Finite Group Databasebeta

← #34080498

Subgroups — #34080498

Order 19328.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752769C211yesmaximal, characteristic, complemented
2#23752762C211yesmaximal, characteristic
3#23752508C212yesmaximal, complemented
4#23752493C212yesmaximal, complemented
5#23752458C214yesmaximal, complemented
6#23752418C212yesmaximal, complemented
7#23752413C212yesmaximal, complemented
8#423×C151C211yesmaximal, characteristic, complemented
9C2×#14559004—21no—
10C2×#14558993C2214yes—
11#18012739C2211yescharacteristic
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012736C2211yescharacteristic
15#18012731—21no—
16#18012727—21no—
17#18012718—21no—
18#18012718C2212yes—
19#18012713—21no—
20#18012713C2212yes—
21C4×Dic302—21no—
22C4×Dic302C2212yes—
23C4×D604—21no—
24C4×D604C2212yes—
25#18012698—21no—
26#18012673C2214yes—
27#18012664C2214yes—
28#18012661C2214yes—
29C2×M16×C151C2212yes—
30C2×C42×C151C2211yescharacteristic
31C4⋊C8×C151C2212yes—
32C4⋊C8×C151C2212yes—
33#14559004—44no—
34C2×Dic302—21no—
35C2×Dic302—21no—
36C2×Dic302C2312yes—
37C2×D604—21no—
38C2×D604—21no—
39C2×D604C2312yes—
40C2×C22⋊D151—22no—
41C2×C4×D151—22no—
42#14558993—44no—
43C4⋊Dic151—21no—
44C4⋊Dic151—21no—
45C4⋊Dic151—21no—
46C4⋊Dic151—21no—
47C4⋊Dic151C2312yes—
48C4⋊Dic151C2312yes—
49Dic151⋊C4—22no—
50Dic151⋊C4—22no—
51C22⋊Dic151—22no—
52(C2×D151)⋊C4—22no—
53(C2×D151)⋊C4—22no—
54C4×Dic151—22no—
55C22×C4×C151D411yescharacteristic
56C22×C4×C151D411yescharacteristic
57C22×C4×C151C2311yescharacteristic
58M16×C151—42no—
59C2×C8×C151C2314yes—
60C42×C151D411yescharacteristic
61C42×C151D411yescharacteristic
62C42×C151C2311yescharacteristic
63C42×C151C2311yescharacteristic
64C22×D151—22no—
65Dic302—22no—
66Dic302—22no—
67Dic302—42no—
68Dic302—42no—
69D604—22no—
70D604—22no—
71D604—42no—
72D604—42no—
73C22⋊D151—44no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C2×Dic151—22no—
77C4×D151—44no—
78C23×C151C2×D411yescharacteristic
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151—21no—
82C2×C4×C151—21no—
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2×D411yescharacteristic
87C2×C4×C151C2×D411yescharacteristic
88C2×C4×C151C2411yescharacteristic
89C8×C151—24no—
90C22×C151—21no—
91C22×C151—21no—
92C22×C151—21no—
93C22×C151C22×D411yescharacteristic
94C2×D151—42no—
95C2×D151—42no—
96C2×D151—42no—
97C4×C151—21no—
98C4×C151—21no—
99C4×C151—21no—
100C4×C151AGL(1,ℤ/8)12yes—
101C4×C151#13712yes—
102C4×C151H(5,𝔽2)11yescharacteristic
103C4×C1512−1+411yescharacteristic
104Dic151—42no—
105Dic151—42no—
106Dic151—42no—
107C2×C151—41no—
108C2×C151#53711yescharacteristic
109C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C151C2×#13711yescharacteristic
111D151—82no—
112C151#325411yescharacteristic, complemented, Sylow
113#3254—1511nomaximal, Sylow
114#533—1511no—
115#532—1511no—
116#477—1512no—
117#474—1512no—
118#468—1514no—
119#461—1512no—
120#460—1512no—
121#423D15111yescharacteristic, complemented
122C2×#41—3021no—
123C2×SD16—1514no—
124C2×M16C2×D15112yes—
125C4⋊Q8—1511no—
126C4⋊Q8—1511no—
127C4⋊Q8—1511no—
128#127—1511no—
129#125—3021no—
130#124—3021no—
131C22⋊Q8—3021no—
132C22⋊Q8—1512no—
133#121—3021no—
134#121—1512no—
135C4×Q8—3021no—
136C4×Q8—1512no—
137C4×D4—3021no—
138C4×D4—1512no—
139#117—3021no—
140C2×C42C2×D15111yescharacteristic
141#107—1514no—
142C4⋊C8C2×D15112yes—
143C4⋊C8C2×D15112yes—
144#103—1514no—
145#102—1514no—
146#41—6044no—
147C2×Q8—3021no—
148C2×Q8—3021no—
149C2×Q8—1512no—
150C2×D4—3022no—
151C2×D4—3021no—
152C2×D4—3021no—
153C2×D4—1512no—
154C22×C4—3022no—
155C22×C4D60411yescharacteristic
156C22×C4D60411yescharacteristic
157C22×C4C22×D15111yescharacteristic
158SD16—6044no—
159M16—42no—
160C2×C8C22×D15114yes—
161C4⋊C4—3022no—
162C4⋊C4—3022no—
163C4⋊C4—3021no—
164C4⋊C4—3021no—
165C4⋊C4—3021no—
166C4⋊C4—3021no—
167C4⋊C4—1512no—
168C4⋊C4—1512no—
169C22⋊C4—3022no—
170C22⋊C4—3022no—
171C22⋊C4—3022no—
172C42—3022no—
173C42D60411yescharacteristic
174C42D60411yescharacteristic
175C42C22×D15111yescharacteristic
176C42C22×D15111yescharacteristic
177C23—3022no—
178C23C2×D60411yescharacteristic
179Q8—3022no—
180Q8—3022no—
181Q8—6042no—
182Q8—6042no—
183D4—3022no—
184D4—3022no—
185D4—6042no—
186D4—6044no—
187D4—6042no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—3022no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—6044no—
196C2×C4C2×D60411yescharacteristic
197C2×C4C2×D60411yescharacteristic
198C2×C4C2×D60411yescharacteristic
199C2×C4C2×D60411yescharacteristic
200C2×C4C2×D60411yescharacteristic
201C2×C4C23×D15111yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—6042no—
207C22—6042no—
208C22—6042no—
209C22C22×D60411yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—6042no—
214C4—6042no—
215C4—6042no—
216C4#1801276712yes—
217C4#1801277212yes—
218C4#1801278411yescharacteristic
219C4#1801278711yescharacteristic
220C2—41no—
221C2—12082no—
222C2#2375279311yescharacteristic
223C2C2×#1801276711yescharacteristic
224C2C2×#1801277211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#423×C151C2
socleC22×C151C22×D4
prime radical#23752762C2
hypercenter#423D151
hypocenterC151#3254
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #23752769C2semidirect
3. #23752508C2semidirect
4. #23752493C2semidirect
5. #23752458C2semidirect
6. #23752418C2semidirect
7. #23752413C2semidirect
8. #423×C151C2semidirect
112. C151#3254semidirect
121. #423D151semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237527622
#237525082
#237524932
#237524582
#237524182
#237524132
#423×C1512
#3254151