Finite Group Databasebeta

← #37583315

Subgroups — #37583315

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#27133175C211yesmaximal, characteristic, complemented
3#27133006C211yesmaximal, characteristic, complemented
4#27132989C211yesmaximal, characteristic, complemented
5#27132987C211yesmaximal, characteristic, complemented
6#27132903C211yesmaximal, characteristic, complemented
7#27132900C211yesmaximal, characteristic, complemented
8#27132895C211yesmaximal, characteristic, complemented
9#27132893C211yesmaximal, characteristic, complemented
10#27132828C211yesmaximal, characteristic, complemented
11#27132823C211yesmaximal, characteristic, complemented
12#27132811C211yesmaximal, characteristic, complemented
13#27132810C211yesmaximal, characteristic, complemented
14C22⋊C8×D191C211yesmaximal, characteristic, complemented
15#485×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C22×C4×D191C2211yescharacteristic
19C2×#15690277C2211yescharacteristic, complemented
20C2×#15690276C2211yescharacteristic, complemented
21C2×#15690274C2211yescharacteristic, complemented
22C2×D1528C2211yescharacteristic, complemented
23C2×C8×D191C2211yescharacteristic
24C2×C8×D191C2211yescharacteristic
25#20259307—21no—
26#20259306—21no—
27#20259302C2211yescharacteristic
28#20259302C2211yescharacteristic
29#20259298C2211yescharacteristic
30#20259297C2211yescharacteristic
31#20259297C2211yescharacteristic
32#20259297C2211yescharacteristic
33#20259296C2211yescharacteristic
34#20259292—21no—
35#20259292—21no—
36C4×D764—21no—
37C4×D764—21no—
38#20259284—21no—
39(C22⋊D191)⋊C4—21no—
40#20259280C2211yescharacteristic
41#20259255C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259247C2211yescharacteristic, complemented
44#20259245C2211yescharacteristic, complemented
45#20259244C2211yescharacteristic, complemented
46#20259242C2211yescharacteristic, complemented
47#20259242C2211yescharacteristic, complemented
48#20259242C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C22⋊Q8×C191C2211yescharacteristic
53#117×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic, complemented
55#106×C191C2211yescharacteristic, complemented
56#103×C191C2211yescharacteristic, complemented
57#103×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic
59C23×D191D411yescharacteristic
60#15690288—41no—
61#15690288—41no—
62#15690287—41no—
63#15690287—41no—
64C2×Dic382C2311yescharacteristic
65C2×D764—21no—
66C2×D764—21no—
67C2×D764—21no—
68C2×D764—21no—
69C2×D764C2311yescharacteristic
70C2×D764C2311yescharacteristic
71C2×C22⋊D191—21no—
72C2×C22⋊D191—21no—
73C22×Dic191D411yescharacteristic
74C2×C4×D191—21no—
75C2×C4×D191—21no—
76C2×C4×D191—41no—
77C2×C4×D191—41no—
78C2×C4×D191D411yescharacteristic
79C2×C4×D191D411yescharacteristic
80C2×C4×D191C2311yescharacteristic
81C2×C4×D191C2311yescharacteristic
82#15690277—41no—
83#15690276—41no—
84#15690274—41no—
85D1528—41no—
86C2×C191⋊C8C2311yescharacteristic
87C2×C191⋊C8C2311yescharacteristic
88C8×D191—41no—
89C8×D191—41no—
90C4⋊Dic191—21no—
91C4⋊Dic191—21no—
92C4⋊Dic191C2311yescharacteristic
93Dic191⋊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—
99(C2×D191)⋊C4—21no—
100(C2×D191)⋊C4—21no—
101(C2×D191)⋊C4—21no—
102C4×Dic191—21no—
103C2×Q8×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C2×C8×C191C2311yescharacteristic
106C2×C8×C191C2311yescharacteristic
107C4⋊C4×C191—21no—
108C4⋊C4×C191C2311yescharacteristic
109C4⋊C4×C191C2311yescharacteristic
110C4⋊C4×C191C2311yescharacteristic
111C22⋊C4×C191—21no—
112C22⋊C4×C191—21no—
113C42×C191—21no—
114C22×D191—22no—
115C22×D191—21no—
116C22×D191—21no—
117C22×D191—41no—
118C22×D191—41no—
119C22×D191C2×D411yescharacteristic
120C22×D191C2×D411yescharacteristic
121Dic382—21no—
122Dic382—21no—
123D764—21no—
124D764—21no—
125D764—21no—
126D764—21no—
127D764—42no—
128D764—42no—
129D764—42no—
130D764—42no—
131C22⋊D191—42no—
132C22⋊D191—42no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—41no—
136C2×Dic191C2×D411yescharacteristic
137C2×Dic191C2×D411yescharacteristic
138C4×D191—21no—
139C4×D191—21no—
140C4×D191—21no—
141C4×D191—21no—
142C4×D191—41no—
143C4×D191—41no—
144C4×D191—42no—
145C4×D191—42no—
146C191⋊C8—21no—
147C191⋊C8—21no—
148C23×C191C2×D411yescharacteristic
149Q8×C191—21no—
150Q8×C191—21no—
151C2×C4×C191—21no—
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—21no—
164C22×C191C22×D411yescharacteristic
165C2×D191—21no—
166C2×D191—21no—
167C2×D191—21no—
168C2×D191—21no—
169C2×D191—21no—
170C2×D191—44no—
171C2×D191—41no—
172C2×D191—41no—
173C2×D191—41no—
174C2×D191—41no—
175C2×D191—41no—
176C2×D191—41no—
177C2×D191#13512yes—
178C4×C191—21no—
179C4×C191—41no—
180C4×C191—41no—
181C4×C191—41no—
182C4×C191—41no—
183C4×C191H(5,𝔽2)11yescharacteristic
184C4×C191H(5,𝔽2)11yescharacteristic
185Dic191—21no—
186Dic191—21no—
187Dic191—41no—
188Dic191—41no—
189C2×C191—41no—
190C2×C191#53411yescharacteristic
191C2×C191C2×#13511yescharacteristic
192C2×C191#57511yescharacteristic
193D191—22no—
194D191—41no—
195D191—81no—
196D191—81no—
197C191#319111yescharacteristic, complemented, Sylow
198#3191—1911nomaximal, Sylow
199#525—1911no—
200#525—1911no—
201#485—1911no—
202#485D19111yescharacteristic, complemented
203#482—1911no—
204#482—1911no—
205#467—1911no—
206#466—1911no—
207#465—1911no—
208#465—1911no—
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×SD16—1911no—
220C2×D8—1911no—
221C22×C8—1911no—
222C22×C8—1911no—
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#121—1911no—
233#120—3821no—
234#120—3821no—
235C4×D4—3821no—
236C4×D4—3821no—
237C4×D4—3821no—
238C4×D4—3821no—
239#117—1911no—
240#117C2×D19111yescharacteristic
241#107—1911no—
242#107C2×D19111yescharacteristic, complemented
243#106—1911no—
244#106C2×D19111yescharacteristic, complemented
245#103—1911no—
246#103—1911no—
247#103C2×D19111yescharacteristic, complemented
248#103C2×D19111yescharacteristic, complemented
249#102—1911no—
250#102—1911no—
251#102—1911no—
252#102—1911no—
253C22⋊C8—1911no—
254C22⋊C8—1911no—
255C22⋊C8—1911no—
256C22⋊C8C2×D19111yescharacteristic
257C24—1911no—
258#41—7641no—
259#41—7641no—
260#41—7641no—
261#41—7641no—
262C2×Q8—1911no—
263C2×Q8C22×D19111yescharacteristic
264C2×D4—3821no—
265C2×D4—3821no—
266C2×D4—3821no—
267C2×D4—3821no—
268C2×D4—3821no—
269C2×D4—3821no—
270C2×D4—1911no—
271C2×D4—1911no—
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—7641no—
284SD16—7641no—
285D8—7641no—
286C2×C8—1911no—
287C2×C8—1911no—
288C2×C8—7641no—
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⋊C4C22×D19111yescharacteristic
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—21no—
311C42—3821no—
312C23—3822no—
313C23—3821no—
314C23—3821no—
315C23—1911no—
316C23—1911no—
317C23—7641no—
318C23—7641no—
319C23D4×D19111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3821no—
323Q8—3821no—
324D4—3821no—
325D4—3821no—
326D4—3821no—
327D4—3821no—
328D4—7642no—
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—21no—
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—7642no—
352C2×C4—7641no—
353C2×C4D4×D19111yescharacteristic
354C2×C4C23×D19111yescharacteristic
355C8—21no—
356C8—21no—
357C8—3821no—
358C8—3821no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—3821no—
363C22—3821no—
364C22—3821no—
365C22—3821no—
366C22—3821no—
367C22—1912no—
368C22—7644no—
369C22—7641no—
370C22—7641no—
371C22—7641no—
372C22—7641no—
373C22—7641no—
374C22—7641no—
375C22C2×D4×D19111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—3821no—
382C4—3821no—
383C4—7641no—
384C4—7641no—
385C4#2025936811yescharacteristic
386C4#2025936811yescharacteristic
387C2—41no—
388C2—3822no—
389C2—15281no—
390C2—15281no—
391C2—7641no—
392C2#2713322411yescharacteristic
393C2#135×D19111yescharacteristic
394C2#2713346211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#485×C191C2
socleC22×C191C22×D4
hypercenter#485D191
hypocenterC191#3191
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #27133176C2semidirect
2. #27133175C2semidirect
3. #27133006C2semidirect
4. #27132989C2semidirect
5. #27132987C2semidirect
6. #27132903C2semidirect
7. #27132900C2semidirect
8. #27132895C2semidirect
9. #27132893C2semidirect
10. #27132828C2semidirect
11. #27132823C2semidirect
12. #27132811C2semidirect
13. #27132810C2semidirect
14. C22⋊C8×D191C2semidirect
15. #485×C191C2semidirect
19. C2×#15690277C22semidirect
20. C2×#15690276C22semidirect
21. C2×#15690274C22semidirect
22. C2×D1528C22semidirect
41. #20259255C22semidirect
42. #20259253C22semidirect
43. #20259247C22semidirect
44. #20259245C22semidirect
45. #20259244C22semidirect
46. #20259242C22semidirect
47. #20259242C22semidirect
48. #20259242C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
56. #103×C191C22semidirect
57. #103×C191C22semidirect
197. C191#3191semidirect
202. #485D191semidirect
242. #107C2×D191semidirect
244. #106C2×D191semidirect
247. #103C2×D191semidirect
248. #103C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331762
#271331752
#271330062
#271329892
#271329872
#271329032
#271329002
#271328952
#271328932
#271328282
#271328232
#271328112
#271328102
C22⋊C8×D1912
#485×C1912
#3191191