Finite Group Databasebeta

← #34068258

Subgroups — #34068258

Order 19328.

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

normal subgroups only

This group has 234 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#23752865C211yesmaximal, characteristic
2#23752499C211yesmaximal, characteristic, complemented
3#23752499C211yesmaximal, characteristic, complemented
4#23751958C211yesmaximal, characteristic, complemented
5#23751941C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7#487×C151C211yesmaximal, characteristic, complemented
8C2×#14559005—21no—
9#18012724—22no—
10#18012715—21no—
11#18012714—21no—
12C4×D604C2211yescharacteristic
13C4×D604C2211yescharacteristic
14C4⋊C4×D151—21no—
15#18012670—21no—
16#18012670—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012659—21no—
20#18012659—21no—
21C4⋊Q8×C151C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23#103×C151—22no—
24C4×C8×C151C2211yescharacteristic
25#14559005—42no—
26#14559005—42no—
27C2×D604—22no—
28C2×D604D411yescharacteristic
29C2×D604D411yescharacteristic
30C2×C4×D151—22no—
31C2×C4×D151—21no—
32C2×C4×D151—21no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151D411yescharacteristic
36C4⋊Dic151D411yescharacteristic
37Dic151⋊C4—22no—
38(C2×D151)⋊C4—22no—
39(C2×D151)⋊C4—21no—
40(C2×D151)⋊C4—21no—
41C2×Q8×C151—21no—
42C2×Q8×C151—21no—
43C2×C8×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D412yes—
48C42×C151C2311yescharacteristic
49C22×D151—21no—
50C22×D151—21no—
51D604—21no—
52D604—21no—
53D604—21no—
54D604—44no—
55D604SD1612yes—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C4×D151—44no—
59C4×D151—41no—
60C4×D151—41no—
61C4×D151—41no—
62C4×D151—41no—
63C151⋊C8—41no—
64C151⋊C8—41no—
65Q8×C151—42no—
66Q8×C151—41no—
67Q8×C151—41no—
68C2×C4×C151—22no—
69C2×C4×C151—41no—
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C8×C151—41no—
74C22×C151#12011yescharacteristic
75C2×D151—22no—
76C2×D151—41no—
77C2×D151—41no—
78C2×D151—41no—
79C2×D151—41no—
80C2×D151—41no—
81C4×C151—21no—
82C4×C151—42no—
83C4×C151—81no—
84C4×C151C2×SD1611yescharacteristic
85C4×C151#13511yescharacteristic
86C4×C151AGL(1,ℤ/8)11yescharacteristic
87C4×C151#13711yescharacteristic
88Dic151—41no—
89Dic151—41no—
90C2×C151#45011yescharacteristic
91C2×C151#45211yescharacteristic
92C2×C151#45411yescharacteristic
93D151—42no—
94D151—81no—
95C151#163511yescharacteristic, complemented, Sylow
96#1635—1511nomaximal, Sylow
97#547—1511no—
98#487D15111yescharacteristic, complemented
99#476—1511no—
100#476—1511no—
101#332—1511no—
102D4⋊C8—1511no—
103D4⋊C8—1511no—
104C2×#41—3021no—
105C4⋊Q8C2×D15111yescharacteristic
106C4⋊Q8C2×D15111yescharacteristic
107#123—3022no—
108C22⋊Q8—3021no—
109#121—3021no—
110C4×D4—1511no—
111C4×D4—1511no—
112C2×C4⋊C4—3021no—
113#106—3021no—
114#106—3021no—
115C4⋊C8—1511no—
116C4⋊C8—1511no—
117#103—22no—
118#102—3021no—
119#102—3021no—
120C4×C8C2×D15111yescharacteristic
121#41—6042no—
122#41—6042no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—3022no—
126C2×D4—1511no—
127C2×D4—1511no—
128C22×C4—3022no—
129C22×C4—3021no—
130C22×C4—3021no—
131C2×C8—21no—
132C2×C8—3021no—
133C2×C8—3021no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—3022no—
138C4⋊C4—1511no—
139C4⋊C4—1511no—
140C4⋊C4C22⋊D15112yes—
141C22⋊C4—3022no—
142C22⋊C4—3021no—
143C22⋊C4—3021no—
144C42C22×D15111yescharacteristic
145C23—3021no—
146C23—3021no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—3021no—
151D4—3021no—
152D4—3021no—
153D4—6044no—
154D4—1512no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—3021no—
158C2×C4—3021no—
159C2×C4—6044no—
160C2×C4—6041no—
161C2×C4—6041no—
162C2×C4—6041no—
163C2×C4—6041no—
164C2×C4D4×D15111yescharacteristic
165C2×C4D4×D15111yescharacteristic
166C2×C4C2×C22⋊D15111yescharacteristic
167C8—41no—
168C8—6041no—
169C8—6041no—
170C22—3022no—
171C22—6041no—
172C22—6041no—
173C22—6041no—
174C22—6041no—
175C22—6041no—
176C22#1801270711yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—6041no—
181C4—6041no—
182C4SD16×D15111yescharacteristic
183C4#1801276211yescharacteristic
184C4#1801276611yescharacteristic
185C4#1801277111yescharacteristic
186C2—6042no—
187C2—12081no—
188C2#2375236111yescharacteristic
189C2#2375237311yescharacteristic
190C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#487×C151C2
socleC22×C151#120
prime radical#23752865C2
hypercenter#487D151
hypocenterC151#1635
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #23752499C2semidirect
3. #23752499C2semidirect
4. #23751958C2semidirect
5. #23751941C2semidirect
6. #23751941C2semidirect
7. #487×C151C2semidirect
95. C151#1635semidirect
98. #487D151semidirect

Maximal subgroups

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

subgroupindex
#237528652
#237524992
#237519582
#237519412
#487×C1512
#1635151