—61no—
815C8—181no—
816C8—181no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—81no—
823C2×C3—121no—
824C2×C3—121no—
825C2×C3C4×D3×D411yescharacteristic
826C2×C3C4×D3×D411yescharacteristic
827C2×C3C2×#90111yescharacteristic
828C2×C3C2×#90711yescharacteristic
829C2×C3D3×#13111yescharacteristic
830C2×C3D3×#13111yescharacteristic
831D3—41no—
832D3—41no—
833D3—62no—
834D3—62no—
835D3—122no—
836D3—121no—
837D3—121no—
838D3—241no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—61no—
847C22—61no—
848C22—92no—
849C22—181no—
850C22—181no—
851C22—181no—
852C22—181no—
853C22—181no—
854C22C2×C4×D3211yescharacteristic
855C4—21no—
856C4—32no—
857C4—32no—
858C4—61no—
859C4—61no—
860C4—61no—
861C4—61no—
862C4—92no—
863C4—181no—
864C4D32×D411yescharacteristic
865C4#6431211yescharacteristic
866C3—21no—
867C3#7942211yescharacteristic, complemented
868C3#7953811yescharacteristic, complemented
869C2—41no—
870C2—121no—
871C2—121no—
872C2—182no—
873C2—361no—
874C2#1059425511yescharacteristic
875C2D3×#90111yescharacteristic
876C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radical#10595017C2
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C2×#63804C2semidirect
4. #10592426C2semidirect
5. C3×#4729C2semidirect
6. C3×#67⋊C8C2semidirect
7. #10591156C2semidirect
8. C3⋊C8×#67C2semidirect
9. #10590958C2semidirect
10. #10590731C2semidirect
11. #10590730C2semidirect
12. #10590721C2semidirect
13. #10590720C2semidirect
14. #10590666C2semidirect
15. C8×#624C2semidirect
82. #4729D3semidirect
89. #67⋊C8D3semidirect
151. #3710D4semidirect
471. C3×Dic3#131semidirect
472. C3×Dic3#131semidirect
767. Dic3#901semidirect
768. Dic3#907semidirect
769. C32#2931semidirect
867. C3#79422semidirect
868. C3#79538semidirect

Maximal subgroups

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

subgroupindex
#105950172
C2×#638172
C2×#638042
#105924262
C3×#47292
C3×#67⋊C82
#105911562
C3⋊C8×#672
#105909582
#105907312
#105907302
#105907212
#105907202
#105906662
C8×#6242
#795383
#794223