Finite Group Databasebeta

← #34068178

Subgroups — #34068178

Order 19328.

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

normal subgroups only

This group has 278 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#23752883C211yesmaximal, characteristic, complemented
2#23752589C211yesmaximal, characteristic, complemented
3#23752413C211yesmaximal, characteristic, complemented
4#23752407C211yesmaximal, characteristic, complemented
5#23751955C211yesmaximal, characteristic, complemented
6#23751944C211yesmaximal, characteristic, complemented
7D4⋊C8×C151C211yesmaximal, characteristic, complemented
8C2×#14559004—21no—
9C2×#14558993—21no—
10C2×D1208—22no—
11C2×#14558989—21no—
12#18012736C2211yescharacteristic
13#18012736C2211yescharacteristic
14#18012735—21no—
15#18012713—21no—
16#18012712—22no—
17C4×Dic302C2211yescharacteristic
18#18012701—21no—
19C4⋊(C151⋊C8)C2211yescharacteristic
20#18012661—21no—
21#18012659—21no—
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4×C8×C151C2211yescharacteristic
25#14559004—42no—
26#14559004—42no—
27C2×Dic302D411yescharacteristic
28C2×D604—21no—
29C2×D604—21no—
30C2×D604—21no—
31C2×D604—21no—
32C2×D604—21no—
33C2×D604D412yes—
34C2×C22⋊D151—22no—
35C2×C22⋊D151—22no—
36C2×C4×D151—22no—
37#14558993—42no—
38D1208—44no—
39#14558989—42no—
40C2×C151⋊C8—21no—
41C4⋊Dic151D411yescharacteristic
42Dic151⋊C4—21no—
43(C2×D151)⋊C4—22no—
44C4×Dic151—21no—
45C2×D4×C151D411yescharacteristic
46C22×C4×C151—21no—
47C2×C8×C151—21no—
48C2×C8×C151—21no—
49C4⋊C4×C151D411yescharacteristic
50C22⋊C4×C151—21no—
51C42×C151C2311yescharacteristic
52C22×D151—22no—
53C22×D151—41no—
54Dic302—21no—
55Dic302D812yescomplemented
56D604—42no—
57D604—42no—
58D604—41no—
59D604—41no—
60D604—41no—
61D604—41no—
62D604—41no—
63D604—41no—
64D604—41no—
65D604—41no—
66C22⋊D151—44no—
67C22⋊D151—82no—
68C2×Dic151—21no—
69C2×Dic151—21no—
70C4×D151—44no—
71C151⋊C8—41no—
72C23×C151—21no—
73D4×C151—21no—
74D4×C151—21no—
75C2×C4×C151—21no—
76C2×C4×C151—41no—
77C2×C4×C151—41no—
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C8×C151—22no—
82C8×C151—41no—
83C22×C151—41no—
84C22×C151—41no—
85C22×C151—41no—
86C22×C151#12011yescharacteristic
87C2×D151—42no—
88C2×D151—42no—
89C2×D151—42no—
90C2×D151—81no—
91C2×D151—81no—
92C2×D151—81no—
93C4×C151—21no—
94C4×C151—41no—
95C4×C151C2×D811yescharacteristic
96C4×C151#13511yescharacteristic
97C4×C151AGL(1,ℤ/8)11yescharacteristic
98C4×C151AGL(1,ℤ/8)11yescharacteristic
99Dic151—22no—
100Dic151—41no—
101C2×C151—81no—
102C2×C151#44711yescharacteristic
103C2×C151#44911yescharacteristic
104C2×C151#45311yescharacteristic
105D151—82no—
106D151—161no—
107C151#162111yescharacteristic, complemented, Sylow
108#1621—1511nomaximal, Sylow
109#550—1511no—
110#493—1511no—
111#460—1511no—
112#459—1511no—
113#331—1511no—
114Q8⋊C8—1511no—
115D4⋊C8D15111yescharacteristic, complemented
116C2×#41—3021no—
117C2×SD16—3021no—
118C2×D8—3022no—
119C2×D8—3021no—
120#127—3021no—
121#127—1511no—
122#127—1511no—
123#121—3022no—
124#121—3021no—
125C4×Q8—1511no—
126C4×D4—3021no—
127C4×D4C2×D15111yescharacteristic
128C4⋊C8—1511no—
129C4⋊C8C2×D15111yescharacteristic
130#102—3021no—
131#102—3021no—
132C4×C8C2×D15111yescharacteristic
133#41—6042no—
134#41—6042no—
135C2×Q8—1511no—
136C2×D4—3022no—
137C2×D4—3022no—
138C2×D4—3021no—
139C2×D4—3021no—
140C2×D4—3021no—
141C2×D4—3021no—
142C2×D4—3021no—
143C2×D4—1512no—
144C2×D4D60411yescharacteristic
145C22×C4—21no—
146C22×C4—3022no—
147SD16—6042no—
148D8—6044no—
149D8—6042no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3021no—
153C4⋊C4—3021no—
154C4⋊C4—1511no—
155C4⋊C4D60411yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—3022no—
158C42—3021no—
159C42C22×D15111yescharacteristic
160C23—21no—
161C23—3022no—
162C23—6041no—
163Q8—3021no—
164Q8—1512no—
165D4—21no—
166D4—21no—
167D4—6042no—
168D4—6042no—
169D4—6044no—
170D4—6041no—
171D4—6041no—
172D4—6041no—
173D4—6041no—
174D4—6041no—
175D4—6041no—
176D4—6041no—
177D4—6041no—
178D4—12082no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—3021no—
183C2×C4—3021no—
184C2×C4—6044no—
185C2×C4D4×D15111yescharacteristic
186C2×C4D4×D15111yescharacteristic
187C2×C4C2×D60411yescharacteristic
188C8—22no—
189C8—41no—
190C8—6041no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—6042no—
195C22—6042no—
196C22—6042no—
197C22—12081no—
198C22—12081no—
199C22—12081no—
200C22#1801270911yescharacteristic
201C4—21no—
202C4—41no—
203C4—3022no—
204C4—6041no—
205C4D8×D15111yescharacteristic
206C4#1801276111yescharacteristic
207C4#1801276611yescharacteristic
208C4#1801276711yescharacteristic
209C2—81no—
210C2—24161no—
211C2—12082no—
212C2#2375234711yescharacteristic
213C2#2375235911yescharacteristic
214C2#2375238111yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
FittingD4⋊C8×C151C2
socleC22×C151#120
hypercenterD4⋊C8D151
hypocenterC151#1621
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #23752883C2semidirect
2. #23752589C2semidirect
3. #23752413C2semidirect
4. #23752407C2semidirect
5. #23751955C2semidirect
6. #23751944C2semidirect
7. D4⋊C8×C151C2semidirect
55. Dic302D8semidirect
107. C151#1621semidirect
115. D4⋊C8D151semidirect

Maximal subgroups

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

subgroupindex
#237528832
#237525892
#237524132
#237524072
#237519552
#237519442
D4⋊C8×C1512
#1621151