Finite Group Databasebeta

← #37583309

Subgroups — #37583309

Order 24448.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133176C211yesmaximal, characteristic, complemented
2#27133173C211yesmaximal, characteristic, complemented
3#27133007C211yesmaximal, characteristic, complemented
4#27133002C211yesmaximal, characteristic, complemented
5#27132989C211yesmaximal, characteristic, complemented
6#27132986C211yesmaximal, characteristic, complemented
7#27132902C211yesmaximal, characteristic, complemented
8#27132897C211yesmaximal, characteristic, complemented
9#27132892C211yesmaximal, characteristic, complemented
10#27132828C211yesmaximal, characteristic, complemented
11#27132822C211yesmaximal, characteristic, complemented
12#27132809C211yesmaximal, characteristic, complemented
13#27132807C211yesmaximal, characteristic, complemented
14C2×(C2×D191)⋊C8C211yesmaximal, characteristic, complemented
15#465×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690286C2211yescharacteristic
18C22×C4×D191C2211yescharacteristic
19C2×#15690277C2211yescharacteristic, complemented
20C2×#15690276C2211yescharacteristic, complemented
21C2×#15690272C2211yescharacteristic, complemented
22C22×C191⋊C8C2211yescharacteristic
23#20259307—21no—
24#20259304—21no—
25#20259302C2211yescharacteristic
26#20259301C2211yescharacteristic
27#20259298C2211yescharacteristic
28#20259297C2211yescharacteristic
29#20259296C2211yescharacteristic
30#20259293C2211yescharacteristic
31#20259292—21no—
32#20259290—21no—
33D4×Dic191—21no—
34#20259284—21no—
35(C22⋊D191)⋊C4—21no—
36(C22⋊D191)⋊C4—21no—
37#20259280C2211yescharacteristic
38#20259280C2211yescharacteristic
39#20259255C2211yescharacteristic, complemented
40#20259255C2211yescharacteristic, complemented
41#20259254C2211yescharacteristic, complemented
42#20259247C2211yescharacteristic, complemented
43#20259246C2211yescharacteristic, complemented
44#20259245C2211yescharacteristic, complemented
45#20259244C2211yescharacteristic, complemented
46#20259243C2211yescharacteristic, complemented
47#20259242C2211yescharacteristic, complemented
48(C2×D191)⋊C8C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic, complemented
53C22×C8×C191C2211yescharacteristic
54C22⋊Q8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56#106×C191C2211yescharacteristic, complemented
57#103×C191C2211yescharacteristic, complemented
58#102×C191C2211yescharacteristic, complemented
59C23×D191D411yescharacteristic
60#15690288—41no—
61#15690288—41no—
62#15690286—41no—
63#15690286—41no—
64C2×Dic382C2311yescharacteristic
65C2×D764—21no—
66C2×D764—21no—
67C2×D764C2311yescharacteristic
68C2×C22⋊D191—21no—
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C22×Dic191—21no—
72C22×Dic191D411yescharacteristic
73C2×C4×D191—21no—
74C2×C4×D191—41no—
75C2×C4×D191—41no—
76C2×C4×D191D411yescharacteristic
77C2×C4×D191D411yescharacteristic
78C2×C4×D191C2311yescharacteristic
79C2×C4×D191C2311yescharacteristic
80#15690277—41no—
81#15690276—41no—
82#15690272—41no—
83C2×C191⋊C8—41no—
84C2×C191⋊C8C2311yescharacteristic
85C2×C191⋊C8C2311yescharacteristic
86C4⋊Dic191—21no—
87C4⋊Dic191C2311yescharacteristic
88C4⋊Dic191C2311yescharacteristic
89Dic191⋊C4—21no—
90Dic191⋊C4—21no—
91C22⋊Dic191—21no—
92C22⋊Dic191—21no—
93(C2×D191)⋊C4—21no—
94(C2×D191)⋊C4—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99C4×Dic191—21no—
100C4×Dic191—21no—
101C2×Q8×C191C2311yescharacteristic
102C2×D4×C191—21no—
103C2×D4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105SD16×C191—41no—
106C2×C8×C191—41no—
107C2×C8×C191C2311yescharacteristic
108C2×C8×C191C2311yescharacteristic
109C4⋊C4×C191—21no—
110C4⋊C4×C191C2311yescharacteristic
111C4⋊C4×C191C2311yescharacteristic
112C22⋊C4×C191—21no—
113C22⋊C4×C191—21no—
114C22×D191—22no—
115C22×D191—21no—
116C22×D191—41no—
117C22×D191—41no—
118C22×D191C2×D411yescharacteristic
119C22×D191C2×D411yescharacteristic
120Dic382—21no—
121Dic382—21no—
122D764—21no—
123D764—21no—
124D764—42no—
125D764—42no—
126C22⋊D191—42no—
127C22⋊D191—42no—
128C22⋊D191—42no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—41no—
133C2×Dic191—42no—
134C2×Dic191C2×D411yescharacteristic
135C2×Dic191C2×D411yescharacteristic
136C4×D191—21no—
137C4×D191—21no—
138C4×D191—21no—
139C4×D191—21no—
140C4×D191—41no—
141C4×D191—41no—
142C4×D191—42no—
143C191⋊C8—21no—
144C191⋊C8—21no—
145C23×C191—21no—
146C23×C191C2×D411yescharacteristic
147Q8×C191—21no—
148Q8×C191—21no—
149D4×C191—21no—
150D4×C191—21no—
151D4×C191—42no—
152C2×C4×C191—21no—
153C2×C4×C191—21no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191C2×D411yescharacteristic
158C2×C4×C191C2411yescharacteristic
159C8×C191—21no—
160C8×C191—21no—
161C22×C191—21no—
162C22×C191—21no—
163C22×C191—41no—
164C22×C191—41no—
165C22×C191—41no—
166C22×C191#13512yes—
167C22×C191C22×D411yescharacteristic
168C2×D191—21no—
169C2×D191—21no—
170C2×D191—21no—
171C2×D191—21no—
172C2×D191—21no—
173C2×D191—21no—
174C2×D191—44no—
175C2×D191—41no—
176C2×D191—41no—
177C2×D191—41no—
178C4×C191—21no—
179C4×C191—41no—
180C4×C191—41no—
181C4×C191—41no—
182C4×C191H(5,𝔽2)11yescharacteristic
183C4×C191H(5,𝔽2)11yescharacteristic
184Dic191—21no—
185Dic191—21no—
186Dic191—41no—
187Dic191—41no—
188Dic191—41no—
189C2×C191—22no—
190C2×C191—81no—
191C2×C191#53411yescharacteristic
192C2×C191C2×#13511yescharacteristic
193C2×C191#57511yescharacteristic
194D191—41no—
195D191—41no—
196D191—81no—
197C191#319111yescharacteristic, complemented, Sylow
198#3191—1911nomaximal, Sylow
199#525—1911no—
200#525—1911no—
201#485—1911no—
202#485—1911no—
203#482—1911no—
204#482—1911no—
205#467—1911no—
206#466—1911no—
207#465—1911no—
208#465D19111yescharacteristic, complemented
209#452—1911no—
210#452—1911no—
211#449—1911no—
212#449—1911no—
213C2×C22⋊C8—1911no—
214C2×#41—1911no—
215C2×#41—1911no—
216C23×C4—1911no—
217C2×Q16—1911no—
218C2×SD16—1911no—
219C2×SD16C2×D19111yescharacteristic, complemented
220C2×D8—1911no—
221C22×C8—1911no—
222C22×C8C2×D19111yescharacteristic
223#123—3821no—
224#123—3821no—
225C22⋊Q8—1911no—
226C22⋊Q8—1911no—
227C22⋊Q8—1911no—
228C22⋊Q8C2×D19111yescharacteristic
229#121—1911no—
230#121—1911no—
231#121—1911no—
232#121C2×D19111yescharacteristic
233#120—3821no—
234#120—3821no—
235C4×D4—3821no—
236C4×D4—3821no—
237C4×D4—3821no—
238C4×D4—3821no—
239#117—1911no—
240#117—1911no—
241#107—1911no—
242#107—1911no—
243#106—1911no—
244#106C2×D19111yescharacteristic, complemented
245#103—1911no—
246#103—1911no—
247#103—1911no—
248#103C2×D19111yescharacteristic, complemented
249#102—1911no—
250#102—1911no—
251#102—1911no—
252#102C2×D19111yescharacteristic, complemented
253C22⋊C8—1911no—
254C22⋊C8—1911no—
255C22⋊C8—1911no—
256C22⋊C8—1911no—
257C24—1911no—
258#41—7641no—
259#41—7641no—
260#41—7641no—
261#41—7641no—
262C2×Q8—1911no—
263C2×Q8C22×D19111yescharacteristic
264C2×D4—21no—
265C2×D4—3821no—
266C2×D4—3821no—
267C2×D4—3821no—
268C2×D4—3821no—
269C2×D4—3821no—
270C2×D4—1911no—
271C2×D4C22×D19111yescharacteristic
272C22×C4—3821no—
273C22×C4—3821no—
274C22×C4—1911no—
275C22×C4—1911no—
276C22×C4—1911no—
277C22×C4—1911no—
278C22×C4—1911no—
279C22×C4—7641no—
280C22×C4—7641no—
281C22×C4C22×D19111yescharacteristic
282Q16—7641no—
283SD16—41no—
284SD16—7641no—
285D8—7641no—
286C2×C8—41no—
287C2×C8—1911no—
288C2×C8—1911no—
289C2×C8—7641no—
290C2×C8C22×D19111yescharacteristic
291C2×C8C22×D19111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—3821no—
294C4⋊C4—3821no—
295C4⋊C4—3821no—
296C4⋊C4—1911no—
297C4⋊C4—1911no—
298C4⋊C4C22×D19111yescharacteristic
299C4⋊C4C22×D19111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—3821no—
303C22⋊C4—3821no—
304C22⋊C4—3821no—
305C22⋊C4—3821no—
306C22⋊C4—3821no—
307C22⋊C4—3821no—
308C22⋊C4—3821no—
309C22⋊C4—3821no—
310C42—3821no—
311C42—3821no—
312C23—21no—
313C23—3822no—
314C23—3821no—
315C23—1911no—
316C23—1911no—
317C23—7641no—
318C23—7641no—
319C23D4×D19111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3821no—
323Q8—3821no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3821no—
328D4—3821no—
329D4—7642no—
330D4—7642no—
331D4—7642no—
332D4—7642no—
333D4—7642no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—3821no—
340C2×C4—3821no—
341C2×C4—3821no—
342C2×C4—3821no—
343C2×C4—3821no—
344C2×C4—3821no—
345C2×C4—3821no—
346C2×C4—1911no—
347C2×C4—1911no—
348C2×C4—7641no—
349C2×C4—7641no—
350C2×C4—7642no—
351C2×C4—7641no—
352C2×C4—7642no—
353C2×C4D4×D19111yescharacteristic
354C2×C4C23×D19111yescharacteristic
355C8—21no—
356C8—21no—
357C8—3821no—
358C8—3821no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—3821no—
365C22—3821no—
366C22—3821no—
367C22—3821no—
368C22—3821no—
369C22—3821no—
370C22—7644no—
371C22—7641no—
372C22—7641no—
373C22—7641no—
374C22#2025934312yes—
375C22C2×D4×D19111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3821no—
381C4—3821no—
382C4—7641no—
383C4—7641no—
384C4—7641no—
385C4#2025936711yescharacteristic
386C4#2025936811yescharacteristic
387C2—22no—
388C2—81no—
389C2—15281no—
390C2—7641no—
391C2—7641no—
392C2#2713322111yescharacteristic
393C2C2×#2025934311yescharacteristic
394C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#465×C191C2
socleC22×C191C22×D4
hypercenter#465D191
hypocenterC191#3191
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #27133176C2semidirect
2. #27133173C2semidirect
3. #27133007C2semidirect
4. #27133002C2semidirect
5. #27132989C2semidirect
6. #27132986C2semidirect
7. #27132902C2semidirect
8. #27132897C2semidirect
9. #27132892C2semidirect
10. #27132828C2semidirect
11. #27132822C2semidirect
12. #27132809C2semidirect
13. #27132807C2semidirect
14. C2×(C2×D191)⋊C8C2semidirect
15. #465×C191C2semidirect
19. C2×#15690277C22semidirect
20. C2×#15690276C22semidirect
21. C2×#15690272C22semidirect
39. #20259255C22semidirect
40. #20259255C22semidirect
41. #20259254C22semidirect
42. #20259247C22semidirect
43. #20259246C22semidirect
44. #20259245C22semidirect
45. #20259244C22semidirect
46. #20259243C22semidirect
47. #20259242C22semidirect
52. C2×SD16×C191C22semidirect
56. #106×C191C22semidirect
57. #103×C191C22semidirect
58. #102×C191C22semidirect
197. C191#3191semidirect
208. #465D191semidirect
219. C2×SD16C2×D191semidirect
244. #106C2×D191semidirect
248. #103C2×D191semidirect
252. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331762
#271331732
#271330072
#271330022
#271329892
#271329862
#271329022
#271328972
#271328922
#271328282
#271328222
#271328092
#271328072
C2×(C2×D191)⋊C82
#465×C1912
#3191191