Finite Group Databasebeta

← #34077143

Subgroups — #34077143

Order 19328.

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

normal subgroups only

This group has 528 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×#18012717C211yesmaximal, characteristic, complemented
2C2×#18012714C211yesmaximal, characteristic
3#23752147C212yesmaximal, complemented
4#23752143C211yesmaximal, characteristic, complemented
5#23752130C212yesmaximal, complemented
6#23752130C211yesmaximal, characteristic, complemented
7#23752129C212yesmaximal, complemented
8#23752129C211yesmaximal, characteristic, complemented
9#23752125C212yesmaximal, complemented
10#23752074C211yesmaximal, characteristic, complemented
11#398×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×D604C2212yes—
14C22×D604C2211yescharacteristic
15C22×C4×D151C2211yescharacteristic
16#18012717—24no—
17#18012714—24no—
18C2×Dic151⋊C4C2211yescharacteristic
19C2×Dic151⋊C4C2211yescharacteristic
20C2×Dic151⋊C4C2212yes—
21C2×(C2×D151)⋊C4C2212yes—
22C2×(C2×D151)⋊C4C2211yescharacteristic
23C2×(C2×D151)⋊C4C2211yescharacteristic
24C2×(C2×D151)⋊C4C2212yes—
25C2×(C2×D151)⋊C4C2212yes—
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C2×(C2×D151)⋊C4C2212yes—
29C151⋊#95C2212yes—
30C151⋊#95C2211yescharacteristic
31C151⋊#95C2212yes—
32C2×C4⋊C4×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2211yescharacteristic
34C2×C4⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37C23×D151C2312yes—
38C23×D151C2311yescharacteristic
39C2×Dic302—22no—
40C2×Dic302—42no—
41C2×D604—24no—
42C2×D604—22no—
43C2×D604—42no—
44C2×D604—42no—
45C2×D604—42no—
46C22×Dic151C2311yescharacteristic
47C22×Dic151C2311yescharacteristic
48C22×Dic151C2312yes—
49C22×Dic151C2311yescharacteristic
50C2×C4×D151—42no—
51C2×C4×D151D414yes—
52Dic151⋊C4—22no—
53Dic151⋊C4—22no—
54Dic151⋊C4—42no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—24no—
58(C2×D151)⋊C4—42no—
59(C2×D151)⋊C4—42no—
60(C2×D151)⋊C4—42no—
61(C2×D151)⋊C4—42no—
62(C2×D151)⋊C4—42no—
63C22×C4×C151C2311yescharacteristic
64C22×C4×C151C2311yescharacteristic
65C22×C4×C151C2312yes—
66C22×C4×C151C2312yes—
67C22×C4×C151C2311yescharacteristic
68C4⋊C4×C151—22no—
69C4⋊C4×C151—22no—
70C4⋊C4×C151—42no—
71C22×D151—22no—
72C22×D151—21no—
73C22×D151—21no—
74C22×D151—22no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151—22no—
78C22×D151—22no—
79C22×D151—22no—
80C22×D151—22no—
81C22×D151—22no—
82C22×D151C2×D412yes—
83Dic302—44no—
84D604—44no—
85D604—48no—
86C2×Dic151—22no—
87C2×Dic151—21no—
88C2×Dic151—21no—
89C2×Dic151—21no—
90C2×Dic151—22no—
91C2×Dic151—22no—
92C2×Dic151—22no—
93C2×Dic151—21no—
94C2×Dic151—22no—
95C2×Dic151C2×D412yes—
96C4×D151—44no—
97C23×C151C2411yescharacteristic
98C2×C4×C151—22no—
99C2×C4×C151—21no—
100C2×C4×C151—22no—
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—22no—
104C2×C4×C151—22no—
105C2×C4×C151—22no—
106C2×C4×C151—22no—
107C2×C4×C151—22no—
108C2×C4×C151—21no—
109C2×C4×C151—22no—
110C2×C4×C151C2×D412yes—
111C22×C151C22×D411yescharacteristic
112C22×C151H(5,𝔽2)11yescharacteristic
113C22×C151H(5,𝔽2)12yes—
114C22×C151H(5,𝔽2)11yescharacteristic
115C22×C1512−1+412yes—
116C2×D151—22no—
117C2×D151—22no—
118C2×D151—22no—
119C2×D151—42no—
120C2×D151—42no—
121C2×D151—42no—
122C2×D151—42no—
123C2×D151—42no—
124C2×D151—42no—
125C2×D151—42no—
126C2×D151—42no—
127C2×D151—42no—
128C4×C151—22no—
129C4×C151—41no—
130C4×C151—41no—
131C4×C151—42no—
132C4×C151—42no—
133Dic151—22no—
134Dic151—41no—
135Dic151—41no—
136Dic151—42no—
137C2×C151#53411yescharacteristic
138C2×C151#53511yescharacteristic
139C2×C151#53611yescharacteristic
140C2×C151#56212yes—
141C2×C151#56212yes—
142D151—42no—
143D151—82no—
144C151#281611yescharacteristic, complemented, Sylow
145#2816—1511nomaximal, Sylow
146C2×C22⋊Q8—1511no—
147C2×#121—1511no—
148#399—1512no—
149#398—1511no—
150#398D15111yescharacteristic, complemented
151#394—1511no—
152#394—1512no—
153#394—1511no—
154#394—1512no—
155#393—1512no—
156#381—1511no—
157C22×Q8—1511no—
158C22×D4—1512no—
159C22×D4—1511no—
160C23×C4—1511no—
161C22⋊Q8—3024no—
162#121—3024no—
163C2×C4⋊C4—1511no—
164C2×C4⋊C4—1511no—
165C2×C4⋊C4—1512no—
166C2×C4⋊C4C2×D15111yescharacteristic
167C2×C4⋊C4C2×D15111yescharacteristic
168C2×C4⋊C4C2×D15112yes—
169C2×C22⋊C4—1512no—
170C2×C22⋊C4—1511no—
171C2×C22⋊C4—1511no—
172C2×C22⋊C4—1512no—
173C2×C22⋊C4—1512no—
174C2×C22⋊C4—1512no—
175C2×C22⋊C4—1512no—
176C2×C22⋊C4—1512no—
177#95—1512no—
178#95—1511no—
179#95—1512no—
180#95C2×D15111yescharacteristic
181#95C2×D15112yes—
182C24—1512no—
183C24—1511no—
184C2×Q8—3022no—
185C2×Q8—6042no—
186C2×D4—3024no—
187C2×D4—3022no—
188C2×D4—6042no—
189C2×D4—6042no—
190C2×D4—6042no—
191C22×C4—6042no—
192C22×C4—1512no—
193C22×C4—1511no—
194C22×C4—1511no—
195C22×C4—1511no—
196C22×C4—1514no—
197C22×C4C22×D15112yes—
198C22×C4C22×D15112yes—
199C22×C4C22×D15111yescharacteristic
200C22×C4C22×D15111yescharacteristic
201C22×C4C22×D15111yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—3022no—
206C4⋊C4—3022no—
207C4⋊C4—6042no—
208C22⋊C4—3022no—
209C22⋊C4—3022no—
210C22⋊C4—3024no—
211C22⋊C4—6042no—
212C22⋊C4—6042no—
213C22⋊C4—6042no—
214C22⋊C4—6042no—
215C22⋊C4—6042no—
216C23—3021no—
217C23—3022no—
218C23—3021no—
219C23—3022no—
220C23—3022no—
221C23—3022no—
222C23—3022no—
223C23—3022no—
224C23—3022no—
225C23—3022no—
226C23—3022no—
227C23—1512no—
228C23C23×D15111yescharacteristic
229Q8—6044no—
230D4—6044no—
231D4—6048no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—3022no—
245C2×C4—3021no—
246C2×C4—3021no—
247C2×C4—3021no—
248C2×C4—3022no—
249C2×C4—3022no—
250C2×C4—3022no—
251C2×C4—3021no—
252C2×C4—3022no—
253C2×C4—6044no—
254C2×C4—1512no—
255C2×C4D4×D15112yes—
256C22—3022no—
257C22—3022no—
258C22—3022no—
259C22—6042no—
260C22—6042no—
261C22—6042no—
262C22—6042no—
263C22—6042no—
264C22—6042no—
265C22—6042no—
266C22—6042no—
267C22—6042no—
268C22C2×D4×D15111yescharacteristic
269C22#1801278411yescharacteristic
270C22#1801278511yescharacteristic
271C22#1801278512yes—
272C22#1801278712yes—
273C4—22no—
274C4—41no—
275C4—42no—
276C4—41no—
277C4—42no—
278C4—3022no—
279C4—6042no—
280C4—6041no—
281C4—6041no—
282C2—6042no—
283C2—12082no—
284C2#2375277311yescharacteristic
285C2#2375277811yescharacteristic
286C2#2375278711yescharacteristic
287C2#2375295812yes—
288C2#2375296012yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#398×C151C2
prime radicalC2×#18012714C2
hypercenter#398D151
hypocenterC151#2816
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#18012717C2semidirect
3. #23752147C2semidirect
4. #23752143C2semidirect
5. #23752130C2semidirect
6. #23752130C2semidirect
7. #23752129C2semidirect
8. #23752129C2semidirect
9. #23752125C2semidirect
10. #23752074C2semidirect
11. #398×C151C2semidirect
144. C151#2816semidirect
150. #398D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127172
C2×#180127142
#237521472
#237521432
#237521302
#237521292
#237521252
#237520742
#398×C1512
#2816151