Finite Group Databasebeta

← #34070804

Subgroups — #34070804

Order 19328.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#23752783C211yesmaximal, characteristic
2#23752196C211yesmaximal, characteristic
3#23752010C214yesmaximal, complemented
4#413×C151C211yesmaximal, characteristic
5C22×Dic302C411yescharacteristic
6C2×#14558988—21no—
7#18012737C2212yes—
8#18012726C412yes—
9#18012720—21no—
10#18012720—21no—
11#18012718—21no—
12#18012718—21no—
13#18012698C411yescharacteristic
14#18012658C2212yes—
15#18012656—21no—
16C2×#41×C151C2211yescharacteristic
17C2×M16×C151—21no—
18#101×C151C2212yes—
19#100×C151—21no—
20C2×Dic302—21no—
21C2×Dic302—41no—
22C2×Dic302—41no—
23C2×Dic302C2×C412yes—
24C22×Dic151—21no—
25#14558988—22no—
26#14558988—41no—
27C2×C151⋊C8—41no—
28C4⋊Dic151—21no—
29Dic151⋊C4—22no—
30Dic151⋊C4—22no—
31C22⋊Dic151—21no—
32C22⋊Dic151—22no—
33C22⋊Dic151—22no—
34C4×Dic151C2×C412yes—
35#41×C151—41no—
36#41×C151—41no—
37C2×Q8×C151C2311yescharacteristic
38C2×D4×C151C2×C411yescharacteristic
39C2×D4×C151D411yescharacteristic
40C2×D4×C151D411yescharacteristic
41C22×C4×C151C2×C411yescharacteristic
42C22×C4×C151D411yescharacteristic
43C22×C4×C151D411yescharacteristic
44M16×C151—22no—
45M16×C151—41no—
46C2×C8×C151—41no—
47Dic302—41no—
48Dic302—41no—
49Dic302—42no—
50C2×Dic151—22no—
51C2×Dic151—22no—
52C2×Dic151—42no—
53C151⋊C8—42no—
54C23×C151C22⋊C411yescharacteristic
55C23×C151C22⋊C411yescharacteristic
56C23×C151C22⋊C411yescharacteristic
57Q8×C151—41no—
58D4×C151—41no—
59D4×C151—41no—
60D4×C151—41no—
61C2×C4×C151—21no—
62C2×C4×C151—21no—
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151C22⋊C411yescharacteristic
68C2×C4×C151C22×C411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×D411yescharacteristic
71C8×C151—42no—
72C22×C151—21no—
73C22×C151—21no—
74C22×C151—21no—
75C22×C151—41no—
76C22×C151—41no—
77C22×C151—41no—
78C22×C151C2×C22⋊C411yescharacteristic
79C4×C151—21no—
80C4×C151—21no—
81C4×C151—21no—
82C4×C151#9911yescharacteristic
83C4×C151#9911yescharacteristic
84Dic151—42no—
85Dic151—42no—
86C2×C151—21no—
87C2×C151—41no—
88C2×C151—41no—
89C2×C151—41no—
90C2×C151C2×#9911yescharacteristic
91C151#213511yescharacteristic, complemented, Sylow
92#2135—1511nomaximal, Sylow
93#536—1511no—
94#413—1511no—
95#413D15111yescharacteristic
96#356—1514no—
97C2×#41C2×D15111yescharacteristic
98C22×Q8—1511no—
99C2×M16—21no—
100C2×M16—3021no—
101C4⋊Q8—1512no—
102#124—1512no—
103#123—3021no—
104#123—3021no—
105C22⋊Q8—3021no—
106C22⋊Q8—3021no—
107#117—1511no—
108#101—1512no—
109#101C2×D15112yes—
110#100—21no—
111#100—3021no—
112#41—41no—
113#41—41no—
114C2×Q8—3021no—
115C2×Q8—6041no—
116C2×Q8—6041no—
117C2×Q8—1512no—
118C2×Q8C22×D15111yescharacteristic
119C2×D4C4×D15111yescharacteristic
120C2×D4C22⋊D15111yescharacteristic
121C2×D4D60411yescharacteristic
122C22×C4—3021no—
123C22×C4C4×D15111yescharacteristic
124C22×C4C22⋊D15111yescharacteristic
125C22×C4D60411yescharacteristic
126M16—22no—
127M16—41no—
128M16—3022no—
129M16—6041no—
130C2×C8—41no—
131C2×C8—6041no—
132C4⋊C4—3021no—
133C4⋊C4—3022no—
134C4⋊C4—3022no—
135C22⋊C4—3021no—
136C22⋊C4—3022no—
137C22⋊C4—3022no—
138C42—1512no—
139C23(C2×D151)⋊C411yescharacteristic
140C23(C2×D151)⋊C411yescharacteristic
141C23(C2×D151)⋊C411yescharacteristic
142Q8—41no—
143Q8—6042no—
144Q8—6041no—
145Q8—6041no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—3022no—
156C2×C4—3022no—
157C2×C4—6042no—
158C2×C4(C2×D151)⋊C411yescharacteristic
159C2×C4C2×C4×D15111yescharacteristic
160C2×C4C2×C22⋊D15111yescharacteristic
161C2×C4C2×D60411yescharacteristic
162C8—42no—
163C8—6042no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D151)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—6042no—
175C4—6042no—
176C4#1801265311yescharacteristic
177C4#1801265311yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1801265311yescharacteristic
subgroupG/H
centerC2C2×#18012653
commutatorC2×C4×C151C22×C4
FrattiniC2×Q8C22×D151
Fitting#413×C151C2
socleC2×C151C2×#99
prime radicalC2×#41×C151C22
cosocleC2×Q8×C151C23
hypercenter#413D151
hypocenterC151#2135
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #23752010C2semidirect
91. C151#2135semidirect

Maximal subgroups

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

subgroupindex
#237527832
#237521962
#237520102
#413×C1512
#2135151