Finite Group Databasebeta

← #34077172

Subgroups — #34077172

Order 19328.

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

normal subgroups only

This group has 430 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
1C2×#18012737C211yesmaximal, characteristic, complemented
2C2×#18012732C211yesmaximal, characteristic
3#23752154C212yesmaximal, complemented
4#23752148C212yesmaximal
5#23752146C212yesmaximal, complemented
6#23752140C212yesmaximal
7#23752133C211yesmaximal, characteristic, complemented
8#23752131C211yesmaximal, characteristic, complemented
9#23752124C211yesmaximal, characteristic
10#23752079C211yesmaximal, characteristic, complemented
11#393×C151C211yesmaximal, characteristic
12C22×Dic302C2211yescharacteristic
13#18012737—24no—
14#18012732—24no—
15C2×C4⋊Dic151C2211yescharacteristic
16C2×C4⋊Dic151C2212yes—
17C2×Dic151⋊C4C2211yescharacteristic
18C2×Dic151⋊C4C2211yescharacteristic
19C2×Dic151⋊C4C2212yes—
20C2×Dic151⋊C4C2212yes—
21C2×Dic151⋊C4C2212yes—
22C2×C22⋊Dic151C2211yescharacteristic
23C2×C22⋊Dic151C2211yescharacteristic
24C2×C22⋊Dic151C2212yes—
25C2×C4×Dic151C2211yescharacteristic
26C151⋊#95C2211yescharacteristic
27C151⋊#95C2212yes—
28C151⋊#95C2212yes—
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×Q8×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37C2×Dic302—22no—
38C2×Dic302—42no—
39C22×Dic151C2311yescharacteristic
40C22×Dic151C2312yes—
41C22×Dic151C2311yescharacteristic
42C22×Dic151C2312yes—
43C22×Dic151C2311yescharacteristic
44C22×Dic151C2311yescharacteristic
45C4⋊Dic151—22no—
46C4⋊Dic151—42no—
47Dic151⋊C4—22no—
48Dic151⋊C4—24no—
49Dic151⋊C4—24no—
50Dic151⋊C4—22no—
51Dic151⋊C4—42no—
52C22⋊Dic151—22no—
53C22⋊Dic151—22no—
54C22⋊Dic151—42no—
55C4×Dic151D414yes—
56C24×C151C2311yescharacteristic
57C2×Q8×C151—22no—
58C2×Q8×C151—42no—
59C22×C4×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61C22×C4×C151C2312yes—
62C22×C4×C151C2311yescharacteristic
63C22⋊C4×C151—22no—
64C22⋊C4×C151—42no—
65Dic302—44no—
66C2×Dic151—22no—
67C2×Dic151—21no—
68C2×Dic151—21no—
69C2×Dic151—21no—
70C2×Dic151—21no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C2×Dic151—21no—
77C2×Dic151—22no—
78C2×Dic151—21no—
79C2×Dic151—22no—
80C2×Dic151C2×D412yes—
81C2×Dic151C2×D412yes—
82C23×C151—21no—
83C23×C151—22no—
84C23×C151—21no—
85C23×C151—22no—
86C23×C151—21no—
87C23×C151C2411yescharacteristic
88Q8×C151—44no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—21no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151C2×D412yes—
99C22×C151—41no—
100C22×C151—41no—
101C22×C151—41no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151C22×D411yescharacteristic
105C22×C151H(5,𝔽2)12yes—
106C22×C1512−1+411yescharacteristic
107C22×C1512−1+412yes—
108C22×C1512−1+411yescharacteristic
109C4×C151—22no—
110C4×C151—42no—
111C4×C151—41no—
112C4×C151—42no—
113Dic151—22no—
114Dic151—22no—
115Dic151—41no—
116Dic151—42no—
117Dic151—41no—
118Dic151—42no—
119C2×C151—81no—
120C2×C151#53511yescharacteristic
121C2×C151#53611yescharacteristic
122C2×C151#53611yescharacteristic
123C2×C151#56312yes—
124C2×C151#56312yes—
125C151#282111yescharacteristic, complemented, Sylow
126#2821—1511nomaximal, Sylow
127C2×C4⋊Q8—1511no—
128C2×#126—1511no—
129#400—1512no—
130#399—1512no—
131#398—1512no—
132#397—1512no—
133#395—1511no—
134#395—1511no—
135#393—1511no—
136#393D15111yescharacteristic
137#383—1511no—
138C22×Q8—1511no—
139C22×Q8C2×D15111yescharacteristic
140C4⋊Q8—3024no—
141#126—3024no—
142C2×C4⋊C4—1511no—
143C2×C4⋊C4—1511no—
144C2×C4⋊C4—1511no—
145C2×C4⋊C4—1512no—
146C2×C4⋊C4—1512no—
147C2×C4⋊C4—1512no—
148C2×C4⋊C4—1512no—
149C2×C22⋊C4—1511no—
150C2×C22⋊C4—1511no—
151C2×C22⋊C4—1512no—
152C2×C22⋊C4C2×D15111yescharacteristic
153C2×C22⋊C4C2×D15112yes—
154C2×C42—1511no—
155#95—1511no—
156#95—1512no—
157#95—1512no—
158#95—1512no—
159#95—1512no—
160#95—1512no—
161#95C2×D15111yescharacteristic
162#95C2×D15112yes—
163C24C22×D15111yescharacteristic
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—3022no—
167C2×Q8—6042no—
168C22×C4—1512no—
169C22×C4—1511no—
170C22×C4—1512no—
171C22×C4—1511no—
172C22×C4—1511no—
173C22×C4—1511no—
174C22×C4C22×D15112yes—
175C22×C4C22×D15111yescharacteristic
176C22×C4C22×D15112yes—
177C22×C4C22×D15111yescharacteristic
178C4⋊C4—3022no—
179C4⋊C4—3024no—
180C4⋊C4—3024no—
181C4⋊C4—3022no—
182C4⋊C4—3022no—
183C4⋊C4—6042no—
184C4⋊C4—6042no—
185C22⋊C4—22no—
186C22⋊C4—42no—
187C22⋊C4—3022no—
188C22⋊C4—3022no—
189C22⋊C4—6042no—
190C42—1514no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23C23×D15111yescharacteristic
197Q8—44no—
198Q8—6044no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—3022no—
209C2×C4—3021no—
210C2×C4—3021no—
211C2×C4—3021no—
212C2×C4—3021no—
213C2×C4—3022no—
214C2×C4—3022no—
215C2×C4—3022no—
216C2×C4—3022no—
217C2×C4—3022no—
218C2×C4—3022no—
219C2×C4—3021no—
220C2×C4—3022no—
221C2×C4—3021no—
222C2×C4—1512no—
223C2×C4—1512no—
224C2×C4D4×D15112yes—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22C2×D4×D15111yescharacteristic
231C22#1801278412yes—
232C22#1801278611yescharacteristic
233C22#1801278612yes—
234C22#1801278711yescharacteristic
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—3022no—
240C4—3022no—
241C4—6042no—
242C4—6042no—
243C4—6041no—
244C4—6041no—
245C2—81no—
246C2#2375277711yescharacteristic
247C2#2375278211yescharacteristic
248C2#2375278511yescharacteristic
249C2#2375296212yes—
250C2#2375296312yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#393×C151C2
prime radicalC24×C151C23
hypercenter#393D151
hypocenterC151#2821
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#18012737C2semidirect
3. #23752154C2semidirect
5. #23752146C2semidirect
7. #23752133C2semidirect
8. #23752131C2semidirect
10. #23752079C2semidirect
125. C151#2821semidirect

Maximal subgroups

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

subgroupindex
C2×#180127372
C2×#180127322
#237521542
#237521482
#237521462
#237521402
#237521332
#237521312
#237521242
#237520792
#393×C1512
#2821151