Finite Group Databasebeta

← #34077055

Subgroups — #34077055

Order 19328.

480 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#23752151C211yesmaximal, characteristic, complemented
2#23752125C212yesmaximal, complemented
3#23752125C212yesmaximal, complemented
4#23752116C212yesmaximal, complemented
5#23752113C211yesmaximal, characteristic
6#23752090C212yesmaximal
7#23752086C212yesmaximal, complemented
8#23752083C212yesmaximal, complemented
9#400×C151C211yesmaximal, characteristic, complemented
10C22×Dic302C2212yes—
11C22×D604C2211yescharacteristic
12C22×C4×D151C2212yes—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4C2212yes—
15C2×(C2×D151)⋊C4C2212yes—
16C2×(C2×D151)⋊C4C2212yes—
17C2×(C2×D151)⋊C4C2212yes—
18C2×(C2×D151)⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×C4×Dic151C2211yescharacteristic
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28#95×C151C2212yes—
29#95×C151C2212yes—
30#95×C151C2211yescharacteristic
31C23×D151C2312yes—
32C2×Dic302—24no—
33C2×Dic302—42no—
34C2×Dic302—42no—
35C2×D604—41no—
36C2×D604—41no—
37C2×D604Q814yescomplemented
38C22×Dic151C2312yes—
39C22×Dic151C2312yes—
40C22×Dic151C2312yes—
41C2×C4×D151—42no—
42C2×C4×D151—42no—
43C2×C4×D151—42no—
44C4⋊Dic151—41no—
45Dic151⋊C4—42no—
46(C2×D151)⋊C4—24no—
47(C2×D151)⋊C4—24no—
48(C2×D151)⋊C4—42no—
49(C2×D151)⋊C4—42no—
50(C2×D151)⋊C4—42no—
51C4×Dic151—41no—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2312yes—
54C22×C4×C151C2311yescharacteristic
55C22×C4×C151C2312yes—
56C22×C4×C151C2311yescharacteristic
57C4⋊C4×C151—41no—
58C4⋊C4×C151—41no—
59C22×D151—22no—
60C22×D151—22no—
61C22×D151—22no—
62C22×D151—22no—
63C22×D151—22no—
64C22×D151—22no—
65C22×D151C2×Q814yes—
66Dic302—48no—
67D604—44no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C2×Dic151#4114yes—
77C4×D151—48no—
78C23×C151C2411yescharacteristic
79C2×C4×C151—21no—
80C2×C4×C151—21no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151—21no—
89C2×C4×C151—22no—
90C2×C4×C151—21no—
91C2×C4×C151C2×Q812yes—
92C22×C151C22×Q811yescharacteristic
93C22×C151C2×#4112yes—
94C22×C151H(5,𝔽2)11yescharacteristic
95C22×C151H(5,𝔽2)11yescharacteristic
96C22×C151H(5,𝔽2)12yes—
97C2×D151—24no—
98C2×D151—24no—
99C2×D151—24no—
100C2×D151—42no—
101C2×D151—42no—
102C2×D151—42no—
103C2×D151—42no—
104C4×C151—22no—
105C4×C151—42no—
106C4×C151—41no—
107C4×C151—41no—
108C4×C151—42no—
109Dic151—24no—
110Dic151—42no—
111Dic151—42no—
112C2×C151#53812yes—
113C2×C151#54311yescharacteristic
114C2×C151#55412yes—
115C2×C151#55911yescharacteristic
116C2×C151H(3,𝔽4)11yescharacteristic
117D151—44no—
118C151#280411yescharacteristic, complemented, Sylow
119#2804—1511nomaximal, Sylow
120#400—1511no—
121#400D15111yescharacteristic, complemented
122#393—1512no—
123#393—1512no—
124#391—1512no—
125#390—1511no—
126#386—1512no—
127#385—1512no—
128#385—1512no—
129C22×Q8—1512no—
130C22×D4—1511no—
131C23×C4—1512no—
132C2×C4⋊C4—1512no—
133C2×C4⋊C4—1511no—
134C2×C4⋊C4C2×D15111yescharacteristic
135C2×C4⋊C4C2×D15111yescharacteristic
136C2×C22⋊C4—1512no—
137C2×C22⋊C4—1512no—
138C2×C22⋊C4—1512no—
139C2×C22⋊C4—1512no—
140C2×C22⋊C4—1512no—
141C2×C42—1511no—
142#95—1512no—
143#95—1512no—
144#95—1512no—
145#95—1512no—
146#95—1511no—
147#95C2×D15112yes—
148#95C2×D15112yes—
149#95C2×D15111yescharacteristic
150C24—1512no—
151C2×Q8—3024no—
152C2×Q8—6042no—
153C2×Q8—6042no—
154C2×D4—6041no—
155C2×D4—6041no—
156C2×D4—1514no—
157C22×C4—6042no—
158C22×C4—6042no—
159C22×C4—6042no—
160C22×C4—1512no—
161C22×C4—1512no—
162C22×C4—1512no—
163C22×C4C22×D15111yescharacteristic
164C22×C4C22×D15112yes—
165C22×C4C22×D15111yescharacteristic
166C22×C4C22×D15112yes—
167C22×C4C22×D15111yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—6042no—
171C4⋊C4—6041no—
172C22⋊C4—3024no—
173C22⋊C4—3024no—
174C22⋊C4—6042no—
175C22⋊C4—6042no—
176C22⋊C4—6042no—
177C42—6041no—
178C23—3022no—
179C23—3022no—
180C23—3022no—
181C23—3022no—
182C23—3022no—
183C23—3022no—
184C23—1514no—
185C23C23×D15111yescharacteristic
186Q8—6048no—
187D4—6044no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—3022no—
201C2×C4—3022no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—3022no—
206C2×C4—3022no—
207C2×C4—3022no—
208C2×C4—6048no—
209C2×C4—1514no—
210C2×C4Q8×D15112yes—
211C22—3024no—
212C22—3024no—
213C22—3024no—
214C22—6042no—
215C22—6042no—
216C22—6042no—
217C22—6042no—
218C22C2×Q8×D15111yescharacteristic
219C22#41×D15112yes—
220C22#1801278411yescharacteristic
221C22#1801278511yescharacteristic
222C22#1801278512yes—
223C4—22no—
224C4—42no—
225C4—41no—
226C4—41no—
227C4—42no—
228C4—3024no—
229C4—6042no—
230C4—6042no—
231C2—6044no—
232C2#2375280112yes—
233C2#2375283711yescharacteristic
234C2#2375291812yes—
235C2#2375294611yescharacteristic
236C2#2375295411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#400×C151C2
prime radicalC22×D604C22
hypercenter#400D151
hypocenterC151#2804
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #23752151C2semidirect
2. #23752125C2semidirect
3. #23752125C2semidirect
4. #23752116C2semidirect
7. #23752086C2semidirect
8. #23752083C2semidirect
9. #400×C151C2semidirect
37. C2×D604Q8semidirect
118. C151#2804semidirect
121. #400D151semidirect

Maximal subgroups

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

subgroupindex
#237521512
#237521252
#237521162
#237521132
#237520902
#237520862
#237520832
#400×C1512
#2804151