Finite Group Databasebeta

← #34080302

Subgroups — #34080302

Order 19328.

368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752762C211yesmaximal, characteristic
2C2×#18012731C211yesmaximal, characteristic, complemented
3#23752621C212yesmaximal, complemented
4#23752577C212yesmaximal, complemented
5#23752531C212yesmaximal, complemented
6#23752526C212yesmaximal, complemented
7#23752513C214yesmaximal, complemented
8#432×C151C211yesmaximal, characteristic, complemented
9C2×#14559004—21no—
10#18012739C2211yescharacteristic
11#18012736C2211yescharacteristic
12#18012731—21no—
13#18012731—21no—
14#18012731C2212yes—
15#18012731C2212yes—
16#18012727—21no—
17#18012713—21no—
18#18012713C2212yes—
19C4×D604—21no—
20C4×D604C2212yes—
21C2×C4⋊Dic151C2211yescharacteristic
22C2×C4⋊Dic151C2211yescharacteristic
23C2×Dic151⋊C4—21no—
24C2×Dic151⋊C4—21no—
25#18012673C2214yes—
26#18012671C2214yes—
27#18012661C2214yes—
28#18012661C2214yes—
29C2×C42×C151C2211yescharacteristic
30C4⋊C8×C151C2212yes—
31C22⋊C8×C151C2212yes—
32#97×C151C2212yes—
33#14559004—44no—
34C2×Dic302—21no—
35C2×D604—21no—
36C2×D604—21no—
37C2×D604C2312yes—
38C2×C22⋊D151—22no—
39C22×Dic151—21no—
40C22×Dic151—21no—
41C2×C4×D151—22no—
42C4⋊Dic151—21no—
43C4⋊Dic151—21no—
44C4⋊Dic151—21no—
45C4⋊Dic151C2312yes—
46C4⋊Dic151C2312yes—
47C4⋊Dic151C2312yes—
48Dic151⋊C4—22no—
49Dic151⋊C4—22no—
50Dic151⋊C4—22no—
51Dic151⋊C4—22no—
52(C2×D151)⋊C4—22no—
53(C2×D151)⋊C4—22no—
54C22×C4×C151D411yescharacteristic
55C22×C4×C151D411yescharacteristic
56C22×C4×C151C2311yescharacteristic
57C2×C8×C151C2314yes—
58C42×C151D411yescharacteristic
59C42×C151D411yescharacteristic
60C42×C151C2311yescharacteristic
61C42×C151C2311yescharacteristic
62C22×D151—22no—
63Dic302—42no—
64D604—24no—
65D604—42no—
66D604—42no—
67C22⋊D151—44no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—42no—
72C2×Dic151—42no—
73C4×D151—44no—
74C23×C151C2×D411yescharacteristic
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—41no—
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2411yescharacteristic
84C8×C151—24no—
85C22×C151—21no—
86C22×C151—21no—
87C22×C151AGL(1,ℤ/8)12yes—
88C22×C151C22×D411yescharacteristic
89C2×D151—42no—
90C2×D151—42no—
91C2×D151—42no—
92C4×C151—21no—
93C4×C151—21no—
94C4×C151—21no—
95C4×C151—21no—
96C4×C151—21no—
97C4×C1512−1+412yes—
98Dic151—42no—
99Dic151—42no—
100Dic151—42no—
101C2×C151—22no—
102C2×C151#53611yescharacteristic
103C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
104C2×C151#57511yescharacteristic
105D151—82no—
106C151#323411yescharacteristic, complemented, Sylow
107#3234—1511nomaximal, Sylow
108#532—1511no—
109C2×#125—1511no—
110#501—1512no—
111#490—1512no—
112#481—1512no—
113#480—1512no—
114#478—1514no—
115#432D15111yescharacteristic, complemented
116C2×#41—3021no—
117C4⋊Q8—1511no—
118#127—1511no—
119#125—3021no—
120#125—3021no—
121#125—1512no—
122#125—1512no—
123#124—3021no—
124#121—3021no—
125#121—1512no—
126C4×D4—3021no—
127C4×D4—1512no—
128C2×C4⋊C4—3021no—
129C2×C4⋊C4—3021no—
130C2×C4⋊C4—1511no—
131C2×C4⋊C4—1511no—
132C2×C42C2×D15111yescharacteristic
133#107—1514no—
134#106—1514no—
135C4⋊C8C2×D15112yes—
136#102—1514no—
137#102—1514no—
138C22⋊C8C2×D15112yes—
139#97C2×D15112yes—
140#41—6044no—
141C2×Q8—3021no—
142C2×D4—3022no—
143C2×D4—3021no—
144C2×D4—3021no—
145C2×D4—1512no—
146C22×C4—3021no—
147C22×C4—3021no—
148C22×C4—3022no—
149C22×C4D60411yescharacteristic
150C22×C4D60411yescharacteristic
151C22×C4C22×D15111yescharacteristic
152C2×C8C22×D15114yes—
153C4⋊C4—3022no—
154C4⋊C4—3022no—
155C4⋊C4—3022no—
156C4⋊C4—3022no—
157C4⋊C4—3021no—
158C4⋊C4—3021no—
159C4⋊C4—3021no—
160C4⋊C4—1512no—
161C4⋊C4—1512no—
162C4⋊C4—1512no—
163C22⋊C4—3022no—
164C22⋊C4—3022no—
165C42D60411yescharacteristic
166C42D60411yescharacteristic
167C42C22×D15111yescharacteristic
168C42C22×D15111yescharacteristic
169C23—3022no—
170C23C2×D60411yescharacteristic
171Q8—6042no—
172D4—3024no—
173D4—6042no—
174D4—6042no—
175D4—6044no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—6044no—
183C2×C4—6042no—
184C2×C4—6042no—
185C2×C4C2×D60411yescharacteristic
186C2×C4C2×D60411yescharacteristic
187C2×C4C2×D60411yescharacteristic
188C2×C4C2×D60411yescharacteristic
189C2×C4C2×D60411yescharacteristic
190C2×C4C23×D15111yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—6042no—
195C22—6042no—
196C22—6042no—
197C22#1801276712yes—
198C22C22×D60411yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—6042no—
205C4—6042no—
206C4—6042no—
207C4#1801278612yes—
208C2—22no—
209C2—12082no—
210C2#2375278811yescharacteristic
211C2C2×#1801276711yescharacteristic
212C2#2375301211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#432×C151C2
socleC22×C151C22×D4
prime radical#23752762C2
hypercenter#432D151
hypocenterC151#3234
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#18012731C2semidirect
3. #23752621C2semidirect
4. #23752577C2semidirect
5. #23752531C2semidirect
6. #23752526C2semidirect
7. #23752513C2semidirect
8. #432×C151C2semidirect
106. C151#3234semidirect
115. #432D151semidirect

Maximal subgroups

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

subgroupindex
#237527622
C2×#180127312
#237526212
#237525772
#237525312
#237525262
#237525132
#432×C1512
#3234151