Finite Group Databasebeta

← #34079055

Subgroups — #34079055

Order 19328.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D151C211yesmaximal, characteristic
2C2×#18012697C211yesmaximal, characteristic
3#23752555C212yesmaximal, complemented
4#23752551C212yesmaximal, complemented
5#23752547C211yesmaximal, characteristic, complemented
6#23752543C211yesmaximal, characteristic, complemented
7#23752540C211yesmaximal, characteristic, complemented
8#23752253C212yesmaximal, complemented
9#23752219C212yesmaximal, complemented
10#23752174C211yesmaximal, characteristic
11#484×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151C2211yescharacteristic
13C22×C4×D151C2211yescharacteristic
14C2×#14558987C2212yes—
15#18012719C2211yescharacteristic
16#18012718C2211yescharacteristic
17#18012717—21no—
18#18012716—21no—
19#18012715C2211yescharacteristic
20#18012697—21no—
21#18012697—21no—
22#18012697C2212yes—
23#18012697C2212yes—
24C2×C4⋊Dic151C2211yescharacteristic
25C4⋊C4×D151—21no—
26C4⋊C4×D151C2211yescharacteristic
27C2×(C2×D151)⋊C4—21no—
28C22⋊C4×D151—21no—
29C2×C4×Dic151—21no—
30#18012672C2212yescomplemented
31#18012671C2212yescomplemented
32#18012670C2212yescomplemented
33#18012664C2212yescomplemented
34#18012663C2212yescomplemented
35#18012662C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yes—
38C22⋊Q8×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40#107×C151C2212yescomplemented
41#103×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44C2×Dic302—21no—
45C2×Dic302C2311yescharacteristic
46Q8×D151—24no—
47C22×Dic151—21no—
48C22×Dic151D411yescharacteristic
49C2×C4×D151—24no—
50C2×C4×D151—21no—
51C2×C4×D151—21no—
52C2×C4×D151D411yescharacteristic
53C2×C4×D151D411yescharacteristic
54C2×C4×D151C2311yescharacteristic
55C2×C4×D151C2311yescharacteristic
56#14558987—24no—
57C2×C151⋊C8C2312yes—
58C4⋊Dic151—21no—
59C4⋊Dic151—21no—
60C4⋊Dic151C2311yescharacteristic
61C4⋊Dic151C2312yes—
62Dic151⋊C4—21no—
63Dic151⋊C4—21no—
64Dic151⋊C4—21no—
65C22⋊Dic151—21no—
66(C2×D151)⋊C4—21no—
67(C2×D151)⋊C4—21no—
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4—22no—
70C4×Dic151—22no—
71C4×Dic151—22no—
72C2×Q8×C151C2311yescharacteristic
73C22×C4×C151—21no—
74C22×C4×C151C2311yescharacteristic
75C2×C8×C151C2312yes—
76C4⋊C4×C151—21no—
77C4⋊C4×C151—21no—
78C4⋊C4×C151C2312yes—
79C4⋊C4×C151C2311yescharacteristic
80C22⋊C4×C151—21no—
81C22×D151—22no—
82C22×D151—22no—
83C22×D151—41no—
84C22×D151C2×D411yescharacteristic
85C22×D151C2×D411yescharacteristic
86Dic302—22no—
87Dic302—42no—
88C2×Dic151—22no—
89C2×Dic151—22no—
90C2×Dic151—21no—
91C2×Dic151—21no—
92C2×Dic151—42no—
93C2×Dic151C2×D411yescharacteristic
94C2×Dic151C2×D411yescharacteristic
95C4×D151—22no—
96C4×D151—22no—
97C4×D151—22no—
98C4×D151—42no—
99C4×D151—42no—
100C4×D151#4114yes—
101C151⋊C8—22no—
102C23×C151C2×D411yescharacteristic
103Q8×C151—22no—
104C2×C4×C151—22no—
105C2×C4×C151—21no—
106C2×C4×C151—22no—
107C2×C4×C151—21no—
108C2×C4×C151—42no—
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2411yescharacteristic
111C8×C151—22no—
112C22×C151—21no—
113C22×C151—21no—
114C22×C151#13712yes—
115C22×C151C22×D411yescharacteristic
116C2×D151—21no—
117C2×D151—21no—
118C2×D151—21no—
119C2×D151—21no—
120C2×D151—21no—
121C2×D151—44no—
122C2×D151#12312yes—
123C4×C151—21no—
124C4×C151—41no—
125C4×C151—42no—
126C4×C151—41no—
127C4×C151C2×#4112yes—
128Dic151—21no—
129Dic151—41no—
130Dic151—42no—
131Dic151—41no—
132Dic151#12312yes—
133C2×C151—22no—
134C2×C151C2×#12311yescharacteristic
135C2×C151C2×#13711yescharacteristic
136C2×C151#57511yescharacteristic
137D151—22no—
138D151—41no—
139C151#309511yescharacteristic, complemented, Sylow
140#3095—1511nomaximal, Sylow
141C2×C22⋊Q8—1511no—
142C2×#117—1511no—
143#485—1512no—
144#485—1512no—
145#484—1511no—
146#484D15111yescharacteristic, complemented
147#483—1511no—
148#483—1511no—
149#428—1512no—
150#419—1512no—
151#407—1511no—
152C22×Q8—1511no—
153C23×C4—1511no—
154C2×M16—1512no—
155C22⋊Q8—3021no—
156C22⋊Q8—3021no—
157C22⋊Q8—1511no—
158C22⋊Q8—1511no—
159C22⋊Q8—1511no—
160C22⋊Q8C2×D15111yescharacteristic
161#117—3021no—
162#117—3021no—
163#117—1512no—
164#117—1512no—
165C2×C4⋊C4—3021no—
166C2×C4⋊C4—1511no—
167C2×C4⋊C4—1511no—
168C2×C4⋊C4C2×D15111yescharacteristic
169C2×C22⋊C4—3021no—
170C2×C22⋊C4—3021no—
171C2×C42—3021no—
172#107—1512no—
173#107C2×D15112yescomplemented
174#106—1512no—
175#106—1512no—
176#103—1512no—
177#103—1512no—
178#103—1512no—
179#103C2×D15112yescomplemented
180C22⋊C8—1511no—
181C22⋊C8—1512no—
182C22⋊C8C2×D15111yescharacteristic
183C24—1511no—
184C2×Q8—3021no—
185C2×Q8—3024no—
186C2×Q8—1511no—
187C2×Q8C22×D15111yescharacteristic
188C22×C4—21no—
189C22×C4—3024no—
190C22×C4—3021no—
191C22×C4—3021no—
192C22×C4—3021no—
193C22×C4—1511no—
194C22×C4—1511no—
195C22×C4—1511no—
196C22×C4—1511no—
197C22×C4—1511no—
198C22×C4C22×D15111yescharacteristic
199M16—3024no—
200C2×C8—1512no—
201C2×C8C22×D15112yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—3021no—
205C4⋊C4—3021no—
206C4⋊C4—3021no—
207C4⋊C4—3021no—
208C4⋊C4—3021no—
209C4⋊C4—1512no—
210C4⋊C4—1511no—
211C4⋊C4C22×D15112yes—
212C4⋊C4C22×D15111yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—3022no—
215C22⋊C4—3022no—
216C22⋊C4—3021no—
217C22⋊C4—3021no—
218C22⋊C4—3021no—
219C42—3022no—
220C42—3022no—
221C23—3022no—
222C23—3022no—
223C23—6041no—
224C23—1511no—
225C23—1511no—
226C23D4×D15111yescharacteristic
227Q8—22no—
228Q8—3022no—
229Q8—6042no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—3022no—
236C2×C4—3022no—
237C2×C4—3022no—
238C2×C4—3022no—
239C2×C4—3022no—
240C2×C4—3021no—
241C2×C4—3021no—
242C2×C4—6042no—
243C2×C4—6042no—
244C2×C4—6042no—
245C2×C4—1511no—
246C2×C4—1511no—
247C2×C4—1514no—
248C2×C4D4×D15111yescharacteristic
249C2×C4C23×D15111yescharacteristic
250C8—22no—
251C8—3022no—
252C22—21no—
253C22—21no—
254C22—3021no—
255C22—3021no—
256C22—3021no—
257C22—3021no—
258C22—3021no—
259C22—6044no—
260C22—1512no—
261C22#1801277112yes—
262C22C2×D4×D15111yescharacteristic
263C4—21no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—3021no—
268C4—6041no—
269C4—6042no—
270C4—6041no—
271C4—1512no—
272C4#41×D15112yes—
273C2—22no—
274C2—3022no—
275C2—6041no—
276C2#123×D15111yescharacteristic
277C2C2×#1801277111yescharacteristic
278C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#484×C151C2
socleC22×C151C22×D4
prime radicalC23×D151D4
hypercenter#484D151
hypocenterC151#3095
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #23752555C2semidirect
4. #23752551C2semidirect
5. #23752547C2semidirect
6. #23752543C2semidirect
7. #23752540C2semidirect
8. #23752253C2semidirect
9. #23752219C2semidirect
11. #484×C151C2semidirect
30. #18012672C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. #18012664C22semidirect
34. #18012663C22semidirect
35. #18012662C22semidirect
40. #107×C151C22semidirect
41. #103×C151C22semidirect
139. C151#3095semidirect
146. #484D151semidirect
173. #107C2×D151semidirect
179. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1512
C2×#180126972
#237525552
#237525512
#237525472
#237525432
#237525402
#237522532
#237522192
#237521742
#484×C1512
#3095151