Finite Group Databasebeta

← #34080557

Subgroups — #34080557

Order 19328.

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

normal subgroups only

This group has 346 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#23752824C211yesmaximal, characteristic, complemented
2#23752817C211yesmaximal, characteristic
3#23752520C212yesmaximal, complemented
4#23752513C212yesmaximal, complemented
5#23752458C212yesmaximal, complemented
6#23752441C212yesmaximal, complemented
7#23752418C212yesmaximal, complemented
8#23752413C212yesmaximal, complemented
9#424×C151C211yesmaximal, characteristic, complemented
10C2×#14558993C2212yes—
11C2×#14558993C2212yes—
12#18012739C2211yescharacteristic
13#18012736C2211yescharacteristic
14#18012732—22no—
15#18012731C2211yescharacteristic
16#18012731C2211yescharacteristic
17#18012729—22no—
18#18012724—22no—
19#18012718C2212yes—
20#18012713C2212yes—
21#18012712—22no—
22C4×Dic302C2212yes—
23C4×D604C2212yes—
24#18012673C2212yes—
25#18012671C2212yes—
26#18012664C2212yes—
27#18012664C2212yes—
28#18012661C2212yes—
29#18012661C2212yes—
30C2×M16×C151C2211yescharacteristic
31C22×C8×C151C2211yescharacteristic
32#117×C151C2211yescharacteristic
33C4⋊C8×C151C2212yes—
34C4⋊C8×C151C2212yes—
35C2×Dic302C2312yes—
36C2×D604—22no—
37C2×D604C2312yes—
38C2×C22⋊D151—22no—
39C2×C4×D151—22no—
40#14558993—42no—
41#14558993—42no—
42C4⋊Dic151—22no—
43C4⋊Dic151C2312yes—
44C4⋊Dic151C2312yes—
45Dic151⋊C4—22no—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48Dic151⋊C4—22no—
49C22⋊Dic151—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊C4—22no—
52C4×Dic151—22no—
53C22×C4×C151C2311yescharacteristic
54M16×C151—41no—
55C2×C8×C151—41no—
56C2×C8×C151C2312yes—
57C2×C8×C151C2312yes—
58C4⋊C4×C151D412yes—
59C22⋊C4×C151D412yes—
60C42×C151C2311yescharacteristic
61C42×C151C2311yescharacteristic
62C22×D151—22no—
63Dic302—22no—
64Dic302—22no—
65D604—22no—
66D604—22no—
67D604—82no—
68C22⋊D151—82no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C4×D151—82no—
73C23×C151C2×D411yescharacteristic
74C2×C4×C151—21no—
75C2×C4×C151—21no—
76C2×C4×C151C2×D412yes—
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×D412yes—
79C2×C4×C151C2411yescharacteristic
80C8×C151—22no—
81C8×C151—22no—
82C22×C151—21no—
83C22×C151—22no—
84C22×C151C22×D411yescharacteristic
85C2×D151—42no—
86C2×D151—42no—
87C2×D151—42no—
88C4×C151—21no—
89C4×C151—22no—
90C4×C151—22no—
91C4×C151H(5,𝔽2)11yescharacteristic
92C4×C1512−1+411yescharacteristic
93Dic151—42no—
94Dic151—42no—
95Dic151—42no—
96C2×C151—41no—
97C2×C151#53711yescharacteristic
98C2×C151#57712yes—
99D151—82no—
100C151#326011yescharacteristic, complemented, Sylow
101#3260—1511nomaximal, Sylow
102#541—1511no—
103#540—1511no—
104#479—1512no—
105#478—1512no—
106#468—1512no—
107#465—1512no—
108#461—1512no—
109#460—1512no—
110#424D15111yescharacteristic, complemented
111C2×SD16—1512no—
112C2×SD16—1512no—
113C2×M16C2×D15111yescharacteristic
114C22×C8C2×D15111yescharacteristic
115C4⋊Q8—1511no—
116#127—1511no—
117#126—3022no—
118#125—3022no—
119#125—1511no—
120#125—1511no—
121#123—3022no—
122C22⋊Q8—1512no—
123#121—3022no—
124#121—1512no—
125C4×Q8—1512no—
126C4×D4—1512no—
127#117C2×D15111yescharacteristic
128#107—1512no—
129#106—1512no—
130C4⋊C8C2×D15112yes—
131C4⋊C8C2×D15112yes—
132#103—1512no—
133#103—1512no—
134#102—1512no—
135#102—1512no—
136C2×Q8—1512no—
137C2×D4—3022no—
138C2×D4—3022no—
139C2×D4—1512no—
140C22×C4—3022no—
141C22×C4C22×D15111yescharacteristic
142SD16—6042no—
143SD16—6042no—
144M16—41no—
145C2×C8—41no—
146C2×C8C22×D15112yes—
147C2×C8C22×D15112yes—
148C4⋊C4—3022no—
149C4⋊C4—3022no—
150C4⋊C4—3022no—
151C4⋊C4—3022no—
152C4⋊C4—3022no—
153C4⋊C4—1512no—
154C4⋊C4—1512no—
155C4⋊C4D60412yes—
156C22⋊C4—3022no—
157C22⋊C4—3022no—
158C22⋊C4—3022no—
159C22⋊C4D60412yes—
160C42—3022no—
161C42C22×D15111yescharacteristic
162C42C22×D15111yescharacteristic
163C23—3022no—
164C23C2×D60411yescharacteristic
165Q8—3022no—
166Q8—3022no—
167D4—3022no—
168D4—3022no—
169D4—12082no—
170D4—12082no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—3022no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—12082no—
177C2×C4C2×D60412yes—
178C2×C4C2×D60412yes—
179C2×C4C2×D60411yescharacteristic
180C2×C4C23×D15111yescharacteristic
181C8—22no—
182C8—22no—
183C22—22no—
184C22—21no—
185C22—6042no—
186C22—6042no—
187C22—6042no—
188C22C22×D60411yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—6042no—
193C4—6042no—
194C4—6042no—
195C4#1801278411yescharacteristic
196C4#1801278711yescharacteristic
197C2—41no—
198C2—12082no—
199C2#2375279311yescharacteristic
200C2#2375302412yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#424×C151C2
socleC22×C151C22×D4
prime radical#23752817C2
hypercenter#424D151
hypocenterC151#3260
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #23752824C2semidirect
3. #23752520C2semidirect
4. #23752513C2semidirect
5. #23752458C2semidirect
6. #23752441C2semidirect
7. #23752418C2semidirect
8. #23752413C2semidirect
9. #424×C151C2semidirect
100. C151#3260semidirect
110. #424D151semidirect

Maximal subgroups

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

subgroupindex
#237528242
#237528172
#237525202
#237525132
#237524582
#237524412
#237524182
#237524132
#424×C1512
#3260151