Finite Group Databasebeta

← #34080511

Subgroups — #34080511

Order 19328.

354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752746C212yesmaximal, complemented
2#23752520C212yesmaximal, complemented
3#23752513C212yesmaximal, complemented
4#23752470C211yesmaximal, characteristic, complemented
5#23752465C211yesmaximal, characteristic
6#23752458C212yesmaximal, complemented
7#23752435C212yesmaximal, complemented
8#23752428C212yesmaximal, complemented
9#423×C151C211yesmaximal, characteristic, complemented
10C2×Dic604C2211yescharacteristic
11C2×#14558993C2212yes—
12C2×D1208C2211yescharacteristic
13#18012733—22no—
14#18012731C2212yes—
15#18012727C2212yes—
16#18012722—22no—
17#18012718C2212yes—
18#18012713C2212yes—
19C4×Dic302C2212yes—
20C4×D604C2212yes—
21C4×C22⋊D151—22no—
22#18012696—22no—
23#18012673C2212yes—
24#18012671C2211yescharacteristic
25#18012671C2211yescharacteristic
26#18012664C2212yes—
27#18012664C2212yes—
28#18012661C2212yes—
29#18012661C2212yes—
30C2×M16×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic
32C2×C42×C151C2211yescharacteristic
33C4⋊C8×C151C2212yes—
34C4⋊C8×C151C2212yes—
35C2×Dic302C2312yes—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C4×D151—22no—
39Dic604—41no—
40#14558993—42no—
41D1208—41no—
42C4⋊Dic151C2312yes—
43C4⋊Dic151C2312yes—
44Dic151⋊C4—22no—
45Dic151⋊C4—22no—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48C22⋊Dic151—22no—
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
54C22×C4×C151D412yes—
55C22×C4×C151C2311yescharacteristic
56M16×C151—41no—
57M16×C151—41no—
58C2×C8×C151C2312yes—
59C2×C8×C151C2311yescharacteristic
60C2×C8×C151C2311yescharacteristic
61C42×C151D411yescharacteristic
62C42×C151D411yescharacteristic
63C42×C151C2312yes—
64C22×D151—22no—
65Dic302—22no—
66Dic302—22no—
67D604—22no—
68D604—22no—
69C22⋊D151—44no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C4×D151—44no—
74C23×C151C2×D411yescharacteristic
75C2×C4×C151—21no—
76C2×C4×C151—21no—
77C2×C4×C151—42no—
78C2×C4×C151C2×D412yes—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D412yes—
81C2×C4×C151C2411yescharacteristic
82C8×C151—21no—
83C8×C151—22no—
84C8×C151—21no—
85C22×C151—21no—
86C22×C151—22no—
87C22×C151C22×D411yescharacteristic
88C2×D151—42no—
89C2×D151—42no—
90C2×D151—42no—
91C4×C151—21no—
92C4×C151—22no—
93C4×C151—22no—
94C4×C151H(5,𝔽2)11yescharacteristic
95C4×C1512−1+411yescharacteristic
96Dic151—42no—
97Dic151—42no—
98Dic151—42no—
99C2×C151—41no—
100C2×C151#53711yescharacteristic
101C2×C151#57512yes—
102D151—82no—
103C151#325611yescharacteristic, complemented, Sylow
104#3256—1511nomaximal, Sylow
105#529—1512no—
106#479—1512no—
107#478—1512no—
108#470—1511no—
109#469—1511no—
110#468—1512no—
111#464—1512no—
112#463—1512no—
113#423D15111yescharacteristic, complemented
114C2×Q16—1511no—
115C2×SD16—1512no—
116C2×D8—1511no—
117C2×M16C2×D15111yescharacteristic
118C2×M16C2×D15111yescharacteristic
119#126—3022no—
120#125—1512no—
121#124—1512no—
122#123—3022no—
123C22⋊Q8—1512no—
124#121—1512no—
125C4×Q8—1512no—
126C4×D4—3022no—
127C4×D4—1512no—
128#117—3022no—
129C2×C42C2×D15111yescharacteristic
130#107—1512no—
131#106—1511no—
132#106—1511no—
133C4⋊C8C2×D15112yes—
134C4⋊C8C2×D15112yes—
135#103—1512no—
136#103—1512no—
137#102—1512no—
138#102—1512no—
139C2×Q8—1512no—
140C2×D4—3022no—
141C2×D4—1512no—
142C22×C4—3022no—
143C22×C4D60412yes—
144C22×C4C22×D15111yescharacteristic
145Q16—6041no—
146SD16—6042no—
147D8—6041no—
148M16—41no—
149M16—41no—
150C2×C8C22×D15111yescharacteristic
151C2×C8C22×D15112yes—
152C2×C8C22×D15111yescharacteristic
153C4⋊C4—3022no—
154C4⋊C4—3022no—
155C4⋊C4—3022no—
156C4⋊C4—3022no—
157C4⋊C4—1512no—
158C4⋊C4—1512no—
159C22⋊C4—3022no—
160C22⋊C4—3022no—
161C22⋊C4—3022no—
162C22⋊C4—3022no—
163C22⋊C4—3022no—
164C42—3022no—
165C42D60411yescharacteristic
166C42D60411yescharacteristic
167C42C22×D15112yes—
168C23—3022no—
169C23C2×D60411yescharacteristic
170Q8—3022no—
171Q8—3022no—
172D4—3022no—
173D4—3022no—
174D4—6044no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—3022no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—6044no—
182C2×C4C2×D60412yes—
183C2×C4C2×D60411yescharacteristic
184C2×C4C2×D60412yes—
185C2×C4C23×D15111yescharacteristic
186C8—21no—
187C8—22no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—6042no—
192C22—6042no—
193C22—6042no—
194C22C22×D60411yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—6042no—
199C4—6042no—
200C4—6042no—
201C4#1801278411yescharacteristic
202C4#1801278711yescharacteristic
203C2—41no—
204C2—12082no—
205C2#2375279311yescharacteristic
206C2#2375301212yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#423×C151C2
socleC22×C151C22×D4
prime radical#23752465C2
hypercenter#423D151
hypocenterC151#3256
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. #23752746C2semidirect
2. #23752520C2semidirect
3. #23752513C2semidirect
4. #23752470C2semidirect
6. #23752458C2semidirect
7. #23752435C2semidirect
8. #23752428C2semidirect
9. #423×C151C2semidirect
103. C151#3256semidirect
113. #423D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237525202
#237525132
#237524702
#237524652
#237524582
#237524352
#237524282
#423×C1512
#3256151