Finite Group Databasebeta

← #34068150

Subgroups — #34068150

Order 19328.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#23752841C211yesmaximal, characteristic
2#23752547C211yesmaximal, characteristic
3#23752150C211yesmaximal, characteristic
4#23751950C211yesmaximal, characteristic
5#23751949C211yesmaximal, characteristic
6#23751937C211yesmaximal, characteristic
7#484×C151C211yesmaximal, characteristic
8#18012738—21no—
9#18012737—21no—
10#18012729—21no—
11#18012729—21no—
12#18012718C2211yescharacteristic
13#18012716—21no—
14#18012695—21no—
15C2×Dic151⋊C4C2211yescharacteristic
16#18012672—21no—
17#18012662—21no—
18C22⋊(C151⋊C8)C2211yescharacteristic
19C151⋊#95—21no—
20C151⋊#95—21no—
21C151⋊#95C2211yescharacteristic
22C22⋊Q8×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2211yescharacteristic
24#107×C151—21no—
25#103×C151—21no—
26C22⋊C8×C151C2211yescharacteristic
27C2×Dic302—21no—
28C2×Dic302D411yescharacteristic
29C22×Dic151—21no—
30C22×Dic151D411yescharacteristic
31C22×Dic151D411yescharacteristic
32C2×C151⋊C8—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151D411yescharacteristic
35Dic151⋊C4—21no—
36Dic151⋊C4—21no—
37Dic151⋊C4—21no—
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41Dic151⋊C4—21no—
42C22⋊Dic151—21no—
43C4×Dic151—21no—
44C4×Dic151—21no—
45C2×Q8×C151D411yescharacteristic
46C22×C4×C151—21no—
47C22×C4×C151C2311yescharacteristic
48C2×C8×C151—21no—
49C4⋊C4×C151—21no—
50C4⋊C4×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151D411yescharacteristic
53C22⋊C4×C151—21no—
54Dic302—41no—
55Dic302—81no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—41no—
62C2×Dic151—41no—
63C2×Dic151—41no—
64C2×Dic151—41no—
65C2×Dic151Q1612yes—
66C151⋊C8—41no—
67C23×C151C2×D411yescharacteristic
68Q8×C151—41no—
69C2×C4×C151—21no—
70C2×C4×C151—21no—
71C2×C4×C151—41no—
72C2×C4×C151—42no—
73C2×C4×C151—41no—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151C2×D411yescharacteristic
76C8×C151—41no—
77C22×C151—21no—
78C22×C151—21no—
79C22×C151#12011yescharacteristic
80C22×C151C2×Q1611yescharacteristic
81C22×C151#13711yescharacteristic
82C4×C151—21no—
83C4×C151—21no—
84C4×C151—41no—
85C4×C151—41no—
86C4×C151—81no—
87Dic151—22no—
88Dic151—41no—
89Dic151—41no—
90Dic151—41no—
91Dic151—81no—
92C2×C151—21no—
93C2×C151—21no—
94C2×C151#45111yescharacteristic
95C2×C151#45411yescharacteristic
96C2×C151#45811yescharacteristic
97C151#161711yescharacteristic, complemented, Sylow
98#1617—1511nomaximal, Sylow
99#544—1511no—
100#484—1511no—
101#484D15111yescharacteristic
102#400—1511no—
103#328—1511no—
104#328—1511no—
105#324—1511no—
106C4⋊Q8—3021no—
107C4⋊Q8—3021no—
108#125—3021no—
109#125—3021no—
110C22⋊Q8—3021no—
111C22⋊Q8—1511no—
112C22⋊Q8C2×D15111yescharacteristic
113#117—3021no—
114C2×C4⋊C4—1511no—
115C2×C4⋊C4C2×D15111yescharacteristic
116#107—21no—
117#107—3021no—
118#103—21no—
119#103—3021no—
120C22⋊C8—1511no—
121C22⋊C8C2×D15111yescharacteristic
122#95—3021no—
123#95—3021no—
124#95—1511no—
125C2×Q8—3021no—
126C2×Q8—1511no—
127C2×Q8C22⋊D15111yescharacteristic
128C22×C4—21no—
129C22×C4—3021no—
130C22×C4—1511no—
131C22×C4—1511no—
132C22×C4C22×D15111yescharacteristic
133C2×C8—21no—
134C2×C8—3021no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3021no—
139C4⋊C4—3021no—
140C4⋊C4—3021no—
141C4⋊C4—3021no—
142C4⋊C4—3021no—
143C4⋊C4—3021no—
144C4⋊C4—3021no—
145C4⋊C4—3021no—
146C4⋊C4—1511no—
147C4⋊C4C22⋊D15111yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3021no—
150C42—3021no—
151C42—3021no—
152C23D4×D15111yescharacteristic
153Q8—41no—
154Q8—6041no—
155Q8—12081no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—3021no—
162C2×C4—3021no—
163C2×C4—3021no—
164C2×C4—3021no—
165C2×C4—3021no—
166C2×C4—6041no—
167C2×C4—6041no—
168C2×C4—6041no—
169C2×C4—6041no—
170C2×C4—1512no—
171C2×C4D4×D15111yescharacteristic
172C2×C4C2×C22⋊D15111yescharacteristic
173C8—41no—
174C8—6041no—
175C22—21no—
176C22—21no—
177C22#1801270711yescharacteristic
178C22Q16×D15111yescharacteristic
179C22#1801277111yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3022no—
186C4—6041no—
187C4—6041no—
188C4—6041no—
189C4—12081no—
190C2—21no—
191C2—21no—
192C2#2375236611yescharacteristic
193C2#2375238311yescharacteristic
194C2#2375240111yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#484×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#484D151
hypocenterC151#1617
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C151#1617semidirect

Maximal subgroups

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

subgroupindex
#237528412
#237525472
#237521502
#237519502
#237519492
#237519372
#484×C1512
#1617151