Finite Group Databasebeta

← #37583409

Subgroups — #37583409

Order 24448.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133244C211yesmaximal, characteristic
2#27133236C211yesmaximal, characteristic, complemented
3#27133007C211yesmaximal, characteristic, complemented
4#27132998C211yesmaximal, characteristic, complemented
5#27132989C211yesmaximal, characteristic, complemented
6#27132922C211yesmaximal, characteristic, complemented
7#27132912C211yesmaximal, characteristic, complemented
8#27132903C211yesmaximal, characteristic, complemented
9#27132893C211yesmaximal, characteristic, complemented
10#27132827C211yesmaximal, characteristic, complemented
11#27132823C211yesmaximal, characteristic, complemented
12#27132820C211yesmaximal, characteristic, complemented
13#27132803C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#483×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×Q8×D191C2211yescharacteristic
19C2×Dic764C2211yescharacteristic
20C2×#15690277C2211yescharacteristic
21C2×#15690276C2211yescharacteristic
22C2×#15690274C2211yescharacteristic
23C2×#15690270C2211yescharacteristic
24C2×C8×D191C2211yescharacteristic
25#20259321—21no—
26#20259308—21no—
27#20259307—21no—
28#20259304—21no—
29#20259302—21no—
30#20259302C2211yescharacteristic
31#20259302C2211yescharacteristic
32#20259302C2211yescharacteristic
33#20259301C2211yescharacteristic
34#20259298C2211yescharacteristic
35#20259297—21no—
36#20259297C2211yescharacteristic
37#20259297C2211yescharacteristic
38#20259296—21no—
39#20259296—21no—
40#20259280C2211yescharacteristic
41#20259255C2211yescharacteristic
42#20259255C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259245C2211yescharacteristic
45#20259245C2211yescharacteristic
46#20259245C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259242C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C22⋊Q8×C191C2211yescharacteristic
53C2×C4⋊C4×C191C2211yescharacteristic
54#106×C191C2211yescharacteristic
55#106×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690287—41no—
60#15690287—41no—
61#15690287—41no—
62#15690287—41no—
63C2×Dic382—21no—
64C2×Dic382D411yescharacteristic
65C2×Dic382C2311yescharacteristic
66C2×Dic382C2311yescharacteristic
67Q8×D191—41no—
68Q8×D191—41no—
69C2×D764—21no—
70C2×D764—21no—
71C2×D764D411yescharacteristic
72C2×D764C2311yescharacteristic
73C2×C22⋊D191—21no—
74C2×C22⋊D191D411yescharacteristic
75C2×C22⋊D191D411yescharacteristic
76C2×C4×D191—21no—
77C2×C4×D191—21no—
78C2×C4×D191C2311yescharacteristic
79C2×C4×D191C2311yescharacteristic
80Dic764—41no—
81#15690277—41no—
82#15690276—41no—
83#15690274—41no—
84#15690270—41no—
85C2×C191⋊C8C2311yescharacteristic
86C2×C191⋊C8C2311yescharacteristic
87C8×D191—41no—
88C4⋊Dic191—21no—
89C4⋊Dic191—21no—
90C4⋊Dic191—21no—
91C4⋊Dic191C2311yescharacteristic
92Dic191⋊C4—21no—
93Dic191⋊C4—21no—
94C22⋊Dic191—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×C191—21no—
105C22×C4×C191C2311yescharacteristic
106C2×C8×C191C2311yescharacteristic
107C2×C8×C191C2311yescharacteristic
108C4⋊C4×C191—21no—
109C4⋊C4×C191—21no—
110C4⋊C4×C191C2311yescharacteristic
111C4⋊C4×C191C2311yescharacteristic
112C4⋊C4×C191C2311yescharacteristic
113C22⋊C4×C191—21no—
114C22×D191—21no—
115C22×D191C2×D411yescharacteristic
116C22×D191C2×D411yescharacteristic
117Dic382—21no—
118Dic382—21no—
119Dic382—21no—
120Dic382—21no—
121Dic382—41no—
122Dic382—42no—
123D764—21no—
124D764—21no—
125D764—41no—
126D764—81no—
127D764—81no—
128C22⋊D191—41no—
129C22⋊D191—41no—
130C22⋊D191—42no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191C2×D411yescharacteristic
135C2×Dic191C2×D411yescharacteristic
136C4×D191—21no—
137C4×D191—21no—
138C4×D191—21no—
139C4×D191—21no—
140C4×D191—42no—
141C4×D191—42no—
142C191⋊C8—21no—
143C191⋊C8—21no—
144C23×C191C2×D411yescharacteristic
145Q8×C191—21no—
146Q8×C191—21no—
147C2×C4×C191—21no—
148C2×C4×C191—21no—
149C2×C4×C191—21no—
150C2×C4×C191—21no—
151C2×C4×C191—21no—
152C2×C4×C191—21no—
153C2×C4×C191—81no—
154C2×C4×C191C2×D411yescharacteristic
155C2×C4×C191C2411yescharacteristic
156C8×C191—21no—
157C8×C191—21no—
158C22×C191—21no—
159C22×C191—21no—
160C22×C191—21no—
161C22×C191C22×D411yescharacteristic
162C2×D191—21no—
163C2×D191—21no—
164C2×D191—21no—
165C2×D191—21no—
166C2×D191—21no—
167C2×D191—21no—
168C2×D191—41no—
169C2×D191—41no—
170C2×D191—41no—
171C4×C191—21no—
172C4×C191—41no—
173C4×C191—41no—
174C4×C191—41no—
175C4×C191—41no—
176C4×C191H(5,𝔽2)11yescharacteristic
177C4×C191H(5,𝔽2)11yescharacteristic
178Dic191—21no—
179Dic191—21no—
180Dic191—41no—
181Dic191—41no—
182Dic191—41no—
183C2×C191—41no—
184C2×C191#53411yescharacteristic
185C2×C191#57711yescharacteristic
186C2×C191#57811yescharacteristic
187D191—41no—
188D191—41no—
189D191—81no—
190C191#320111yescharacteristic, complemented, Sylow
191#3201—1911nomaximal, Sylow
192#537—1911no—
193#536—1911no—
194#485—1911no—
195#484—1911no—
196#483D19111yescharacteristic, complemented
197#482—1911no—
198#470—1911no—
199#468—1911no—
200#467—1911no—
201#465—1911no—
202#452—1911no—
203#452—1911no—
204#451—1911no—
205#448—1911no—
206#408—1911no—
207C2×#41—1911no—
208C2×#41—1911no—
209C22×Q8—1911no—
210C2×Q16—1911no—
211C2×Q16—1911no—
212C2×SD16—1911no—
213C2×SD16—1911no—
214C2×M16—1911no—
215C22×C8—1911no—
216C4⋊Q8—3821no—
217#124—3821no—
218#123—3821no—
219#123—3821no—
220C22⋊Q8—3821no—
221C22⋊Q8—1911no—
222C22⋊Q8—1911no—
223C22⋊Q8—1911no—
224C22⋊Q8—1911no—
225C22⋊Q8—1911no—
226C22⋊Q8C2×D19111yescharacteristic
227#121—3821no—
228#121—3821no—
229#121—3821no—
230#121—1911no—
231#121—1911no—
232#117—1911no—
233C2×C4⋊C4C2×D19111yescharacteristic
234#107—1911no—
235#107—1911no—
236#106C2×D19111yescharacteristic
237#106C2×D19111yescharacteristic
238#103—1911no—
239#103—1911no—
240#103—1911no—
241#103—1911no—
242#103C2×D19111yescharacteristic
243#103C2×D19111yescharacteristic
244#102—1911no—
245#102—1911no—
246C22⋊C8—1911no—
247C22⋊C8—1911no—
248C22⋊C8—1911no—
249C22⋊C8C2×D19111yescharacteristic
250#41—7641no—
251#41—7641no—
252#41—7641no—
253#41—7641no—
254C2×Q8—3821no—
255C2×Q8—1911no—
256C2×Q8—1911no—
257C2×Q8—1911no—
258C2×Q8—7641no—
259C2×Q8—7641no—
260C2×Q8C22×D19111yescharacteristic
261C2×D4—3821no—
262C2×D4—3821no—
263C2×D4—3821no—
264C2×D4—1911no—
265C2×D4—1911no—
266C2×D4—1911no—
267C2×D4—1911no—
268C22×C4—21no—
269C22×C4—3821no—
270C22×C4—3821no—
271C22×C4—1911no—
272C22×C4—1911no—
273C22×C4C22×D19111yescharacteristic
274Q16—7641no—
275Q16—7641no—
276SD16—7641no—
277SD16—7641no—
278M16—7641no—
279C2×C8—1911no—
280C2×C8—1911no—
281C2×C8—7641no—
282C2×C8C22×D19111yescharacteristic
283C2×C8C22×D19111yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—3821no—
287C4⋊C4—3821no—
288C4⋊C4—3821no—
289C4⋊C4—3821no—
290C4⋊C4—3821no—
291C4⋊C4—1911no—
292C4⋊C4C22×D19111yescharacteristic
293C4⋊C4C22×D19111yescharacteristic
294C4⋊C4C22×D19111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—3821no—
297C22⋊C4—3821no—
298C22⋊C4—3821no—
299C22⋊C4—3821no—
300C22⋊C4—3821no—
301C22⋊C4—3821no—
302C22⋊C4—3821no—
303C22⋊C4—3821no—
304C42—3821no—
305C23—3821no—
306C23—1911no—
307C23—1911no—
308C23D4×D19111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—3821no—
312Q8—3821no—
313Q8—3821no—
314Q8—3821no—
315Q8—7641no—
316Q8—7642no—
317D4—3821no—
318D4—3821no—
319D4—15281no—
320D4—15281no—
321D4—7641no—
322D4—7641no—
323D4—7641no—
324D4—7642no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—3821no—
333C2×C4—3821no—
334C2×C4—3821no—
335C2×C4—3821no—
336C2×C4—3821no—
337C2×C4—3821no—
338C2×C4—3821no—
339C2×C4—1911no—
340C2×C4—1911no—
341C2×C4—7642no—
342C2×C4—7642no—
343C2×C4D4×D19111yescharacteristic
344C2×C4C23×D19111yescharacteristic
345C8—21no—
346C8—21no—
347C8—3821no—
348C8—3821no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—3821no—
353C22—3821no—
354C22—3821no—
355C22—3821no—
356C22—3821no—
357C22—3821no—
358C22—7641no—
359C22—7641no—
360C22—7641no—
361C22C2×D4×D19111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—3821no—
368C4—3821no—
369C4—7641no—
370C4—7641no—
371C4—7641no—
372C4#2025936811yescharacteristic
373C4#2025936811yescharacteristic
374C2—41no—
375C2—15281no—
376C2—7641no—
377C2—7641no—
378C2#2713322411yescharacteristic
379C2#2713346911yescharacteristic
380C2#2713347911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#483×C191C2
socleC22×C191C22×D4
prime radical#27133244C2
hypercenter#483D191
hypocenterC191#3201
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #27133236C2semidirect
3. #27133007C2semidirect
4. #27132998C2semidirect
5. #27132989C2semidirect
6. #27132922C2semidirect
7. #27132912C2semidirect
8. #27132903C2semidirect
9. #27132893C2semidirect
10. #27132827C2semidirect
11. #27132823C2semidirect
12. #27132820C2semidirect
13. #27132803C2semidirect
14. #27132628C2semidirect
15. #483×C191C2semidirect
190. C191#3201semidirect
196. #483D191semidirect

Maximal subgroups

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

subgroupindex
#271332442
#271332362
#271330072
#271329982
#271329892
#271329222
#271329122
#271329032
#271328932
#271328272
#271328232
#271328202
#271328032
#271326282
#483×C1912
#3201191