Finite Group Databasebeta

← #34077163

Subgroups — #34077163

Order 19328.

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

normal subgroups only

This group has 464 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×#18012729C211yesmaximal, characteristic, complemented
2C2×#18012726C211yesmaximal, characteristic
3#23752148C212yesmaximal, complemented
4#23752140C212yesmaximal, complemented
5#23752135C212yesmaximal, complemented
6#23752135C212yesmaximal, complemented
7#23752133C211yesmaximal, characteristic, complemented
8#23752132C211yesmaximal, characteristic, complemented
9#23752126C211yesmaximal, characteristic
10#23752076C211yesmaximal, characteristic, complemented
11#394×C151C211yesmaximal, characteristic
12C22×Dic302C2211yescharacteristic
13#18012729—24no—
14#18012726—24no—
15C2×C4⋊Dic151C2211yescharacteristic
16C2×C4⋊Dic151C2212yes—
17C2×Dic151⋊C4C2211yescharacteristic
18C2×Dic151⋊C4C2211yescharacteristic
19C2×Dic151⋊C4C2211yescharacteristic
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2212yes—
22C2×Dic151⋊C4C2212yes—
23C2×C22⋊Dic151C2212yes—
24C2×C22⋊Dic151C2212yes—
25C2×C22⋊Dic151C2212yes—
26C2×C22⋊Dic151C2212yes—
27C2×C4×Dic151C2211yescharacteristic
28C151⋊#95C2211yescharacteristic
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×D4×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2212yes—
35C2×C22⋊C4×C151C2212yes—
36#95×C151C2211yescharacteristic
37C2×Dic302—22no—
38C2×Dic302—42no—
39C22×Dic151C2311yescharacteristic
40C22×Dic151C2311yescharacteristic
41C22×Dic151C2312yes—
42C22×Dic151C2312yes—
43C22×Dic151C2311yescharacteristic
44C22×Dic151C2311yescharacteristic
45C4⋊Dic151—22no—
46C4⋊Dic151—42no—
47Dic151⋊C4—22no—
48Dic151⋊C4—22no—
49Dic151⋊C4—22no—
50Dic151⋊C4—22no—
51Dic151⋊C4—42no—
52Dic151⋊C4—42no—
53C22⋊Dic151—24no—
54C22⋊Dic151—24no—
55C22⋊Dic151—42no—
56C22⋊Dic151—42no—
57C4×Dic151D414yes—
58C24×C151C2312yes—
59C2×D4×C151—22no—
60C2×D4×C151—42no—
61C22×C4×C151C2311yescharacteristic
62C22×C4×C151C2311yescharacteristic
63C22×C4×C151C2312yes—
64C22×C4×C151C2311yescharacteristic
65C4⋊C4×C151—22no—
66C22⋊C4×C151—42no—
67C22⋊C4×C151—42no—
68Dic302—44no—
69C2×Dic151—21no—
70C2×Dic151—22no—
71C2×Dic151—21no—
72C2×Dic151—22no—
73C2×Dic151—21no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—22no—
77C2×Dic151—22no—
78C2×Dic151—22no—
79C2×Dic151—22no—
80C2×Dic151—22no—
81C2×Dic151—21no—
82C2×Dic151—22no—
83C2×Dic151C2×D412yes—
84C2×Dic151C2×D412yes—
85C23×C151—22no—
86C23×C151—22no—
87C23×C151—22no—
88C23×C151—22no—
89C23×C151—22no—
90C23×C151—22no—
91C23×C151—22no—
92C23×C151C2411yescharacteristic
93D4×C151—44no—
94C2×C4×C151—22no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—22no—
98C2×C4×C151—22no—
99C2×C4×C151—22no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151—22no—
103C2×C4×C151C2×D412yes—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151—42no—
108C22×C151—42no—
109C22×C151—42no—
110C22×C151—42no—
111C22×C151C22×D411yescharacteristic
112C22×C151H(5,𝔽2)12yes—
113C22×C151H(5,𝔽2)11yescharacteristic
114C22×C1512−1+412yes—
115C22×C1512−1+411yescharacteristic
116C4×C151—22no—
117C4×C151—41no—
118C4×C151—41no—
119C4×C151—42no—
120Dic151—22no—
121Dic151—22no—
122Dic151—41no—
123Dic151—42no—
124Dic151—41no—
125Dic151—42no—
126C2×C151—82no—
127C2×C151#53511yescharacteristic
128C2×C151#53611yescharacteristic
129C2×C151#53711yescharacteristic
130C2×C151#56212yes—
131C2×C151#56312yes—
132C151#282011yescharacteristic, complemented, Sylow
133#2820—1511nomaximal, Sylow
134C2×#125—1511no—
135C2×#124—1511no—
136#399—1512no—
137#397—1512no—
138#396—1512no—
139#396—1512no—
140#395—1511no—
141#395—1511no—
142#394—1511no—
143#394D15111yescharacteristic
144#382—1511no—
145C22×Q8—1511no—
146C22×D4C2×D15111yescharacteristic
147#125—3024no—
148#124—3024no—
149C2×C4⋊C4—1511no—
150C2×C4⋊C4—1511no—
151C2×C4⋊C4—1511no—
152C2×C4⋊C4—1511no—
153C2×C4⋊C4—1511no—
154C2×C4⋊C4—1512no—
155C2×C4⋊C4—1512no—
156C2×C4⋊C4—1512no—
157C2×C4⋊C4C2×D15111yescharacteristic
158C2×C22⋊C4—1512no—
159C2×C22⋊C4—1512no—
160C2×C22⋊C4—1512no—
161C2×C22⋊C4—1512no—
162C2×C22⋊C4C2×D15112yes—
163C2×C22⋊C4C2×D15112yes—
164C2×C42—1511no—
165#95—1511no—
166#95—1512no—
167#95—1512no—
168#95—1512no—
169#95C2×D15111yescharacteristic
170C24C22×D15112yes—
171C2×Q8—3022no—
172C2×Q8—6042no—
173C2×D4—22no—
174C2×D4—42no—
175C22×C4—1512no—
176C22×C4—1511no—
177C22×C4—1512no—
178C22×C4—1511no—
179C22×C4—1511no—
180C22×C4—1511no—
181C22×C4C22×D15112yes—
182C22×C4C22×D15111yescharacteristic
183C22×C4C22×D15111yescharacteristic
184C22×C4C22×D15111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—3022no—
187C4⋊C4—3022no—
188C4⋊C4—3022no—
189C4⋊C4—3022no—
190C4⋊C4—3022no—
191C4⋊C4—6042no—
192C4⋊C4—6042no—
193C4⋊C4—6042no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C22⋊C4—3024no—
197C22⋊C4—3024no—
198C22⋊C4—6042no—
199C22⋊C4—6042no—
200C42—1514no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23C23×D15111yescharacteristic
209Q8—6044no—
210D4—44no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—3021no—
221C2×C4—3022no—
222C2×C4—3021no—
223C2×C4—3022no—
224C2×C4—3021no—
225C2×C4—3021no—
226C2×C4—3021no—
227C2×C4—3022no—
228C2×C4—3022no—
229C2×C4—3022no—
230C2×C4—3022no—
231C2×C4—3022no—
232C2×C4—3021no—
233C2×C4—3022no—
234C2×C4—1512no—
235C2×C4—1512no—
236C2×C4D4×D15112yes—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D15111yescharacteristic
245C22#1801278412yes—
246C22#1801278411yescharacteristic
247C22#1801278611yescharacteristic
248C22#1801278612yes—
249C4—22no—
250C4—41no—
251C4—41no—
252C4—42no—
253C4—3022no—
254C4—3022no—
255C4—6042no—
256C4—6041no—
257C4—6041no—
258C4—6042no—
259C2—82no—
260C2#2375277711yescharacteristic
261C2#2375278211yescharacteristic
262C2#2375279111yescharacteristic
263C2#2375295712yes—
264C2#2375296512yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#394×C151C2
prime radicalC22×D4×C151C22
hypercenter#394D151
hypocenterC151#2820
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#18012729C2semidirect
3. #23752148C2semidirect
4. #23752140C2semidirect
5. #23752135C2semidirect
6. #23752135C2semidirect
7. #23752133C2semidirect
8. #23752132C2semidirect
10. #23752076C2semidirect
132. C151#2820semidirect

Maximal subgroups

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

subgroupindex
C2×#180127292
C2×#180127262
#237521482
#237521402
#237521352
#237521332
#237521322
#237521262
#237520762
#394×C1512
#2820151