Finite Group Databasebeta

← #34077125

Subgroups — #34077125

Order 19328.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18012722C211yesmaximal, characteristic
2C2×#18012718C211yesmaximal, characteristic, complemented
3#23752144C211yesmaximal, characteristic, complemented
4#23752142C212yesmaximal, complemented
5#23752139C211yesmaximal, characteristic, complemented
6#23752137C212yesmaximal, complemented
7#23752134C212yesmaximal, complemented
8#23752133C211yesmaximal, characteristic, complemented
9#23752128C212yesmaximal
10#23752125C211yesmaximal, characteristic, complemented
11#380×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×C22⋊D151C2211yescharacteristic
14#18012722—24no—
15#18012718—24no—
16C2×C4⋊Dic151C2211yescharacteristic
17C2×C4⋊Dic151C2212yes—
18C2×C4⋊Dic151C2212yes—
19C2×Dic151⋊C4C2212yes—
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×C22⋊Dic151C2212yes—
23C2×C22⋊Dic151C2211yescharacteristic
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C151⋊#95C2212yes—
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C23×C4×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2212yes—
34C2×C22⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2211yescharacteristic
37C23×D151C2311yescharacteristic
38C2×Dic302—22no—
39C2×Dic302—42no—
40C2×C22⋊D151—22no—
41C2×C22⋊D151—42no—
42C22×Dic151C2311yescharacteristic
43C22×Dic151C2312yes—
44C22×Dic151C2312yes—
45C22×Dic151C2311yescharacteristic
46C22×Dic151C2311yescharacteristic
47C4⋊Dic151—22no—
48C4⋊Dic151—42no—
49C4⋊Dic151—42no—
50Dic151⋊C4—24no—
51Dic151⋊C4—22no—
52Dic151⋊C4—22no—
53C22⋊Dic151—24no—
54C22⋊Dic151—22no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—42no—
58(C2×D151)⋊C4—42no—
59C24×C151C2311yescharacteristic
60C22×C4×C151—42no—
61C22×C4×C151D414yes—
62C22×C4×C151C2312yes—
63C22×C4×C151C2312yes—
64C22×C4×C151C2311yescharacteristic
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151—42no—
67C22⋊C4×C151—42no—
68C22×D151—21no—
69C22×D151—21no—
70C22×D151—22no—
71C22×D151—22no—
72C22×D151—21no—
73Dic302—44no—
74C22⋊D151—44no—
75C2×Dic151—21no—
76C2×Dic151—21no—
77C2×Dic151—22no—
78C2×Dic151—22no—
79C2×Dic151—21no—
80C2×Dic151—22no—
81C2×Dic151—22no—
82C2×Dic151—21no—
83C2×Dic151—22no—
84C2×Dic151—22no—
85C2×Dic151—22no—
86C2×Dic151—21no—
87C2×Dic151—22no—
88C23×C151—22no—
89C23×C151—21no—
90C23×C151—22no—
91C23×C151—21no—
92C23×C151C2×D412yes—
93C23×C151C2411yescharacteristic
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—22no—
99C2×C4×C151—22no—
100C2×C4×C151—22no—
101C2×C4×C151—22no—
102C2×C4×C151—44no—
103C2×C4×C151C2×D412yes—
104C2×C4×C151C2×D412yes—
105C22×C151—22no—
106C22×C151—22no—
107C22×C151—22no—
108C22×C151—42no—
109C22×C151—42no—
110C22×C151C22×D411yescharacteristic
111C22×C151H(5,𝔽2)12yes—
112C22×C151H(5,𝔽2)11yescharacteristic
113C22×C1512−1+412yes—
114C22×C1512−1+411yescharacteristic
115C2×D151—41no—
116C2×D151—41no—
117C2×D151—41no—
118C2×D151—42no—
119C2×D151—42no—
120C4×C151—22no—
121C4×C151—22no—
122C4×C151—42no—
123C4×C151—42no—
124Dic151—41no—
125Dic151—42no—
126Dic151—41no—
127Dic151—41no—
128Dic151—42no—
129C2×C151—42no—
130C2×C151#53411yescharacteristic
131C2×C151#53611yescharacteristic
132C2×C151#53711yescharacteristic
133C2×C151#56212yes—
134C2×C151#56312yes—
135D151—81no—
136C151#281411yescharacteristic, complemented, Sylow
137#2814—1511nomaximal, Sylow
138C2×#123—1511no—
139C2×C22⋊Q8—1511no—
140#398—1512no—
141#398—1511no—
142#397—1512no—
143#397—1511no—
144#396—1512no—
145#395—1511no—
146#394—1512no—
147#393—1511no—
148#380D15111yescharacteristic, complemented
149C22×Q8—1511no—
150C22×D4—1511no—
151C23×C4C2×D15111yescharacteristic
152#123—3024no—
153C22⋊Q8—3024no—
154C2×C4⋊C4—1512no—
155C2×C4⋊C4—1511no—
156C2×C4⋊C4—1511no—
157C2×C4⋊C4—1511no—
158C2×C4⋊C4—1512no—
159C2×C4⋊C4—1512no—
160C2×C4⋊C4C2×D15112yes—
161C2×C22⋊C4—1512no—
162C2×C22⋊C4—1511no—
163C2×C22⋊C4—1511no—
164C2×C22⋊C4—1511no—
165C2×C22⋊C4—1512no—
166C2×C22⋊C4—1512no—
167C2×C22⋊C4C2×D15112yes—
168#95—1512no—
169#95—1512no—
170#95—1512no—
171#95—1512no—
172#95C2×D15111yescharacteristic
173#95C2×D15111yescharacteristic
174C24—1511no—
175C24C22×D15111yescharacteristic
176C2×Q8—3022no—
177C2×Q8—6042no—
178C2×D4—3022no—
179C2×D4—6042no—
180C22×C4—42no—
181C22×C4—1511no—
182C22×C4—1511no—
183C22×C4—1512no—
184C22×C4—1512no—
185C22×C4—1511no—
186C22×C4D60414yes—
187C22×C4C22×D15112yes—
188C22×C4C22×D15112yes—
189C22×C4C22×D15111yescharacteristic
190C22×C4C22×D15111yescharacteristic
191C4⋊C4—42no—
192C4⋊C4—3024no—
193C4⋊C4—3022no—
194C4⋊C4—3022no—
195C4⋊C4—3022no—
196C4⋊C4—6042no—
197C4⋊C4—6042no—
198C22⋊C4—42no—
199C22⋊C4—3024no—
200C22⋊C4—3022no—
201C22⋊C4—3022no—
202C22⋊C4—3022no—
203C22⋊C4—6042no—
204C22⋊C4—6042no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—3021no—
210C23—3021no—
211C23—3022no—
212C23—3022no—
213C23—3021no—
214C23C2×D60412yes—
215C23C23×D15111yescharacteristic
216Q8—6044no—
217D4—6044no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—3021no—
228C2×C4—3021no—
229C2×C4—3022no—
230C2×C4—3022no—
231C2×C4—3021no—
232C2×C4—3022no—
233C2×C4—3022no—
234C2×C4—3021no—
235C2×C4—3022no—
236C2×C4—3022no—
237C2×C4—3022no—
238C2×C4—3021no—
239C2×C4—3022no—
240C2×C4C2×D60412yes—
241C2×C4C2×D60412yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—6042no—
248C22—6041no—
249C22—6041no—
250C22—6041no—
251C22—6042no—
252C22C22×D60411yescharacteristic
253C22#1801278412yes—
254C22#1801278411yescharacteristic
255C22#1801278612yes—
256C22#1801278711yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—6041no—
262C4—6042no—
263C4—6041no—
264C4—6041no—
265C4—6042no—
266C2—42no—
267C2—12081no—
268C2#2375277411yescharacteristic
269C2#2375278811yescharacteristic
270C2#2375279311yescharacteristic
271C2#2375295712yes—
272C2#2375296312yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#380×C151C2
prime radicalC22×C22⋊D151C22
hypercenter#380D151
hypocenterC151#2814
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#18012718C2semidirect
3. #23752144C2semidirect
4. #23752142C2semidirect
5. #23752139C2semidirect
6. #23752137C2semidirect
7. #23752134C2semidirect
8. #23752133C2semidirect
10. #23752125C2semidirect
11. #380×C151C2semidirect
136. C151#2814semidirect
148. #380D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127222
C2×#180127182
#237521442
#237521422
#237521392
#237521372
#237521342
#237521332
#237521282
#237521252
#380×C1512
#2814151