Finite Group Databasebeta

← #34070242

Subgroups — #34070242

Order 19328.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#23752774C211yesmaximal, characteristic
2C2×#18012723C212yesmaximal, complemented
3C2×#18012653C212yesmaximal, complemented
4#23752073C211yesmaximal, characteristic, complemented
5#342×C151C211yesmaximal, characteristic, complemented
6C22×C22⋊D151C2212yes—
7C23×Dic151C2211yescharacteristic
8#18012723—24no—
9#18012723—22no—
10#18012723—24no—
11#18012713—22no—
12#18012709—22no—
13C2×C4⋊Dic151—22no—
14C2×C22⋊Dic151C2211yescharacteristic
15C2×(C2×D151)⋊C4—22no—
16#18012653—24no—
17C151⋊#95—22no—
18C2×C22⋊C4×C151C2211yescharacteristic
19C2×C22⋊C4×C151C2212yes—
20C23×D151D412yes—
21C2×D604—22no—
22C2×C22⋊D151—22no—
23C2×C22⋊D151—22no—
24C2×C22⋊D151—22no—
25C2×C22⋊D151—22no—
26C2×C22⋊D151—22no—
27C2×C22⋊D151—22no—
28C22×Dic151—22no—
29C22×Dic151—22no—
30C22×Dic151—21no—
31C22×Dic151—21no—
32C22×Dic151—21no—
33C22×Dic151D412yes—
34C22×Dic151D412yescomplemented
35C4⋊Dic151—28no—
36C4⋊Dic151—22no—
37C22⋊Dic151—22no—
38(C2×D151)⋊C4—28no—
39(C2×D151)⋊C4—24no—
40C24×C151C2311yescharacteristic
41C22×C4×C151—22no—
42C22×C4×C151D412yes—
43C22⋊C4×C151—22no—
44C22⋊C4×C151—22no—
45C22⋊C4×C151D414yescomplemented
46C22×D151—22no—
47C22×D151—22no—
48C22×D151—22no—
49C22×D151—44no—
50D604—82no—
51C22⋊D151—42no—
52C22⋊D151—42no—
53C22⋊D151—42no—
54C22⋊D151—42no—
55C2×Dic151—24no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—41no—
61C2×Dic151—42no—
62C2×Dic151—41no—
63C2×Dic151—42no—
64C2×Dic151—41no—
65C23×C151—42no—
66C23×C151C2×D412yes—
67C23×C151C2×D411yescharacteristic
68C23×C151C2×D411yescharacteristic
69C23×C151C2×D412yes—
70C23×C151#4111yescharacteristic
71C2×C4×C151—24no—
72C2×C4×C151—22no—
73C2×C4×C151—44no—
74C2×C4×C151—42no—
75C22×C151—22no—
76C22×C151—24no—
77C22×C151—41no—
78C22×C151—42no—
79C22×C151—41no—
80C22×C151#12012yes—
81C22×C151#12011yescharacteristic
82C22×C151#12111yescharacteristic
83C22×C151#12112yes—
84C22×C151#12711yescharacteristic
85C2×D151—44no—
86C2×D151—42no—
87C2×D151—44no—
88C2×D151—82no—
89C4×C151—44no—
90C4×C151—42no—
91Dic151—42no—
92Dic151—42no—
93Dic151—81no—
94C2×C151—21no—
95C2×C151—22no—
96C2×C151—22no—
97C2×C151—21no—
98C2×C151#39211yescharacteristic
99C2×C151#45812yes—
100D151—82no—
101C151#202211yescharacteristic, complemented, Sylow
102#2022—1511nomaximal, Sylow
103#534—1511no—
104C2×#123—1512no—
105C2×#99—1512no—
106#381—1511no—
107#342D15111yescharacteristic, complemented
108C22×D4—1512no—
109C23×C4—1511no—
110#123—3024no—
111#123—3022no—
112#123—3024no—
113#121—3022no—
114#120—3022no—
115C2×C4⋊C4—3022no—
116C2×C22⋊C4—3022no—
117C2×C22⋊C4—1511no—
118C2×C22⋊C4C2×D15111yescharacteristic
119C2×C22⋊C4C2×D15112yes—
120#99—3024no—
121#95—3022no—
122C24—1512no—
123C24C22×D15111yescharacteristic
124C2×D4—3022no—
125C2×D4—3022no—
126C2×D4—3022no—
127C2×D4—3022no—
128C2×D4—3022no—
129C2×D4—3022no—
130C2×D4—3022no—
131C22×C4—22no—
132C22×C4—3022no—
133C22×C4—3021no—
134C22×C4—3022no—
135C22×C4—3021no—
136C22×C4—3021no—
137C22×C4—1512no—
138C22×C4—1512no—
139C22×C4D60412yes—
140C4⋊C4—3028no—
141C4⋊C4—3022no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—3028no—
145C22⋊C4—3024no—
146C22⋊C4—3022no—
147C22⋊C4D60414yescomplemented
148C23—42no—
149C23—3022no—
150C23—3022no—
151C23—3022no—
152C23—6044no—
153C23D4×D15112yes—
154C23D4×D15111yescharacteristic
155C23C2×D60411yescharacteristic
156C23C2×D60412yes—
157C23#1455900511yescharacteristic
158D4—6042no—
159D4—6042no—
160D4—6042no—
161D4—6042no—
162D4—12082no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—3024no—
168C2×C4—3022no—
169C2×C4—3022no—
170C2×C4—3022no—
171C2×C4—3022no—
172C2×C4—6041no—
173C2×C4—6042no—
174C2×C4—6041no—
175C2×C4—6042no—
176C2×C4—6041no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—6044no—
183C22—6042no—
184C22—6044no—
185C22—12082no—
186C22#1801270912yes—
187C22#1801270911yescharacteristic
188C22#1801271411yescharacteristic
189C22#1801271412yes—
190C22#1801273611yescharacteristic
191C4—44no—
192C4—42no—
193C4—6042no—
194C4—6042no—
195C4—12081no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—12082no—
201C2#2375212211yescharacteristic
202C2#2375240312yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC24×C151C23
FrattiniC24C22×D151
Fitting#342×C151C2
socleC22×C151#120
prime radical#23752774C2
hypercenter#342D151
hypocenterC151#2022
LCSG ▷ C24×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#18012723C2semidirect
3. C2×#18012653C2semidirect
4. #23752073C2semidirect
5. #342×C151C2semidirect
34. C22×Dic151D4semidirect
45. C22⋊C4×C151D4semidirect
101. C151#2022semidirect
107. #342D151semidirect
147. C22⋊C4D604semidirect

Maximal subgroups

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

subgroupindex
#237527742
C2×#180127232
C2×#180126532
#237520732
#342×C1512
#2022151