Finite Group Databasebeta

← #37582626

Subgroups — #37582626

Order 24448.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133192C211yesmaximal, characteristic, complemented
2C4×#15690286C211yesmaximal, characteristic, complemented
3#27133002C211yesmaximal, characteristic, complemented
4#27132985C211yesmaximal, characteristic, complemented
5#27132971C211yesmaximal, characteristic, complemented
6#27132963C211yesmaximal, characteristic, complemented
7#27132882C211yesmaximal, characteristic, complemented
8#27132822C211yesmaximal, characteristic, complemented
9#27132805C211yesmaximal, characteristic
10#27132775C211yesmaximal, characteristic, complemented
11#27132767C211yesmaximal, characteristic, complemented
12#27132764C211yesmaximal, characteristic, complemented
13#27132760C211yesmaximal, characteristic, complemented
14#27132719C211yesmaximal, characteristic, complemented
15#463×C191C211yesmaximal, characteristic, complemented
16C2×#15690286C2211yescharacteristic
17C2×#15690277C2211yescharacteristic
18C2×#15690275C2211yescharacteristic
19#20259315—21no—
20#20259314C2211yescharacteristic
21#20259304—21no—
22#20259298C2211yescharacteristic
23#20259293C2211yescharacteristic
24Q8×Dic191C2211yescharacteristic
25C4×Dic382C2211yescharacteristic
26#20259287C2211yescharacteristic
27D4×Dic191C2211yescharacteristic
28D4×Dic191C2211yescharacteristic
29C4×C22⋊D191—21no—
30(C22⋊D191)⋊C4—21no—
31(C22⋊D191)⋊C4—21no—
32#20259280C2211yescharacteristic
33#20259278—21no—
34#20259278—21no—
35C2×C4×Dic191—21no—
36C42×D191C2211yescharacteristic
37#20259256C2211yescharacteristic
38#20259255C2211yescharacteristic
39#20259254C2211yescharacteristic
40#20259253C2211yescharacteristic
41C4⋊(C191⋊C8)C2211yescharacteristic
42#20259247C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259243C2211yescharacteristic
46#20259243C2211yescharacteristic
47#20259243C2211yescharacteristic
48(C2×D191)⋊C8C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50#20259232C2211yescharacteristic
51#20259232C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic
53C2×D8×C191C2211yescharacteristic
54#124×C191C2211yescharacteristic
55C4×D4×C191C2211yescharacteristic
56C4⋊C8×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58#102×C191C2211yescharacteristic
59#15690286—22no—
60#15690286—22no—
61C2×Dic382C2311yescharacteristic
62C2×C22⋊D191—21no—
63C2×C22⋊D191—21no—
64C22×Dic191—21no—
65C22×Dic191—21no—
66C22×Dic191—21no—
67C2×C4×D191D411yescharacteristic
68C2×C4×D191D411yescharacteristic
69C2×C4×D191C2311yescharacteristic
70#15690277—22no—
71#15690275—22no—
72C2×C191⋊C8C2311yescharacteristic
73C2×C191⋊C8C2311yescharacteristic
74C4⋊Dic191—21no—
75C4⋊Dic191C2311yescharacteristic
76C4⋊Dic191C2311yescharacteristic
77C4⋊Dic191C2311yescharacteristic
78Dic191⋊C4—21no—
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83C22⋊Dic191—21no—
84C22⋊Dic191—21no—
85C22⋊Dic191—21no—
86(C2×D191)⋊C4—21no—
87(C2×D191)⋊C4—21no—
88C4×Dic191—21no—
89C4×Dic191—21no—
90C4×Dic191—21no—
91C4×Dic191—21no—
92C4×Dic191D411yescharacteristic
93C4×Dic191D411yescharacteristic
94C4×Dic191C2311yescharacteristic
95C2×Q8×C191C2311yescharacteristic
96C2×D4×C191C2311yescharacteristic
97C2×D4×C191C2311yescharacteristic
98C22×C4×C191—21no—
99SD16×C191—22no—
100D8×C191—22no—
101C2×C8×C191C2311yescharacteristic
102C2×C8×C191C2311yescharacteristic
103C4⋊C4×C191C2311yescharacteristic
104C22⋊C4×C191—21no—
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191C2×D411yescharacteristic
109Dic382—21no—
110Dic382#4112yes—
111C22⋊D191—24no—
112C22⋊D191—42no—
113C2×Dic191—24no—
114C2×Dic191—21no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C2×Dic191—42no—
119C2×Dic191—42no—
120C2×Dic191C2×D411yescharacteristic
121C2×Dic191C2×D411yescharacteristic
122C2×Dic191C2×D411yescharacteristic
123C4×D191—21no—
124C4×D191—21no—
125C4×D191—41no—
126C4×D191—41no—
127C191⋊C8—21no—
128C191⋊C8—21no—
129C23×C191—21no—
130C23×C191—21no—
131Q8×C191—21no—
132Q8×C191—21no—
133D4×C191—21no—
134D4×C191—21no—
135D4×C191—21no—
136D4×C191#4112yes—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—42no—
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2411yescharacteristic
143C8×C191—21no—
144C8×C191—21no—
145C22×C191—22no—
146C22×C191—41no—
147C22×C191—41no—
148C22×C191—41no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191C22×D411yescharacteristic
152C2×D191—21no—
153C2×D191—21no—
154C2×D191—21no—
155C4×C191—21no—
156C4×C191—21no—
157C4×C191—41no—
158C4×C191—41no—
159C4×C191C2×#4111yescharacteristic
160C4×C191C2×#4111yescharacteristic
161Dic191—21no—
162Dic191—22no—
163Dic191—21no—
164Dic191—21no—
165Dic191—41no—
166Dic191—41no—
167Dic191—41no—
168C2×C191—42no—
169C2×C191—81no—
170C2×C191#52511yescharacteristic
171C2×C191#57511yescharacteristic
172C2×C191#57511yescharacteristic
173D191—41no—
174C191#311111yescharacteristic, complemented, Sylow
175#3111—1911nomaximal, Sylow
176#529—1911no—
177C4×#41—1911no—
178#485—1911no—
179#482—1911no—
180#479—1911no—
181#478—1911no—
182#464—1911no—
183#463D19111yescharacteristic, complemented
184#452—1911no—
185#449—1911no—
186#442—1911no—
187#441—1911no—
188#440—1911no—
189#440—1911no—
190#432—1911no—
191C2×#41—1911no—
192C2×Q16—1911no—
193C2×SD16—1911no—
194C2×SD16C2×D19111yescharacteristic
195C2×D8C2×D19111yescharacteristic
196#126—3821no—
197#125—1911no—
198#124C2×D19111yescharacteristic
199#123—3821no—
200C22⋊Q8—1911no—
201#121—1911no—
202C4×Q8—1911no—
203C4×Q8—1911no—
204C4×Q8—1911no—
205C4×D4—3821no—
206C4×D4—3821no—
207C4×D4—3821no—
208C4×D4—1911no—
209C4×D4—1911no—
210C4×D4C2×D19111yescharacteristic
211#117—3821no—
212#117—3821no—
213#117—1911no—
214C2×C42—3821no—
215C2×C42—1911no—
216#107—1911no—
217#107—1911no—
218#106—1911no—
219#106—1911no—
220C4⋊C8—1911no—
221C4⋊C8C2×D19111yescharacteristic
222#103—1911no—
223#103—1911no—
224#103—1911no—
225#103C2×D19111yescharacteristic
226#102—1911no—
227#102—1911no—
228#102—1911no—
229#102C2×D19111yescharacteristic
230C22⋊C8—1911no—
231C22⋊C8—1911no—
232#97—1911no—
233#97—1911no—
234#41—3822no—
235#41—3822no—
236C2×Q8—1911no—
237C2×Q8C22×D19111yescharacteristic
238C2×D4—3821no—
239C2×D4—3821no—
240C2×D4C22×D19111yescharacteristic
241C2×D4C22×D19111yescharacteristic
242C22×C4—21no—
243C22×C4—3821no—
244C22×C4—3821no—
245C22×C4—3821no—
246C22×C4—1911no—
247C22×C4—1911no—
248C22×C4—1911no—
249Q16—3822no—
250SD16—22no—
251SD16—3822no—
252D8—22no—
253C2×C8—1911no—
254C2×C8—1911no—
255C2×C8C22×D19111yescharacteristic
256C2×C8C22×D19111yescharacteristic
257C4⋊C4—3821no—
258C4⋊C4—3821no—
259C4⋊C4—3821no—
260C4⋊C4—3821no—
261C4⋊C4—3821no—
262C4⋊C4—3821no—
263C4⋊C4—1911no—
264C4⋊C4—1911no—
265C4⋊C4—1911no—
266C4⋊C4C22×D19111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—3821no—
271C22⋊C4—3821no—
272C22⋊C4—3821no—
273C22⋊C4—3821no—
274C22⋊C4—3821no—
275C42—3821no—
276C42—3821no—
277C42—3821no—
278C42—3821no—
279C42—1911no—
280C42—1911no—
281C42—1911no—
282C42C22×D19111yescharacteristic
283C23—21no—
284C23—21no—
285C23—1911no—
286Q8—21no—
287Q8—21no—
288Q8—3821no—
289Q8—1912no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—3824no—
294D4—7642no—
295D4#1569028612yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—3824no—
300C2×C4—3821no—
301C2×C4—3821no—
302C2×C4—3821no—
303C2×C4—3821no—
304C2×C4—3821no—
305C2×C4—3821no—
306C2×C4—1911no—
307C2×C4—1911no—
308C2×C4—1911no—
309C2×C4—7641no—
310C2×C4—7641no—
311C2×C4—7642no—
312C2×C4—7642no—
313C2×C4D4×D19111yescharacteristic
314C2×C4D4×D19111yescharacteristic
315C2×C4C23×D19111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3821no—
319C8—3821no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3821no—
327C22—3821no—
328C22—3821no—
329C22C2×D4×D19111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—3821no—
335C4—3821no—
336C4—3821no—
337C4—3822no—
338C4—7641no—
339C4—7641no—
340C4—7641no—
341C4#41×D19111yescharacteristic
342C4C2×#1569028611yescharacteristic
343C2—42no—
344C2—81no—
345C2—7641no—
346C2#2713317311yescharacteristic
347C2#2713345911yescharacteristic
348C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#463×C191C2
socleC22×C191C22×D4
prime radical#27132805C2
hypercenter#463D191
hypocenterC191#3111
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #27133192C2semidirect
2. C4×#15690286C2semidirect
3. #27133002C2semidirect
4. #27132985C2semidirect
5. #27132971C2semidirect
6. #27132963C2semidirect
7. #27132882C2semidirect
8. #27132822C2semidirect
10. #27132775C2semidirect
11. #27132767C2semidirect
12. #27132764C2semidirect
13. #27132760C2semidirect
14. #27132719C2semidirect
15. #463×C191C2semidirect
174. C191#3111semidirect
183. #463D191semidirect

Maximal subgroups

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

subgroupindex
#271331922
C4×#156902862
#271330022
#271329852
#271329712
#271329632
#271328822
#271328222
#271328052
#271327752
#271327672
#271327642
#271327602
#271327192
#463×C1912
#3111191