Finite Group Databasebeta

← #37584062

Subgroups — #37584062

Order 24448.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259349C211yesmaximal, characteristic, complemented
2C2×#20259343C211yesmaximal, characteristic, complemented
3#27133335C211yesmaximal, characteristic, complemented
4#27133308C211yesmaximal, characteristic, complemented
5#27133052C211yesmaximal, characteristic, complemented
6#27132910C211yesmaximal, characteristic, complemented
7#27132900C211yesmaximal, characteristic, complemented
8#27132885C211yesmaximal, characteristic, complemented
9#27132858C211yesmaximal, characteristic, complemented
10#27132828C211yesmaximal, characteristic, complemented
11#27132811C211yesmaximal, characteristic, complemented
12#27132809C211yesmaximal, characteristic, complemented
13#27132798C211yesmaximal, characteristic, complemented
14#27132736C211yesmaximal, characteristic, complemented
15#440×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690288C2211yescharacteristic, complemented
18C2×#15690286C2211yescharacteristic
19C2×D4×D191C2211yescharacteristic
20#20259349—24no—
21#20259343—24no—
22C2×#15690277C2211yescharacteristic, complemented
23C2×#15690276C2211yescharacteristic, complemented
24C2×#15690276C2211yescharacteristic, complemented
25C2×#15690274C2211yescharacteristic
26C2×D1528C2211yescharacteristic
27C2×D1528C2211yescharacteristic
28C2×#15690272C2211yescharacteristic
29C2×#15690272C2211yescharacteristic
30C2×#15690270C2211yescharacteristic
31C2×C8×D191C2211yescharacteristic, complemented
32#20259319—21no—
33#20259319C2211yescharacteristic, complemented
34#20259310C2211yescharacteristic
35#20259306—21no—
36#20259302C2211yescharacteristic
37#20259297—21no—
38#20259297—21no—
39#20259297C2211yescharacteristic
40#20259297C2211yescharacteristic
41#20259297C2211yescharacteristic, complemented
42#20259296—21no—
43#20259292—21no—
44C4×D764—21no—
45C4×D764C2211yescharacteristic
46C2×(C2×D191)⋊C4—21no—
47C4⋊(C191⋊C8)C2211yescharacteristic, complemented
48#20259245C2211yescharacteristic, complemented
49#20259242C2211yescharacteristic
50#20259242C2211yescharacteristic, complemented
51#20259242C2211yescharacteristic, complemented
52(C2×D191)⋊C8C2211yescharacteristic
53(C2×D191)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C191C2211yescharacteristic
55C4×Q8×C191C2211yescharacteristic, complemented
56C4×D4×C191C2211yescharacteristic
57#107×C191C2211yescharacteristic, complemented
58#103×C191C2211yescharacteristic, complemented
59#102×C191C2211yescharacteristic
60#97×C191C2211yescharacteristic, complemented
61C23×D191—21no—
62#15690288—22no—
63#15690288—22no—
64#15690288—41no—
65#15690288—41no—
66#15690286—22no—
67#15690286—41no—
68C2×Dic382C2311yescharacteristic
69C2×D764—21no—
70C2×D764—21no—
71C2×D764—21no—
72C2×D764—21no—
73C2×D764—21no—
74C2×D764—21no—
75C2×D764—21no—
76C2×D764D411yescharacteristic
77C2×D764C2311yescharacteristic
78C2×D764C2311yescharacteristic
79C2×D764C2311yescharacteristic
80C2×C22⋊D191—21no—
81C2×C22⋊D191—21no—
82D4×D191—22no—
83D4×D191—41no—
84C22×Dic191—21no—
85C2×C4×D191—21no—
86C2×C4×D191—21no—
87C2×C4×D191C2311yescharacteristic
88C2×C4×D191C2311yescharacteristic
89#15690277—22no—
90#15690276—22no—
91#15690276—41no—
92#15690274—22no—
93D1528—22no—
94D1528—41no—
95#15690272—22no—
96#15690272—22no—
97#15690270—22no—
98C2×C191⋊C8C2311yescharacteristic
99C2×C191⋊C8C2311yescharacteristic
100C8×D191—22no—
101C4⋊Dic191—21no—
102C4⋊Dic191D411yescharacteristic
103(C2×D191)⋊C4—21no—
104(C2×D191)⋊C4—21no—
105(C2×D191)⋊C4—21no—
106(C2×D191)⋊C4—21no—
107(C2×D191)⋊C4—21no—
108(C2×D191)⋊C4—21no—
109(C2×D191)⋊C4D411yescharacteristic
110(C2×D191)⋊C4D411yescharacteristic
111C2×Q8×C191C2311yescharacteristic
112C2×D4×C191C2311yescharacteristic
113C22×C4×C191—21no—
114SD16×C191D414yescomplemented
115C2×C8×C191C2311yescharacteristic
116C2×C8×C191C2311yescharacteristic
117C4⋊C4×C191—21no—
118C4⋊C4×C191C2311yescharacteristic
119C4⋊C4×C191C2311yescharacteristic
120C22⋊C4×C191—21no—
121C42×C191—21no—
122C42×C191C2311yescharacteristic
123C22×D191—21no—
124C22×D191—21no—
125C22×D191—21no—
126C22×D191—42no—
127C22×D191—42no—
128C22×D191—81no—
129C22×D191C2×D411yescharacteristic
130C22×D191C2×D411yescharacteristic
131Dic382—21no—
132Dic382—21no—
133D764—21no—
134D764—21no—
135D764—21no—
136D764—21no—
137D764—21no—
138D764—21no—
139D764—41no—
140D764—42no—
141D764—42no—
142D764—42no—
143D764—81no—
144D764—81no—
145D764—81no—
146D764—81no—
147C22⋊D191—42no—
148C22⋊D191—42no—
149C2×Dic191—21no—
150C2×Dic191—42no—
151C2×Dic191C2×D411yescharacteristic
152C2×Dic191C2×D411yescharacteristic
153C4×D191—21no—
154C4×D191—21no—
155C4×D191—21no—
156C4×D191—21no—
157C4×D191—42no—
158C4×D191—42no—
159C191⋊C8—21no—
160C191⋊C8—21no—
161C23×C191—21no—
162Q8×C191—21no—
163Q8×C191C2×D412yes—
164D4×C191—21no—
165D4×C191C2×D412yes—
166C2×C4×C191—21no—
167C2×C4×C191—21no—
168C2×C4×C191—21no—
169C2×C4×C191—81no—
170C2×C4×C191C2×D411yescharacteristic
171C2×C4×C191C2×D411yescharacteristic
172C2×C4×C191C2411yescharacteristic
173C8×C191—21no—
174C8×C191C2×D412yes—
175C22×C191—22no—
176C22×C191—41no—
177C22×C191—41no—
178C22×C191C22×D411yescharacteristic
179C2×D191—21no—
180C2×D191—21no—
181C2×D191—21no—
182C2×D191—21no—
183C2×D191—21no—
184C2×D191—21no—
185C2×D191—41no—
186C2×D191—41no—
187C2×D191—41no—
188C2×D191—41no—
189C2×D191—41no—
190C2×D191—41no—
191C2×D191—41no—
192C2×D191—41no—
193C2×D191—41no—
194C2×D191—84no—
195C4×C191—22no—
196C4×C191—21no—
197C4×C191—21no—
198C4×C191—41no—
199C4×C191—41no—
200C4×C191C22×D411yescharacteristic
201C4×C191H(5,𝔽2)11yescharacteristic
202Dic191—21no—
203Dic191—21no—
204Dic191—41no—
205C2×C191—42no—
206C2×C191D4211yescharacteristic
207C2×C191#57511yescharacteristic
208C2×C191#57611yescharacteristic
209D191—41no—
210D191—41no—
211D191—81no—
212D191—81no—
213D191—81no—
214C191#326811yescharacteristic, complemented, Sylow
215#3268—1911nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1911no—
217C2×#135—1911no—
218#550—1911no—
219#546—1911no—
220#496—1911no—
221#468—1911no—
222#466—1911no—
223#464—1911no—
224#459—1911no—
225#452—1911no—
226#449—1911no—
227#449—1911no—
228#447—1911no—
229#440D19111yescharacteristic, complemented
230#435—1911no—
231C2×#41—1911no—
232C2×#41—1911no—
233C2×#41—1911no—
234C22×D4—1911no—
235AGL(1,ℤ/8)—3824no—
236#135—3824no—
237C2×Q16—1911no—
238C2×SD16—1911no—
239C2×SD16—1911no—
240C2×SD16—1911no—
241C2×SD16C2×D19111yescharacteristic
242C2×D8—1911no—
243C2×D8—1911no—
244C2×D8—1911no—
245C2×D8—1911no—
246C2×M16—1911no—
247C22×C8—1911no—
248#127—3821no—
249#127—1911no—
250#124—1911no—
251#123—3821no—
252C22⋊Q8—1911no—
253#121—3821no—
254#121—3821no—
255#121—3821no—
256#121—1911no—
257#121—1911no—
258#121—1911no—
259#120—3821no—
260C4×Q8C2×D19111yescharacteristic, complemented
261C4×D4—3821no—
262C4×D4—1911no—
263C4×D4C2×D19111yescharacteristic
264C2×C22⋊C4—3821no—
265#107C2×D19111yescharacteristic, complemented
266C4⋊C8—1911no—
267#103—1911no—
268#103C2×D19111yescharacteristic, complemented
269#102—1911no—
270#102—1911no—
271#102—1911no—
272#102C2×D19111yescharacteristic
273C22⋊C8—1911no—
274C22⋊C8—1911no—
275#97C2×D19111yescharacteristic, complemented
276C24—3821no—
277#41—3822no—
278#41—3822no—
279#41—3822no—
280#41—7641no—
281#41—7641no—
282#41—7641no—
283C2×Q8—1911no—
284C2×Q8C22×D19111yescharacteristic
285C2×D4—3821no—
286C2×D4—3821no—
287C2×D4—3821no—
288C2×D4—3821no—
289C2×D4—3821no—
290C2×D4—3822no—
291C2×D4—3821no—
292C2×D4—3821no—
293C2×D4—3821no—
294C2×D4—3821no—
295C2×D4—1911no—
296C2×D4—1911no—
297C2×D4—1911no—
298C2×D4—1911no—
299C2×D4—7641no—
300C2×D4C22×D19111yescharacteristic
301C22×C4—21no—
302C22×C4—3821no—
303C22×C4—3821no—
304C22×C4—3821no—
305C22×C4—1911no—
306C22×C4—1911no—
307Q16—3822no—
308SD16—3822no—
309SD16—3822no—
310SD16—7641no—
311SD16D76414yescomplemented
312D8—3822no—
313D8—3822no—
314D8—3822no—
315D8—7641no—
316M16—3822no—
317C2×C8—3822no—
318C2×C8—1911no—
319C2×C8—1911no—
320C2×C8C22×D19111yescharacteristic
321C2×C8C22×D19111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—3821no—
324C4⋊C4—1911no—
325C4⋊C4C22×D19111yescharacteristic
326C4⋊C4C22×D19111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—3821no—
329C22⋊C4—3821no—
330C22⋊C4—3821no—
331C22⋊C4—3821no—
332C22⋊C4—3821no—
333C22⋊C4—3821no—
334C22⋊C4—1911no—
335C22⋊C4—1911no—
336C42—21no—
337C42C22×D19111yescharacteristic
338C23—21no—
339C23—3821no—
340C23—3821no—
341C23—3821no—
342C23—1911no—
343C23—1911no—
344C23—15281no—
345C23—7642no—
346C23—7642no—
347Q8—21no—
348Q8—3821no—
349Q8—3821no—
350Q8C2×D76412yes—
351D4—21no—
352D4—3821no—
353D4—3821no—
354D4—3821no—
355D4—3821no—
356D4—3821no—
357D4—3821no—
358D4—15281no—
359D4—15281no—
360D4—15281no—
361D4—15281no—
362D4—7641no—
363D4—7642no—
364D4—7642no—
365D4—7642no—
366D4—7642no—
367D4—7642no—
368D4C2×D76412yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—3821no—
374C2×C4—3821no—
375C2×C4—3821no—
376C2×C4—3821no—
377C2×C4—3821no—
378C2×C4—1911no—
379C2×C4—1911no—
380C2×C4—7642no—
381C2×C4—7642no—
382C2×C4—7642no—
383C2×C4D4×D19111yescharacteristic
384C2×C4D4×D19111yescharacteristic
385C2×C4C23×D19111yescharacteristic
386C8—21no—
387C8—3821no—
388C8—3821no—
389C8C2×D76412yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—3821no—
394C22—3821no—
395C22—3821no—
396C22—3821no—
397C22—3821no—
398C22—3821no—
399C22—15284no—
400C22—7641no—
401C22—7641no—
402C22—7641no—
403C22—7641no—
404C22—7641no—
405C22—7641no—
406C22—7641no—
407C22—7641no—
408C22—7641no—
409C22C2×D4×D19111yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—3821no—
416C4—3821no—
417C4—7641no—
418C4C22×D76411yescharacteristic
419C4#2025936811yescharacteristic
420C2—42no—
421C2—15281no—
422C2—15281no—
423C2—15281no—
424C2—7641no—
425C2—7641no—
426C2D4×D76411yescharacteristic
427C2#2713346211yescharacteristic
428C2#2713346711yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#440×C191C2
socleC22×C191C22×D4
hypercenter#440D191
hypocenterC191#3268
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#20259349C2semidirect
2. C2×#20259343C2semidirect
3. #27133335C2semidirect
4. #27133308C2semidirect
5. #27133052C2semidirect
6. #27132910C2semidirect
7. #27132900C2semidirect
8. #27132885C2semidirect
9. #27132858C2semidirect
10. #27132828C2semidirect
11. #27132811C2semidirect
12. #27132809C2semidirect
13. #27132798C2semidirect
14. #27132736C2semidirect
15. #440×C191C2semidirect
17. C2×#15690288C22semidirect
22. C2×#15690277C22semidirect
23. C2×#15690276C22semidirect
24. C2×#15690276C22semidirect
31. C2×C8×D191C22semidirect
33. #20259319C22semidirect
41. #20259297C22semidirect
47. C4⋊(C191⋊C8)C22semidirect
48. #20259245C22semidirect
50. #20259242C22semidirect
51. #20259242C22semidirect
53. (C2×D191)⋊C8C22semidirect
55. C4×Q8×C191C22semidirect
57. #107×C191C22semidirect
58. #103×C191C22semidirect
60. #97×C191C22semidirect
114. SD16×C191D4semidirect
214. C191#3268semidirect
229. #440D191semidirect
260. C4×Q8C2×D191semidirect
265. #107C2×D191semidirect
268. #103C2×D191semidirect
275. #97C2×D191semidirect
311. SD16D764semidirect

Maximal subgroups

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

subgroupindex
C2×#202593492
C2×#202593432
#271333352
#271333082
#271330522
#271329102
#271329002
#271328852
#271328582
#271328282
#271328112
#271328092
#271327982
#271327362
#440×C1912
#3268191