Finite Group Databasebeta

← #34077367

Subgroups — #34077367

Order 19328.

396 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 133 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#23752154C212yesmaximal, complemented
2#23752148C211yesmaximal, characteristic
3#23752146C212yesmaximal, complemented
4#23752144C212yesmaximal, complemented
5#23752135C212yesmaximal
6#23752133C212yesmaximal, complemented
7#23752124C211yesmaximal, characteristic
8#23752072C212yesmaximal
9#381×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×C4⋊Dic151C2212yes—
12C2×C4⋊Dic151C2212yes—
13C2×C4⋊Dic151C2212yes—
14C2×C4⋊Dic151C2211yescharacteristic
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×Dic151⋊C4C2212yes—
18C2×C22⋊Dic151C2212yes—
19C2×C22⋊Dic151C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2211yescharacteristic
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C23×C4×C151C2211yescharacteristic
27C2×C22⋊C4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2211yescharacteristic
29#95×C151C2212yes—
30#95×C151C2212yes—
31C2×Dic302—42no—
32C2×Dic302—41no—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C4⋊Dic151—42no—
38C4⋊Dic151—42no—
39C4⋊Dic151—42no—
40C4⋊Dic151—41no—
41Dic151⋊C4—42no—
42Dic151⋊C4—42no—
43Dic151⋊C4—42no—
44C22⋊Dic151—42no—
45C22⋊Dic151—42no—
46C24×C151C2311yescharacteristic
47C22×C4×C151—41no—
48C22×C4×C151—41no—
49C22×C4×C151Q814yescomplemented
50C22×C4×C151C2312yes—
51C22×C4×C151C2311yescharacteristic
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2312yes—
54C22⋊C4×C151—41no—
55C22⋊C4×C151—41no—
56Dic302—44no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C23×C151—22no—
70C23×C151—21no—
71C23×C151—21no—
72C23×C151—22no—
73C23×C151C2×Q812yes—
74C23×C151C2411yescharacteristic
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—21no—
81C2×C4×C151—21no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151—44no—
85C2×C4×C151C2×Q814yes—
86C22×C151—22no—
87C22×C151—24no—
88C22×C151—41no—
89C22×C151—42no—
90C22×C151—41no—
91C22×C151C22×Q811yescharacteristic
92C22×C151H(5,𝔽2)11yescharacteristic
93C22×C151H(5,𝔽2)11yescharacteristic
94C22×C151H(5,𝔽2)12yes—
95C22×C1512−1+412yes—
96C4×C151—24no—
97C4×C151—41no—
98C4×C151—42no—
99C4×C151—41no—
100Dic151—42no—
101Dic151—42no—
102Dic151—42no—
103Dic151—42no—
104C2×C151—42no—
105C2×C151#54311yescharacteristic
106C2×C151#54412yes—
107C2×C151#56011yescharacteristic
108C2×C151#56212yes—
109C2×C151#56311yescharacteristic
110C151#284111yescharacteristic, complemented, Sylow
111#2841—1511nomaximal, Sylow
112#400—1512no—
113#399—1511no—
114#398—1512no—
115#398—1512no—
116#396—1512no—
117#395—1512no—
118#393—1511no—
119#381D15111yescharacteristic
120#380—1512no—
121C22×Q8—1511no—
122C23×C4C2×D15111yescharacteristic
123C2×C4⋊C4—1512no—
124C2×C4⋊C4—1512no—
125C2×C4⋊C4—1512no—
126C2×C4⋊C4—1512no—
127C2×C4⋊C4—1512no—
128C2×C4⋊C4—1512no—
129C2×C4⋊C4—1511no—
130C2×C22⋊C4—1512no—
131C2×C22⋊C4—1512no—
132C2×C22⋊C4C2×D15111yescharacteristic
133C2×C22⋊C4C2×D15111yescharacteristic
134#95—1512no—
135#95—1512no—
136#95—1511no—
137#95—1512no—
138#95—1512no—
139#95—1511no—
140#95C2×D15112yes—
141#95C2×D15112yes—
142C24C22×D15111yescharacteristic
143C2×Q8—6041no—
144C2×Q8—6042no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—1512no—
148C22×C4—1512no—
149C22×C4—1512no—
150C22×C4—1512no—
151C22×C4Dic30214yescomplemented
152C22×C4C22×D15111yescharacteristic
153C22×C4C22×D15112yes—
154C22×C4C22×D15111yescharacteristic
155C22×C4C22×D15112yes—
156C4⋊C4—6042no—
157C4⋊C4—6042no—
158C4⋊C4—6042no—
159C4⋊C4—6042no—
160C4⋊C4—6042no—
161C4⋊C4—6041no—
162C4⋊C4—6042no—
163C22⋊C4—41no—
164C22⋊C4—41no—
165C22⋊C4—6042no—
166C22⋊C4—6042no—
167C23—21no—
168C23—21no—
169C23—22no—
170C23—22no—
171C23C2×Dic30212yes—
172C23C23×D15111yescharacteristic
173Q8—6044no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—44no—
184C2×C4—3022no—
185C2×C4—3022no—
186C2×C4—3022no—
187C2×C4—3022no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—3022no—
191C2×C4—3022no—
192C2×C4—3022no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—3022no—
196C2×C4C2×Dic30214yes—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22C22×Dic30211yescharacteristic
203C22#1801278411yescharacteristic
204C22#1801278411yescharacteristic
205C22#1801278512yes—
206C22#1801278612yes—
207C4—24no—
208C4—41no—
209C4—41no—
210C4—42no—
211C4—6042no—
212C4—6042no—
213C4—6042no—
214C4—6042no—
215C2—42no—
216C2#2375283811yescharacteristic
217C2#2375284012yes—
218C2#2375295211yescharacteristic
219C2#2375295912yes—
220C2#2375296511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#381×C151C2
prime radicalC24×C151C23
hypercenter#381D151
hypocenterC151#2841
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #23752154C2semidirect
3. #23752146C2semidirect
4. #23752144C2semidirect
6. #23752133C2semidirect
49. C22×C4×C151Q8semidirect
110. C151#2841semidirect
151. C22×C4Dic302semidirect

Maximal subgroups

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

subgroupindex
#237521542
#237521482
#237521462
#237521442
#237521352
#237521332
#237521242
#237520722
#381×C1512
#2841151