Finite Group Databasebeta

← #11859330

Subgroups — #11859330

Order 1152.

1107 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595002C211yesmaximal, characteristic
2C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
3C2×#63805C211yesmaximal, characteristic, complemented
4#10592424C211yesmaximal, characteristic, complemented
5C3×#4730C211yesmaximal, characteristic, complemented
6C3×#4726C211yesmaximal, characteristic, complemented
7#10591157C211yesmaximal, characteristic, complemented
8#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9#10590955C211yesmaximal, characteristic, complemented
10#10590909C211yesmaximal, characteristic, complemented
11#10590906C211yesmaximal, characteristic, complemented
12#10590728C211yesmaximal, characteristic, complemented
13#10590724C211yesmaximal, characteristic, complemented
14#10590718C211yesmaximal, characteristic, complemented
15#10590695C211yesmaximal, characteristic, complemented
16#79478—31nomaximal
17#78626—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C4×#638C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C3×C4×#67C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28#63978C411yescharacteristic
29#63977C411yescharacteristic
30#63976C411yescharacteristic
31#63964C411yescharacteristic
32#63906C411yescharacteristic
33#63905C411yescharacteristic
34C4×#626C2211yescharacteristic
35C4×#625C2211yescharacteristic
36#63855C2211yescharacteristic
37#63851C411yescharacteristic
38#63850C411yescharacteristic
39C2×#3712C2211yescharacteristic, complemented
40C2×D3×C3⋊C8—24no—
41C2×D3×C3⋊C8C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic, complemented
46#63805—24no—
47C32×C22⋊C8C2211yescharacteristic
48#63647C2211yescharacteristic, complemented
49#63641C2211yescharacteristic, complemented
50C8×C3⋊Dic3C2211yescharacteristic, complemented
51C3×#830C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63555C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63#5791—31no—
64C23×C3⋊C8—31no—
65C2×#907—31no—
66C2×#907—31no—
67C22×D3×C8—31no—
68#5547—31no—
69C3×#435—31no—
70C3×#407—31no—
71#5129—31no—
72#5127—31no—
73#5122—31no—
74#5119—31no—
75#5111—31no—
76D4×C3⋊C8—31no—
77#4839—31no—
78#4834—31no—
79#4730—31no—
80#4730—31no—
81#4730—31no—
82#4730D311yescharacteristic, complemented
83#4727—31no—
84#4726D311yescharacteristic, complemented
85#67⋊C8—31no—
86#67⋊C8—31no—
87#67⋊C8—31no—
88#67⋊C8—31no—
89#67⋊C8—31no—
90#67⋊C8—31no—
91#67⋊C8—61no—
92#4708—31no—
93#4706—31no—
94C23×C3×D3C2×C411yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638C2×C411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67C2×C411yescharacteristic
99C22×C3×Dic3C2×C411yescharacteristic
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3C2×C411yescharacteristic
103C2×C3×C4×D3C2×C411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#627C2×C411yescharacteristic
108C2×#626C2×C411yescharacteristic
109C2×#626C2×C411yescharacteristic
110C2×#626C2×C411yescharacteristic
111C2×#625C2×C411yescharacteristic
112C2×#625C2×C411yescharacteristic
113#3798—22no—
114#3798—22no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117#3757C2×C411yescharacteristic
118#3752C2×C411yescharacteristic
119#3750C2×C411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)—22no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C8×C3⋊D3—22no—
125C3×#217C2×C411yescharacteristic
126C3×(C2×D3)⋊C4C2×C411yescharacteristic
127C3×Dic3⋊C4C2×C411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8—22no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×ΓL(1,𝔽25)—22no—
135C3×ΓL(1,𝔽25)—22no—
136C3×ΓL(1,𝔽25)—22no—
137#3724C2×C411yescharacteristic
138Dic3⋊Dic3C2×C411yescharacteristic
139Dic3⋊Dic3C2×C411yescharacteristic
140Dic3⋊Dic3C2×C411yescharacteristic
141#3722C2×C411yescharacteristic
142(C2×D3)⋊Dic3C2×C411yescharacteristic
143(C2×D3)⋊Dic3C2×C411yescharacteristic
144(C2×D3)⋊Dic3C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147#3712—22no—
148D3×C3⋊C8—22no—
149D3×C3⋊C8—22no—
150D3×C3⋊C8—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8D414yescomplemented
153#2929—91noSylow
154C23×C3×C4—31no—
155C2×#235—31no—
156C2×#235—31no—
157C22×C4×D3C2×D311yescharacteristic
158C2×C3×M16—31no—
159C2×C3×M16—31no—
160C2×C3×M16—31no—
161C22×C3×C8—31no—
162C3×C4×D4—31no—
163#953—31no—
164#953—31no—
165#939—31no—
166#937—31no—
167#930—31no—
168#930—31no—
169#929—31no—
170#929—31no—
171C4×#67—31no—
172C4×#67—31no—
173C4×#67—31no—
174C4×#67—31no—
175C4×#67—31no—
176C4×#67—61no—
177C4×#67C2×D311yescharacteristic
178#926—31no—
179#924—31no—
180#924—31no—
181C22×C3⋊C8—31no—
182C22×C3⋊C8—31no—
183C22×C3⋊C8—31no—
184C22×C3⋊C8—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C22×C3⋊C8—64no—
190C22×C3⋊C8C2×D311yescharacteristic
191#907—64no—
192#907—64no—
193C2×ΓL(1,𝔽25)—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)C2×D311yescharacteristic
196C2×ΓL(1,𝔽25)C2×D311yescharacteristic
197C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204C2×D3×C8—31no—
205C2×D3×C8—61no—
206C2×D3×C8—64no—
207#896—31no—
208#894—31no—
209#884—31no—
210#883—31no—
211#882—31no—
212#878—31no—
213C4×D12—31no—
214#872—31no—
215C3×C4⋊C8—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C2×D311yescharacteristic
223C3×#97—31no—
224#830—31no—
225#830C2×D311yescharacteristic
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—61no—
232(C2×D3)⋊C8C2×D311yescharacteristic
233(C2×D3)⋊C8C2×D311yescharacteristic
234(C2×D3)⋊C8C2×D311yescharacteristic, complemented
235#815—31no—
236#815—31no—
237#815C2×D311yescharacteristic, complemented
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—61no—
244Dic3⋊C8C2×D311yescharacteristic, complemented
245C8×Dic3—31no—
246C8×Dic3—31no—
247C8×Dic3—31no—
248C8×Dic3—61no—
249C4⋊(C3⋊C8)—31no—
250C4×C3⋊C8—31no—
251C23×C32C22×C411yescharacteristic
252C22×C3⋊D3C22×C411yescharacteristic
253C22×C3×D3—22no—
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3C22×C411yescharacteristic
257C22×C3×D3C22×C411yescharacteristic
258C22×C3×D3C22×C411yescharacteristic
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C22×C411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263#638—22no—
264C2×C3⋊Dic3C22×C411yescharacteristic
265C2×C3⋊Dic3C22×C411yescharacteristic
266C2×C3⋊Dic3C22×C411yescharacteristic
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C3×#67—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3C22×C411yescharacteristic
272C2×C3×Dic3C22×C411yescharacteristic
273C2×C3×Dic3C22×C411yescharacteristic
274C2×C3×Dic3C22×C411yescharacteristic
275C2×C3×Dic3C22×C411yescharacteristic
276C3×C4×D3—22no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×C4×D3—22no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284#627—22no—
285#626—22no—
286#626—22no—
287#626—22no—
288#625—22no—
289#625—22no—
290C32×C8—21no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)C2×D412yes—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C23×C8—91no—
300#525—91no—
301#435—31no—
302#435—91no—
303#435—91no—
304#435—91no—
305C8×D4—91no—
306C8×D4—91no—
307C8×D4—91no—
308C8×D4—91no—
309#424—91no—
310#408—91no—
311#407—31no—
312#405—91no—
313C24×C3—31no—
314C23×D3C4×D311yescharacteristic
315C2×C3×D4—31no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—31no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—31no—
331C2×#67—31no—
332C2×#67—31no—
333C2×#67—31no—
334C2×#67—31no—
335C2×#67—31no—
336C2×#67—61no—
337C2×#67C4×D311yescharacteristic
338C22×Dic3C4×D311yescharacteristic
339#235—62no—
340#235—62no—
341#235—62no—
342#235—62no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—31no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3C4×D311yescharacteristic
352C2×C4×D3C4×D311yescharacteristic
353C2×C4×D3C22×D311yescharacteristic
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—31no—
357C2×Dic6—31no—
358C3×M16—62no—
359C3×M16—62no—
360C3×M16—62no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—62no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C3×C4⋊C4—31no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C42—31no—
376#217—31no—
377#217—31no—
378#217—31no—
379#217—31no—
380#217—31no—
381#217—31no—
382#217—31no—
383#217—61no—
384#217C4×D311yescharacteristic
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4C4×D311yescharacteristic
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—61no—
407Dic3⋊C4C4×D311yescharacteristic
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—61no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—22no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—34no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—62no—
421C2×C3⋊C8—62no—
422C2×C3⋊C8—62no—
423C2×C3⋊C8—62no—
424C2×C3⋊C8—62no—
425C2×C3⋊C8—62no—
426C2×C3⋊C8—122no—
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431ΓL(1,𝔽25)—22no—
432ΓL(1,𝔽25)—22no—
433ΓL(1,𝔽25)—22no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)—62no—
436D3×C8—34no—
437D3×C8—62no—
438D3×C8—62no—
439D3×C8—62no—
440D3×C8—62no—
441D3×C8—62no—
442D3×C8—62no—
443D3×C8—122no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32#13112yescomplemented
447C22×C32C23×C411yescharacteristic
448C2×C3⋊D3—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3×D3—28no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3C4×D412yes—
460C2×C3×D3#13112yescomplemented
461C32×C4—21no—
462C32×C4C22×D411yescharacteristic
463C32×C4C2×#4111yescharacteristic
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3C4×D412yes—
472C2×#41—91no—
473C23×C4—31no—
474#131—184no—
475C2×M16—31no—
476C2×M16—31no—
477C2×M16—31no—
478C2×M16—91no—
479C22×C8—31no—
480C22×C8—91no—
481C22×C8—91no—
482C22×C8—91no—
483C22×C8—91no—
484C22×C8—91no—
485C22×C8—91no—
486C22×C8—91no—
487C22×C8—184no—
488#123—91no—
489#123—91no—
490C22⋊Q8—91no—
491C22⋊Q8—91no—
492#121—91no—
493#121—91no—
494#120—91no—
495#120—91no—
496C4×D4—31no—
497C4×D4—91no—
498C4×D4—91no—
499C4×D4—91no—
500#117—91no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505C22⋊C8—31no—
506C22⋊C8—31no—
507C22⋊C8—31no—
508C22⋊C8—31no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512C22⋊C8D3211yescharacteristic
513#97—31no—
514#97—91no—
515C4×C8—91no—
516C4×C8—91no—
517C23×C3—21no—
518C23×C3—31no—
519C23×C3—31no—
520C23×C3—31no—
521C23×C3—62no—
522C23×C3—62no—
523C23×C3—62no—
524C23×C3C2×C4×D311yescharacteristic
525C23×C3C2×C4×D311yescharacteristic
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—31no—
530C22×D3—31no—
531C22×D3—61no—
532C22×D3C2×C4×D311yescharacteristic
533C22×D3C2×C4×D311yescharacteristic
534C22×D3C2×C4×D311yescharacteristic
535C3×D4—62no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—62no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4C2×C4×D311yescharacteristic
559C2×C3×C4C2×C4×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—22no—
563#67—62no—
564#67—62no—
565#67—62no—
566#67—62no—
567#67—64no—
568#67—62no—
569#67—62no—
570#67—62no—
571#67—62no—
572#67—62no—
573C2×Dic3—22no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3C2×C4×D311yescharacteristic
584C2×Dic3C2×C4×D311yescharacteristic
585C2×Dic3C2×C4×D311yescharacteristic
586C2×Dic3C2×C4×D311yescharacteristic
587C2×Dic3C2×C4×D311yescharacteristic
588D12—62no—
589D12—62no—
590D12—62no—
591C4×D3—22no—
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—22no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—61no—
600C4×D3—61no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3D3×D412yes—
604C4×D3#23712yes—
605Dic6—62no—
606Dic6—62no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—32no—
612C3×C8—41no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C3⋊C8—32no—
621C3⋊C8—32no—
622C3⋊C8—62no—
623C3⋊C8—61no—
624C3⋊C8—61no—
625C3⋊C8—121no—
626C3⋊C8D3×D412yes—
627C2×C32—22no—
628C2×C32C2×C4×D411yescharacteristic
629C2×C32C2×#13111yescharacteristic
630C2×C32C2×#13111yescharacteristic
631C3⋊D3—41no—
632C3×D3—22no—
633C3×D3—22no—
634C3×D3—41no—
635C24—31no—
636#41—182no—
637#41—182no—
638C2×Q8—91no—
639C2×D4—31no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—91no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—91no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—91no—
655C22×C4C2×D3211yescharacteristic
656M16—62no—
657M16—62no—
658M16—62no—
659M16—182no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—31no—
663C2×C8—31no—
664C2×C8—62no—
665C2×C8—94no—
666C2×C8—91no—
667C2×C8—91no—
668C2×C8—182no—
669C2×C8—182no—
670C2×C8—182no—
671C2×C8—182no—
672C2×C8—182no—
673C2×C8—182no—
674C2×C8C2×D3211yescharacteristic
675C2×C8C2×D3211yescharacteristic
676C4⋊C4—31no—
677C4⋊C4—91no—
678C4⋊C4—91no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C42—31no—
693C42—91no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—22no—
700C22×C3—32no—
701C22×C3—32no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—68no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3#90712yescomplemented
713C22×C3#90712yescomplemented
714C22×C3C22×C4×D311yescharacteristic
715C22×C3C22×C4×D311yescharacteristic
716C2×D3—28no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—62no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3#67⋊C412yes—
734C2×D3#90712yescomplemented
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—32no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4C2×D3×D411yescharacteristic
746C3×C4C2×D3×D411yescharacteristic
747C3×C4C2×#23711yescharacteristic
748C3×C4D3×#4111yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—21no—
752Dic3—21no—
753Dic3—62no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—121no—
761Dic3—121no—
762Dic3#67⋊C412yes—
763C32#292911yescharacteristic, complemented, Sylow
764C23—31no—
765C23—31no—
766C23—31no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—91no—
771C23C4×D3211yescharacteristic
772Q8—182no—
773D4—62no—
774D4—182no—
775D4—182no—
776D4—182no—
777D4—182no—
778D4—182no—
779D4—182no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—31no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—91no—
797C2×C4—91no—
798C2×C4—91no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4C4×D3211yescharacteristic
802C2×C4C22×D3211yescharacteristic
803C8—21no—
804C8—21no—
805C8—32no—
806C8—61no—
807C8—61no—
808C8—61no—
809C8—92no—
810C8—181no—
811C2×C3—22no—
812C2×C3—22no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—42no—
817C2×C3—62no—
818C2×C3—62no—
819C2×C3—121no—
820C2×C3C2×#67⋊C411yescharacteristic
821C2×C3C4×D3×D411yescharacteristic
822C2×C3C2×#90711yescharacteristic
823C2×C3C2×#90711yescharacteristic
824C2×C3C2×#90711yescharacteristic
825C2×C3D3×#13111yescharacteristic
826D3—22no—
827D3—22no—
828D3—41no—
829D3—122no—
830D3—121no—
831D3—121no—
832C22—21no—
833C22—21no—
834C22—32no—
835C22—32no—
836C22—68no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—181no—
845C22—181no—
846C22—181no—
847C22#6380512yescomplemented
848C22C2×C4×D3211yescharacteristic
849C4—21no—
850C4—32no—
851C4—61no—
852C4—61no—
853C4—61no—
854C4—61no—
855C4—181no—
856C4—181no—
857C4—181no—
858C4D32×D411yescharacteristic
859C4D3×#23711yescharacteristic
860C3—21no—
861C3#7862611yescharacteristic, complemented
862C3#7947811yescharacteristic, complemented
863C2—22no—
864C2—62no—
865C2—62no—
866C2—121no—
867C2—361no—
868C2D3×#67⋊C411yescharacteristic
869C2C2×#6380511yescharacteristic
870C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radical#10595002C2
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×D3×C3⋊C8C2semidirect
3. C2×#63805C2semidirect
4. #10592424C2semidirect
5. C3×#4730C2semidirect
6. C3×#4726C2semidirect
7. #10591157C2semidirect
8. #67⋊(C3⋊C8)C2semidirect
9. #10590955C2semidirect
10. #10590909C2semidirect
11. #10590906C2semidirect
12. #10590728C2semidirect
13. #10590724C2semidirect
14. #10590718C2semidirect
15. #10590695C2semidirect
22. C2×C8×C3⋊D3C22semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C2×#3712C22semidirect
45. C2×D3×C3⋊C8C22semidirect
48. #63647C22semidirect
49. #63641C22semidirect
50. C8×C3⋊Dic3C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×#815C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63555C22semidirect
62. Dic3×C3⋊C8C22semidirect
82. #4730D3semidirect
84. #4726D3semidirect
152. D3×C3⋊C8D4semidirect
197. C2×ΓL(1,𝔽25)C2×D3semidirect
234. (C2×D3)⋊C8C2×D3semidirect
237. #815C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
446. C22×C32#131semidirect
460. C2×C3×D3#131semidirect
712. C22×C3#907semidirect
713. C22×C3#907semidirect
734. C2×D3#907semidirect
763. C32#2929semidirect
847. C22#63805semidirect
861. C3#78626semidirect
862. C3#79478semidirect

Maximal subgroups

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

subgroupindex
#105950022
C22×D3×C3⋊C82
C2×#638052
#105924242
C3×#47302
C3×#47262
#105911572
#67⋊(C3⋊C8)2
#105909552
#105909092
#105909062
#105907282
#105907242
#105907182
#105906952
#794783
#786263