Finite Group Databasebeta

← #34069494

Subgroups — #34069494

Order 19328.

332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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#23752979C211yesmaximal, characteristic, complemented
2#23752229C212yesmaximal, complemented
3#23752186C211yesmaximal, characteristic, complemented
4#23751972C212yesmaximal, complemented
5#532×C151C211yesmaximal, characteristic
6#18012746—24no—
7C2×#14558988—22no—
8C2×#14558988C2212yes—
9#18012698C2212yes—
10#18012666—24no—
11#18012654—22no—
12C2×#41×C151C2211yescharacteristic
13C2×#41×C151C2211yescharacteristic
14C4⋊Q8×C151C411yescharacteristic, complemented
15#127×C151C411yescharacteristic, complemented
16#124×C151C411yescharacteristic, complemented
17#124×C151C411yescharacteristic, complemented
18#121×C151—22no—
19C4×D4×C151—22no—
20C2×C42×C151C2211yescharacteristic
21#14558988—24no—
22#14558988—22no—
23#14558988D414yescomplemented
24C2×C151⋊C8—24no—
25C2×C151⋊C8—22no—
26C4⋊Dic151—22no—
27C22⋊Dic151—22no—
28C4×Dic151—22no—
29#41×C151—22no—
30#41×C151—22no—
31#41×C151—22no—
32#41×C151—22no—
33C2×Q8×C151C2×C411yescharacteristic
34C2×Q8×C151C2×C411yescharacteristic
35C2×D4×C151—22no—
36C2×D4×C151—21no—
37C2×D4×C151C2×C411yescharacteristic
38C2×D4×C151C2×C411yescharacteristic
39C2×D4×C151D412yes—
40C22×C4×C151—21no—
41C22×C4×C151—21no—
42C22×C4×C151D412yes—
43C22×C4×C151C2311yescharacteristic
44C4⋊C4×C151—22no—
45C22⋊C4×C151—22no—
46C22⋊C4×C151—22no—
47C42×C151—21no—
48C42×C151C2×C411yescharacteristic
49C42×C151C2×C411yescharacteristic
50C2×Dic151—42no—
51C151⋊C8—24no—
52C23×C151—21no—
53C23×C151C22⋊C412yes—
54C23×C151C2×D411yescharacteristic
55Q8×C151—22no—
56Q8×C151—22no—
57D4×C151—24no—
58D4×C151—22no—
59D4×C151—22no—
60D4×C151—44no—
61D4×C151—42no—
62C2×C4×C151—21no—
63C2×C4×C151—22no—
64C2×C4×C151—22no—
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—42no—
68C2×C4×C151—41no—
69C2×C4×C151—41no—
70C2×C4×C151C22⋊C412yes—
71C2×C4×C151C22×C411yescharacteristic
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151#4112yes—
75C22×C151—22no—
76C22×C151—41no—
77C22×C151—42no—
78C22×C151—42no—
79C22×C151—41no—
80C22×C151C2×C22⋊C411yescharacteristic
81C22×C151#12112yes—
82C4×C151—22no—
83C4×C151—22no—
84C4×C151—41no—
85C4×C151—41no—
86C4×C151C4×D412yes—
87C4×C151#12011yescharacteristic
88C4×C151#12311yescharacteristic
89Dic151—82no—
90C2×C151—22no—
91C2×C151—21no—
92C2×C151—42no—
93C2×C151—81no—
94C2×C151#38611yescharacteristic
95C151#188411yescharacteristic, complemented, Sylow
96#1884—1511nomaximal, Sylow
97#568—1511no—
98#532D15111yescharacteristic
99#421—1512no—
100#410—1511no—
101#339—1512no—
102C2×#41C2×D15111yescharacteristic
103C2×#41C2×D15111yescharacteristic
104#131—3024no—
105C2×M16—3022no—
106C2×M16—1512no—
107C4⋊Q8Dic15111yescharacteristic, complemented
108#127Dic15111yescharacteristic, complemented
109#124Dic15111yescharacteristic, complemented
110#124Dic15111yescharacteristic, complemented
111#121—22no—
112C4×D4—22no—
113#117—1512no—
114C2×C42C2×D15111yescharacteristic
115#104—3024no—
116#99—3022no—
117#41—22no—
118#41—22no—
119#41—22no—
120#41—22no—
121C2×Q8C2×Dic15111yescharacteristic
122C2×Q8C2×Dic15111yescharacteristic
123C2×D4—22no—
124C2×D4—21no—
125C2×D4C2×Dic15111yescharacteristic
126C2×D4C2×Dic15111yescharacteristic
127C2×D4C22⋊D15112yes—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4C22⋊D15112yes—
131C22×C4C22×D15111yescharacteristic
132M16—3024no—
133M16—3022no—
134M16—1514no—
135C2×C8—3024no—
136C2×C8—3022no—
137C4⋊C4—22no—
138C4⋊C4—3022no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—3022no—
142C42—21no—
143C42—3022no—
144C42C2×Dic15111yescharacteristic
145C42C2×Dic15111yescharacteristic
146C23—21no—
147C23C22⋊Dic15112yes—
148C23C2×C22⋊D15111yescharacteristic
149Q8—22no—
150Q8—22no—
151D4—24no—
152D4—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—6042no—
165C2×C4C22⋊Dic15112yes—
166C2×C4C22×Dic15111yescharacteristic
167C2×C4D4×D15112yes—
168C2×C4C2×C22⋊D15111yescharacteristic
169C2×C4#1455900312yes—
170C8—3024no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic15111yescharacteristic
177C22#1801271112yes—
178C4—22no—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—12082no—
183C4D4×Dic15112yes—
184C4#1801270711yescharacteristic
185C4#1801272011yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—81no—
190C2#2375209211yescharacteristic
subgroupG/H
centerC4#18012707
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting, prime radical#532×C151C2
socleC2×C151#386
cosocleC22×C4×C151C23
hypercenter#532D151
hypocenterC151#1884
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #23752979C2semidirect
2. #23752229C2semidirect
3. #23752186C2semidirect
4. #23751972C2semidirect
14. C4⋊Q8×C151C4semidirect
15. #127×C151C4semidirect
16. #124×C151C4semidirect
17. #124×C151C4semidirect
23. #14558988D4semidirect
95. C151#1884semidirect
107. C4⋊Q8Dic151semidirect
108. #127Dic151semidirect
109. #124Dic151semidirect
110. #124Dic151semidirect

Maximal subgroups

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

subgroupindex
#237529792
#237522292
#237521862
#237519722
#532×C1512
#1884151