Finite Group Databasebeta

← #34079932

Subgroups — #34079932

Order 19328.

410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#18012715C211yesmaximal, characteristic
2C22⋊Q8×D151C211yesmaximal, characteristic
3#23752543C211yesmaximal, characteristic, complemented
4#23752541C212yesmaximal, complemented
5#23752540C211yesmaximal, characteristic, complemented
6#23752469C212yesmaximal, complemented
7#23752467C212yesmaximal, complemented
8#23752368C211yesmaximal, characteristic, complemented
9#23752366C212yesmaximal, complemented
10#23752174C211yesmaximal, characteristic
11#451×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151C2211yescharacteristic
13C22×C4×D151C2211yescharacteristic
14C2×#14558994C2212yescomplemented
15C2×#14558987C2212yes—
16#18012719C2211yescharacteristic
17#18012718C2211yescharacteristic
18#18012717—21no—
19#18012716—21no—
20#18012715—21no—
21#18012715—21no—
22#18012715C2211yescharacteristic
23#18012715C2212yes—
24#18012715C2212yes—
25C2×C4⋊Dic151C2211yescharacteristic
26C2×Dic151⋊C4—21no—
27C4⋊C4×D151—21no—
28C4⋊C4×D151C2211yescharacteristic
29C2×(C2×D151)⋊C4—21no—
30C22⋊C4×D151—21no—
31#18012671C2212yescomplemented
32#18012670C2212yescomplemented
33#18012664C2212yescomplemented
34#18012663C2212yescomplemented
35#18012663C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yes—
38C22×Q8×C151C2211yescharacteristic
39C2×Q16×C151C2212yescomplemented
40C22⋊Q8×C151C2211yescharacteristic
41#103×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44C2×Dic302—21no—
45C2×Dic302C2311yescharacteristic
46Q8×D151—42no—
47C22×Dic151—21no—
48C22×Dic151D411yescharacteristic
49C2×C4×D151—21no—
50C2×C4×D151—21no—
51C2×C4×D151—42no—
52C2×C4×D151D411yescharacteristic
53C2×C4×D151D411yescharacteristic
54C2×C4×D151C2311yescharacteristic
55C2×C4×D151C2311yescharacteristic
56#14558994—42no—
57#14558987—42no—
58C2×C151⋊C8C2312yes—
59C4⋊Dic151—21no—
60C4⋊Dic151—21no—
61C4⋊Dic151C2311yescharacteristic
62C4⋊Dic151C2312yes—
63Dic151⋊C4—21no—
64Dic151⋊C4—21no—
65Dic151⋊C4—22no—
66Dic151⋊C4—22no—
67Dic151⋊C4—21no—
68C22⋊Dic151—21no—
69(C2×D151)⋊C4—21no—
70(C2×D151)⋊C4—21no—
71(C2×D151)⋊C4—22no—
72(C2×D151)⋊C4—22no—
73C2×Q8×C151—21no—
74C2×Q8×C151—42no—
75C2×Q8×C151C2312yes—
76C2×Q8×C151C2311yescharacteristic
77C22×C4×C151—21no—
78C22×C4×C151C2311yescharacteristic
79Q16×C151—42no—
80C2×C8×C151C2312yes—
81C4⋊C4×C151—21no—
82C4⋊C4×C151C2311yescharacteristic
83C22⋊C4×C151—21no—
84C22×D151—22no—
85C22×D151—22no—
86C22×D151—41no—
87C22×D151C2×D411yescharacteristic
88C22×D151C2×D411yescharacteristic
89Dic302—22no—
90Dic302—42no—
91C2×Dic151—22no—
92C2×Dic151—21no—
93C2×Dic151—21no—
94C2×Dic151—41no—
95C2×Dic151—42no—
96C2×Dic151C2×D411yescharacteristic
97C2×Dic151C2×D411yescharacteristic
98C4×D151—22no—
99C4×D151—22no—
100C4×D151—41no—
101C4×D151—41no—
102C4×D151—42no—
103C4×D151—42no—
104C151⋊C8—22no—
105C23×C151C2×D411yescharacteristic
106Q8×C151—22no—
107Q8×C151—22no—
108Q8×C151—22no—
109Q8×C151—42no—
110C2×C4×C151—22no—
111C2×C4×C151—22no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—42no—
115C2×C4×C151C2×D411yescharacteristic
116C2×C4×C151C2411yescharacteristic
117C8×C151—22no—
118C22×C151—21no—
119C22×C151—21no—
120C22×C151#13712yes—
121C22×C151C22×D411yescharacteristic
122C2×D151—21no—
123C2×D151—21no—
124C2×D151—21no—
125C2×D151—21no—
126C2×D151—21no—
127C2×D151—44no—
128C2×D151#13712yes—
129C4×C151—21no—
130C4×C151—42no—
131C4×C151—41no—
132C4×C151—41no—
133C4×C151H(5,𝔽2)12yes—
134Dic151—21no—
135Dic151—21no—
136Dic151—41no—
137Dic151—41no—
138Dic151—42no—
139C2×C151—22no—
140C2×C151#53411yescharacteristic
141C2×C151C2×#13711yescharacteristic
142C2×C151C2×#13711yescharacteristic
143D151—22no—
144D151—41no—
145C151#319511yescharacteristic, complemented, Sylow
146#3195—1511nomaximal, Sylow
147C2×C22⋊Q8—1511no—
148C2×C22⋊Q8—1511no—
149#483—1511no—
150#483—1512no—
151#483—1511no—
152#470—1512no—
153#470—1512no—
154#451—1511no—
155#451—1512no—
156#451D15111yescharacteristic, complemented
157#407—1511no—
158C22×Q8—1511no—
159C22×Q8C2×D15111yescharacteristic
160C23×C4—1511no—
161C2×Q16—1512no—
162C2×Q16C2×D15112yescomplemented
163C2×M16—1512no—
164C22⋊Q8—3021no—
165C22⋊Q8—3021no—
166C22⋊Q8—3021no—
167C22⋊Q8—3021no—
168C22⋊Q8—1512no—
169C22⋊Q8—1511no—
170C22⋊Q8—1512no—
171C22⋊Q8—1511no—
172C22⋊Q8—1511no—
173C22⋊Q8C2×D15111yescharacteristic
174C2×C4⋊C4—3021no—
175C2×C4⋊C4—3021no—
176C2×C4⋊C4—1511no—
177C2×C4⋊C4—1511no—
178C2×C22⋊C4—3021no—
179C2×C22⋊C4—3021no—
180#106—1512no—
181#106—1512no—
182#103—1512no—
183#103—1512no—
184#103—1512no—
185#103C2×D15112yescomplemented
186C22⋊C8—1511no—
187C22⋊C8—1512no—
188C22⋊C8C2×D15111yescharacteristic
189C24—1511no—
190C2×Q8—21no—
191C2×Q8—42no—
192C2×Q8—3021no—
193C2×Q8—6042no—
194C2×Q8—1511no—
195C2×Q8C22×D15111yescharacteristic
196C2×Q8C22×D15112yes—
197C22×C4—21no—
198C22×C4—3021no—
199C22×C4—3021no—
200C22×C4—3021no—
201C22×C4—6042no—
202C22×C4—1511no—
203C22×C4—1511no—
204C22×C4—1511no—
205C22×C4—1511no—
206C22×C4—1511no—
207C22×C4C22×D15111yescharacteristic
208Q16—42no—
209Q16—6042no—
210M16—6042no—
211C2×C8—1512no—
212C2×C8C22×D15112yes—
213C4⋊C4—21no—
214C4⋊C4—3021no—
215C4⋊C4—3022no—
216C4⋊C4—3022no—
217C4⋊C4—3021no—
218C4⋊C4—3021no—
219C4⋊C4—3021no—
220C4⋊C4—3021no—
221C4⋊C4—1511no—
222C4⋊C4—1512no—
223C4⋊C4C22×D15111yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—3021no—
226C22⋊C4—3021no—
227C22⋊C4—3022no—
228C22⋊C4—3022no—
229C22⋊C4—3021no—
230C23—3022no—
231C23—3022no—
232C23—6041no—
233C23—1511no—
234C23—1511no—
235C23D4×D15111yescharacteristic
236Q8—22no—
237Q8—22no—
238Q8—22no—
239Q8—42no—
240Q8—3022no—
241Q8—6042no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—3022no—
248C2×C4—3022no—
249C2×C4—3021no—
250C2×C4—3022no—
251C2×C4—3021no—
252C2×C4—6041no—
253C2×C4—6041no—
254C2×C4—6042no—
255C2×C4—6042no—
256C2×C4—6041no—
257C2×C4—6042no—
258C2×C4—1511no—
259C2×C4—1511no—
260C2×C4D4×D15111yescharacteristic
261C2×C4C23×D15111yescharacteristic
262C8—22no—
263C8—3022no—
264C22—21no—
265C22—21no—
266C22—3021no—
267C22—3021no—
268C22—3021no—
269C22—3021no—
270C22—3021no—
271C22—6044no—
272C22—1512no—
273C22#1801277112yes—
274C22C2×D4×D15111yescharacteristic
275C4—21no—
276C4—41no—
277C4—42no—
278C4—41no—
279C4—3021no—
280C4—3021no—
281C4—6041no—
282C4—6042no—
283C4—6041no—
284C4#1801278412yes—
285C2—22no—
286C2—3022no—
287C2—6041no—
288C2#2375277211yescharacteristic
289C2#137×D15111yescharacteristic
290C2C2×#1801277111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
prime radicalC23×D151D4
hypercenter#451D151
hypocenterC151#3195
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #23752543C2semidirect
4. #23752541C2semidirect
5. #23752540C2semidirect
6. #23752469C2semidirect
7. #23752467C2semidirect
8. #23752368C2semidirect
9. #23752366C2semidirect
11. #451×C151C2semidirect
14. C2×#14558994C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. #18012664C22semidirect
34. #18012663C22semidirect
35. #18012663C22semidirect
39. C2×Q16×C151C22semidirect
41. #103×C151C22semidirect
145. C151#3195semidirect
156. #451D151semidirect
162. C2×Q16C2×D151semidirect
185. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127152
C22⋊Q8×D1512
#237525432
#237525412
#237525402
#237524692
#237524672
#237523682
#237523662
#237521742
#451×C1512
#3195151