Finite Group Databasebeta

← #37583310

Subgroups — #37583310

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#27133173C211yesmaximal, characteristic, complemented
2#27133170C211yesmaximal, characteristic, complemented
3#27133005C211yesmaximal, characteristic, complemented
4#27133003C211yesmaximal, characteristic, complemented
5#27132986C211yesmaximal, characteristic, complemented
6#27132984C211yesmaximal, characteristic, complemented
7#27132903C211yesmaximal, characteristic, complemented
8#27132896C211yesmaximal, characteristic, complemented
9#27132891C211yesmaximal, characteristic, complemented
10#27132889C211yesmaximal, characteristic, complemented
11#27132825C211yesmaximal, characteristic, complemented
12#27132822C211yesmaximal, characteristic, complemented
13#27132805C211yesmaximal, characteristic, complemented
14C22⋊C8×D191C211yesmaximal, characteristic, complemented
15#449×C191C211yesmaximal, characteristic, complemented
16C2×#15690286C2211yescharacteristic
17C22×C4×D191C2211yescharacteristic
18C2×#15690277C2211yescharacteristic, complemented
19C2×#15690275C2211yescharacteristic, complemented
20C2×C8×D191C2211yescharacteristic
21C2×C8×D191C2211yescharacteristic
22#20259304—21no—
23#20259303—21no—
24#20259302C2211yescharacteristic
25#20259301C2211yescharacteristic
26#20259298C2211yescharacteristic
27#20259298C2211yescharacteristic
28#20259293C2211yescharacteristic
29#20259293C2211yescharacteristic
30#20259293C2211yescharacteristic
31#20259290—21no—
32#20259290—21no—
33D4×Dic191—21no—
34C4×C22⋊D191—21no—
35C4×C22⋊D191—21no—
36(C22⋊D191)⋊C4—21no—
37#20259281C2211yescharacteristic
38#20259280C2211yescharacteristic
39#20259256C2211yescharacteristic, complemented
40#20259255C2211yescharacteristic, complemented
41#20259254C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259247C2211yescharacteristic, complemented
44#20259247C2211yescharacteristic, complemented
45#20259246C2211yescharacteristic, complemented
46#20259243C2211yescharacteristic, complemented
47#20259243C2211yescharacteristic, complemented
48#20259243C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C2×#41×C191C2211yescharacteristic
53C2×SD16×C191C2211yescharacteristic, complemented
54C2×D8×C191C2211yescharacteristic, complemented
55#121×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic
59C23×D191D411yescharacteristic
60#15690286—41no—
61#15690286—41no—
62C2×Dic382C2311yescharacteristic
63C2×C22⋊D191—21no—
64C2×C22⋊D191—21no—
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67C22×Dic191—21no—
68C22×Dic191D411yescharacteristic
69C2×C4×D191—41no—
70C2×C4×D191—41no—
71C2×C4×D191D411yescharacteristic
72C2×C4×D191D411yescharacteristic
73C2×C4×D191C2311yescharacteristic
74C2×C4×D191C2311yescharacteristic
75#15690277—41no—
76#15690275—41no—
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C8×D191—41no—
80C8×D191—41no—
81C4⋊Dic191—21no—
82C4⋊Dic191C2311yescharacteristic
83C4⋊Dic191C2311yescharacteristic
84C4⋊Dic191C2311yescharacteristic
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88C22⋊Dic191—21no—
89C22⋊Dic191—21no—
90C22⋊Dic191—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—
97C4×Dic191—21no—
98C4×Dic191—21no—
99#41×C191—41no—
100#41×C191—41no—
101C2×Q8×C191C2311yescharacteristic
102C2×D4×C191—21no—
103C2×D4×C191—21no—
104C2×D4×C191C2311yescharacteristic
105C2×D4×C191C2311yescharacteristic
106C22×C4×C191—21no—
107C22×C4×C191C2311yescharacteristic
108SD16×C191—41no—
109D8×C191—41no—
110C2×C8×C191C2311yescharacteristic
111C2×C8×C191C2311yescharacteristic
112C4⋊C4×C191C2311yescharacteristic
113C22⋊C4×C191—21no—
114C22×D191—22no—
115C22×D191—41no—
116C22×D191—41no—
117C22×D191C2×D411yescharacteristic
118C22×D191C2×D411yescharacteristic
119Dic382—21no—
120Dic382—21no—
121C22⋊D191—42no—
122C22⋊D191—42no—
123C22⋊D191—42no—
124C22⋊D191—42no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—41no—
130C2×Dic191—42no—
131C2×Dic191C2×D411yescharacteristic
132C2×Dic191C2×D411yescharacteristic
133C4×D191—21no—
134C4×D191—21no—
135C4×D191—21no—
136C4×D191—21no—
137C4×D191—41no—
138C4×D191—41no—
139C191⋊C8—21no—
140C191⋊C8—21no—
141C23×C191—21no—
142C23×C191—21no—
143C23×C191C2×D411yescharacteristic
144Q8×C191—21no—
145Q8×C191—21no—
146D4×C191—21no—
147D4×C191—21no—
148D4×C191—21no—
149D4×C191—21no—
150D4×C191—42no—
151D4×C191—42no—
152C2×C4×C191—21no—
153C2×C4×C191—21no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—42no—
157C2×C4×C191C2×D411yescharacteristic
158C2×C4×C191C2411yescharacteristic
159C8×C191—21no—
160C8×C191—21no—
161C22×C191—21no—
162C22×C191—21no—
163C22×C191—21no—
164C22×C191—41no—
165C22×C191—41no—
166C22×C191—41no—
167C22×C191—41no—
168C22×C191—41no—
169C22×C191—41no—
170C22×C191C22×D411yescharacteristic
171C2×D191—21no—
172C2×D191—21no—
173C2×D191—21no—
174C2×D191—21no—
175C2×D191—21no—
176C2×D191—44no—
177C2×D191#13512yes—
178C4×C191—21no—
179C4×C191—41no—
180C4×C191—41no—
181C4×C191H(5,𝔽2)11yescharacteristic
182C4×C191H(5,𝔽2)11yescharacteristic
183Dic191—21no—
184Dic191—21no—
185Dic191—41no—
186Dic191—41no—
187Dic191—41no—
188Dic191—41no—
189C2×C191—41no—
190C2×C191—81no—
191C2×C191—81no—
192C2×C191#53411yescharacteristic
193C2×C191C2×#13511yescharacteristic
194C2×C191#57511yescharacteristic
195D191—22no—
196D191—41no—
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#465—1911no—
209#452—1911no—
210#452—1911no—
211#449—1911no—
212#449D19111yescharacteristic, complemented
213C2×C22⋊C8—1911no—
214C2×#41—1911no—
215C2×#41C2×D19111yescharacteristic
216C23×C4—1911no—
217C2×Q16—1911no—
218C2×SD16—1911no—
219C2×SD16C2×D19111yescharacteristic, complemented
220C2×D8C2×D19111yescharacteristic, complemented
221C22×C8—1911no—
222C22×C8—1911no—
223#123—3821no—
224#123—3821no—
225C22⋊Q8—1911no—
226C22⋊Q8—1911no—
227C22⋊Q8—1911no—
228C22⋊Q8—1911no—
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#106—1911no—
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⋊C8C2×D19111yescharacteristic
257C24—1911no—
258#41—41no—
259#41—41no—
260#41—7641no—
261#41—7641no—
262C2×Q8—1911no—
263C2×Q8C22×D19111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—3821no—
267C2×D4—3821no—
268C2×D4—3821no—
269C2×D4—3821no—
270C2×D4C22×D19111yescharacteristic
271C2×D4C22×D19111yescharacteristic
272C22×C4—21no—
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—41no—
286C2×C8—1911no—
287C2×C8—1911no—
288C2×C8—7641no—
289C2×C8—7641no—
290C2×C8C22×D19111yescharacteristic
291C2×C8C22×D19111yescharacteristic
292C4⋊C4—3821no—
293C4⋊C4—3821no—
294C4⋊C4—3821no—
295C4⋊C4—3821no—
296C4⋊C4—1911no—
297C4⋊C4—1911no—
298C4⋊C4—1911no—
299C4⋊C4C22×D19111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—3821no—
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—21no—
314C23—3822no—
315C23—1911no—
316C23—1911no—
317C23—7641no—
318C23—7641no—
319C23D4×D19111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3821no—
323Q8—3821no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—7642no—
331D4—7642no—
332D4—7642no—
333D4—7642no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—3821no—
340C2×C4—3821no—
341C2×C4—3821no—
342C2×C4—3821no—
343C2×C4—3821no—
344C2×C4—3821no—
345C2×C4—3821no—
346C2×C4—3821no—
347C2×C4—1911no—
348C2×C4—1911no—
349C2×C4—7641no—
350C2×C4—7641no—
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—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—3821no—
369C22—3821no—
370C22—3821no—
371C22—3821no—
372C22—3821no—
373C22—1912no—
374C22—7644no—
375C22C2×D4×D19111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3821no—
380C4—3821no—
381C4—7641no—
382C4—7641no—
383C4—7641no—
384C4—7641no—
385C4#2025936711yescharacteristic
386C4#2025936711yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—3822no—
391C2—7641no—
392C2#2713322311yescharacteristic
393C2#135×D19111yescharacteristic
394C2#2713345911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#449×C191C2
socleC22×C191C22×D4
hypercenter#449D191
hypocenterC191#3191
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #27133173C2semidirect
2. #27133170C2semidirect
3. #27133005C2semidirect
4. #27133003C2semidirect
5. #27132986C2semidirect
6. #27132984C2semidirect
7. #27132903C2semidirect
8. #27132896C2semidirect
9. #27132891C2semidirect
10. #27132889C2semidirect
11. #27132825C2semidirect
12. #27132822C2semidirect
13. #27132805C2semidirect
14. C22⋊C8×D191C2semidirect
15. #449×C191C2semidirect
18. C2×#15690277C22semidirect
19. C2×#15690275C22semidirect
39. #20259256C22semidirect
40. #20259255C22semidirect
41. #20259254C22semidirect
42. #20259253C22semidirect
43. #20259247C22semidirect
44. #20259247C22semidirect
45. #20259246C22semidirect
46. #20259243C22semidirect
47. #20259243C22semidirect
48. #20259243C22semidirect
53. C2×SD16×C191C22semidirect
54. C2×D8×C191C22semidirect
56. #103×C191C22semidirect
57. #102×C191C22semidirect
197. C191#3191semidirect
212. #449D191semidirect
219. C2×SD16C2×D191semidirect
220. C2×D8C2×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
#271331732
#271331702
#271330052
#271330032
#271329862
#271329842
#271329032
#271328962
#271328912
#271328892
#271328252
#271328222
#271328052
C22⋊C8×D1912
#449×C1912
#3191191