Finite Group Databasebeta

← #37583396

Subgroups — #37583396

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#27133234C211yesmaximal, characteristic, complemented
2#27133001C211yesmaximal, characteristic, complemented
3#27132998C211yesmaximal, characteristic, complemented
4#27132993C211yesmaximal, characteristic, complemented
5#27132984C211yesmaximal, characteristic, complemented
6#27132919C211yesmaximal, characteristic, complemented
7#27132907C211yesmaximal, characteristic, complemented
8#27132902C211yesmaximal, characteristic, complemented
9#27132890C211yesmaximal, characteristic, complemented
10#27132825C211yesmaximal, characteristic, complemented
11#27132825C211yesmaximal, characteristic, complemented
12#27132818C211yesmaximal, characteristic, complemented
13#27132801C211yesmaximal, characteristic, complemented
14#27132630C211yesmaximal, characteristic, complemented
15#537×C191C211yesmaximal, characteristic
16C22×Dic382C2211yescharacteristic
17C2×#15690277C2211yescharacteristic
18C2×#15690277C2211yescharacteristic
19C2×#15690275C2211yescharacteristic
20C2×#15690275C2211yescharacteristic
21C2×#15690271C2211yescharacteristic
22C22×C191⋊C8C2211yescharacteristic
23#20259320—21no—
24#20259309—21no—
25#20259303—21no—
26#20259303—21no—
27#20259301C2211yescharacteristic
28#20259301C2211yescharacteristic
29#20259301C2211yescharacteristic
30#20259301C2211yescharacteristic
31#20259281C2211yescharacteristic
32#20259255C2211yescharacteristic
33#20259255C2211yescharacteristic
34#20259253C2211yescharacteristic
35#20259253C2211yescharacteristic
36#20259246C2211yescharacteristic
37#20259246C2211yescharacteristic
38#20259245C2211yescharacteristic
39#20259245C2211yescharacteristic
40#20259245C2211yescharacteristic
41#20259245C2211yescharacteristic
42#20259243C2211yescharacteristic
43#20259243C2211yescharacteristic
44C22⋊(C191⋊C8)C2211yescharacteristic
45C22⋊(C191⋊C8)C2211yescharacteristic
46C22⋊(C191⋊C8)C2211yescharacteristic
47C22⋊(C191⋊C8)C2211yescharacteristic
48C2×#41×C191C2211yescharacteristic
49C2×#41×C191C2211yescharacteristic
50C22⋊Q8×C191—21no—
51C22⋊Q8×C191C2211yescharacteristic
52C22⋊Q8×C191C2211yescharacteristic
53#121×C191—21no—
54#121×C191—21no—
55#121×C191—21no—
56#121×C191C2211yescharacteristic
57#121×C191C2211yescharacteristic
58C2×C4⋊C4×C191C2211yescharacteristic
59C2×Dic382—21no—
60C2×Dic382—41no—
61C2×Dic382—41no—
62C2×Dic382C2311yescharacteristic
63C2×Dic382C2311yescharacteristic
64C22×Dic191—21no—
65#15690277—41no—
66#15690277—41no—
67#15690275—41no—
68#15690275—41no—
69#15690271—41no—
70C2×C191⋊C8—41no—
71C2×C191⋊C8C2311yescharacteristic
72C2×C191⋊C8C2311yescharacteristic
73C2×C191⋊C8C2311yescharacteristic
74C2×C191⋊C8C2311yescharacteristic
75C4⋊Dic191C2311yescharacteristic
76C4⋊Dic191C2311yescharacteristic
77Dic191⋊C4—21no—
78Dic191⋊C4—21no—
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81C22⋊Dic191—21no—
82C22⋊Dic191—21no—
83C22⋊Dic191—21no—
84C22⋊Dic191—21no—
85C22⋊Dic191—21no—
86C4×Dic191—21no—
87#41×C191—41no—
88#41×C191—41no—
89#41×C191—41no—
90#41×C191—41no—
91C2×Q8×C191D411yescharacteristic
92C2×Q8×C191C2311yescharacteristic
93C2×D4×C191—21no—
94C2×D4×C191—21no—
95C2×D4×C191—21no—
96C2×D4×C191D411yescharacteristic
97C2×D4×C191D411yescharacteristic
98C2×D4×C191D411yescharacteristic
99C2×D4×C191C2311yescharacteristic
100C22×C4×C191—21no—
101C22×C4×C191—21no—
102C22×C4×C191C2311yescharacteristic
103C22×C4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C4⋊C4×C191—21no—
106C4⋊C4×C191—21no—
107C4⋊C4×C191—21no—
108C4⋊C4×C191C2311yescharacteristic
109C4⋊C4×C191C2311yescharacteristic
110C22⋊C4×C191—21no—
111C22⋊C4×C191—21no—
112C22⋊C4×C191—21no—
113C22⋊C4×C191—21no—
114Dic382—21no—
115Dic382—21no—
116Dic382—21no—
117Dic382—21no—
118Dic382—42no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—42no—
124C191⋊C8—21no—
125C191⋊C8—21no—
126C191⋊C8—21no—
127C191⋊C8—21no—
128C23×C191—21no—
129C23×C191C2×D411yescharacteristic
130C23×C191C2×D411yescharacteristic
131C23×C191C2×D411yescharacteristic
132Q8×C191—21no—
133Q8×C191—21no—
134Q8×C191—41no—
135D4×C191—21no—
136D4×C191—21no—
137D4×C191—41no—
138D4×C191—41no—
139D4×C191—41no—
140D4×C191—42no—
141D4×C191—81no—
142D4×C191—81no—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191—21no—
146C2×C4×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—42no—
153C2×C4×C191—81no—
154C2×C4×C191C2×D411yescharacteristic
155C2×C4×C191C2×D411yescharacteristic
156C2×C4×C191C2×D411yescharacteristic
157C2×C4×C191C2411yescharacteristic
158C22×C191—21no—
159C22×C191—21no—
160C22×C191—21no—
161C22×C191—21no—
162C22×C191—21no—
163C22×C191—21no—
164C22×C191—21no—
165C22×C191—21no—
166C22×C191—21no—
167C22×C191—41no—
168C22×C191—41no—
169C22×C191—41no—
170C22×C191C22×D411yescharacteristic
171C4×C191—21no—
172C4×C191—21no—
173C4×C191—21no—
174C4×C191—41no—
175C4×C191—41no—
176C4×C191—41no—
177C4×C191H(5,𝔽2)11yescharacteristic
178C4×C191H(5,𝔽2)11yescharacteristic
179Dic191—41no—
180Dic191—41no—
181Dic191—41no—
182Dic191—41no—
183C2×C191—41no—
184C2×C191—41no—
185C2×C191—41no—
186C2×C191—81no—
187C2×C191#53411yescharacteristic
188C2×C191#57711yescharacteristic
189C2×C191#57811yescharacteristic
190C191#320111yescharacteristic, complemented, Sylow
191#3201—1911nomaximal, Sylow
192#537D19111yescharacteristic
193#536—1911no—
194#485—1911no—
195#484—1911no—
196#483—1911no—
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×#41C2×D19111yescharacteristic
208C2×#41C2×D19111yescharacteristic
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—21no—
221C22⋊Q8—1911no—
222C22⋊Q8—1911no—
223C22⋊Q8—1911no—
224C22⋊Q8—1911no—
225C22⋊Q8C2×D19111yescharacteristic
226C22⋊Q8C2×D19111yescharacteristic
227#121—21no—
228#121—21no—
229#121—21no—
230#121C2×D19111yescharacteristic
231#121C2×D19111yescharacteristic
232#117—1911no—
233C2×C4⋊C4C2×D19111yescharacteristic
234#107—1911no—
235#107—1911no—
236#106—1911no—
237#106—1911no—
238#103—1911no—
239#103—1911no—
240#103—1911no—
241#103—1911no—
242#103—1911no—
243#103—1911no—
244#102—1911no—
245#102—1911no—
246C22⋊C8—1911no—
247C22⋊C8—1911no—
248C22⋊C8—1911no—
249C22⋊C8—1911no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—3821no—
255C2×Q8—1911no—
256C2×Q8—1911no—
257C2×Q8—7641no—
258C2×Q8—7641no—
259C2×Q8C22⋊D19111yescharacteristic
260C2×Q8C22×D19111yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊D19111yescharacteristic
265C2×D4C22⋊D19111yescharacteristic
266C2×D4C22⋊D19111yescharacteristic
267C2×D4C22×D19111yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—3821no—
271C22×C4C22×D19111yescharacteristic
272C22×C4C22×D19111yescharacteristic
273C22×C4C22×D19111yescharacteristic
274Q16—7641no—
275Q16—7641no—
276SD16—7641no—
277SD16—7641no—
278M16—7641no—
279C2×C8—1911no—
280C2×C8—1911no—
281C2×C8—1911no—
282C2×C8—1911no—
283C2×C8—7641no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—3821no—
288C4⋊C4—3821no—
289C4⋊C4—3821no—
290C4⋊C4—3821no—
291C4⋊C4—1911no—
292C4⋊C4—1911no—
293C4⋊C4C22×D19111yescharacteristic
294C4⋊C4C22×D19111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—3821no—
300C22⋊C4—3821no—
301C22⋊C4—3821no—
302C22⋊C4—3821no—
303C22⋊C4—3821no—
304C42—3821no—
305C23—21no—
306C23C2×C22⋊D19111yescharacteristic
307C23C2×C22⋊D19111yescharacteristic
308C23C2×C22⋊D19111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—41no—
312Q8—3821no—
313Q8—3821no—
314Q8—3821no—
315Q8—3821no—
316Q8—7642no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—3821no—
337C2×C4—3821no—
338C2×C4—3821no—
339C2×C4—3821no—
340C2×C4—7642no—
341C2×C4C2×C22⋊D19111yescharacteristic
342C2×C4C2×C22⋊D19111yescharacteristic
343C2×C4C2×C22⋊D19111yescharacteristic
344C2×C4C23×D19111yescharacteristic
345C8—3821no—
346C8—3821no—
347C8—3821no—
348C8—3821no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×C22⋊D19111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—7641no—
369C4—7641no—
370C4—7641no—
371C4—7641no—
372C4#2025936711yescharacteristic
373C4#2025936711yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2#2713322211yescharacteristic
379C2#2713347411yescharacteristic
380C2#2713347811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting, prime radical#537×C191C2
socleC22×C191C22×D4
hypercenter#537D191
hypocenterC191#3201
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #27133234C2semidirect
2. #27133001C2semidirect
3. #27132998C2semidirect
4. #27132993C2semidirect
5. #27132984C2semidirect
6. #27132919C2semidirect
7. #27132907C2semidirect
8. #27132902C2semidirect
9. #27132890C2semidirect
10. #27132825C2semidirect
11. #27132825C2semidirect
12. #27132818C2semidirect
13. #27132801C2semidirect
14. #27132630C2semidirect
190. C191#3201semidirect

Maximal subgroups

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

subgroupindex
#271332342
#271330012
#271329982
#271329932
#271329842
#271329192
#271329072
#271329022
#271328902
#271328252
#271328182
#271328012
#271326302
#537×C1912
#3201191