Finite Group Databasebeta

← #34080330

Subgroups — #34080330

Order 19328.

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

normal subgroups only

This group has 362 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
1C4⋊Q8×D151C211yesmaximal, characteristic, complemented
2#23752744C211yesmaximal, characteristic
3#23752619C212yesmaximal, complemented
4#23752570C212yesmaximal, complemented
5#23752544C212yesmaximal, complemented
6#23752524C212yesmaximal
7#23752508C211yesmaximal, characteristic, complemented
8#23752504C211yesmaximal, characteristic, complemented
9#23752502C211yesmaximal, characteristic, complemented
10#23752268C211yesmaximal, characteristic, complemented
11#476×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151—21no—
13#18012739C2211yescharacteristic
14#18012738—21no—
15#18012738C2212yes—
16#18012737—21no—
17#18012732—21no—
18#18012730C2211yescharacteristic
19#18012726C2211yescharacteristic
20#18012721—21no—
21#18012719C2211yescharacteristic
22#18012710C2211yescharacteristic
23C4×Dic302C2211yescharacteristic
24C4×C22⋊D151—21no—
25#18012698—21no—
26C4⋊C4×D151—21no—
27C4⋊C4×D151C2212yes—
28C42×D151C2211yescharacteristic
29#18012673C2212yes—
30#18012672C2212yes—
31#18012670C2212yes—
32C4⋊(C151⋊C8)C2211yescharacteristic
33#18012664C2212yes—
34#18012662C2212yes—
35#18012660C2212yes—
36(C2×D151)⋊C8C2212yes—
37#18012649C2212yes—
38C4⋊Q8×C151C2211yescharacteristic
39C4×D4×C151C2211yescharacteristic
40#106×C151C2212yes—
41C4⋊C8×C151C2211yescharacteristic
42#102×C151C2212yes—
43C2×Dic302—22no—
44C2×Dic302—21no—
45C2×Dic302C2311yescharacteristic
46Q8×D151—44no—
47C2×C22⋊D151—21no—
48C2×C4×D151—22no—
49C2×C4×D151D411yescharacteristic
50C2×C4×D151D411yescharacteristic
51C2×C4×D151C2311yescharacteristic
52C2×C151⋊C8C2312yes—
53C4⋊Dic151—21no—
54C4⋊Dic151—21no—
55C4⋊Dic151—21no—
56C4⋊Dic151C2311yescharacteristic
57C4⋊Dic151C2312yes—
58Dic151⋊C4—22no—
59Dic151⋊C4—22no—
60Dic151⋊C4—21no—
61Dic151⋊C4—21no—
62C22⋊Dic151—21no—
63C22⋊Dic151—21no—
64C22⋊Dic151—21no—
65(C2×D151)⋊C4—21no—
66C4×Dic151—21no—
67C4×Dic151D411yescharacteristic
68C4×Dic151D411yescharacteristic
69C4×Dic151C2311yescharacteristic
70C2×Q8×C151—21no—
71C2×D4×C151C2311yescharacteristic
72C22×C4×C151—21no—
73C2×C8×C151C2312yes—
74C4⋊C4×C151—21no—
75C4⋊C4×C151C2312yes—
76C4⋊C4×C151C2311yescharacteristic
77C22⋊C4×C151—21no—
78C42×C151C2311yescharacteristic
79C22×D151C2×D411yescharacteristic
80Dic302—21no—
81Dic302—21no—
82Dic302—44no—
83Dic302—42no—
84C22⋊D151—42no—
85C2×Dic151—21no—
86C2×Dic151—21no—
87C2×Dic151—22no—
88C2×Dic151C2×D411yescharacteristic
89C2×Dic151C2×D411yescharacteristic
90C2×Dic151C2×D411yescharacteristic
91C4×D151—22no—
92C4×D151—22no—
93C4×D151—21no—
94C4×D151—21no—
95C4×D151—44no—
96C151⋊C8—22no—
97C23×C151—21no—
98Q8×C151—42no—
99D4×C151—21no—
100D4×C151—21no—
101C2×C4×C151—22no—
102C2×C4×C151—21no—
103C2×C4×C151—42no—
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151C2×D411yescharacteristic
106C2×C4×C151C2411yescharacteristic
107C8×C151—22no—
108C22×C151—41no—
109C22×C151—41no—
110C22×C151—41no—
111C22×C151C22×D411yescharacteristic
112C2×D151—21no—
113C2×D151—21no—
114C2×D151AGL(1,ℤ/8)12yes—
115C4×C151—21no—
116C4×C151—42no—
117C4×C151—41no—
118C4×C151#13712yes—
119C4×C1512−1+411yescharacteristic
120C4×C1512−1+411yescharacteristic
121Dic151—21no—
122Dic151—21no—
123Dic151—21no—
124Dic151—41no—
125Dic151—42no—
126Dic151—41no—
127C2×C151—81no—
128C2×C151#53611yescharacteristic
129C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C151C2×#13711yescharacteristic
131D151—22no—
132C151#323811yescharacteristic, complemented, Sylow
133#3238—1511nomaximal, Sylow
134C2×C4⋊Q8—1511no—
135#529—1511no—
136#501—1512no—
137#489—1512no—
138#483—1512no—
139#480—1512no—
140#477—1511no—
141#477—1511no—
142#476—1511no—
143#476D15111yescharacteristic, complemented
144#432—1511no—
145C22×Q8—3021no—
146C4⋊Q8—3021no—
147C4⋊Q8—3021no—
148C4⋊Q8—1512no—
149C4⋊Q8—1511no—
150C4⋊Q8C2×D15111yescharacteristic
151#126—3021no—
152#125—1511no—
153#124—1511no—
154#123—3021no—
155C22⋊Q8—1511no—
156#121—1511no—
157C4×Q8—1511no—
158C4×D4—3021no—
159C4×D4C2×D15111yescharacteristic
160#117—3021no—
161C2×C4⋊C4—3021no—
162C2×C4⋊C4—1512no—
163C2×C42—1511no—
164#107—1512no—
165#107—1512no—
166#106—1512no—
167#106C2×D15112yes—
168C4⋊C8—1511no—
169C4⋊C8C2×D15111yescharacteristic
170#103—1512no—
171#103—1512no—
172#102—1512no—
173#102C2×D15112yes—
174C22⋊C8—1512no—
175#97—1512no—
176C2×Q8—21no—
177C2×Q8—3022no—
178C2×Q8—3021no—
179C2×Q8—6044no—
180C2×Q8—1511no—
181C2×D4—3021no—
182C2×D4C22×D15111yescharacteristic
183C22×C4—21no—
184C22×C4—3022no—
185C22×C4—1511no—
186C22×C4—1511no—
187C22×C4—1511no—
188C2×C8—1512no—
189C2×C8C22×D15112yes—
190C4⋊C4—21no—
191C4⋊C4—3022no—
192C4⋊C4—3022no—
193C4⋊C4—3021no—
194C4⋊C4—3021no—
195C4⋊C4—3021no—
196C4⋊C4—3021no—
197C4⋊C4—3021no—
198C4⋊C4—1512no—
199C4⋊C4—1511no—
200C4⋊C4C22×D15112yes—
201C4⋊C4C22×D15111yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—3021no—
204C22⋊C4—3021no—
205C22⋊C4—3021no—
206C22⋊C4—3021no—
207C42—3021no—
208C42—1511no—
209C42—1511no—
210C42—1511no—
211C42C22×D15111yescharacteristic
212C23—21no—
213C23—1511no—
214Q8—42no—
215Q8—3021no—
216Q8—3021no—
217Q8—6042no—
218Q8—6044no—
219D4—21no—
220D4—21no—
221D4—6042no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—3022no—
226C2×C4—3022no—
227C2×C4—3021no—
228C2×C4—3021no—
229C2×C4—3021no—
230C2×C4—3021no—
231C2×C4—3022no—
232C2×C4—6044no—
233C2×C4—1511no—
234C2×C4—1511no—
235C2×C4—1511no—
236C2×C4D4×D15111yescharacteristic
237C2×C4D4×D15111yescharacteristic
238C2×C4C23×D15111yescharacteristic
239C8—22no—
240C8—3022no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—3021no—
245C22—3021no—
246C22—1512no—
247C22C2×D4×D15111yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—3021no—
252C4—3021no—
253C4—3021no—
254C4—6042no—
255C4—6041no—
256C4—6041no—
257C4#1801276812yes—
258C4#1801278611yescharacteristic
259C4#1801278711yescharacteristic
260C2—81no—
261C2—3022no—
262C2#2375278511yescharacteristic
263C2AGL(1,ℤ/8)×D15111yescharacteristic
264C2C2×#1801276811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#476×C151C2
socleC22×C151C22×D4
prime radical#18012710C22
hypercenter#476D151
hypocenterC151#3238
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D151C2semidirect
3. #23752619C2semidirect
4. #23752570C2semidirect
5. #23752544C2semidirect
7. #23752508C2semidirect
8. #23752504C2semidirect
9. #23752502C2semidirect
10. #23752268C2semidirect
11. #476×C151C2semidirect
132. C151#3238semidirect
143. #476D151semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1512
#237527442
#237526192
#237525702
#237525442
#237525242
#237525082
#237525042
#237525022
#237522682
#476×C1512
#3238151