Finite Group Databasebeta

← #34070774

Subgroups — #34070774

Order 19328.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752761C211yesmaximal, characteristic
2#23752184C212yesmaximal, complemented
3#23752007C211yesmaximal, characteristic, complemented
4#23752004C212yesmaximal, complemented
5#354×C151C211yesmaximal, characteristic, complemented
6C2×#14559005C411yescharacteristic, complemented
7C2×#14559003C2211yescharacteristic
8#18012737C411yescharacteristic, complemented
9#18012735C2211yescharacteristic
10#18012727C411yescharacteristic, complemented
11#18012712—22no—
12(C22⋊D151)⋊C4—22no—
13#18012695—22no—
14C42×D151C411yescharacteristic, complemented
15#18012654C2212yes—
16#18012653—22no—
17#124×C151C2211yescharacteristic
18#99×C151C2212yes—
19#14559005—41no—
20#14559005—41no—
21#14559003—41no—
22#14559003—41no—
23C2×Dic302C2×C411yescharacteristic
24C2×D604—21no—
25C2×D604C2×C411yescharacteristic
26C2×C22⋊D151—22no—
27C2×C22⋊D151D412yes—
28C22×Dic151D412yes—
29C2×C4×D151—21no—
30C2×C4×D151—21no—
31C2×C4×D151C2×C411yescharacteristic
32Dic151⋊C4—22no—
33Dic151⋊C4—42no—
34C22⋊Dic151—22no—
35(C2×D151)⋊C4—22no—
36C4×Dic151—21no—
37C4×Dic151—42no—
38C4×Dic151C2×C411yescharacteristic
39C2×Q8×C151C2×C411yescharacteristic
40C2×D4×C151C2311yescharacteristic
41C22⋊C4×C151—22no—
42C22⋊C4×C151—22no—
43C42×C151C2×C411yescharacteristic
44C22×D151—21no—
45C22×D151C22⋊C411yescharacteristic
46Dic302—41no—
47D604—41no—
48D604—42no—
49C22⋊D151—42no—
50C22⋊D151—44no—
51C2×Dic151—21no—
52C2×Dic151—22no—
53C2×Dic151—22no—
54C2×Dic151—42no—
55C2×Dic151C22⋊C412yes—
56C2×Dic151C22⋊C411yescharacteristic
57C4×D151—21no—
58C4×D151—21no—
59C4×D151—42no—
60C4×D151—41no—
61C4×D151—41no—
62C23×C151C2×D412yes—
63Q8×C151—41no—
64D4×C151—41no—
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—42no—
68C2×C4×C151C22×C411yescharacteristic
69C22×C151—22no—
70C22×C151—42no—
71C22×C151C2×C22⋊C411yescharacteristic
72C2×D151—21no—
73C2×D151—41no—
74C2×D151—42no—
75C2×D151—41no—
76C4×C151—21no—
77C4×C151—41no—
78C4×C151—41no—
79C4×C151—82no—
80Dic151—22no—
81Dic151—22no—
82Dic151—82no—
83Dic151#9911yescharacteristic
84Dic151#9911yescharacteristic
85C2×C151—21no—
86C2×C151—42no—
87C2×C151C2×#9911yescharacteristic
88D151—41no—
89D151—81no—
90C151#212611yescharacteristic, complemented, Sylow
91#2126—1511nomaximal, Sylow
92#532—1511no—
93#410—1512no—
94#354—1511no—
95#354D15111yescharacteristic, complemented
96#353—1512no—
97C2×#41—1511no—
98C2×#41—1511no—
99C4⋊Q8—1511no—
100#127—1511no—
101#124—1511no—
102#124C2×D15111yescharacteristic
103#121—3022no—
104C4×D4—3022no—
105#117—3022no—
106C2×C42—1511no—
107#99—3022no—
108#99—1512no—
109#99C2×D15112yes—
110#41—6041no—
111#41—6041no—
112#41—6041no—
113#41—6041no—
114C2×Q8—1511no—
115C2×Q8C4×D15111yescharacteristic
116C2×D4—3021no—
117C2×D4—3022no—
118C2×D4—1512no—
119C2×D4—1511no—
120C2×D4C22×D15111yescharacteristic
121C22×C4—3021no—
122C22×C4—3021no—
123C22×C4—1512no—
124C22×C4—1511no—
125C4⋊C4—3022no—
126C4⋊C4—6042no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—3022no—
130C22⋊C4—3022no—
131C42—3021no—
132C42—6042no—
133C42—1511no—
134C42C4×D15111yescharacteristic
135C23—3021no—
136C23—1511no—
137C23D4×D15112yes—
138Q8—41no—
139Q8—6041no—
140D4—41no—
141D4—6041no—
142D4—6042no—
143D4—6042no—
144D4—6044no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—3021no—
149C2×C4—3021no—
150C2×C4—3021no—
151C2×C4—3022no—
152C2×C4—3022no—
153C2×C4—6042no—
154C2×C4—6041no—
155C2×C4—6041no—
156C2×C4—6042no—
157C2×C4—1512no—
158C2×C4—1511no—
159C2×C4C2×C4×D15111yescharacteristic
160C22—22no—
161C22—42no—
162C22—3021no—
163C22—6041no—
164C22—6042no—
165C22—6041no—
166C22C22⋊C4×D15111yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—3022no—
172C4—3022no—
173C4—1511no—
174C4—1511no—
175C4—12082no—
176C2—21no—
177C2—42no—
178C2—6041no—
179C2—12081no—
180C2#99×D15111yescharacteristic
subgroupG/H
centerC2#99×D151
commutatorC2×C4×C151C22×C4
FrattiniC2×D4C22×D151
Fitting#354×C151C2
socleC2×C151C2×#99
prime radical#23752761C2
cosocleC2×D4×C151C23
hypercenter#354D151
hypocenterC151#2126
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #23752184C2semidirect
3. #23752007C2semidirect
4. #23752004C2semidirect
5. #354×C151C2semidirect
6. C2×#14559005C4semidirect
8. #18012737C4semidirect
10. #18012727C4semidirect
14. C42×D151C4semidirect
90. C151#2126semidirect
95. #354D151semidirect

Maximal subgroups

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

subgroupindex
#237527612
#237521842
#237520072
#237520042
#354×C1512
#2126151