Finite Group Databasebeta

← #34068228

Subgroups — #34068228

Order 19328.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D604C211yesmaximal, characteristic
2#23752585C211yesmaximal, characteristic, complemented
3#23752503C211yesmaximal, characteristic, complemented
4#23752502C211yesmaximal, characteristic, complemented
5#23751955C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7D4⋊C8×C151C211yesmaximal, characteristic, complemented
8C22×D604—21no—
9C2×D4×D151—21no—
10C2×#14558993—22no—
11#18012739C2211yescharacteristic, complemented
12#18012736C2211yescharacteristic
13#18012714—21no—
14#18012713—21no—
15#18012709—22no—
16C4×D604C2211yescharacteristic
17#18012671—21no—
18#18012670—21no—
19C4⋊(C151⋊C8)C2211yescharacteristic, complemented
20#18012661—21no—
21#18012660—21no—
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic, complemented
24C4×C8×C151C2211yescharacteristic, complemented
25C23×D151—22no—
26C2×Dic302—21no—
27C2×D604—22no—
28C2×D604—21no—
29C2×D604—21no—
30C2×D604—42no—
31C2×D604—42no—
32C2×D604D411yescharacteristic
33C2×D604D412yes—
34C2×C22⋊D151—22no—
35D4×D151—42no—
36D4×D151—42no—
37C2×C4×D151—21no—
38#14558993—44no—
39C2×C151⋊C8—21no—
40C4⋊Dic151—21no—
41C4⋊Dic151—21no—
42C4⋊Dic151D411yescharacteristic
43(C2×D151)⋊C4—22no—
44(C2×D151)⋊C4—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—21no—
53C22×D151—22no—
54C22×D151—44no—
55C22×D151—44no—
56C22×D151—82no—
57Dic302—42no—
58D604—21no—
59D604—42no—
60D604—44no—
61D604—41no—
62D604—41no—
63D604—41no—
64D604—41no—
65D604SD1612yescomplemented
66C22⋊D151—44no—
67C2×Dic151—21no—
68C2×Dic151—41no—
69C4×D151—41no—
70C4×D151—41no—
71C151⋊C8—41no—
72C23×C151—21no—
73D4×C151—21no—
74D4×C151SD1612yescomplemented
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—22no—
84C22×C151—41no—
85C22×C151—41no—
86C22×C151#12011yescharacteristic
87C2×D151—22no—
88C2×D151—41no—
89C2×D151—41no—
90C2×D151—42no—
91C2×D151—42no—
92C2×D151—42no—
93C2×D151—88no—
94C4×C151—21no—
95C4×C151—41no—
96C4×C151C2×SD1611yescharacteristic
97C4×C151C2×SD1611yescharacteristic
98C4×C151AGL(1,ℤ/8)11yescharacteristic
99C4×C151AGL(1,ℤ/8)11yescharacteristic
100Dic151—41no—
101Dic151—81no—
102C2×C151—42no—
103C2×C151#45011yescharacteristic
104C2×C151#45011yescharacteristic
105C2×C151#45311yescharacteristic
106D151—42no—
107D151—82no—
108C151#162911yescharacteristic, complemented, Sylow
109#1629—1511nomaximal, Sylow
110D42—1511no—
111#492—1511no—
112#476—1511no—
113#476—1511no—
114#331—1511no—
115D4⋊C8—1511no—
116D4⋊C8D15111yescharacteristic, complemented
117C22×D4—3021no—
118C22×D4—3021no—
119C2×SD16—3022no—
120C4⋊Q8—1511no—
121#127—1511no—
122#121—3021no—
123#121—3021no—
124#120—3022no—
125C4×D4—1511no—
126C4×D4C2×D15111yescharacteristic
127#106—3021no—
128#106—3021no—
129C4⋊C8—1511no—
130C4⋊C8C2×D15111yescharacteristic, complemented
131#102—3021no—
132#102—3021no—
133C4×C8C2×D15111yescharacteristic, complemented
134C24—3022no—
135C2×Q8—3021no—
136C2×D4—3022no—
137C2×D4—3022no—
138C2×D4—3021no—
139C2×D4—3021no—
140C2×D4—6042no—
141C2×D4—6042no—
142C2×D4—6042no—
143C2×D4—6042no—
144C2×D4—1511no—
145C2×D4—1512no—
146C2×D4D60411yescharacteristic
147C22×C4—21no—
148C22×C4—3021no—
149SD16—6044no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3021no—
153C4⋊C4—3021no—
154C4⋊C4—3021no—
155C4⋊C4—1511no—
156C4⋊C4D60411yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—3022no—
159C22⋊C4—3021no—
160C42C22×D15111yescharacteristic
161C23—21no—
162C23—3021no—
163C23—3022no—
164C23—6044no—
165C23—6044no—
166C23—12082no—
167Q8—6042no—
168D4—21no—
169D4—3021no—
170D4—6042no—
171D4—6044no—
172D4—6044no—
173D4—6041no—
174D4—6041no—
175D4—6041no—
176D4—6041no—
177D4—1512no—
178D4#1455899312yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—3021no—
183C2×C4—6041no—
184C2×C4—6041no—
185C2×C4—6041no—
186C2×C4D4×D15111yescharacteristic
187C2×C4D4×D15111yescharacteristic
188C2×C4C2×D60411yescharacteristic
189C8—22no—
190C8—41no—
191C8—6041no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—3022no—
196C22—6041no—
197C22—6041no—
198C22—6042no—
199C22—6042no—
200C22—6042no—
201C22—12088no—
202C22#1801270911yescharacteristic
203C4—21no—
204C4—41no—
205C4—6041no—
206C4—12081no—
207C4SD16×D15111yescharacteristic
208C4C2×#1455899311yescharacteristic
209C4#1801276311yescharacteristic
210C4#1801276711yescharacteristic
211C2—42no—
212C2—6042no—
213C2—12082no—
214C2#2375236411yescharacteristic
215C2#2375236511yescharacteristic
216C2#2375238111yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
FittingD4⋊C8×C151C2
socleC22×C151#120
prime radicalD4×D604C2
hypercenterD4⋊C8D151
hypocenterC151#1629
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
2. #23752585C2semidirect
3. #23752503C2semidirect
4. #23752502C2semidirect
5. #23751955C2semidirect
6. #23751941C2semidirect
7. D4⋊C8×C151C2semidirect
11. #18012739C22semidirect
19. C4⋊(C151⋊C8)C22semidirect
23. C4⋊C8×C151C22semidirect
24. C4×C8×C151C22semidirect
65. D604SD16semidirect
74. D4×C151SD16semidirect
108. C151#1629semidirect
116. D4⋊C8D151semidirect
130. C4⋊C8C2×D151semidirect
133. C4×C8C2×D151semidirect
178. D4#14558993semidirect

Maximal subgroups

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

subgroupindex
D4×D6042
#237525852
#237525032
#237525022
#237519552
#237519412
D4⋊C8×C1512
#1629151