Finite Group Databasebeta

← #37583398

Subgroups — #37583398

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#27133242C211yesmaximal, characteristic
2#27133237C211yesmaximal, characteristic, complemented
3#27133005C211yesmaximal, characteristic, complemented
4#27132997C211yesmaximal, characteristic, complemented
5#27132992C211yesmaximal, characteristic, complemented
6#27132984C211yesmaximal, characteristic, complemented
7#27132920C211yesmaximal, characteristic, complemented
8#27132906C211yesmaximal, characteristic, complemented
9#27132903C211yesmaximal, characteristic, complemented
10#27132889C211yesmaximal, characteristic, complemented
11#27132822C211yesmaximal, characteristic, complemented
12#27132822C211yesmaximal, characteristic, complemented
13#27132819C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#448×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690286C2211yescharacteristic
18C2×#15690277C2211yescharacteristic
19C2×#15690277C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×C8×D191C2211yescharacteristic
22#20259320—21no—
23#20259311—21no—
24#20259305—21no—
25#20259305—21no—
26#20259302C2211yescharacteristic
27#20259301C2211yescharacteristic
28#20259299—21no—
29#20259298C2211yescharacteristic
30#20259298C2211yescharacteristic
31#20259298C2211yescharacteristic
32#20259298C2211yescharacteristic
33#20259295—21no—
34#20259294—21no—
35#20259293—21no—
36#20259293C2211yescharacteristic
37#20259281C2211yescharacteristic
38C4⋊C4×D191C2211yescharacteristic
39#20259256C2211yescharacteristic
40#20259255C2211yescharacteristic
41#20259254C2211yescharacteristic
42#20259253C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259247C2211yescharacteristic
45#20259246C2211yescharacteristic
46#20259246C2211yescharacteristic
47#20259243C2211yescharacteristic
48#20259243C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C22×Q8×C191C2211yescharacteristic
53C2×SD16×C191C2211yescharacteristic
54C2×SD16×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690287—41no—
60#15690287—41no—
61#15690286—41no—
62#15690286—41no—
63C2×Dic382D411yescharacteristic
64C2×Dic382C2311yescharacteristic
65C2×D764D411yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C22⋊D191D411yescharacteristic
69C2×C22⋊D191D411yescharacteristic
70C22×Dic191—21no—
71C2×C4×D191—21no—
72C2×C4×D191C2311yescharacteristic
73C2×C4×D191C2311yescharacteristic
74#15690277—41no—
75#15690277—41no—
76#15690270—41no—
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C8×D191—41no—
80C4⋊Dic191—21no—
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—
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—
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×D4×C191—21no—
105C2×D4×C191C2311yescharacteristic
106C22×C4×C191—21no—
107C22×C4×C191C2311yescharacteristic
108SD16×C191—41no—
109SD16×C191—41no—
110C2×C8×C191C2311yescharacteristic
111C2×C8×C191C2311yescharacteristic
112C4⋊C4×C191C2311yescharacteristic
113C22⋊C4×C191—21no—
114C22×D191C2×D411yescharacteristic
115C22×D191C2×D411yescharacteristic
116Dic382—21no—
117Dic382—21no—
118Dic382—41no—
119D764—41no—
120C22⋊D191—41no—
121C22⋊D191—41no—
122C22⋊D191—42no—
123C22⋊D191—81no—
124C2×Dic191—21no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—42no—
129C2×Dic191C2×D411yescharacteristic
130C2×Dic191C2×D411yescharacteristic
131C4×D191—21no—
132C4×D191—21no—
133C4×D191—21no—
134C4×D191—21no—
135C4×D191—81no—
136C191⋊C8—21no—
137C191⋊C8—21no—
138C23×C191—21no—
139C23×C191C2×D411yescharacteristic
140Q8×C191—21no—
141Q8×C191—21no—
142Q8×C191—21no—
143Q8×C191—21no—
144Q8×C191—42no—
145D4×C191—21no—
146D4×C191—21no—
147D4×C191—81no—
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×C191—41no—
162C22×C191—41no—
163C22×C191—41no—
164C22×C191C22×D411yescharacteristic
165C2×D191—21no—
166C2×D191—21no—
167C2×D191—21no—
168C2×D191—21no—
169C2×D191—21no—
170C2×D191—21no—
171C4×C191—21no—
172C4×C191—41no—
173C4×C191—41no—
174C4×C191—41no—
175C4×C191H(5,𝔽2)11yescharacteristic
176C4×C191H(5,𝔽2)11yescharacteristic
177Dic191—21no—
178Dic191—21no—
179Dic191—41no—
180Dic191—41no—
181Dic191—41no—
182Dic191—41no—
183C2×C191—41no—
184C2×C191—81no—
185C2×C191#53411yescharacteristic
186C2×C191#57711yescharacteristic
187C2×C191#57811yescharacteristic
188D191—41no—
189D191—41no—
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#451—1911no—
205#448D19111yescharacteristic, complemented
206#408—1911no—
207C2×#41—1911no—
208C2×#41—1911no—
209C22×Q8C2×D19111yescharacteristic
210C2×Q16—1911no—
211C2×Q16—1911no—
212C2×SD16C2×D19111yescharacteristic
213C2×SD16C2×D19111yescharacteristic
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⋊Q8—1911no—
227#121—3821no—
228#121—3821no—
229#121—3821no—
230#121—1911no—
231#121C2×D19111yescharacteristic
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×Q8—1911no—
259C2×Q8C22×D19111yescharacteristic
260C2×Q8C22×D19111yescharacteristic
261C2×D4—21no—
262C2×D4—3821no—
263C2×D4—3821no—
264C2×D4—1911no—
265C2×D4—1911no—
266C2×D4—1911no—
267C2×D4C22×D19111yescharacteristic
268C22×C4—21no—
269C22×C4—3821no—
270C22×C4—3821no—
271C22×C4—1911no—
272C22×C4—1911no—
273C22×C4C22×D19111yescharacteristic
274Q16—7641no—
275Q16—7641no—
276SD16—41no—
277SD16—41no—
278M16—7641no—
279C2×C8—1911no—
280C2×C8—1911no—
281C2×C8—7641no—
282C2×C8C22×D19111yescharacteristic
283C2×C8C22×D19111yescharacteristic
284C4⋊C4—3821no—
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—21no—
306C23—1911no—
307C23—1911no—
308C23D4×D19111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—42no—
314Q8—3821no—
315Q8—3821no—
316Q8—7641no—
317D4—21no—
318D4—21no—
319D4—81no—
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—42no—
331C2×C4—3821no—
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—41no—
353C22—41no—
354C22—41no—
355C22—3821no—
356C22—3821no—
357C22—3821no—
358C22—3821no—
359C22—3821no—
360C22—3821no—
361C22C2×D4×D19111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—3821no—
367C4—3821no—
368C4—7641no—
369C4—7641no—
370C4—7641no—
371C4—7641no—
372C4#2025936711yescharacteristic
373C4#2025936711yescharacteristic
374C2—41no—
375C2—81no—
376C2—7641no—
377C2—7641no—
378C2#2713322311yescharacteristic
379C2#2713346911yescharacteristic
380C2#2713347911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#448×C191C2
socleC22×C191C22×D4
prime radical#27133242C2
hypercenter#448D191
hypocenterC191#3201
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #27133237C2semidirect
3. #27133005C2semidirect
4. #27132997C2semidirect
5. #27132992C2semidirect
6. #27132984C2semidirect
7. #27132920C2semidirect
8. #27132906C2semidirect
9. #27132903C2semidirect
10. #27132889C2semidirect
11. #27132822C2semidirect
12. #27132822C2semidirect
13. #27132819C2semidirect
14. #27132628C2semidirect
15. #448×C191C2semidirect
190. C191#3201semidirect
205. #448D191semidirect

Maximal subgroups

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

subgroupindex
#271332422
#271332372
#271330052
#271329972
#271329922
#271329842
#271329202
#271329062
#271329032
#271328892
#271328222
#271328192
#271326282
#448×C1912
#3201191