Finite Group Databasebeta

← #34071863

Subgroups — #34071863

Order 19328.

484 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×#18012718C211yesmaximal, characteristic
2#23752116C212yesmaximal, complemented
3#23752106C212yesmaximal
4#23752100C212yesmaximal
5#23752095C212yesmaximal, complemented
6#23752094C212yesmaximal, complemented
7#23752063C212yesmaximal, complemented
8C4×C22⋊Dic151C211yesmaximal, characteristic
9#381×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11#18012718C418yescomplemented
12C2×C4⋊Dic151C2211yescharacteristic
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×C22⋊Dic151C2212yes—
17C2×C22⋊Dic151C2212yes—
18C2×C4×Dic151C2212yes—
19C2×C4×Dic151C2211yescharacteristic
20C2×C4×Dic151C2211yescharacteristic
21C2×C4×Dic151C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2212yes—
26C151⋊#95C2212yes—
27C23×C4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2211yescharacteristic
29C2×C22⋊C4×C151C2211yescharacteristic
30#95×C151C2212yes—
31#95×C151C2212yes—
32C2×Dic302—41no—
33C2×Dic302—41no—
34C2×Dic302C2×C414yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C22×Dic151C2312yes—
38C22×Dic151C2312yes—
39C4⋊Dic151C2×C414yes—
40Dic151⋊C4—24no—
41Dic151⋊C4—42no—
42Dic151⋊C4C2×C418yes—
43C22⋊Dic151—24no—
44C22⋊Dic151C2×C418yes—
45C4×Dic151—24no—
46C4×Dic151—41no—
47C4×Dic151—41no—
48C4×Dic151—42no—
49C24×C151C2311yescharacteristic
50C22×C4×C151—41no—
51C22×C4×C151—41no—
52C22×C4×C151C2×C414yes—
53C22×C4×C151C2312yes—
54C22×C4×C151C2312yes—
55C22×C4×C151C2311yescharacteristic
56C22×C4×C151C2311yescharacteristic
57C22⋊C4×C151—41no—
58C22⋊C4×C151—41no—
59Dic302—44no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151C22×C414yes—
70C2×Dic151C22×C414yes—
71C2×Dic151#4114yes—
72C23×C151—22no—
73C23×C151—21no—
74C23×C151—21no—
75C23×C151—22no—
76C23×C151C22×C412yes—
77C23×C151C2411yescharacteristic
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—21no—
81C2×C4×C151—21no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151—44no—
89C2×C4×C151C22×C412yes—
90C2×C4×C151C22×C412yes—
91C22×C151—22no—
92C22×C151—22no—
93C22×C151—22no—
94C22×C151—42no—
95C22×C151—42no—
96C22×C151C23×C411yescharacteristic
97C22×C151C2×#4112yes—
98C22×C151H(5,𝔽2)11yescharacteristic
99C22×C151H(5,𝔽2)11yescharacteristic
100C22×C1512−1+412yes—
101C4×C151—22no—
102C4×C151—22no—
103C4×C151—42no—
104C4×C151—42no—
105Dic151—24no—
106Dic151—24no—
107Dic151—24no—
108Dic151—42no—
109C2×C151—42no—
110C2×C151C4×#4111yescharacteristic
111C2×C151#51811yescharacteristic
112C2×C151#51911yescharacteristic
113C2×C151#53912yes—
114C2×C151#54212yes—
115C151#233211yescharacteristic, complemented, Sylow
116#2332—1511nomaximal, Sylow
117C2×C22⋊Q8—1511no—
118#391—1512no—
119#388—1512no—
120#388—1512no—
121#387—1512no—
122#387—1512no—
123#381D15111yescharacteristic
124C4×C4⋊C4—1512no—
125C4×C22⋊C4—1511no—
126C22×Q8—1511no—
127C23×C4C2×D15111yescharacteristic
128C22⋊Q8—1518no—
129C2×C4⋊C4—1512no—
130C2×C4⋊C4—1512no—
131C2×C4⋊C4—1512no—
132C2×C4⋊C4—1511no—
133C2×C22⋊C4—1512no—
134C2×C22⋊C4—1512no—
135C2×C22⋊C4C2×D15111yescharacteristic
136C2×C22⋊C4C2×D15111yescharacteristic
137C2×C42—1512no—
138C2×C42—1511no—
139C2×C42—1511no—
140C2×C42—1512no—
141#95—1512no—
142#95—1512no—
143#95—1512no—
144#95—1512no—
145#95—1512no—
146#95C2×D15112yes—
147#95C2×D15112yes—
148C24C22×D15111yescharacteristic
149C2×Q8—6041no—
150C2×Q8—6041no—
151C2×Q8—1514no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—1512no—
155C22×C4—1512no—
156C22×C4—1512no—
157C22×C4—1512no—
158C22×C4C4×D15114yes—
159C22×C4C22×D15112yes—
160C22×C4C22×D15112yes—
161C22×C4C22×D15111yescharacteristic
162C22×C4C22×D15111yescharacteristic
163C4⋊C4—3024no—
164C4⋊C4—6042no—
165C4⋊C4—1518no—
166C4⋊C4—1514no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—3024no—
170C22⋊C4—1518no—
171C42—3024no—
172C42—6041no—
173C42—6041no—
174C42—6042no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D15112yes—
180C23C23×D15111yescharacteristic
181Q8—6044no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—44no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—3022no—
196C2×C4—3022no—
197C2×C4—3022no—
198C2×C4—3022no—
199C2×C4—3022no—
200C2×C4—3022no—
201C2×C4—3022no—
202C2×C4—1514no—
203C2×C4—1514no—
204C2×C4—1514no—
205C2×C4C2×C4×D15112yes—
206C2×C4C2×C4×D15112yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D15111yescharacteristic
213C22#41×D15112yes—
214C22#1801278411yescharacteristic
215C22#1801278411yescharacteristic
216C22#1801278612yes—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—42no—
221C4—3024no—
222C4—3024no—
223C4—3024no—
224C4—6042no—
225C2—42no—
226C2#2375268011yescharacteristic
227C2#2375268511yescharacteristic
228C2#2375268911yescharacteristic
229C2#2375280512yes—
230C2#2375283012yes—
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#381×C151C2
socle, cosocleC23×C151C24
prime radicalC24×C151C23
hypercenter#381D151
hypocenterC151#2332
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #23752116C2semidirect
5. #23752095C2semidirect
6. #23752094C2semidirect
7. #23752063C2semidirect
11. #18012718C4semidirect
115. C151#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#180127182
#237521162
#237521062
#237521002
#237520952
#237520942
#237520632
C4×C22⋊Dic1512
#381×C1512
#2332151