Finite Group Databasebeta

← #34070174

Subgroups — #34070174

Order 19328.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#23752719C212yesmaximal, complemented
2#23752229C212yesmaximal, complemented
3#23752175C211yesmaximal, characteristic, complemented
4#23751969C211yesmaximal, characteristic, complemented
5#575×C151C211yesmaximal, characteristic, complemented
6C22×C4×D151C2211yescharacteristic
7C2×#14558988C2211yescharacteristic
8#18012720—22no—
9#18012715—22no—
10#18012710—22no—
11#18012707—22no—
12C4×C22⋊D151—24no—
13#18012698C2212yes—
14#18012666—24no—
15(C2×D151)⋊C8—22no—
16C2×#41×C151C2212yes—
17#137×C151—22no—
18AGL(1,ℤ/8)×C151—22no—
19#135×C151—22no—
20C2×M16×C151C2211yescharacteristic
21C23×D151D411yescharacteristic
22C2×C22⋊D151—24no—
23C22×Dic151D411yescharacteristic
24C2×C4×D151—22no—
25C2×C4×D151—22no—
26C2×C4×D151—21no—
27C2×C4×D151—21no—
28#14558988—22no—
29C2×C151⋊C8—21no—
30C4⋊Dic151—22no—
31Dic151⋊C4—24no—
32C22⋊Dic151—24no—
33C22⋊Dic151—22no—
34(C2×D151)⋊C4—24no—
35C4×Dic151D414yescomplemented
36#41×C151—22no—
37#41×C151—22no—
38#41×C151—22no—
39#41×C151—22no—
40C2×Q8×C151D412yescomplemented
41C2×D4×C151—22no—
42C2×D4×C151D412yescomplemented
43C22×C4×C151—22no—
44C22×C4×C151C2311yescharacteristic
45Q16×C151—22no—
46SD16×C151—24no—
47D8×C151—22no—
48M16×C151—22no—
49C2×C8×C151D412yescomplemented
50C22×D151—22no—
51C22×D151—21no—
52C22×D151—42no—
53C22⋊D151—48no—
54C2×Dic151—24no—
55C2×Dic151—22no—
56C2×Dic151—21no—
57C4×D151—41no—
58C4×D151—42no—
59C4×D151—41no—
60C151⋊C8—41no—
61C23×C151—22no—
62C23×C151C2×D411yescharacteristic
63Q8×C151—22no—
64Q8×C151—22no—
65D4×C151—22no—
66D4×C151—22no—
67D4×C151—42no—
68D4×C151—42no—
69C2×C4×C151—22no—
70C2×C4×C151—42no—
71C2×C4×C151—42no—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151#4111yescharacteristic
76C8×C151—22no—
77C22×C151—41no—
78C22×C151—44no—
79C22×C151—42no—
80C22×C151#12012yes—
81C22×C151#12111yescharacteristic
82C2×D151—24no—
83C2×D151—22no—
84C2×D151—42no—
85C2×D151—41no—
86C2×D151—41no—
87C4×C151—42no—
88C4×C151#12011yescharacteristic
89C4×C151#12112yes—
90C4×C151#12711yescharacteristic
91Dic151—44no—
92Dic151—41no—
93C2×C151—22no—
94C2×C151—21no—
95C2×C151—82no—
96C2×C151#39211yescharacteristic
97D151—42no—
98C151#201011yescharacteristic, complemented, Sylow
99#2010—1511nomaximal, Sylow
100#575D15111yescharacteristic, complemented
101#525—1512no—
102#421—1512no—
103#407—1511no—
104H(3,ℤ/4)—1511no—
105C2×#41C2×D15112yes—
106C23×C4—1511no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1511no—
111C2×M16C2×D15111yescharacteristic
112#123—3022no—
113C22⋊Q8—3022no—
114#121—3022no—
115#120—3022no—
116C4×D4—3024no—
117#117—1512no—
118#104—3024no—
119C22⋊C8—3022no—
120C24—1511no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D15112yescomplemented
126C2×D4—22no—
127C2×D4—3024no—
128C2×D4C22⋊D15112yescomplemented
129C22×C4—22no—
130C22×C4—3022no—
131C22×C4—3021no—
132C22×C4—3022no—
133C22×C4—3021no—
134C22×C4—1511no—
135C22×C4C22×D15111yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—3022no—
141C2×C8—3021no—
142C2×C8C22⋊D15112yescomplemented
143C4⋊C4—3024no—
144C4⋊C4—3022no—
145C22⋊C4—3024no—
146C22⋊C4—3024no—
147C22⋊C4—3022no—
148C42—1514no—
149C23—22no—
150C23—3022no—
151C23—3021no—
152C23—6042no—
153C23D4×D15111yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—6048no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—3024no—
165C2×C4—3022no—
166C2×C4—3021no—
167C2×C4—6041no—
168C2×C4—6042no—
169C2×C4—6041no—
170C2×C4D4×D15112yes—
171C2×C4C2×C22⋊D15112yes—
172C2×C4C2×C22⋊D15111yescharacteristic
173C2×C4#1455900311yescharacteristic
174C8—22no—
175C8—6041no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—3024no—
180C22—3022no—
181C22—6042no—
182C22—6041no—
183C22—6041no—
184C22#1801270712yes—
185C22#1801271011yescharacteristic
186C4—42no—
187C4—6044no—
188C4—6041no—
189C4#1801270811yescharacteristic
190C4#1801271112yes—
191C4#1801273511yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—6042no—
196C2#2375212011yescharacteristic
subgroupG/H
centerC4#18012735
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#575×C151C2
socleC2×C151#392
hypercenter#575D151
hypocenterC151#2010
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23752719C2semidirect
2. #23752229C2semidirect
3. #23752175C2semidirect
4. #23751969C2semidirect
5. #575×C151C2semidirect
35. C4×Dic151D4semidirect
40. C2×Q8×C151D4semidirect
42. C2×D4×C151D4semidirect
49. C2×C8×C151D4semidirect
98. C151#2010semidirect
100. #575D151semidirect
125. C2×Q8C22⋊D151semidirect
128. C2×D4C22⋊D151semidirect
142. C2×C8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237527192
#237522292
#237521752
#237519692
#575×C1512
#2010151