Finite Group Databasebeta

← #34077282

Subgroups — #34077282

Order 19328.

416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752150C212yesmaximal, complemented
2#23752141C212yesmaximal, complemented
3#23752129C211yesmaximal, characteristic
4#23752129C212yesmaximal
5#23752125C212yesmaximal, complemented
6#23752123C212yesmaximal, complemented
7#23752117C211yesmaximal, characteristic, complemented
8#23752101C212yesmaximal, complemented
9#395×C151C211yesmaximal, characteristic, complemented
10C22×Dic302C2211yescharacteristic
11C22×D604C2211yescharacteristic
12C2×Dic151⋊C4C2212yes—
13C2×(C2×D151)⋊C4C2212yes—
14C2×(C2×D151)⋊C4C2212yes—
15C2×(C2×D151)⋊C4C2212yes—
16C2×(C2×D151)⋊C4C2212yes—
17C2×(C2×D151)⋊C4C2212yes—
18C2×(C2×D151)⋊C4C2212yes—
19C2×C4×Dic151C2211yescharacteristic
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C22×Q8×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2212yes—
29#95×C151C2212yes—
30#95×C151C2211yescharacteristic
31C23×D151C2312yes—
32C2×Dic302—22no—
33C2×Dic302—41no—
34C2×Dic302—41no—
35C2×D604—41no—
36C2×D604—42no—
37C22×Dic151C2312yes—
38C22×Dic151C2312yes—
39C22×Dic151C2312yes—
40Dic151⋊C4—42no—
41(C2×D151)⋊C4—24no—
42(C2×D151)⋊C4—42no—
43(C2×D151)⋊C4—42no—
44(C2×D151)⋊C4—42no—
45(C2×D151)⋊C4—42no—
46(C2×D151)⋊C4—42no—
47C4×Dic151—41no—
48C2×Q8×C151—41no—
49C2×Q8×C151—42no—
50C22×C4×C151C2312yes—
51C22×C4×C151C2312yes—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2311yescharacteristic
54C22×C4×C151C2311yescharacteristic
55C4⋊C4×C151—41no—
56C4⋊C4×C151—42no—
57C22×D151—22no—
58C22×D151—22no—
59C22×D151—22no—
60C22×D151—22no—
61C22×D151—22no—
62C22×D151—22no—
63C22×D151—22no—
64Dic302—44no—
65D604—44no—
66C2×Dic151—22no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C23×C151C2411yescharacteristic
76Q8×C151—44no—
77C2×C4×C151—21no—
78C2×C4×C151—21no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—21no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—21no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151#4112yes—
90C22×C151C2×#4111yescharacteristic
91C22×C151H(5,𝔽2)11yescharacteristic
92C22×C151H(5,𝔽2)12yes—
93C22×C151H(5,𝔽2)11yescharacteristic
94C22×C1512−1+412yes—
95C2×D151—42no—
96C2×D151—42no—
97C2×D151—42no—
98C2×D151—42no—
99C2×D151—42no—
100C2×D151—42no—
101C2×D151—42no—
102C4×C151—22no—
103C4×C151—42no—
104C4×C151—41no—
105C4×C151—41no—
106C4×C151—42no—
107Dic151—42no—
108Dic151—42no—
109Dic151—42no—
110C2×C151#53811yescharacteristic
111C2×C151#54212yes—
112C2×C151H(3,𝔽4)11yescharacteristic
113C2×C151#56212yes—
114C2×C151#56311yescharacteristic
115D151—82no—
116C151#283211yescharacteristic, complemented, Sylow
117#2832—1511nomaximal, Sylow
118#400—1512no—
119#397—1512no—
120#395D15111yescharacteristic, complemented
121#394—1512no—
122#394—1511no—
123#393—1512no—
124#393—1512no—
125#391—1511no—
126#388—1512no—
127C22×Q8—1511no—
128C22×Q8C2×D15111yescharacteristic
129C22×D4—1511no—
130C2×C4⋊C4—1512no—
131C2×C4⋊C4C2×D15111yescharacteristic
132C2×C4⋊C4C2×D15112yes—
133C2×C22⋊C4—1512no—
134C2×C22⋊C4—1512no—
135C2×C22⋊C4—1512no—
136C2×C22⋊C4—1512no—
137C2×C22⋊C4—1512no—
138C2×C22⋊C4—1512no—
139C2×C42—1511no—
140#95—1512no—
141#95—1512no—
142#95—1512no—
143#95—1512no—
144#95—1512no—
145#95—1511no—
146#95C2×D15112yes—
147#95C2×D15111yescharacteristic
148C24—1512no—
149C2×Q8—41no—
150C2×Q8—42no—
151C2×Q8—3022no—
152C2×Q8—6041no—
153C2×Q8—6041no—
154C2×D4—6041no—
155C2×D4—6042no—
156C22×C4—1512no—
157C22×C4—1512no—
158C22×C4—1512no—
159C22×C4C22×D15111yescharacteristic
160C22×C4C22×D15112yes—
161C22×C4C22×D15111yescharacteristic
162C22×C4C22×D15112yes—
163C22×C4C22×D15111yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—42no—
166C4⋊C4—6042no—
167C22⋊C4—3024no—
168C22⋊C4—6042no—
169C22⋊C4—6042no—
170C22⋊C4—6042no—
171C22⋊C4—6042no—
172C22⋊C4—6042no—
173C42—6041no—
174C23—3022no—
175C23—3022no—
176C23—3022no—
177C23—3022no—
178C23—3022no—
179C23—3022no—
180C23—3022no—
181C23C23×D15111yescharacteristic
182Q8—44no—
183Q8—6044no—
184D4—6044no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—3022no—
198C2×C4—3022no—
199C2×C4—3022no—
200C2×C4—3022no—
201C2×C4—3022no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—3022no—
206C2×C4#1455900512yes—
207C22—6042no—
208C22—6042no—
209C22—6042no—
210C22—6042no—
211C22—6042no—
212C22—6042no—
213C22—6042no—
214C22C2×#1455900511yescharacteristic
215C22#1801278411yescharacteristic
216C22#1801278412yes—
217C22#1801278511yescharacteristic
218C22#1801278712yes—
219C4—22no—
220C4—41no—
221C4—42no—
222C4—41no—
223C4—42no—
224C4—6042no—
225C4—6042no—
226C4—6042no—
227C2—12082no—
228C2#2375280211yescharacteristic
229C2#2375283612yes—
230C2#2375295511yescharacteristic
231C2#2375295812yes—
232C2#2375296111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#395×C151C2
prime radicalC22×D604C22
hypercenter#395D151
hypocenterC151#2832
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #23752150C2semidirect
2. #23752141C2semidirect
5. #23752125C2semidirect
6. #23752123C2semidirect
7. #23752117C2semidirect
8. #23752101C2semidirect
9. #395×C151C2semidirect
116. C151#2832semidirect
120. #395D151semidirect

Maximal subgroups

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

subgroupindex
#237521502
#237521412
#237521292
#237521252
#237521232
#237521172
#237521012
#395×C1512
#2832151