Finite Group Databasebeta

← #37582777

Subgroups — #37582777

Order 24448.

384 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#27133280C211yesmaximal, characteristic, complemented
2#27133144C211yesmaximal, characteristic, complemented
3#27132998C211yesmaximal, characteristic, complemented
4#27132957C211yesmaximal, characteristic, complemented
5#27132942C211yesmaximal, characteristic, complemented
6#27132884C211yesmaximal, characteristic, complemented
7#27132877C211yesmaximal, characteristic, complemented
8#27132827C211yesmaximal, characteristic, complemented
9#27132806C211yesmaximal, characteristic
10#27132762C211yesmaximal, characteristic, complemented
11#27132760C211yesmaximal, characteristic, complemented
12#27132757C211yesmaximal, characteristic, complemented
13#27132743C211yesmaximal, characteristic, complemented
14#27132721C211yesmaximal, characteristic, complemented
15#480×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×Dic764C2211yescharacteristic
18C2×#15690276C2211yescharacteristic
19C2×#15690275C2211yescharacteristic
20C2×#15690272C2211yescharacteristic
21#20259321C2211yescharacteristic
22#20259315—21no—
23#20259309—21no—
24#20259309C2211yescharacteristic
25#20259303—21no—
26#20259301C2211yescharacteristic
27#20259299—21no—
28#20259287C2211yescharacteristic
29#20259287C2211yescharacteristic
30#20259287C2211yescharacteristic
31D4×Dic191C2211yescharacteristic
32#20259284C2211yescharacteristic
33#20259284C2211yescharacteristic
34C4×C22⋊D191—21no—
35C4×C22⋊D191—21no—
36#20259281C2211yescharacteristic
37#20259280—21no—
38C4⋊C4×D191—21no—
39#20259255C2211yescharacteristic
40#20259255C2211yescharacteristic
41Dic191⋊C8C2211yescharacteristic
42Dic191⋊C8C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259245C2211yescharacteristic
45#20259245C2211yescharacteristic
46#20259245C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259242C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50#20259232C2211yescharacteristic
51C8×Dic191C2211yescharacteristic
52#121×C191C2211yescharacteristic
53C2×C4⋊C4×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic
56#102×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690287—22no—
60#15690287—22no—
61C2×Dic382—21no—
62C2×Dic382C2311yescharacteristic
63C2×Dic382C2311yescharacteristic
64C2×D764C2311yescharacteristic
65C2×C22⋊D191—21no—
66C22×Dic191—21no—
67C2×C4×D191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70Dic764—22no—
71#15690276—22no—
72#15690275—22no—
73#15690272—22no—
74C2×C191⋊C8C2311yescharacteristic
75C2×C191⋊C8C2311yescharacteristic
76C4⋊Dic191D411yescharacteristic
77C4⋊Dic191D411yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4—21no—
84C22⋊Dic191—21no—
85C22⋊Dic191—21no—
86C22⋊Dic191—21no—
87C22⋊Dic191—21no—
88C22⋊Dic191D411yescharacteristic
89C22⋊Dic191D411yescharacteristic
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92C4×Dic191—21no—
93C4×Dic191—21no—
94C4×Dic191—21no—
95C4×Dic191C2311yescharacteristic
96C4×Dic191C2311yescharacteristic
97C2×D4×C191—21no—
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100C22×C4×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C2×C8×C191C2311yescharacteristic
103C4⋊C4×C191—21no—
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C4⋊C4×C191C2311yescharacteristic
107C22⋊C4×C191—21no—
108C22×D191—21no—
109Dic382—21no—
110Dic382—21no—
111Dic382—21no—
112Dic382—81no—
113Dic382#4112yes—
114D764—21no—
115D764#4112yes—
116C22⋊D191—24no—
117C2×Dic191—21no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191—81no—
121C2×Dic191C2×D411yescharacteristic
122C2×Dic191C2×D411yescharacteristic
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C4×D191—24no—
126C4×D191—81no—
127C4×D191—81no—
128C191⋊C8—21no—
129C191⋊C8—21no—
130C23×C191—21no—
131C23×C191C2×D411yescharacteristic
132D4×C191—21no—
133D4×C191—21no—
134D4×C191—81no—
135C2×C4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—81no—
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2411yescharacteristic
143C8×C191—21no—
144C8×C191—21no—
145C22×C191—21no—
146C22×C191—21no—
147C22×C191—21no—
148C22×C191—41no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191C22×D411yescharacteristic
152C2×D191—22no—
153C2×D191—41no—
154C2×D191—41no—
155C4×C191—21no—
156C4×C191—41no—
157C4×C191—41no—
158C4×C191—41no—
159C4×C191C2×#4111yescharacteristic
160C4×C191C2×#4111yescharacteristic
161Dic191—22no—
162Dic191—21no—
163Dic191—21no—
164Dic191—21no—
165Dic191—21no—
166Dic191—41no—
167Dic191—41no—
168C2×C191—41no—
169C2×C191—81no—
170C2×C191#52511yescharacteristic
171C2×C191#57611yescharacteristic
172C2×C191#57811yescharacteristic
173D191—42no—
174C191#312411yescharacteristic, complemented, Sylow
175#3124—1911nomaximal, Sylow
176#542—1911no—
177#520—1911no—
178#484—1911no—
179#480D19111yescharacteristic, complemented
180#477—1911no—
181#474—1911no—
182#464—1911no—
183#463—1911no—
184#452—1911no—
185#449—1911no—
186#440—1911no—
187#440—1911no—
188C4×Q16—1911no—
189C4×D8—1911no—
190#433—1911no—
191C2×#41—1911no—
192C2×Q16—1911no—
193C2×SD16—1911no—
194C2×SD16—1911no—
195C2×D8—1911no—
196C4⋊Q8—1911no—
197#126—3821no—
198#124—3821no—
199#124—1911no—
200#123—3821no—
201C22⋊Q8—3821no—
202C22⋊Q8—1911no—
203#121C2×D19111yescharacteristic
204C4×Q8—1911no—
205C4×Q8—1911no—
206C4×Q8—1911no—
207C4×D4—3821no—
208C4×D4—3821no—
209C4×D4—1911no—
210C4×D4—1911no—
211C4×D4—1911no—
212#117—3821no—
213#117—1911no—
214C2×C4⋊C4—3821no—
215C2×C4⋊C4C2×D19111yescharacteristic
216#107—1911no—
217#107—1911no—
218#107C2×D19111yescharacteristic
219#107C2×D19111yescharacteristic
220C4⋊C8—1911no—
221C4⋊C8—1911no—
222#103—1911no—
223#103—1911no—
224#103—1911no—
225#103—1911no—
226#102—1911no—
227#102—1911no—
228#102C2×D19111yescharacteristic
229#102C2×D19111yescharacteristic
230C22⋊C8—1911no—
231C22⋊C8C2×D19111yescharacteristic
232#97—1911no—
233C4×C8—1911no—
234#41—3822no—
235#41—3822no—
236C2×Q8—3821no—
237C2×Q8—1911no—
238C2×Q8—1911no—
239C2×D4—21no—
240C2×D4—3821no—
241C2×D4—1911no—
242C2×D4C22×D19111yescharacteristic
243C22×C4—21no—
244C22×C4—3821no—
245C22×C4—3821no—
246C22×C4—3821no—
247C22×C4—3821no—
248C22×C4C22×D19111yescharacteristic
249Q16—3822no—
250SD16—3822no—
251SD16—3822no—
252D8—3822no—
253C2×C8—1911no—
254C2×C8—1911no—
255C2×C8C22×D19111yescharacteristic
256C2×C8C22×D19111yescharacteristic
257C4⋊C4—21no—
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
267C4⋊C4C22×D19111yescharacteristic
268C4⋊C4C22×D19111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—3821no—
271C22⋊C4—3821no—
272C22⋊C4—3821no—
273C22⋊C4—3821no—
274C22⋊C4—3821no—
275C22⋊C4—3821no—
276C22⋊C4—1911no—
277C22⋊C4—1911no—
278C42—3821no—
279C42—3821no—
280C42—3821no—
281C42—1911no—
282C42—1911no—
283C23—21no—
284C23—3821no—
285C23D4×D19111yescharacteristic
286Q8—3821no—
287Q8—3821no—
288Q8—3821no—
289Q8—1912no—
290Q8—15281no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—3824no—
295D4—3821no—
296D4—1912no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—3824no—
304C2×C4—3821no—
305C2×C4—3821no—
306C2×C4—3821no—
307C2×C4—1911no—
308C2×C4—1911no—
309C2×C4—1911no—
310C2×C4—1911no—
311C2×C4—15281no—
312C2×C4—15281no—
313C2×C4—15281no—
314C2×C4D4×D19111yescharacteristic
315C2×C4C23×D19111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3821no—
319C8—3821no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3822no—
327C22—7641no—
328C22—7641no—
329C22C2×D4×D19111yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—3821no—
335C4—3821no—
336C4—3821no—
337C4—3821no—
338C4—3822no—
339C4—7641no—
340C4—7641no—
341C4#41×D19111yescharacteristic
342C4#41×D19111yescharacteristic
343C2—41no—
344C2—81no—
345C2—7642no—
346C2#2713317111yescharacteristic
347C2#2713346411yescharacteristic
348C2#2713347911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#480×C191C2
socleC22×C191C22×D4
prime radical#27132806C2
hypercenter#480D191
hypocenterC191#3124
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #27133280C2semidirect
2. #27133144C2semidirect
3. #27132998C2semidirect
4. #27132957C2semidirect
5. #27132942C2semidirect
6. #27132884C2semidirect
7. #27132877C2semidirect
8. #27132827C2semidirect
10. #27132762C2semidirect
11. #27132760C2semidirect
12. #27132757C2semidirect
13. #27132743C2semidirect
14. #27132721C2semidirect
15. #480×C191C2semidirect
174. C191#3124semidirect
179. #480D191semidirect

Maximal subgroups

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

subgroupindex
#271332802
#271331442
#271329982
#271329572
#271329422
#271328842
#271328772
#271328272
#271328062
#271327622
#271327602
#271327572
#271327432
#271327212
#480×C1912
#3124191