Finite Group Databasebeta

← #34068427

Subgroups — #34068427

Order 19328.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#23752622C211yesmaximal, characteristic, complemented
2#23752607C211yesmaximal, characteristic, complemented
3#23752571C211yesmaximal, characteristic, complemented
4#23751954C211yesmaximal, characteristic, complemented
5#23751952C211yesmaximal, characteristic, complemented
6#23751952C211yesmaximal, characteristic, complemented
7#562×C151C211yesmaximal, characteristic
8C2×#14558994—21no—
9C2×#14558992—21no—
10#18012739C2211yescharacteristic
11#18012672—21no—
12#18012670—21no—
13#18012663—21no—
14#18012660—21no—
15#18012650C2211yescharacteristic
16#18012650C2211yescharacteristic
17#18012650C2211yescharacteristic
18#125×C151C2211yescharacteristic
19#124×C151C2211yescharacteristic
20#124×C151C2211yescharacteristic
21#123×C151—21no—
22#123×C151—21no—
23C22⋊Q8×C151—21no—
24C22⋊Q8×C151—21no—
25#121×C151—21no—
26#121×C151—21no—
27C2×Dic302—21no—
28#14558994—42no—
29#14558992—42no—
30C2×C151⋊C8—21no—
31C2×C151⋊C8—21no—
32C2×C151⋊C8—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C2×Q8×C151D411yescharacteristic
36C2×Q8×C151D411yescharacteristic
37C2×D4×C151—21no—
38C2×D4×C151—21no—
39C2×D4×C151D411yescharacteristic
40C2×D4×C151D411yescharacteristic
41C22×C4×C151—21no—
42C22×C4×C151—21no—
43C4⋊C4×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D411yescharacteristic
48C4⋊C4×C151D411yescharacteristic
49C22⋊C4×C151—21no—
50C22⋊C4×C151—21no—
51C22⋊C4×C151—21no—
52C22⋊C4×C151—21no—
53C22⋊C4×C151—21no—
54C22⋊C4×C151—21no—
55C42×C151C2311yescharacteristic
56Dic302—41no—
57Dic302—41no—
58C2×Dic151—41no—
59C151⋊C8—22no—
60C151⋊C8—22no—
61C151⋊C8—41no—
62C23×C151—21no—
63C23×C151—21no—
64Q8×C151—41no—
65Q8×C151—41no—
66D4×C151—41no—
67D4×C151—41no—
68D4×C151—81no—
69D4×C151—81no—
70C2×C4×C151—21no—
71C2×C4×C151—21no—
72C2×C4×C151—21no—
73C2×C4×C151—21no—
74C2×C4×C151—81no—
75C2×C4×C151—81no—
76C2×C4×C151C2×D411yescharacteristic
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×D411yescharacteristic
79C22×C151—41no—
80C22×C151—41no—
81C22×C151—41no—
82C22×C151—41no—
83C22×C151—41no—
84C22×C151—41no—
85C22×C151#12011yescharacteristic
86C4×C151—21no—
87C4×C151—21no—
88C4×C151—21no—
89C4×C151—41no—
90C4×C151—41no—
91C4×C151—41no—
92C4×C151—41no—
93Dic151—81no—
94C2×C151—81no—
95C2×C151—81no—
96C2×C151#45311yescharacteristic
97C2×C151#45511yescharacteristic
98C2×C151#45611yescharacteristic
99C151#166111yescharacteristic, complemented, Sylow
100#1661—1511nomaximal, Sylow
101#562D15111yescharacteristic
102#501—1511no—
103#497—1511no—
104#489—1511no—
105#330—1511no—
106#329—1511no—
107#329—1511no—
108C2×Q16—3021no—
109C2×SD16—3021no—
110C4⋊Q8—1511no—
111#125C2×D15111yescharacteristic
112#124C2×D15111yescharacteristic
113#124C2×D15111yescharacteristic
114#123—21no—
115#123—21no—
116C22⋊Q8—21no—
117C22⋊Q8—21no—
118#121—21no—
119#121—21no—
120#107—3021no—
121#106—3021no—
122#103—3021no—
123#102—3021no—
124#97—1511no—
125#97—1511no—
126#97—1511no—
127C2×Q8—3021no—
128C2×Q8C22⋊D15111yescharacteristic
129C2×Q8C22⋊D15111yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4C22⋊D15111yescharacteristic
133C2×D4C22⋊D15111yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136Q16—6042no—
137SD16—6042no—
138C2×C8—3021no—
139C2×C8—3021no—
140C2×C8—3021no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—3021no—
146C4⋊C4—3021no—
147C4⋊C4C22⋊D15111yescharacteristic
148C4⋊C4C22⋊D15111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D15111yescharacteristic
156C23—21no—
157C23—21no—
158Q8—41no—
159Q8—41no—
160Q8—6041no—
161Q8—6041no—
162D4—41no—
163D4—41no—
164D4—81no—
165D4—81no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—6041no—
173C2×C4C2×C22⋊D15111yescharacteristic
174C2×C4C2×C22⋊D15111yescharacteristic
175C2×C4C2×C22⋊D15111yescharacteristic
176C8—3022no—
177C8—3022no—
178C8—6041no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#1801270811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—12081no—
194C2—81no—
195C2—81no—
196C2#2375238011yescharacteristic
197C2#2375239011yescharacteristic
198C2#2375239511yescharacteristic
subgroupG/H
centerC22#18012708
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting, prime radical#562×C151C2
socleC22×C151#120
hypercenter#562D151
hypocenterC151#1661
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #23752622C2semidirect
2. #23752607C2semidirect
3. #23752571C2semidirect
4. #23751954C2semidirect
5. #23751952C2semidirect
6. #23751952C2semidirect
99. C151#1661semidirect

Maximal subgroups

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

subgroupindex
#237526222
#237526072
#237525712
#237519542
#237519522
#562×C1512
#1661151