Finite Group Databasebeta

← #34070159

Subgroups — #34070159

Order 19328.

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

normal subgroups only

This group has 370 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
1C2×#18012772C212yesmaximal, complemented
2#23752793C211yesmaximal, characteristic
3C2×#18012665C212yesmaximal, complemented
4#23752117C211yesmaximal, characteristic, complemented
5#343×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7C22×Dic302C2211yescharacteristic
8#18012772—24no—
9#18012772—24no—
10C2×Dic604—22no—
11C2×#14558993—22no—
12#18012719—22no—
13#18012714—22no—
14#18012713—22no—
15C2×C4×Dic151C2211yescharacteristic
16#18012665—24no—
17C151⋊#95—22no—
18C2×M16×C151C2212yes—
19C2×C4⋊C4×C151C2211yescharacteristic
20#14559004—22no—
21#14559004—22no—
22#14559004—22no—
23#14559004—22no—
24C2×Dic302—22no—
25C2×Dic302—22no—
26C2×Dic302—21no—
27C2×Dic302D412yes—
28C2×Dic302D412yescomplemented
29C2×D604—22no—
30C2×D604D412yes—
31C2×C22⋊D151—22no—
32C22×Dic151—21no—
33C22×Dic151—21no—
34C2×C4×D151—22no—
35Dic604—28no—
36#14558993—28no—
37C4⋊Dic151—22no—
38(C2×D151)⋊C4—24no—
39C4×Dic151—22no—
40C22×C4×C151D412yes—
41C22×C4×C151C2311yescharacteristic
42M16×C151—22no—
43M16×C151D414yescomplemented
44C2×C8×C151—22no—
45C4⋊C4×C151—22no—
46C22×D151—22no—
47Dic302—24no—
48Dic302—22no—
49Dic302—22no—
50Dic302—42no—
51D604—22no—
52D604—22no—
53D604—82no—
54C22⋊D151—42no—
55C22⋊D151—42no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—41no—
60C2×Dic151—41no—
61C2×Dic151—41no—
62C2×Dic151—41no—
63C4×D151—42no—
64C4×D151—42no—
65C23×C151C2×D411yescharacteristic
66C2×C4×C151—22no—
67C2×C4×C151—42no—
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D412yes—
70C2×C4×C151C2×D412yes—
71C2×C4×C151#4111yescharacteristic
72C8×C151—24no—
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#12012yes—
83C4×C151#12112yes—
84Dic151—42no—
85Dic151—42no—
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#391—1511no—
99#343D15111yescharacteristic, complemented
100C2×#41—1512no—
101C22×Q8—1511no—
102#137—3024no—
103#137—3024no—
104C2×Q16—3022no—
105C2×SD16—3022no—
106C2×M16C2×D15112yes—
107C22⋊Q8—3022no—
108#121—3022no—
109#121—3022no—
110C2×C4⋊C4C2×D15111yescharacteristic
111C2×C42—1511no—
112#104—3024no—
113#95—3022no—
114#41—3022no—
115#41—3022no—
116#41—3022no—
117#41—3022no—
118C2×Q8—3021no—
119C2×Q8—3022no—
120C2×Q8—3022no—
121C2×Q8—1512no—
122C2×Q8—1512no—
123C2×D4—3022no—
124C2×D4—3022no—
125C2×D4—1512no—
126C22×C4—3021no—
127C22×C4—3021no—
128C22×C4—3022no—
129C22×C4D60412yes—
130C22×C4C22×D15111yescharacteristic
131Q16—3028no—
132SD16—3028no—
133M16—22no—
134M16D60414yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—3022no—
138C22⋊C4—3024no—
139C42—3022no—
140C23—3022no—
141C23C2×D60411yescharacteristic
142Q8—3024no—
143Q8—3022no—
144Q8—3022no—
145Q8—6042no—
146D4—3022no—
147D4—3022no—
148D4—6042no—
149D4—6042no—
150D4—12082no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—3022no—
154C2×C4—3022no—
155C2×C4—3022no—
156C2×C4—6041no—
157C2×C4—6041no—
158C2×C4—6041no—
159C2×C4—6041no—
160C2×C4—6042no—
161C2×C4—6042no—
162C2×C4D4×D15111yescharacteristic
163C2×C4D4×D15112yes—
164C2×C4C2×D60412yes—
165C2×C4#1455900511yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—6042no—
170C22—6042no—
171C22—6042no—
172C22#1801270911yescharacteristic
173C22#1801271411yescharacteristic
174C22#1801273611yescharacteristic
175C4—42no—
176C4—6042no—
177C4—6042no—
178C4—6042no—
179C4#1801270912yes—
180C4#1801271412yes—
181C2—21no—
182C2—21no—
183C2—12082no—
184C2#2375212211yescharacteristic
185C2#2375239211yescharacteristic
186C2#2375239711yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#343×C151C2
socleC22×C151#120
prime radical#23752793C2
hypercenter#343D151
hypocenterC151#2007
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#18012772C2semidirect
3. C2×#18012665C2semidirect
4. #23752117C2semidirect
5. #343×C151C2semidirect
28. C2×Dic302D4semidirect
43. M16×C151D4semidirect
93. C151#2007semidirect
99. #343D151semidirect
134. M16D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127722
#237527932
C2×#180126652
#237521172
#343×C1512
#2007151