Finite Group Databasebeta

← #34069500

Subgroups — #34069500

Order 19328.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#18012737C211yesmaximal, characteristic
2#23752689C211yesmaximal, characteristic
3#23752221C211yesmaximal, characteristic
4C2×#18012657C211yesmaximal, characteristic
5#23751973C211yesmaximal, characteristic
6#23751971C211yesmaximal, characteristic
7#419×C151C211yesmaximal, characteristic
8C22×Dic302C2211yescharacteristic
9C2×#14558988C2211yescharacteristic
10#18012737—22no—
11#18012737C414yescomplemented
12C4×Dic302—22no—
13#18012704—22no—
14#18012698C2211yescharacteristic
15#18012695—22no—
16C2×Dic151⋊C4—22no—
17C2×C4×Dic151C2211yescharacteristic
18#18012663—22no—
19#18012657—22no—
20C22×Q8×C151C2211yescharacteristic
21C2×M16×C151C2211yescharacteristic
22#117×C151C2211yescharacteristic
23#103×C151—22no—
24C2×Dic302—21no—
25C2×Dic302—21no—
26C2×Dic302—21no—
27C2×Dic302—21no—
28C2×Dic302C2×C412yes—
29C2×Dic302D412yes—
30C22×Dic151—21no—
31C22×Dic151D412yes—
32#14558988—21no—
33#14558988—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151D412yes—
36Dic151⋊C4—24no—
37Dic151⋊C4—28no—
38C22⋊Dic151—21no—
39C4×Dic151—24no—
40C4×Dic151—21no—
41C4×Dic151—21no—
42C4×Dic151C2×C412yes—
43C2×Q8×C151—21no—
44C2×Q8×C151—21no—
45C2×Q8×C151—21no—
46C2×Q8×C151—21no—
47C2×Q8×C151—21no—
48C2×Q8×C151C2×C412yes—
49C22×C4×C151—21no—
50C22×C4×C151C2311yescharacteristic
51M16×C151—21no—
52M16×C151—21no—
53C2×C8×C151—21no—
54C4⋊C4×C151D412yes—
55C22⋊C4×C151—21no—
56C42×C151—21no—
57Dic302—22no—
58Dic302—22no—
59Dic302—22no—
60Dic302—22no—
61C2×Dic151—24no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C2×Dic151C22⋊C414yes—
67C151⋊C8—41no—
68C23×C151C2×D411yescharacteristic
69Q8×C151—22no—
70Q8×C151—22no—
71Q8×C151—41no—
72Q8×C151—41no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—41no—
76C2×C4×C151—41no—
77C2×C4×C151C22×C411yescharacteristic
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151#4111yescharacteristic
82C2×C4×C151#4111yescharacteristic
83C8×C151—41no—
84C22×C151—22no—
85C22×C151C2×C22⋊C411yescharacteristic
86C22×C151#12011yescharacteristic
87C22×C151#12311yescharacteristic
88C4×C151—42no—
89C4×C151—42no—
90C4×C151C4×D411yescharacteristic
91C4×C151C4×D411yescharacteristic
92C4×C151#12111yescharacteristic
93C4×C151#12111yescharacteristic
94Dic151—24no—
95Dic151—24no—
96Dic151—42no—
97C2×C151—21no—
98C2×C151—21no—
99C2×C151#38611yescharacteristic
100C2×C151#45612yes—
101C151#188611yescharacteristic, complemented, Sylow
102#1886—1511nomaximal, Sylow
103C2×C4⋊Q8—1511no—
104#519—1511no—
105#419—1511no—
106#419D15111yescharacteristic
107C2×#101—1511no—
108#339—1511no—
109#339—1511no—
110C22×Q8—1511no—
111C22×Q8C2×D15111yescharacteristic
112C2×M16—1511no—
113C2×M16C2×D15111yescharacteristic
114C4⋊Q8—3022no—
115C4⋊Q8—1514no—
116C4×Q8—3022no—
117C4×Q8—3022no—
118#117—3022no—
119#117—1511no—
120#117C2×D15111yescharacteristic
121C2×C4⋊C4—3022no—
122C2×C42—1511no—
123#103—22no—
124#103—3022no—
125#101—3022no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—3021no—
132C2×Q8—3021no—
133C2×Q8—3021no—
134C2×Q8—3021no—
135C2×Q8—1512no—
136C2×Q8—1512no—
137C2×Q8C4×D15112yes—
138C22×C4—21no—
139C22×C4—3021no—
140C22×C4—1512no—
141C22×C4C22×D15111yescharacteristic
142M16—21no—
143M16—21no—
144M16—3021no—
145M16—3021no—
146C2×C8—21no—
147C2×C8—3021no—
148C4⋊C4—3024no—
149C4⋊C4—3028no—
150C4⋊C4—1512no—
151C4⋊C4C22⋊D15112yes—
152C22⋊C4—21no—
153C22⋊C4—3021no—
154C42—21no—
155C42—3024no—
156C42—3021no—
157C42—3021no—
158C42—1512no—
159C23D4×D15111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—3022no—
165Q8—3022no—
166Q8—3022no—
167Q8—3022no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3024no—
173C2×C4—3022no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—3022no—
177C2×C4—1514no—
178C2×C4C2×C4×D15111yescharacteristic
179C2×C4D4×D15111yescharacteristic
180C2×C4D4×D15111yescharacteristic
181C2×C4C2×C22⋊D15111yescharacteristic
182C2×C4#1455900311yescharacteristic
183C2×C4#1455900411yescharacteristic
184C8—41no—
185C8—6041no—
186C22—22no—
187C22C22⋊C4×D15111yescharacteristic
188C22#1801270711yescharacteristic
189C22#1801272111yescharacteristic
190C4—42no—
191C4—42no—
192C4—3024no—
193C4—3024no—
194C4—6042no—
195C4(C22⋊D151)⋊C411yescharacteristic
196C4C4×C22⋊D15111yescharacteristic
197C4#1801271011yescharacteristic
198C4#1801271211yescharacteristic
199C2—21no—
200C2—21no—
201C2#2375208811yescharacteristic
202C2#2375239312yes—
subgroupG/H
centerC22#18012707
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#419×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
cosocleC22×C4×C151C23
hypercenter#419D151
hypocenterC151#1886
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #18012737C4semidirect
101. C151#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#180127372
#237526892
#237522212
C2×#180126572
#237519732
#237519712
#419×C1512
#1886151