Finite Group Databasebeta

← #34080054

Subgroups — #34080054

Order 19328.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752767C211yesmaximal, characteristic
2C4⋊Q8×D151C211yesmaximal, characteristic
3#23752591C211yesmaximal, characteristic, complemented
4#23752563C211yesmaximal, characteristic, complemented
5#23752562C211yesmaximal, characteristic, complemented
6#23752420C214yesmaximal, complemented
7#23752366C214yesmaximal
8#23752263C211yesmaximal, characteristic
9#494×C151C211yesmaximal, characteristic, complemented
10C2×Q8×D151C2212yes—
11C2×#14558994C2214yes—
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012738—21no—
15#18012738—21no—
16#18012737C2212yes—
17#18012730—21no—
18#18012719—21no—
19#18012715C2212yes—
20Q8×Dic151C2212yes—
21#18012704—21no—
22#18012697—21no—
23C4⋊C4×D151—21no—
24C4⋊C4×D151—21no—
25C42×D151C2211yescharacteristic
26Dic151⋊C8C2212yes—
27#18012664C2214yes—
28#18012663C2214yes—
29(C2×D151)⋊C8C2212yes—
30C4×C151⋊C8C2211yescharacteristic
31C2×Q16×C151C2214yes—
32C4⋊Q8×C151C2211yescharacteristic
33C4⋊Q8×C151C2211yescharacteristic
34C4×C8×C151C2211yescharacteristic
35C2×Dic302—22no—
36C2×Dic302—21no—
37C2×Dic302C2312yes—
38Q8×D151—44no—
39C2×C4×D151—22no—
40C2×C4×D151D411yescharacteristic
41C2×C4×D151D411yescharacteristic
42C2×C4×D151C2311yescharacteristic
43#14558994—44no—
44C2×C151⋊C8C2312yes—
45C4⋊Dic151—22no—
46C4⋊Dic151—21no—
47C4⋊Dic151—21no—
48C4⋊Dic151—21no—
49C4⋊Dic151C2312yes—
50Dic151⋊C4—22no—
51Dic151⋊C4—22no—
52Dic151⋊C4—22no—
53(C2×D151)⋊C4—22no—
54C4×Dic151—22no—
55C4×Dic151D411yescharacteristic
56C4×Dic151D411yescharacteristic
57C4×Dic151C2311yescharacteristic
58C2×Q8×C151C2312yes—
59C2×Q8×C151C2312yes—
60Q16×C151—44no—
61C2×C8×C151C2312yes—
62C4⋊C4×C151—21no—
63C4⋊C4×C151—21no—
64C4⋊C4×C151—21no—
65C4⋊C4×C151—21no—
66C42×C151C2311yescharacteristic
67C22×D151C2×D411yescharacteristic
68Dic302—24no—
69Dic302—44no—
70Dic302—42no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151C2×D411yescharacteristic
74C2×Dic151C2×D411yescharacteristic
75C2×Dic151C2×D411yescharacteristic
76C4×D151—22no—
77C4×D151—22no—
78C4×D151—44no—
79C4×D151Q1614yescomplemented
80C151⋊C8—22no—
81Q8×C151—24no—
82Q8×C151—24no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2×D411yescharacteristic
87C2×C4×C151C2411yescharacteristic
88C8×C151—22no—
89C22×C151C22×D411yescharacteristic
90C2×D151—21no—
91C2×D151—21no—
92C2×D151C2×Q1612yes—
93C4×C151—42no—
94C4×C151—42no—
95C4×C151C2×Q1612yes—
96C4×C151#13712yes—
97C4×C151H(5,𝔽2)12yes—
98Dic151—21no—
99Dic151—21no—
100Dic151—42no—
101Dic151—42no—
102Dic151C2×Q1612yes—
103C2×C151#53511yescharacteristic
104C2×C151C22×Q1611yescharacteristic
105C2×C151C2×#13711yescharacteristic
106D151—22no—
107C151#320911yescharacteristic, complemented, Sylow
108#3209—1511nomaximal, Sylow
109#533—1511no—
110C2×C4⋊Q8—1511no—
111#494—1511no—
112#494D15111yescharacteristic, complemented
113#487—1511no—
114#487—1511no—
115#462—1514no—
116#451—1514no—
117#431—1511no—
118C22×Q8—1512no—
119C2×Q16—1514no—
120C2×Q16C2×D15114yes—
121C4⋊Q8—3021no—
122C4⋊Q8—3021no—
123C4⋊Q8—1512no—
124C4⋊Q8—1511no—
125C4⋊Q8—1511no—
126C4⋊Q8C2×D15111yescharacteristic
127C4⋊Q8C2×D15111yescharacteristic
128#125—3021no—
129C22⋊Q8—3021no—
130C22⋊Q8—1512no—
131C4×Q8—3021no—
132C4×Q8—1512no—
133#117—3021no—
134C2×C4⋊C4—3021no—
135C2×C4⋊C4—3021no—
136C2×C42—1511no—
137C4⋊C8—1512no—
138#103—1514no—
139#103—1514no—
140C22⋊C8—1512no—
141C4×C8—1511no—
142C4×C8C2×D15111yescharacteristic
143C2×Q8—3022no—
144C2×Q8—3021no—
145C2×Q8—6044no—
146C2×Q8—1512no—
147C2×Q8C22×D15112yes—
148C2×Q8C22×D15112yes—
149C22×C4—3022no—
150C22×C4—1511no—
151C22×C4—1511no—
152C22×C4—1511no—
153Q16—44no—
154Q16—6044no—
155C2×C8—1512no—
156C2×C8C22×D15112yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—3022no—
162C4⋊C4—3022no—
163C4⋊C4—3022no—
164C4⋊C4—3022no—
165C4⋊C4—3021no—
166C4⋊C4—3021no—
167C4⋊C4—3021no—
168C4⋊C4—1512no—
169C22⋊C4—3022no—
170C42—3022no—
171C42—1511no—
172C42—1511no—
173C42—1511no—
174C42C22×D15111yescharacteristic
175C23—1511no—
176Q8—24no—
177Q8—24no—
178Q8—3024no—
179Q8—6044no—
180Q8—6042no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—3022no—
184C2×C4—3022no—
185C2×C4—3022no—
186C2×C4—3022no—
187C2×C4—6044no—
188C2×C4—1511no—
189C2×C4—1511no—
190C2×C4—1511no—
191C2×C4—1514no—
192C2×C4D4×D15111yescharacteristic
193C2×C4D4×D15111yescharacteristic
194C2×C4C23×D15111yescharacteristic
195C8—22no—
196C8—3022no—
197C22—3021no—
198C22—3021no—
199C22—1512no—
200C22C2×D4×D15111yescharacteristic
201C4—42no—
202C4—42no—
203C4—3021no—
204C4—3021no—
205C4—6042no—
206C4—6042no—
207C4—1512no—
208C4Q16×D15112yes—
209C4#1801277112yes—
210C4#1801278412yes—
211C2—3022no—
212C2#2375277511yescharacteristic
213C2C2×Q16×D15111yescharacteristic
214C2C2×#1801277111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#494×C151C2
socleC22×C151C22×D4
prime radicalC22×D151C2×D4
hypercenter#494D151
hypocenterC151#3209
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #23752591C2semidirect
4. #23752563C2semidirect
5. #23752562C2semidirect
6. #23752420C2semidirect
9. #494×C151C2semidirect
79. C4×D151Q16semidirect
107. C151#3209semidirect
112. #494D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
C4⋊Q8×D1512
#237525912
#237525632
#237525622
#237524202
#237523662
#237522632
#494×C1512
#3209151