Finite Group Databasebeta

← #37583406

Subgroups — #37583406

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#27133243C211yesmaximal, characteristic
2#27133237C211yesmaximal, characteristic, complemented
3#27133001C211yesmaximal, characteristic, complemented
4#27132997C211yesmaximal, characteristic, complemented
5#27132992C211yesmaximal, characteristic, complemented
6#27132988C211yesmaximal, characteristic, complemented
7#27132918C211yesmaximal, characteristic, complemented
8#27132912C211yesmaximal, characteristic, complemented
9#27132901C211yesmaximal, characteristic, complemented
10#27132895C211yesmaximal, characteristic, complemented
11#27132824C211yesmaximal, characteristic, complemented
12#27132824C211yesmaximal, characteristic, complemented
13#27132802C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#451×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×#15690274C2211yescharacteristic
19C2×#15690274C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×C8×D191C2211yescharacteristic
22#20259320—21no—
23#20259311—21no—
24#20259305—21no—
25#20259305—21no—
26#20259300—21no—
27#20259298C2211yescharacteristic
28#20259298C2211yescharacteristic
29#20259298C2211yescharacteristic
30#20259298C2211yescharacteristic
31#20259298C2211yescharacteristic
32#20259297—21no—
33#20259297C2211yescharacteristic
34#20259296C2211yescharacteristic
35#20259295—21no—
36#20259295—21no—
37#20259281C2211yescharacteristic
38C4⋊C4×D191C2211yescharacteristic
39#20259256C2211yescharacteristic
40#20259255C2211yescharacteristic
41#20259254C2211yescharacteristic
42#20259253C2211yescharacteristic
43#20259246C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259246C2211yescharacteristic
46#20259246C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259244C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C22×Q8×C191C2211yescharacteristic
53C2×Q16×C191C2211yescharacteristic
54C2×Q16×C191C2211yescharacteristic
55C22⋊Q8×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690288—41no—
60#15690288—41no—
61#15690287—41no—
62#15690287—41no—
63C2×Dic382D411yescharacteristic
64C2×D764—21no—
65C2×D764—21no—
66C2×D764D411yescharacteristic
67C2×D764C2311yescharacteristic
68C2×C22⋊D191—21no—
69C2×C22⋊D191D411yescharacteristic
70C2×C22⋊D191D411yescharacteristic
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73C2×C4×D191C2311yescharacteristic
74C2×C4×D191C2311yescharacteristic
75#15690274—41no—
76#15690274—41no—
77#15690270—41no—
78C2×C191⋊C8C2311yescharacteristic
79C2×C191⋊C8C2311yescharacteristic
80C8×D191—41no—
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83C4⋊Dic191C2311yescharacteristic
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88Dic191⋊C4—21no—
89Dic191⋊C4—21no—
90C22⋊Dic191—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94(C2×D191)⋊C4—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98C4×Dic191—21no—
99C2×Q8×C191—21no—
100C2×Q8×C191—41no—
101C2×Q8×C191—41no—
102C2×Q8×C191C2311yescharacteristic
103C2×Q8×C191C2311yescharacteristic
104C2×Q8×C191C2311yescharacteristic
105C22×C4×C191—21no—
106C22×C4×C191C2311yescharacteristic
107Q16×C191—41no—
108Q16×C191—41no—
109C2×C8×C191C2311yescharacteristic
110C2×C8×C191C2311yescharacteristic
111C4⋊C4×C191—21no—
112C4⋊C4×C191C2311yescharacteristic
113C22⋊C4×C191—21no—
114C22×D191—21no—
115C22×D191C2×D411yescharacteristic
116C22×D191C2×D411yescharacteristic
117Dic382—41no—
118D764—21no—
119D764—21no—
120D764—41no—
121D764—42no—
122D764—81no—
123C22⋊D191—41no—
124C22⋊D191—41no—
125C22⋊D191—81no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191C2×D411yescharacteristic
130C2×Dic191C2×D411yescharacteristic
131C4×D191—21no—
132C4×D191—21no—
133C4×D191—21no—
134C4×D191—21no—
135C4×D191—42no—
136C4×D191—81no—
137C191⋊C8—21no—
138C191⋊C8—21no—
139C23×C191C2×D411yescharacteristic
140Q8×C191—21no—
141Q8×C191—21no—
142Q8×C191—21no—
143Q8×C191—21no—
144Q8×C191—21no—
145Q8×C191—21no—
146Q8×C191—42no—
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—42no—
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#483—1911no—
197#482—1911no—
198#470—1911no—
199#468—1911no—
200#467—1911no—
201#465—1911no—
202#452—1911no—
203#452—1911no—
204#451D19111yescharacteristic, complemented
205#448—1911no—
206#408—1911no—
207C2×#41—1911no—
208C2×#41—1911no—
209C22×Q8C2×D19111yescharacteristic
210C2×Q16C2×D19111yescharacteristic
211C2×Q16C2×D19111yescharacteristic
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⋊C4—1911no—
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#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—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—1911no—
258C2×Q8C22×D19111yescharacteristic
259C2×Q8C22×D19111yescharacteristic
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—41no—
275Q16—41no—
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—3821no—
286C4⋊C4—3821no—
287C4⋊C4—3821no—
288C4⋊C4—3821no—
289C4⋊C4—3821no—
290C4⋊C4—3821no—
291C4⋊C4—1911no—
292C4⋊C4—1911no—
293C4⋊C4—1911no—
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—21no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—42no—
316Q8—7641no—
317D4—3821no—
318D4—3821no—
319D4—15281no—
320D4—15281no—
321D4—7641no—
322D4—7642no—
323D4—7641no—
324D4—7641no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
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—15281no—
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#2025936711yescharacteristic
373C4#2025936711yescharacteristic
374C2—41no—
375C2—15281no—
376C2—7641no—
377C2—7641no—
378C2#2713322311yescharacteristic
379C2#2713347211yescharacteristic
380C2#2713347611yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#451×C191C2
socleC22×C191C22×D4
prime radical#27133243C2
hypercenter#451D191
hypocenterC191#3201
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #27133237C2semidirect
3. #27133001C2semidirect
4. #27132997C2semidirect
5. #27132992C2semidirect
6. #27132988C2semidirect
7. #27132918C2semidirect
8. #27132912C2semidirect
9. #27132901C2semidirect
10. #27132895C2semidirect
11. #27132824C2semidirect
12. #27132824C2semidirect
13. #27132802C2semidirect
14. #27132628C2semidirect
15. #451×C191C2semidirect
190. C191#3201semidirect
204. #451D191semidirect

Maximal subgroups

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

subgroupindex
#271332432
#271332372
#271330012
#271329972
#271329922
#271329882
#271329182
#271329122
#271329012
#271328952
#271328242
#271328022
#271326282
#451×C1912
#3201191