Finite Group Databasebeta

← #34068291

Subgroups — #34068291

Order 19328.

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

normal subgroups only

This group has 308 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#23752559C211yesmaximal, characteristic, complemented
3#23752493C211yesmaximal, characteristic, complemented
4#23752417C211yesmaximal, characteristic, complemented
5#23751955C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7D4⋊C8×C151C211yesmaximal, characteristic, complemented
8C22×D604—21no—
9C2×D4×D151—21no—
10C2×#14558992—21no—
11#18012739C2211yescharacteristic, complemented
12#18012736C2211yescharacteristic
13#18012714—21no—
14#18012713—21no—
15#18012709—22no—
16C4×D604C2211yescharacteristic
17#18012673—21no—
18C4⋊(C151⋊C8)C2211yescharacteristic, complemented
19#18012662—21no—
20#18012661—21no—
21#18012661—22no—
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#14558992—42no—
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—41no—
58Dic302—41no—
59D604—21no—
60D604—42no—
61D604—44no—
62D604—41no—
63D604—41no—
64D604—41no—
65D604—41no—
66D604SD1612yescomplemented
67C22⋊D151—44no—
68C2×Dic151—21no—
69C2×Dic151—41no—
70C4×D151—41no—
71C4×D151—41no—
72C151⋊C8—41no—
73C23×C151—21no—
74D4×C151—21no—
75D4×C151D812yes—
76C2×C4×C151—21no—
77C2×C4×C151—41no—
78C2×C4×C151—41no—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C8×C151—41no—
83C8×C151—41no—
84C22×C151—22no—
85C22×C151—41no—
86C22×C151—41no—
87C22×C151#12011yescharacteristic
88C2×D151—22no—
89C2×D151—41no—
90C2×D151—41no—
91C2×D151—42no—
92C2×D151—42no—
93C2×D151—42no—
94C2×D151—88no—
95C4×C151—21no—
96C4×C151—41no—
97C4×C151C2×D811yescharacteristic
98C4×C151C2×SD1611yescharacteristic
99C4×C151AGL(1,ℤ/8)11yescharacteristic
100C4×C151AGL(1,ℤ/8)11yescharacteristic
101Dic151—41no—
102Dic151—81no—
103C2×C151—42no—
104C2×C151#44711yescharacteristic
105C2×C151#45011yescharacteristic
106C2×C151#45511yescharacteristic
107D151—42no—
108D151—82no—
109C151#163911yescharacteristic, complemented, Sylow
110#1639—1511nomaximal, Sylow
111D42—1511no—
112#486—1511no—
113#474—1511no—
114#461—1511no—
115#331—1511no—
116D4⋊C8—1511no—
117D4⋊C8D15111yescharacteristic, complemented
118C22×D4—3021no—
119C22×D4—3021no—
120C2×SD16—3021no—
121C4⋊Q8—1511no—
122#127—1511no—
123#121—3021no—
124#121—3021no—
125#120—3022no—
126C4×D4—1511no—
127C4×D4C2×D15111yescharacteristic
128#107—3021no—
129C4⋊C8—1511no—
130C4⋊C8C2×D15111yescharacteristic, complemented
131#103—3021no—
132#102—3021no—
133#102—3022no—
134C4×C8C2×D15111yescharacteristic, complemented
135C24—3022no—
136C2×Q8—3021no—
137C2×D4—3022no—
138C2×D4—3022no—
139C2×D4—3021no—
140C2×D4—3021no—
141C2×D4—6042no—
142C2×D4—6042no—
143C2×D4—6042no—
144C2×D4—6042no—
145C2×D4—1511no—
146C2×D4—1512no—
147C2×D4D60411yescharacteristic
148C22×C4—21no—
149C22×C4—3021no—
150SD16—6042no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—3021no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—1511no—
157C4⋊C4D60411yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—3022no—
160C22⋊C4—3021no—
161C42C22×D15111yescharacteristic
162C23—21no—
163C23—3021no—
164C23—3022no—
165C23—6044no—
166C23—6044no—
167C23—12082no—
168Q8—6041no—
169Q8—6041no—
170D4—21no—
171D4—3021no—
172D4—6042no—
173D4—6044no—
174D4—6044no—
175D4—6041no—
176D4—6041no—
177D4—6041no—
178D4—6041no—
179D4—1512no—
180D4D120812yes—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—3021no—
185C2×C4—6041no—
186C2×C4—6041no—
187C2×C4—6041no—
188C2×C4D4×D15111yescharacteristic
189C2×C4D4×D15111yescharacteristic
190C2×C4C2×D60411yescharacteristic
191C8—41no—
192C8—41no—
193C8—6041no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—3022no—
198C22—6041no—
199C22—6041no—
200C22—6042no—
201C22—6042no—
202C22—6042no—
203C22—12088no—
204C22#1801270911yescharacteristic
205C4—21no—
206C4—41no—
207C4—6041no—
208C4—12081no—
209C4C2×D120811yescharacteristic
210C4SD16×D15111yescharacteristic
211C4#1801276311yescharacteristic
212C4#1801276711yescharacteristic
213C2—42no—
214C2—6042no—
215C2—12082no—
216C2#2375234811yescharacteristic
217C2#2375236411yescharacteristic
218C2#2375239111yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
FittingD4⋊C8×C151C2
socleC22×C151#120
prime radicalD4×D604C2
hypercenterD4⋊C8D151
hypocenterC151#1639
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. #23752559C2semidirect
3. #23752493C2semidirect
4. #23752417C2semidirect
5. #23751955C2semidirect
6. #23751941C2semidirect
7. D4⋊C8×C151C2semidirect
11. #18012739C22semidirect
18. C4⋊(C151⋊C8)C22semidirect
23. C4⋊C8×C151C22semidirect
24. C4×C8×C151C22semidirect
66. D604SD16semidirect
109. C151#1639semidirect
117. D4⋊C8D151semidirect
130. C4⋊C8C2×D151semidirect
134. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
D4×D6042
#237525592
#237524932
#237524172
#237519552
#237519412
D4⋊C8×C1512
#1639151