Finite Group Databasebeta

← #34077414

Subgroups — #34077414

Order 19328.

696 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 165 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×#18012728C211yesmaximal, characteristic, complemented
2C2×#18012715C211yesmaximal, characteristic, complemented
3C2×#18012714C211yesmaximal, characteristic
4C2×C42×D151C211yesmaximal, characteristic, complemented
5#23752114C211yesmaximal, characteristic, complemented
6#23752101C214yesmaximal, complemented
7#23752090C214yesmaximal, complemented
8#23752077C211yesmaximal, characteristic, complemented
9#391×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11C22×D604C2212yes—
12C22×C4×D151C2212yes—
13C22×C4×D151C2211yescharacteristic
14#18012728—24no—
15#18012715—24no—
16#18012714—24no—
17C2×C4⋊Dic151C2211yescharacteristic
18C2×Dic151⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×(C2×D151)⋊C4C2212yes—
21C2×(C2×D151)⋊C4C2214yes—
22C2×(C2×D151)⋊C4C2214yes—
23C2×C4×Dic151C2212yes—
24C2×C4×Dic151C2211yescharacteristic
25C42×D151—24no—
26C151⋊#95C2214yes—
27C22×Q8×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C42×C151C2211yescharacteristic
30#95×C151C2214yes—
31C23×D151C2312yes—
32C23×D151C2311yescharacteristic
33C2×D604—24no—
34C2×D604—28no—
35C2×D604—22no—
36C2×D604—22no—
37C2×D604—22no—
38C22×Dic151C2312yes—
39C22×Dic151C2311yescharacteristic
40C22×Dic151C2312yes—
41C2×C4×D151—24no—
42C2×C4×D151—24no—
43C2×C4×D151—22no—
44C2×C4×D151—22no—
45C2×C4×D151—24no—
46C2×C4×D151D414yes—
47C4⋊Dic151—22no—
48Dic151⋊C4—24no—
49(C2×D151)⋊C4—24no—
50(C2×D151)⋊C4—24no—
51(C2×D151)⋊C4—28no—
52(C2×D151)⋊C4—28no—
53C4×Dic151—24no—
54C4×Dic151D414yescomplemented
55C2×Q8×C151—22no—
56C2×Q8×C151—22no—
57C2×Q8×C151—22no—
58C22×C4×C151C2312yes—
59C22×C4×C151C2312yes—
60C22×C4×C151C2312yes—
61C22×C4×C151C2311yescharacteristic
62C4⋊C4×C151—22no—
63C42×C151—22no—
64C22×D151—21no—
65C22×D151—21no—
66C22×D151—22no—
67C22×D151—22no—
68C22×D151—22no—
69C22×D151—24no—
70C22×D151—24no—
71C22×D151—22no—
72C22×D151C2×D412yes—
73C22×D151#4114yes—
74D604—48no—
75D604—44no—
76C2×Dic151—21no—
77C2×Dic151—22no—
78C2×Dic151—21no—
79C2×Dic151—22no—
80C2×Dic151—22no—
81C2×Dic151—24no—
82C2×Dic151C2×D414yes—
83C2×Dic151C2×D412yes—
84C4×D151—216no—
85C4×D151—28no—
86C23×C151C2411yescharacteristic
87Q8×C151—44no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—24no—
95C2×C4×C151C2×D412yes—
96C2×C4×C151C2×D412yes—
97C2×C4×C151#4112yes—
98C2×C4×C151#4114yes—
99C22×C151C22×D411yescharacteristic
100C22×C151C22×D411yescharacteristic
101C22×C151C2×#4112yes—
102C22×C151C2×#4111yescharacteristic
103C22×C151C2×#4112yes—
104C2×D151—22no—
105C2×D151—24no—
106C2×D151—24no—
107C2×D151—22no—
108C2×D151—42no—
109C2×D151—44no—
110C2×D151—42no—
111C2×D151—44no—
112C2×D151—42no—
113C2×D151#12414yescomplemented
114C4×C151—24no—
115C4×C151—42no—
116C4×C151—42no—
117C4×C151#12114yes—
118Dic151—22no—
119Dic151—24no—
120Dic151—42no—
121C2×C151C2×#12111yescharacteristic
122C2×C151#52512yes—
123C2×C151C2×#12411yescharacteristic
124C2×C151#52912yes—
125C2×C151#53211yescharacteristic
126D151—24no—
127D151—82no—
128C151#285011yescharacteristic, complemented, Sylow
129#2850—1511nomaximal, Sylow
130C2×#124—1511no—
131C2×C22⋊Q8—1511no—
132C2×#121—1511no—
133C22×C42—1511no—
134#391D15111yescharacteristic, complemented
135#390—1511no—
136#388—1514no—
137#386—1514no—
138#382—1511no—
139C22×Q8C2×D15111yescharacteristic
140C22×D4—1511no—
141C22×D4—1512no—
142C23×C4—1512no—
143C23×C4—1511no—
144#124—3024no—
145C22⋊Q8—3024no—
146#121—3024no—
147C2×C4⋊C4—1512no—
148C2×C4⋊C4—1511no—
149C2×C4⋊C4C2×D15111yescharacteristic
150C2×C22⋊C4—1512no—
151C2×C22⋊C4—1512no—
152C2×C22⋊C4—1514no—
153C2×C22⋊C4—1514no—
154C2×C42—3024no—
155C2×C42—1512no—
156C2×C42—1511no—
157C2×C42C2×D15111yescharacteristic
158#95—1514no—
159#95C2×D15114yes—
160C24—1512no—
161C24—1511no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8—22no—
165C2×D4—3024no—
166C2×D4—3028no—
167C2×D4—3022no—
168C2×D4—3022no—
169C2×D4—3022no—
170C22×C4—3024no—
171C22×C4—3024no—
172C22×C4—3022no—
173C22×C4—3022no—
174C22×C4—3024no—
175C22×C4—1512no—
176C22×C4—1512no—
177C22×C4—1511no—
178C22×C4—1514no—
179C22×C4C22×D15112yes—
180C22×C4C22×D15112yes—
181C22×C4C22×D15112yes—
182C22×C4C22×D15111yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—3024no—
185C4⋊C4—3022no—
186C22⋊C4—3024no—
187C22⋊C4—3024no—
188C22⋊C4—3028no—
189C22⋊C4—3028no—
190C42—22no—
191C42—3024no—
192C42—1514no—
193C23—3021no—
194C23—3021no—
195C23—3022no—
196C23—3022no—
197C23—3022no—
198C23—3024no—
199C23—3022no—
200C23—3024no—
201C23—1512no—
202C23—1514no—
203C23C23×D15111yescharacteristic
204Q8—44no—
205D4—6048no—
206D4—6044no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—24no—
213C2×C4—22no—
214C2×C4—30216no—
215C2×C4—3021no—
216C2×C4—3022no—
217C2×C4—3021no—
218C2×C4—3022no—
219C2×C4—3028no—
220C2×C4—3022no—
221C2×C4—3024no—
222C2×C4—1514no—
223C2×C4—1512no—
224C2×C4D4×D15112yes—
225C2×C4D4×D15112yes—
226C2×C4#1455900412yes—
227C2×C4#1455900514yes—
228C22—3024no—
229C22—3024no—
230C22—3022no—
231C22—3022no—
232C22—6044no—
233C22—6042no—
234C22—6044no—
235C22—6042no—
236C22—6042no—
237C22—1514no—
238C22C2×D4×D15111yescharacteristic
239C22C2×D4×D15111yescharacteristic
240C22#41×D15112yes—
241C22C2×#1455900411yescharacteristic
242C22C2×#1455900512yes—
243C4—24no—
244C4—42no—
245C4—42no—
246C4—3024no—
247C4—3022no—
248C4—6042no—
249C4#1801271214yes—
250C2—3024no—
251C2—12082no—
252C2C2×#1801271211yescharacteristic
253C2#2375272512yes—
254C2#124×D15111yescharacteristic
255C2#2375274912yes—
256C2#2375276311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#391×C151C2
prime radicalC2×#18012714C2
hypercenter#391D151
hypocenterC151#2850
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#18012728C2semidirect
2. C2×#18012715C2semidirect
4. C2×C42×D151C2semidirect
5. #23752114C2semidirect
6. #23752101C2semidirect
7. #23752090C2semidirect
8. #23752077C2semidirect
9. #391×C151C2semidirect
54. C4×Dic151D4semidirect
113. C2×D151#124semidirect
128. C151#2850semidirect
134. #391D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127282
C2×#180127152
C2×#180127142
C2×C42×D1512
#237521142
#237521012
#237520902
#237520772
#391×C1512
#2850151