Finite Group Databasebeta

← #34070259

Subgroups — #34070259

Order 19328.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#18012730C211yesmaximal, characteristic
2C2×#18012663C211yesmaximal, characteristic
3#23752119C211yesmaximal, characteristic
4#23751975C211yesmaximal, characteristic
5#23751974C211yesmaximal, characteristic
6#23751966C211yesmaximal, characteristic
7C2×#103×C151C211yesmaximal, characteristic
8C22×C151⋊C8C2211yescharacteristic
9#18012730—22no—
10#18012730—22no—
11C2×C4⋊Dic151—21no—
12C2×C4⋊Dic151C2211yescharacteristic
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4—21no—
15C2×C4×Dic151C2211yescharacteristic
16#18012663—22no—
17C151⋊#95—21no—
18C151⋊#95—21no—
19C22×Q8×C151C2211yescharacteristic
20C22×C8×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22#103×C151—22no—
23C22×Dic151—21no—
24C22×Dic151—21no—
25C22×Dic151D411yescharacteristic
26C22×Dic151D411yescharacteristic
27C2×C151⋊C8—21no—
28C2×C151⋊C8—21no—
29C2×C151⋊C8—21no—
30C4⋊Dic151—24no—
31C4⋊Dic151—21no—
32C4⋊Dic151—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151D412yes—
35Dic151⋊C4—24no—
36C4×Dic151—21no—
37C4×Dic151—21no—
38C2×Q8×C151—21no—
39C2×Q8×C151—21no—
40C2×Q8×C151—21no—
41C2×Q8×C151—21no—
42C2×Q8×C151—21no—
43C2×Q8×C151Q812yes—
44C22×C4×C151—21no—
45C22×C4×C151—21no—
46C22×C4×C151C2311yescharacteristic
47C2×C8×C151—21no—
48C2×C8×C151—21no—
49C2×C8×C151—21no—
50C4⋊C4×C151—21no—
51C4⋊C4×C151D412yes—
52C2×Dic151—21no—
53C2×Dic151—21no—
54C2×Dic151—22no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—41no—
60C2×Dic151—41no—
61C2×Dic151—41no—
62C2×Dic151—41no—
63C2×Dic151—41no—
64C151⋊C8—41no—
65C23×C151C2×D411yescharacteristic
66Q8×C151—22no—
67Q8×C151—22no—
68Q8×C151—41no—
69Q8×C151—41no—
70C2×C4×C151—22no—
71C2×C4×C151—22no—
72C2×C4×C151—41no—
73C2×C4×C151—41no—
74C2×C4×C151—41no—
75C2×C4×C151—41no—
76C2×C4×C151C2×D411yescharacteristic
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×Q811yescharacteristic
79C2×C4×C151#4111yescharacteristic
80C2×C4×C151#4111yescharacteristic
81C2×C4×C151#4111yescharacteristic
82C8×C151—41no—
83C22×C151#12011yescharacteristic
84C22×C151C22⋊Q811yescharacteristic
85C22×C151#12411yescharacteristic
86C22×C151#13511yescharacteristic
87C22×C151#13511yescharacteristic
88C22×C151#13711yescharacteristic
89C22×C151#13711yescharacteristic
90C4×C151—42no—
91C4×C151—42no—
92C4×C151C22⋊Q811yescharacteristic
93C4×C151C22⋊Q811yescharacteristic
94C4×C151#12411yescharacteristic
95C4×C151#12411yescharacteristic
96Dic151—41no—
97Dic151—41no—
98Dic151—42no—
99Dic151—81no—
100C2×C151#39311yescharacteristic
101C2×C151#45211yescharacteristic
102C2×C151#45211yescharacteristic
103C2×C151#47911yescharacteristic
104C2×C151#47911yescharacteristic
105C2×C151#48811yescharacteristic
106C2×C151#49111yescharacteristic
107C151#202611yescharacteristic, complemented, Sylow
108#2026—1511nomaximal, Sylow
109C2×#125—1511no—
110C2×#103—1511no—
111C2×#103D15111yescharacteristic
112#391—1511no—
113#340—1511no—
114#340—1511no—
115#336—1511no—
116C22×Q8C2×D15111yescharacteristic
117C22×C8—1511no—
118C22×C8C2×D15111yescharacteristic
119#125—3022no—
120#125—3022no—
121C2×C4⋊C4—3021no—
122C2×C4⋊C4—3021no—
123C2×C4⋊C4—1511no—
124C2×C4⋊C4—1511no—
125C2×C4⋊C4C2×D15111yescharacteristic
126C2×C42—1511no—
127#103—22no—
128#103—3022no—
129#95—3021no—
130#95—3021no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic30212yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—3021no—
140C22×C4—3021no—
141C22×C4—1511no—
142C22×C4—1511no—
143C22×C4C22×D15111yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—3021no—
148C2×C8—3021no—
149C2×C8—3021no—
150C4⋊C4—21no—
151C4⋊C4—3024no—
152C4⋊C4—3024no—
153C4⋊C4—3021no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—1512no—
157C4⋊C4C22⋊D15112yes—
158C42—3021no—
159C42—3021no—
160C23D4×D15111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3021no—
172C2×C4—3021no—
173C2×C4—3022no—
174C2×C4—3021no—
175C2×C4—3021no—
176C2×C4—3021no—
177C2×C4—3021no—
178C2×C4—6041no—
179C2×C4—6041no—
180C2×C4—6041no—
181C2×C4—6041no—
182C2×C4—6041no—
183C2×C4D4×D15111yescharacteristic
184C2×C4C2×C22⋊D15111yescharacteristic
185C2×C4C2×Dic30211yescharacteristic
186C2×C4#1455900311yescharacteristic
187C2×C4#1455900311yescharacteristic
188C2×C4#1455900411yescharacteristic
189C8—41no—
190C8—6041no—
191C22#1801270711yescharacteristic
192C22#1801271611yescharacteristic
193C22#1801272511yescharacteristic
194C22#1801276011yescharacteristic
195C22#1801276211yescharacteristic
196C22#1801276811yescharacteristic
197C22#1801277111yescharacteristic
198C4—42no—
199C4—42no—
200C4—6041no—
201C4—6041no—
202C4—6042no—
203C4—12081no—
204C4#1801271611yescharacteristic
205C4#1801271811yescharacteristic
206C4#1801272511yescharacteristic
207C4#1801272611yescharacteristic
208C2#2375212411yescharacteristic
209C2#2375237111yescharacteristic
210C2#2375237311yescharacteristic
211C2#2375251711yescharacteristic
212C2#2375252111yescharacteristic
213C2#2375256811yescharacteristic
214C2#2375257911yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
FittingC2×#103×C151C2
socle, prime radicalC23×C151C2×D4
hypercenterC2×#103D151
hypocenterC151#2026
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
107. C151#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#180127302
C2×#180126632
#237521192
#237519752
#237519742
#237519662
C2×#103×C1512
#2026151