Finite Group Databasebeta

← #34078896

Subgroups — #34078896

Order 19328.

388 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752765C211yesmaximal, characteristic, complemented
2#23752680C211yesmaximal, characteristic
3#23752522C211yesmaximal, characteristic, complemented
4#23752518C211yesmaximal, characteristic, complemented
5#23752515C211yesmaximal, characteristic, complemented
6#23752511C211yesmaximal, characteristic, complemented
7#23752506C211yesmaximal, characteristic, complemented
8#23752501C211yesmaximal, characteristic, complemented
9#23752496C211yesmaximal, characteristic, complemented
10#23752491C211yesmaximal, characteristic, complemented
11#23752248C211yesmaximal, characteristic, complemented
12C2×Dic151⋊C8C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic
14#23752206C211yesmaximal, characteristic
15#427×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×C151⋊C8C2211yescharacteristic
18#18012738C2211yescharacteristic
19#18012738C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012730C2211yescharacteristic
22#18012716—21no—
23#18012716—21no—
24C4×Dic302—21no—
25C4×Dic302—21no—
26#18012704C2211yescharacteristic
27#18012704C2211yescharacteristic
28#18012701C2211yescharacteristic
29#18012701C2211yescharacteristic
30(C22⋊D151)⋊C4—21no—
31(C22⋊D151)⋊C4—21no—
32#18012698C2211yescharacteristic
33#18012696—21no—
34C2×C4×Dic151C2211yescharacteristic
35C42×D151—21no—
36#18012672C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012670C2211yescharacteristic
39#18012670C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52C22×C8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#117×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#106×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic
59#14559004—22no—
60#14559004Q814yescomplemented
61C2×Dic302—21no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C22×Dic151D411yescharacteristic
67C22×Dic151D411yescharacteristic
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C151⋊C8—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87C4×Dic151—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151D411yescharacteristic
91C4×Dic151D411yescharacteristic
92C4×Dic151C2311yescharacteristic
93C4×Dic151C2311yescharacteristic
94C22×C4×C151C2311yescharacteristic
95C2×C8×C151—22no—
96C2×C8×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C22⋊C4×C151—21no—
103C22⋊C4×C151—21no—
104C42×C151—21no—
105C42×C151—21no—
106C22×D151—21no—
107Dic302—21no—
108Dic302—42no—
109Dic302—42no—
110Dic302C2×Q812yes—
111D604—21no—
112D604C2×Q812yes—
113C22⋊D151—24no—
114C2×Dic151—21no—
115C2×Dic151—22no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—41no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—24no—
124C4×D151—42no—
125C4×D151—42no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151C2×D411yescharacteristic
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151C2×D411yescharacteristic
134C2×C4×C151C2×Q812yes—
135C2×C4×C151#4112yes—
136C2×C4×C151C2411yescharacteristic
137C8×C151—21no—
138C8×C151—21no—
139C22×C151—21no—
140C22×C151—21no—
141C22×C151C22⋊Q812yes—
142C22×C151C22×D411yescharacteristic
143C2×D151—22no—
144C2×D151—41no—
145C2×D151—41no—
146C4×C151—41no—
147C4×C151—41no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151C22⋊Q812yes—
151C4×C151C22×Q811yescharacteristic
152C4×C151C2×#4111yescharacteristic
153Dic151—22no—
154Dic151—21no—
155Dic151—21no—
156Dic151—21no—
157Dic151—41no—
158Dic151—41no—
159Dic151#13512yes—
160C2×C151—22no—
161C2×C151C2×C22⋊Q811yescharacteristic
162C2×C151C2×#13511yescharacteristic
163C2×C151#57511yescharacteristic
164D151—42no—
165C151#307611yescharacteristic, complemented, Sylow
166#3076—1511nomaximal, Sylow
167#533—1511no—
168C4×#41—1511no—
169#479—1511no—
170#479—1511no—
171#478—1511no—
172#478—1511no—
173#477—1511no—
174#476—1511no—
175#475—1511no—
176#474—1511no—
177#427—1511no—
178#427D15111yescharacteristic, complemented
179C2×C4⋊C8—1511no—
180#416—1511no—
181#416—1511no—
182C2×#41—1511no—
183C22×C8—1511no—
184C22×C8C2×D15111yescharacteristic
185C4⋊Q8—1511no—
186C4⋊Q8—1511no—
187#125—1511no—
188#125—1511no—
189C22⋊Q8—3021no—
190C22⋊Q8—3021no—
191C4×Q8—3021no—
192C4×Q8—3021no—
193C4×Q8—1511no—
194C4×Q8—1511no—
195C4×D4—3021no—
196C4×D4—3021no—
197C4×D4—1511no—
198C4×D4—1511no—
199#117—3021no—
200#117—1511no—
201#117C2×D15111yescharacteristic
202#117C2×D15111yescharacteristic
203C2×C42—3021no—
204C2×C42—1511no—
205#107—1511no—
206#107—1511no—
207#107C2×D15111yescharacteristic
208#107C2×D15111yescharacteristic
209#106—1511no—
210#106—1511no—
211#106C2×D15111yescharacteristic
212#106C2×D15111yescharacteristic
213C4⋊C8—1511no—
214C4⋊C8—1511no—
215C4⋊C8—1511no—
216C4⋊C8—1511no—
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#103—1511no—
221#102—1511no—
222#102—1511no—
223#102—1511no—
224#102—1511no—
225#41—3022no—
226#41—1514no—
227C2×Q8—3021no—
228C2×Q8—3021no—
229C2×Q8—1511no—
230C2×D4—3021no—
231C2×D4—1511no—
232C22×C4—3021no—
233C22×C4—3021no—
234C22×C4—3021no—
235C22×C4—1511no—
236C22×C4—1511no—
237C22×C4C22×D15111yescharacteristic
238C2×C8—22no—
239C2×C8—3022no—
240C2×C8—1511no—
241C2×C8—1511no—
242C2×C8C22×D15111yescharacteristic
243C2×C8C22×D15111yescharacteristic
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—3021no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—1511no—
253C4⋊C4—1511no—
254C4⋊C4C22×D15111yescharacteristic
255C4⋊C4C22×D15111yescharacteristic
256C4⋊C4C22×D15111yescharacteristic
257C4⋊C4C22×D15111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C42—21no—
264C42—21no—
265C42—3021no—
266C42—3021no—
267C42—3021no—
268C42—1511no—
269C42—1511no—
270C42—1511no—
271C42—1511no—
272C23—3021no—
273C23D4×D15111yescharacteristic
274Q8—3021no—
275Q8—6042no—
276Q8—6042no—
277Q8—1512no—
278D4—3024no—
279D4—3021no—
280D4—1512no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—3021no—
286C2×C4—3022no—
287C2×C4—3024no—
288C2×C4—3021no—
289C2×C4—3021no—
290C2×C4—6042no—
291C2×C4—6042no—
292C2×C4—6041no—
293C2×C4—1511no—
294C2×C4—1511no—
295C2×C4—1511no—
296C2×C4—1511no—
297C2×C4D4×D15111yescharacteristic
298C2×C4Q8×D15112yes—
299C2×C4#1455900412yes—
300C2×C4C23×D15111yescharacteristic
301C8—21no—
302C8—21no—
303C8—3021no—
304C8—3021no—
305C22—21no—
306C22—21no—
307C22—3022no—
308C22—6041no—
309C22—6041no—
310C22#1801271712yes—
311C22C2×D4×D15111yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—3022no—
317C4—3021no—
318C4—3021no—
319C4—3021no—
320C4—6041no—
321C4—6041no—
322C4—1512no—
323C4#1801271712yes—
324C4C2×Q8×D15111yescharacteristic
325C4C2×#1455900411yescharacteristic
326C2—22no—
327C2—6042no—
328C2C2×#1801271711yescharacteristic
329C2#135×D15111yescharacteristic
330C2#2375300911yescharacteristic
subgroupG/H
centerC2×C4D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#427×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#427D151
hypocenterC151#3076
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. #23752765C2semidirect
3. #23752522C2semidirect
4. #23752518C2semidirect
5. #23752515C2semidirect
6. #23752511C2semidirect
7. #23752506C2semidirect
8. #23752501C2semidirect
9. #23752496C2semidirect
10. #23752491C2semidirect
11. #23752248C2semidirect
12. C2×Dic151⋊C8C2semidirect
15. #427×C151C2semidirect
60. #14559004Q8semidirect
165. C151#3076semidirect
178. #427D151semidirect

Maximal subgroups

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

subgroupindex
#237527652
#237526802
#237525222
#237525182
#237525152
#237525112
#237525062
#237525012
#237524962
#237524912
#237522482
C2×Dic151⋊C82
#237522092
#237522062
#427×C1512
#3076151