Finite Group Databasebeta

← #34068272

Subgroups — #34068272

Order 19328.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752877C211yesmaximal, characteristic
2#23752504C211yesmaximal, characteristic, complemented
3#23752499C211yesmaximal, characteristic
4#23751958C211yesmaximal, characteristic, complemented
5#23751944C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic
7#487×C151C211yesmaximal, characteristic, complemented
8C2×Q8×D151—21no—
9#18012738—21no—
10#18012717—22no—
11#18012715—21no—
12C4×Dic302C2211yescharacteristic
13C4×D604C2211yescharacteristic
14#18012701—21no—
15#18012672—21no—
16#18012670—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012662—21no—
20#18012659—21no—
21C4⋊Q8×C151C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23#103×C151—22no—
24C4×C8×C151C2211yescharacteristic
25C2×Dic302—22no—
26C2×Dic302D411yescharacteristic
27Q8×D151—42no—
28Q8×D151—42no—
29C2×D604D411yescharacteristic
30C2×C4×D151—22no—
31C2×C4×D151—21no—
32C2×C151⋊C8—21no—
33C2×C151⋊C8—21no—
34C4⋊Dic151D411yescharacteristic
35C4⋊Dic151D411yescharacteristic
36Dic151⋊C4—22no—
37Dic151⋊C4—21no—
38(C2×D151)⋊C4—22no—
39(C2×D151)⋊C4—21no—
40C4×Dic151—21no—
41C2×Q8×C151—21no—
42C2×Q8×C151—21no—
43C2×C8×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D412yes—
48C42×C151C2311yescharacteristic
49C22×D151—21no—
50Dic302—21no—
51Dic302—44no—
52Dic302SD1612yes—
53D604—21no—
54D604Q1612yes—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C4×D151—44no—
59C4×D151—41no—
60C4×D151—41no—
61C151⋊C8—41no—
62C151⋊C8—41no—
63Q8×C151—42no—
64Q8×C151—41no—
65Q8×C151—41no—
66C2×C4×C151—22no—
67C2×C4×C151—41no—
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×D411yescharacteristic
71C8×C151—41no—
72C22×C151#12011yescharacteristic
73C2×D151—22no—
74C2×D151—41no—
75C2×D151—41no—
76C4×C151—21no—
77C4×C151—42no—
78C4×C151—81no—
79C4×C151C2×SD1611yescharacteristic
80C4×C151C2×Q1611yescharacteristic
81C4×C151AGL(1,ℤ/8)11yescharacteristic
82C4×C151#13711yescharacteristic
83Dic151—22no—
84Dic151—41no—
85Dic151—41no—
86C2×C151#45011yescharacteristic
87C2×C151#45111yescharacteristic
88C2×C151#45411yescharacteristic
89D151—42no—
90C151#163711yescharacteristic, complemented, Sylow
91#1637—1511nomaximal, Sylow
92D4×Q8—1511no—
93#487D15111yescharacteristic, complemented
94#477—1511no—
95#476—1511no—
96#332—1511no—
97Q8⋊C8—1511no—
98D4⋊C8—1511no—
99C22×Q8—3021no—
100C4⋊Q8—3021no—
101C4⋊Q8C2×D15111yescharacteristic
102C4⋊Q8C2×D15111yescharacteristic
103C22⋊Q8—3021no—
104C22⋊Q8—3022no—
105C4×Q8—1511no—
106C4×D4—3021no—
107C4×D4—1511no—
108#107—3021no—
109#106—3021no—
110C4⋊C8—1511no—
111C4⋊C8—1511no—
112#103—22no—
113#103—3021no—
114#102—3021no—
115C4×C8C2×D15111yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—3022no—
119C2×Q8—6042no—
120C2×Q8—6042no—
121C2×Q8—1511no—
122C2×D4—1511no—
123C22×C4—3022no—
124C22×C4—3021no—
125C2×C8—21no—
126C2×C8—3021no—
127C2×C8—3021no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—3022no—
132C4⋊C4—3021no—
133C4⋊C4—1511no—
134C4⋊C4—1511no—
135C4⋊C4C22⋊D15112yes—
136C22⋊C4—3022no—
137C22⋊C4—3021no—
138C42—3021no—
139C42C22×D15111yescharacteristic
140C23—3021no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—3021no—
145Q8—6044no—
146Q8—1512no—
147D4—3021no—
148D4—1512no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—3021no—
152C2×C4—3021no—
153C2×C4—3021no—
154C2×C4—6044no—
155C2×C4—6041no—
156C2×C4—6041no—
157C2×C4D4×D15111yescharacteristic
158C2×C4D4×D15111yescharacteristic
159C2×C4C2×C22⋊D15111yescharacteristic
160C8—41no—
161C8—6041no—
162C8—6041no—
163C22—3022no—
164C22—6041no—
165C22—6041no—
166C22#1801270711yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—3022no—
171C4—6041no—
172C4—6041no—
173C4SD16×D15111yescharacteristic
174C4Q16×D15111yescharacteristic
175C4#1801276611yescharacteristic
176C4#1801277111yescharacteristic
177C2—6042no—
178C2#2375236111yescharacteristic
179C2#2375236611yescharacteristic
180C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#487×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#487D151
hypocenterC151#1637
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #23752504C2semidirect
4. #23751958C2semidirect
5. #23751944C2semidirect
7. #487×C151C2semidirect
90. C151#1637semidirect
93. #487D151semidirect

Maximal subgroups

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

subgroupindex
#237528772
#237525042
#237524992
#237519582
#237519442
#237519412
#487×C1512
#1637151