Finite Group Databasebeta

← #37582689

Subgroups — #37582689

Order 24448.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133195C211yesmaximal, characteristic
2C4×Q8×D191C211yesmaximal, characteristic, complemented
3#27133000C211yesmaximal, characteristic, complemented
4#27132980C211yesmaximal, characteristic
5#27132969C211yesmaximal, characteristic, complemented
6#27132968C211yesmaximal, characteristic, complemented
7#27132884C211yesmaximal, characteristic, complemented
8#27132883C211yesmaximal, characteristic, complemented
9#27132820C211yesmaximal, characteristic, complemented
10#27132800C211yesmaximal, characteristic
11#27132771C211yesmaximal, characteristic, complemented
12#27132768C211yesmaximal, characteristic, complemented
13#27132763C211yesmaximal, characteristic, complemented
14#27132718C211yesmaximal, characteristic, complemented
15#440×C191C211yesmaximal, characteristic, complemented
16C2×Q8×D191C2211yescharacteristic
17C2×Dic764C2211yescharacteristic
18C2×#15690277C2211yescharacteristic
19C2×#15690275C2211yescharacteristic
20#20259315—21no—
21#20259313C2211yescharacteristic
22#20259309C2211yescharacteristic
23#20259304—21no—
24#20259302C2211yescharacteristic
25#20259293C2211yescharacteristic
26Q8×Dic191C2211yescharacteristic
27C4×Dic382—21no—
28C4×Dic382C2211yescharacteristic
29C4×Dic382C2211yescharacteristic
30#20259287—21no—
31#20259287C2211yescharacteristic
32C4×C22⋊D191—21no—
33#20259281—21no—
34C4⋊C4×D191—21no—
35C4⋊C4×D191C2211yescharacteristic
36C42×D191—21no—
37C42×D191C2211yescharacteristic
38#20259255C2211yescharacteristic
39#20259254C2211yescharacteristic
40#20259253C2211yescharacteristic
41Dic191⋊C8C2211yescharacteristic
42Dic191⋊C8C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259247C2211yescharacteristic
45#20259246C2211yescharacteristic
46#20259245C2211yescharacteristic
47#20259245C2211yescharacteristic
48#20259243C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51#20259233C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic
53C4×Q8×C191C2211yescharacteristic
54C4×D4×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58#97×C191C2211yescharacteristic
59C2×Dic382—21no—
60C2×Dic382C2311yescharacteristic
61C2×Dic382C2311yescharacteristic
62Q8×D191—22no—
63Q8×D191—22no—
64C2×C22⋊D191—21no—
65C2×C4×D191—21no—
66C2×C4×D191—21no—
67C2×C4×D191D411yescharacteristic
68C2×C4×D191D411yescharacteristic
69C2×C4×D191C2311yescharacteristic
70Dic764—22no—
71#15690277—22no—
72#15690275—22no—
73C2×C191⋊C8C2311yescharacteristic
74C2×C191⋊C8C2311yescharacteristic
75C4⋊Dic191—21no—
76C4⋊Dic191—21no—
77C4⋊Dic191—21no—
78C4⋊Dic191C2311yescharacteristic
79C4⋊Dic191C2311yescharacteristic
80Dic191⋊C4—21no—
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85C22⋊Dic191—21no—
86C22⋊Dic191—21no—
87C22⋊Dic191—21no—
88(C2×D191)⋊C4—21no—
89C4×Dic191—21no—
90C4×Dic191—21no—
91C4×Dic191—21no—
92C4×Dic191—21no—
93C4×Dic191D411yescharacteristic
94C4×Dic191D411yescharacteristic
95C4×Dic191C2311yescharacteristic
96C2×Q8×C191C2311yescharacteristic
97C2×D4×C191C2311yescharacteristic
98C22×C4×C191—21no—
99SD16×C191—22no—
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191—21no—
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C42×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191C2×D411yescharacteristic
109Dic382—24no—
110Dic382—21no—
111Dic382—21no—
112Dic382—21no—
113Dic382#4112yes—
114C22⋊D191—42no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C2×Dic191—21no—
119C2×Dic191C2×D411yescharacteristic
120C2×Dic191C2×D411yescharacteristic
121C2×Dic191C2×D411yescharacteristic
122C4×D191—24no—
123C4×D191—22no—
124C4×D191—21no—
125C4×D191—21no—
126C4×D191—41no—
127C4×D191—42no—
128C191⋊C8—21no—
129C191⋊C8—21no—
130C23×C191—21no—
131Q8×C191—21no—
132Q8×C191#4112yes—
133D4×C191—21no—
134D4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—42no—
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2411yescharacteristic
142C8×C191—21no—
143C8×C191—21no—
144C22×C191—41no—
145C22×C191—41no—
146C22×C191—41no—
147C22×C191C22×D411yescharacteristic
148C2×D191—21no—
149C2×D191—21no—
150C2×D191#13712yes—
151C4×C191—22no—
152C4×C191—21no—
153C4×C191—21no—
154C4×C191—41no—
155C4×C191—41no—
156C4×C191C2×#4111yescharacteristic
157C4×C191C2×#4111yescharacteristic
158Dic191—22no—
159Dic191—21no—
160Dic191—21no—
161Dic191—21no—
162Dic191—41no—
163Dic191—41no—
164Dic191—41no—
165C2×C191—81no—
166C2×C191#52511yescharacteristic
167C2×C191C2×#13711yescharacteristic
168C2×C191#57511yescharacteristic
169D191—22no—
170C191#311711yescharacteristic, complemented, Sylow
171#3117—1911nomaximal, Sylow
172#529—1911no—
173C2×C4×Q8—1911no—
174#484—1911no—
175#481—1911no—
176#479—1911no—
177#479—1911no—
178#464—1911no—
179#464—1911no—
180#451—1911no—
181#448—1911no—
182#441—1911no—
183#441—1911no—
184#440—1911no—
185#440D19111yescharacteristic, complemented
186#432—1911no—
187C22×Q8—1911no—
188C2×Q16—1911no—
189C2×Q16—1911no—
190C2×SD16—1911no—
191C2×SD16C2×D19111yescharacteristic
192#126—3821no—
193#125—1911no—
194#124—1911no—
195#123—3821no—
196C22⋊Q8—1911no—
197#121—1911no—
198C4×Q8—3821no—
199C4×Q8—3821no—
200C4×Q8—1911no—
201C4×Q8—1911no—
202C4×Q8—1911no—
203C4×Q8—1911no—
204C4×Q8C2×D19111yescharacteristic
205C4×D4—3821no—
206C4×D4C2×D19111yescharacteristic
207#117—3821no—
208C2×C4⋊C4—3821no—
209C2×C4⋊C4—1911no—
210C2×C42—3821no—
211C2×C42—1911no—
212#107—1911no—
213#107C2×D19111yescharacteristic
214#106—1911no—
215#106—1911no—
216C4⋊C8—1911no—
217C4⋊C8—1911no—
218#103—1911no—
219#103—1911no—
220#103—1911no—
221#103—1911no—
222#103—1911no—
223#103C2×D19111yescharacteristic
224#102—1911no—
225#102C2×D19111yescharacteristic
226C22⋊C8—1911no—
227C22⋊C8—1911no—
228#97—1911no—
229#97C2×D19111yescharacteristic
230C2×Q8—3821no—
231C2×Q8—3822no—
232C2×Q8—3822no—
233C2×Q8—1911no—
234C2×Q8—1911no—
235C2×Q8C22×D19111yescharacteristic
236C2×D4—3821no—
237C2×D4C22×D19111yescharacteristic
238C22×C4—21no—
239C22×C4—3821no—
240C22×C4—3821no—
241C22×C4—1911no—
242C22×C4—1911no—
243C22×C4—1911no—
244Q16—3822no—
245Q16—3822no—
246SD16—22no—
247SD16—3822no—
248C2×C8—1911no—
249C2×C8—1911no—
250C2×C8C22×D19111yescharacteristic
251C2×C8C22×D19111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—3821no—
254C4⋊C4—3821no—
255C4⋊C4—3821no—
256C4⋊C4—3821no—
257C4⋊C4—3821no—
258C4⋊C4—3821no—
259C4⋊C4—3821no—
260C4⋊C4—3821no—
261C4⋊C4—1911no—
262C4⋊C4—1911no—
263C4⋊C4C22×D19111yescharacteristic
264C4⋊C4C22×D19111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—3821no—
267C22⋊C4—3821no—
268C22⋊C4—3821no—
269C22⋊C4—3821no—
270C42—21no—
271C42—3821no—
272C42—3821no—
273C42—3821no—
274C42—3821no—
275C42—1911no—
276C42—1911no—
277C42—1911no—
278C42C22×D19111yescharacteristic
279C23—21no—
280C23—1911no—
281Q8—21no—
282Q8—3824no—
283Q8—3821no—
284Q8—3821no—
285Q8—3821no—
286Q8—1912no—
287Q8#1569028712yes—
288D4—21no—
289D4—21no—
290D4—7642no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—3824no—
296C2×C4—3822no—
297C2×C4—3821no—
298C2×C4—3821no—
299C2×C4—3821no—
300C2×C4—3821no—
301C2×C4—3821no—
302C2×C4—3821no—
303C2×C4—1911no—
304C2×C4—1911no—
305C2×C4—1911no—
306C2×C4—7641no—
307C2×C4—7642no—
308C2×C4D4×D19111yescharacteristic
309C2×C4D4×D19111yescharacteristic
310C2×C4C23×D19111yescharacteristic
311C8—21no—
312C8—21no—
313C8—3821no—
314C8—3821no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—3821no—
319C22—3821no—
320C22—1912no—
321C22C2×D4×D19111yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—3821no—
328C4—3821no—
329C4—3822no—
330C4—3821no—
331C4—7641no—
332C4—7641no—
333C4—7641no—
334C4#41×D19111yescharacteristic
335C4C2×#1569028711yescharacteristic
336C2—81no—
337C2—3822no—
338C2#2713317211yescharacteristic
339C2#137×D19111yescharacteristic
340C2#2713345911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#440×C191C2
socleC22×C191C22×D4
prime radical#20259293C22
hypercenter#440D191
hypocenterC191#3117
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D191C2semidirect
3. #27133000C2semidirect
5. #27132969C2semidirect
6. #27132968C2semidirect
7. #27132884C2semidirect
8. #27132883C2semidirect
9. #27132820C2semidirect
11. #27132771C2semidirect
12. #27132768C2semidirect
13. #27132763C2semidirect
14. #27132718C2semidirect
15. #440×C191C2semidirect
170. C191#3117semidirect
185. #440D191semidirect

Maximal subgroups

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

subgroupindex
#271331952
C4×Q8×D1912
#271330002
#271329802
#271329692
#271329682
#271328842
#271328832
#271328202
#271328002
#271327712
#271327682
#271327632
#271327182
#440×C1912
#3117191