Finite Group Databasebeta

← #37582784

Subgroups — #37582784

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#27133284C211yesmaximal, characteristic, complemented
2#27133143C211yesmaximal, characteristic, complemented
3#27132999C211yesmaximal, characteristic, complemented
4#27132977C211yesmaximal, characteristic, complemented
5#27132959C211yesmaximal, characteristic, complemented
6#27132944C211yesmaximal, characteristic, complemented
7#27132886C211yesmaximal, characteristic, complemented
8#27132879C211yesmaximal, characteristic, complemented
9#27132827C211yesmaximal, characteristic, complemented
10#27132810C211yesmaximal, characteristic
11#27132765C211yesmaximal, characteristic, complemented
12#27132765C211yesmaximal, characteristic, complemented
13C4×Dic764C211yesmaximal, characteristic, complemented
14C4×D1528C211yesmaximal, characteristic, complemented
15#433×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×Dic764C2211yescharacteristic
18C2×#15690276C2211yescharacteristic
19C2×#15690276C2211yescharacteristic
20C2×D1528C2211yescharacteristic
21#20259322C2211yescharacteristic
22#20259317—21no—
23#20259310C2211yescharacteristic
24#20259308—21no—
25#20259304—21no—
26#20259301C2211yescharacteristic
27#20259300—21no—
28#20259296C2211yescharacteristic
29C4×Dic382C2211yescharacteristic
30C4×Dic382C2211yescharacteristic
31C4×Dic382C2211yescharacteristic
32C4×D764C2211yescharacteristic
33C4×D764C2211yescharacteristic
34C4×D764C2211yescharacteristic
35(C22⋊D191)⋊C4—21no—
36(C22⋊D191)⋊C4—21no—
37#20259280—21no—
38C2×C4⋊Dic191C2211yescharacteristic
39C4⋊C4×D191—21no—
40#20259256C2211yescharacteristic
41#20259256C2211yescharacteristic
42#20259256C2211yescharacteristic
43#20259256C2211yescharacteristic
44#20259247C2211yescharacteristic
45#20259247C2211yescharacteristic
46#20259247C2211yescharacteristic
47#20259247C2211yescharacteristic
48#20259244C2211yescharacteristic
49#20259244C2211yescharacteristic
50#20259244C2211yescharacteristic
51#20259244C2211yescharacteristic
52#117×C191C2211yescharacteristic
53C4⋊C8×C191C2211yescharacteristic
54C4⋊C8×C191C2211yescharacteristic
55C22⋊C8×C191C2211yescharacteristic
56C22⋊C8×C191C2211yescharacteristic
57#97×C191C2211yescharacteristic
58C4×C8×C191C2211yescharacteristic
59#15690287—22no—
60#15690287—22no—
61C2×Dic382—21no—
62C2×Dic382C2311yescharacteristic
63C2×Dic382C2311yescharacteristic
64C2×D764C2311yescharacteristic
65C2×D764C2311yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C22×Dic191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73Dic764—22no—
74#15690276—22no—
75#15690276—22no—
76D1528—22no—
77C4⋊Dic191—21no—
78C4⋊Dic191—21no—
79C4⋊Dic191C2311yescharacteristic
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87C22⋊Dic191—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94C4×Dic191—21no—
95C4×Dic191—21no—
96C4×Dic191—21no—
97C22×C4×C191C2311yescharacteristic
98C2×C8×C191C2311yescharacteristic
99C2×C8×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191D411yescharacteristic
103C4⋊C4×C191D411yescharacteristic
104C22⋊C4×C191D411yescharacteristic
105C22⋊C4×C191D411yescharacteristic
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110Dic382—21no—
111Dic382—21no—
112Dic382—21no—
113Dic382—81no—
114Dic382#4112yes—
115D764—21no—
116D764—21no—
117D764—21no—
118D764#4112yes—
119C22⋊D191—24no—
120C22⋊D191—81no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—81no—
128C4×D191—24no—
129C4×D191—81no—
130C4×D191—81no—
131C4×D191—81no—
132C23×C191C2×D411yescharacteristic
133C2×C4×C191—21no—
134C2×C4×C191—21no—
135C2×C4×C191C2×D411yescharacteristic
136C2×C4×C191C2×D411yescharacteristic
137C2×C4×C191C2×D411yescharacteristic
138C2×C4×C191C2×D411yescharacteristic
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2411yescharacteristic
141C8×C191—21no—
142C8×C191—21no—
143C8×C191—21no—
144C8×C191—21no—
145C22×C191—21no—
146C22×C191—21no—
147C22×C191—21no—
148C22×C191C22×D411yescharacteristic
149C2×D191—22no—
150C2×D191—41no—
151C2×D191—41no—
152C2×D191—41no—
153C2×D191—41no—
154C2×D191—41no—
155C4×C191—21no—
156C4×C191—21no—
157C4×C191—21no—
158C4×C191—21no—
159C4×C191—21no—
160C4×C191C2×#4111yescharacteristic
161C4×C191C2×#4111yescharacteristic
162Dic191—22no—
163Dic191—41no—
164Dic191—41no—
165Dic191—41no—
166Dic191—41no—
167Dic191—41no—
168C2×C191—41no—
169C2×C191#52511yescharacteristic
170C2×C191#57611yescharacteristic
171C2×C191#57811yescharacteristic
172D191—42no—
173D191—81no—
174C191#312411yescharacteristic, complemented, Sylow
175#3124—1911nomaximal, Sylow
176#542—1911no—
177#520—1911no—
178#484—1911no—
179#480—1911no—
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#433D19111yescharacteristic, complemented
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#121—1911no—
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#117C2×D19111yescharacteristic
214C2×C4⋊C4—3821no—
215C2×C4⋊C4—1911no—
216#107—1911no—
217#107—1911no—
218#107—1911no—
219#107—1911no—
220C4⋊C8C2×D19111yescharacteristic
221C4⋊C8C2×D19111yescharacteristic
222#103—1911no—
223#103—1911no—
224#103—1911no—
225#103—1911no—
226#102—1911no—
227#102—1911no—
228#102—1911no—
229#102—1911no—
230C22⋊C8C2×D19111yescharacteristic
231C22⋊C8C2×D19111yescharacteristic
232#97C2×D19111yescharacteristic
233C4×C8C2×D19111yescharacteristic
234#41—3822no—
235#41—3822no—
236C2×Q8—3821no—
237C2×Q8—1911no—
238C2×Q8—1911no—
239C2×D4—3821no—
240C2×D4—3821no—
241C2×D4—1911no—
242C2×D4—1911no—
243C22×C4—3821no—
244C22×C4—3821no—
245C22×C4—3821no—
246C22×C4—3821no—
247C22×C4—3821no—
248C22×C4C22×D19111yescharacteristic
249Q16—3822no—
250SD16—3822no—
251SD16—3822no—
252D8—3822no—
253C2×C8C22×D19111yescharacteristic
254C2×C8C22×D19111yescharacteristic
255C2×C8C22×D19111yescharacteristic
256C2×C8C22×D19111yescharacteristic
257C4⋊C4—3821no—
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⋊C4—1911no—
267C4⋊C4D76411yescharacteristic
268C4⋊C4D76411yescharacteristic
269C22⋊C4—3821no—
270C22⋊C4—3821no—
271C22⋊C4—3821no—
272C22⋊C4—3821no—
273C22⋊C4—3821no—
274C22⋊C4—3821no—
275C22⋊C4—3821no—
276C22⋊C4D76411yescharacteristic
277C22⋊C4D76411yescharacteristic
278C42—3821no—
279C42—3821no—
280C42—3821no—
281C42C22×D19111yescharacteristic
282C42C22×D19111yescharacteristic
283C23—3821no—
284C23—3821no—
285C23C2×D76411yescharacteristic
286Q8—3821no—
287Q8—3821no—
288Q8—3821no—
289Q8—1912no—
290Q8—15281no—
291D4—3824no—
292D4—3821no—
293D4—3821no—
294D4—3821no—
295D4—1912no—
296D4—15281no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3824no—
300C2×C4—3821no—
301C2×C4—3821no—
302C2×C4—3821no—
303C2×C4—3821no—
304C2×C4—3821no—
305C2×C4—3821no—
306C2×C4—15281no—
307C2×C4—15281no—
308C2×C4—15281no—
309C2×C4—15281no—
310C2×C4C2×D76411yescharacteristic
311C2×C4C2×D76411yescharacteristic
312C2×C4C2×D76411yescharacteristic
313C2×C4C2×D76411yescharacteristic
314C2×C4C2×D76411yescharacteristic
315C2×C4C23×D19111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—3822no—
324C22—7641no—
325C22—7641no—
326C22—7641no—
327C22—7641no—
328C22—7641no—
329C22C22×D76411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—3822no—
336C4—7641no—
337C4—7641no—
338C4—7641no—
339C4—7641no—
340C4—7641no—
341C4#41×D19111yescharacteristic
342C4#41×D19111yescharacteristic
343C2—41no—
344C2—15281no—
345C2—7642no—
346C2#2713317511yescharacteristic
347C2#2713346811yescharacteristic
348C2#2713348011yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#433×C191C2
socleC22×C191C22×D4
prime radical#27132810C2
hypercenter#433D191
hypocenterC191#3124
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #27133284C2semidirect
2. #27133143C2semidirect
3. #27132999C2semidirect
4. #27132977C2semidirect
5. #27132959C2semidirect
6. #27132944C2semidirect
7. #27132886C2semidirect
8. #27132879C2semidirect
9. #27132827C2semidirect
11. #27132765C2semidirect
12. #27132765C2semidirect
13. C4×Dic764C2semidirect
14. C4×D1528C2semidirect
15. #433×C191C2semidirect
174. C191#3124semidirect
190. #433D191semidirect

Maximal subgroups

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

subgroupindex
#271332842
#271331432
#271329992
#271329772
#271329592
#271329442
#271328862
#271328792
#271328272
#271328102
#271327652
C4×Dic7642
C4×D15282
#433×C1912
#3124191