Finite Group Databasebeta

← #34070275

Subgroups — #34070275

Order 19328.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#23752838C211yesmaximal, characteristic, complemented
2#23752067C211yesmaximal, characteristic
3#23752067C212yesmaximal
4#23751978C212yesmaximal, complemented
5#342×C151C211yesmaximal, characteristic, complemented
6C24×D151C2211yescharacteristic
7#18012718—22no—
8#18012716—24no—
9C2×C22⋊Dic151C2211yescharacteristic
10C2×C22⋊Dic151C2212yes—
11C2×(C2×D151)⋊C4—22no—
12C2×(C2×D151)⋊C4—24no—
13C2×C22⋊C4×C151C2212yes—
14C2×C22⋊C4×C151C2211yescharacteristic
15C23×D151—22no—
16C23×D151—21no—
17C23×D151—21no—
18C23×D151—22no—
19C23×D151—44no—
20C23×D151Q812yescomplemented
21C2×Dic302—22no—
22C22×Dic151—21no—
23C22×Dic151D414yes—
24C4⋊Dic151—22no—
25Dic151⋊C4—24no—
26C22⋊Dic151—22no—
27C22⋊Dic151—22no—
28C22⋊Dic151—22no—
29(C2×D151)⋊C4—44no—
30(C2×D151)⋊C4—48no—
31C24×C151C2311yescharacteristic
32C22×C4×C151—22no—
33C22×C4×C151D412yes—
34C22⋊C4×C151—22no—
35C22⋊C4×C151—22no—
36C22⋊C4×C151—22no—
37C22×D151—28no—
38C22×D151—24no—
39C22×D151—24no—
40C22×D151—22no—
41C22×D151—44no—
42C22×D151—44no—
43C22×D151—48no—
44C22×D151—44no—
45C22×D151—42no—
46C22×D151—41no—
47C22×D151—42no—
48C22×D151—41no—
49Dic302—82no—
50C2×Dic151—24no—
51C2×Dic151—44no—
52C2×Dic151—42no—
53C2×Dic151—41no—
54C23×C151—42no—
55C23×C151C2×D412yes—
56C23×C151C2×D411yescharacteristic
57C23×C151C2×Q811yescharacteristic
58C23×C151#4111yescharacteristic
59C23×C151#4112yes—
60C2×C4×C151—22no—
61C2×C4×C151—42no—
62C2×C4×C151—44no—
63C2×C4×C151—42no—
64C22×C151—24no—
65C22×C151—22no—
66C22×C151—41no—
67C22×C151—41no—
68C22×C151—42no—
69C22×C151#12011yescharacteristic
70C22×C151C22⋊Q812yes—
71C22×C151C22⋊Q811yescharacteristic
72C22×C151#12412yes—
73C22×C151#12411yescharacteristic
74C2×D151—28no—
75C2×D151—24no—
76C2×D151—44no—
77C2×D151—48no—
78C2×D151—44no—
79C2×D151—42no—
80C2×D151—42no—
81C2×D151—44no—
82C4×C151—42no—
83C4×C151—82no—
84Dic151—44no—
85Dic151—81no—
86C2×C151—21no—
87C2×C151—22no—
88C2×C151—22no—
89C2×C151—21no—
90C2×C151#39311yescharacteristic
91C2×C151B(4,𝔽2)12yes—
92D151—44no—
93C151#202911yescharacteristic, complemented, Sylow
94#2029—1511nomaximal, Sylow
95#543—1511no—
96#379—1512no—
97#379—1511no—
98#342—1512no—
99#342D15111yescharacteristic, complemented
100C25—1511no—
101C22⋊Q8—3024no—
102C22⋊Q8—3022no—
103C2×C22⋊C4—3024no—
104C2×C22⋊C4—3022no—
105C2×C22⋊C4—1511no—
106C2×C22⋊C4—1512no—
107C2×C22⋊C4C2×D15112yes—
108C2×C22⋊C4C2×D15111yescharacteristic
109C24—3022no—
110C24—3021no—
111C24—3021no—
112C24—3022no—
113C24—6044no—
114C24—1512no—
115C24C22×D15111yescharacteristic
116C2×Q8—3022no—
117C22×C4—22no—
118C22×C4—3021no—
119C22×C4—1514no—
120C22×C4D60412yes—
121C4⋊C4—3024no—
122C4⋊C4—3022no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—3022no—
127C22⋊C4—3022no—
128C22⋊C4—3022no—
129C22⋊C4—6044no—
130C22⋊C4—6048no—
131C23—42no—
132C23—3028no—
133C23—3024no—
134C23—3024no—
135C23—3022no—
136C23—6044no—
137C23—6042no—
138C23—6044no—
139C23—6044no—
140C23—6048no—
141C23—6041no—
142C23—6042no—
143C23—6041no—
144C23D4×D15112yes—
145C23C2×D60411yescharacteristic
146C23Q8×D15111yescharacteristic
147C23#1455900311yescharacteristic
148C23#1455900412yes—
149Q8—12082no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—3024no—
155C2×C4—6044no—
156C2×C4—6042no—
157C2×C4—6041no—
158C22—24no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22—42no—
163C22—3028no—
164C22—3024no—
165C22—6048no—
166C22—6044no—
167C22—6044no—
168C22—6042no—
169C22—6042no—
170C22—6044no—
171C22#1801270911yescharacteristic
172C22#1801271712yes—
173C22#1801271911yescharacteristic
174C22#1801272512yes—
175C22#1801272711yescharacteristic
176C4—42no—
177C4—82no—
178C4—6044no—
179C4—12081no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—6044no—
185C2#2375212511yescharacteristic
186C2#2375240012yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC24×C151C23
FrattiniC24C22×D151
Fitting#342×C151C2
socleC22×C151#120
prime radicalC24×D151C22
hypercenter#342D151
hypocenterC151#2029
LCSG ▷ C24×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #23752838C2semidirect
4. #23751978C2semidirect
5. #342×C151C2semidirect
20. C23×D151Q8semidirect
93. C151#2029semidirect
99. #342D151semidirect

Maximal subgroups

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

subgroupindex
#237528382
#237520672
#237519782
#342×C1512
#2029151