Finite Group Databasebeta

← #34070156

Subgroups — #34070156

Order 19328.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#18012770C212yesmaximal, complemented
2#23752793C211yesmaximal, characteristic
3C2×#18012667C212yesmaximal, complemented
4#23751981C211yesmaximal, characteristic, complemented
5#391×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7#18012770—24no—
8#18012770—24no—
9C2×#14558994—22no—
10C2×#14558991—22no—
11C2×#14558988C2212yes—
12#18012719—22no—
13#18012714—22no—
14#18012713—22no—
15#18012667—24no—
16C22×Q8×C151C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C2×C42×C151C2211yescharacteristic
19#95×C151—22no—
20#14559004—22no—
21#14559004—22no—
22#14559004—22no—
23#14559004—22no—
24C2×Dic302D412yes—
25C2×D604—22no—
26C2×D604D412yes—
27C2×C22⋊D151—22no—
28C2×C4×D151—22no—
29#14558994—28no—
30#14558991—28no—
31#14558988—22no—
32#14558988D414yescomplemented
33C2×C151⋊C8—22no—
34C4⋊Dic151—22no—
35(C2×D151)⋊C4—24no—
36C2×Q8×C151—21no—
37C2×Q8×C151—22no—
38C2×Q8×C151—22no—
39C2×Q8×C151D412yescomplemented
40C22×C4×C151—21no—
41C22×C4×C151—21no—
42C22×C4×C151D412yes—
43C22×C4×C151C2311yescharacteristic
44C4⋊C4×C151—22no—
45C42×C151—22no—
46C22×D151—22no—
47Dic302—22no—
48Dic302—22no—
49D604—22no—
50D604—22no—
51D604—82no—
52C22⋊D151—42no—
53C22⋊D151—42no—
54C2×Dic151—22no—
55C4×D151—42no—
56C4×D151—42no—
57C151⋊C8—24no—
58C23×C151C2×D411yescharacteristic
59Q8×C151—24no—
60Q8×C151—42no—
61C2×C4×C151—22no—
62C2×C4×C151—22no—
63C2×C4×C151—22no—
64C2×C4×C151—41no—
65C2×C4×C151—41no—
66C2×C4×C151—41no—
67C2×C4×C151—41no—
68C2×C4×C151—42no—
69C2×C4×C151C2×D412yes—
70C2×C4×C151C2×D412yes—
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151#4111yescharacteristic
73C22×C151—21no—
74C22×C151—21no—
75C22×C151#12011yescharacteristic
76C22×C151#12111yescharacteristic
77C22×C151#12711yescharacteristic
78C2×D151—42no—
79C2×D151—42no—
80C2×D151—42no—
81C4×C151—42no—
82C4×C151—42no—
83C4×C151—42no—
84C4×C151#12012yes—
85C4×C151#12112yes—
86Dic151—42no—
87C2×C151—21no—
88C2×C151—21no—
89C2×C151#39211yescharacteristic
90C2×C151#45511yescharacteristic
91C2×C151#45611yescharacteristic
92D151—82no—
93C151#200711yescharacteristic, complemented, Sylow
94#2007—1511nomaximal, Sylow
95C2×#137—1512no—
96#537—1511no—
97C2×#104—1512no—
98#391D15111yescharacteristic, complemented
99#343—1511no—
100C2×#41—1512no—
101C22×Q8C2×D15111yescharacteristic
102#137—3024no—
103#137—3024no—
104C2×Q16—3022no—
105C2×SD16—3022no—
106C2×M16—1512no—
107C22⋊Q8—3022no—
108#121—3022no—
109#121—3022no—
110C2×C4⋊C4C2×D15111yescharacteristic
111C2×C42C2×D15111yescharacteristic
112#104—3024no—
113#95—22no—
114#41—3022no—
115#41—3022no—
116#41—3022no—
117#41—3022no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—1512no—
122C2×Q8D60412yescomplemented
123C2×D4—3022no—
124C2×D4—3022no—
125C2×D4—1512no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—3022no—
129C22×C4C22⋊D15112yes—
130C22×C4C22×D15111yescharacteristic
131Q16—3028no—
132SD16—3028no—
133M16—3022no—
134M16—1514no—
135C2×C8—3022no—
136C4⋊C4—22no—
137C4⋊C4—3022no—
138C22⋊C4—3024no—
139C42—22no—
140C23—3022no—
141C23C2×C22⋊D15111yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—3022no—
145Q8—3022no—
146D4—3022no—
147D4—3022no—
148D4—6042no—
149D4—6042no—
150D4—12082no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—3022no—
160C2×C4—6042no—
161C2×C4—6042no—
162C2×C4D4×D15112yes—
163C2×C4D4×D15112yes—
164C2×C4C2×D60411yescharacteristic
165C2×C4#1455900411yescharacteristic
166C8—3024no—
167C22—21no—
168C22—21no—
169C22—6042no—
170C22—6042no—
171C22—6042no—
172C22#1801270711yescharacteristic
173C22#1801271311yescharacteristic
174C22#1801273511yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—6042no—
179C4#1801270912yes—
180C4#1801271212yes—
181C2—21no—
182C2—21no—
183C2—12082no—
184C2#2375212111yescharacteristic
185C2#2375238911yescharacteristic
186C2#2375239411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#391×C151C2
socleC22×C151#120
prime radical#23752793C2
hypercenter#391D151
hypocenterC151#2007
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#18012770C2semidirect
3. C2×#18012667C2semidirect
4. #23751981C2semidirect
5. #391×C151C2semidirect
32. #14558988D4semidirect
39. C2×Q8×C151D4semidirect
93. C151#2007semidirect
98. #391D151semidirect
122. C2×Q8D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127702
#237527932
C2×#180126672
#237519812
#391×C1512
#2007151