Finite Group Databasebeta

← #34077157

Subgroups — #34077157

Order 19328.

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

normal subgroups only

This group has 580 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×#18012726C211yesmaximal, characteristic, complemented
2C2×#18012725C211yesmaximal, characteristic, complemented
3#23752127C212yesmaximal, complemented
4#23752126C212yesmaximal, complemented
5#23752125C211yesmaximal, characteristic, complemented
6#23752124C212yesmaximal, complemented
7#23752124C211yesmaximal, characteristic, complemented
8#23752120C211yesmaximal, characteristic, complemented
9#23752120C212yesmaximal, complemented
10#23752076C211yesmaximal, characteristic, complemented
11#392×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×Dic302C2211yescharacteristic
14C22×C22⋊D151C2211yescharacteristic
15C22×C22⋊D151C2212yes—
16#18012726—24no—
17#18012725—24no—
18C2×Dic151⋊C4C2212yes—
19C2×C22⋊Dic151C2211yescharacteristic
20C2×C22⋊Dic151C2212yes—
21C2×C22⋊Dic151C2212yes—
22C2×C22⋊Dic151C2212yes—
23C2×C22⋊Dic151C2212yes—
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2212yes—
27C2×C4×Dic151C2211yescharacteristic
28C151⋊#95C2211yescharacteristic
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×D4×C151C2211yescharacteristic
33C22×D4×C151C2212yes—
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2212yes—
36#95×C151C2211yescharacteristic
37C23×D151C2311yescharacteristic
38C2×Dic302—22no—
39C2×Dic302—22no—
40C2×Dic302—42no—
41C2×Dic302—42no—
42C2×C22⋊D151—22no—
43C2×C22⋊D151—42no—
44C2×C22⋊D151—42no—
45C2×C22⋊D151—42no—
46C2×C22⋊D151—42no—
47C22×Dic151C2311yescharacteristic
48C22×Dic151C2312yes—
49C22×Dic151C2312yes—
50C22×Dic151C2311yescharacteristic
51C22×Dic151C2311yescharacteristic
52Dic151⋊C4—42no—
53C22⋊Dic151—22no—
54C22⋊Dic151—24no—
55C22⋊Dic151—24no—
56C22⋊Dic151—42no—
57C22⋊Dic151—42no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60(C2×D151)⋊C4—42no—
61C4×Dic151D414yescomplemented
62C24×C151C2312yes—
63C24×C151C2311yescharacteristic
64C2×D4×C151—22no—
65C2×D4×C151—42no—
66C2×D4×C151—42no—
67C2×D4×C151—42no—
68C2×D4×C151—42no—
69C22×C4×C151C2312yes—
70C22×C4×C151C2311yescharacteristic
71C22×C4×C151C2311yescharacteristic
72C22⋊C4×C151—22no—
73C22⋊C4×C151—42no—
74C22×D151—21no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151—21no—
78C22×D151—21no—
79Dic302—44no—
80Dic302—44no—
81C22⋊D151—44no—
82C22⋊D151—48no—
83C2×Dic151—21no—
84C2×Dic151—22no—
85C2×Dic151—21no—
86C2×Dic151—21no—
87C2×Dic151—22no—
88C2×Dic151—22no—
89C2×Dic151—22no—
90C2×Dic151—22no—
91C2×Dic151—22no—
92C2×Dic151—22no—
93C2×Dic151—22no—
94C2×Dic151C2×D412yes—
95C2×Dic151C2×D412yes—
96C23×C151—22no—
97C23×C151—21no—
98C23×C151—22no—
99C23×C151—22no—
100C23×C151—22no—
101C23×C151—22no—
102C23×C151—22no—
103C23×C151—22no—
104C23×C151—22no—
105C23×C151—21no—
106C23×C151—22no—
107C23×C151—21no—
108C23×C151C2411yescharacteristic
109D4×C151—44no—
110D4×C151—48no—
111C2×C4×C151—22no—
112C2×C4×C151—21no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151—22no—
116C2×C4×C151—22no—
117C2×C4×C151C2×D412yes—
118C22×C151—42no—
119C22×C151—42no—
120C22×C151—41no—
121C22×C151—41no—
122C22×C151—42no—
123C22×C151—41no—
124C22×C151—42no—
125C22×C151—42no—
126C22×C151—42no—
127C22×C151—42no—
128C22×C151—42no—
129C22×C151—42no—
130C22×C151C22×D411yescharacteristic
131C22×C151H(5,𝔽2)12yes—
132C22×C151H(5,𝔽2)12yes—
133C22×C151H(5,𝔽2)11yescharacteristic
134C22×C1512−1+411yescharacteristic
135C2×D151—41no—
136C2×D151—41no—
137C2×D151—41no—
138C2×D151—42no—
139C2×D151—42no—
140C4×C151—22no—
141C4×C151—41no—
142C4×C151—42no—
143Dic151—22no—
144Dic151—22no—
145Dic151—41no—
146Dic151—42no—
147Dic151—42no—
148C2×C151—82no—
149C2×C151—81no—
150C2×C151#53511yescharacteristic
151C2×C151#53511yescharacteristic
152C2×C151#53711yescharacteristic
153C2×C151H(3,𝔽4)12yes—
154C2×C151#56212yes—
155D151—81no—
156C151#281911yescharacteristic, complemented, Sylow
157#2819—1511nomaximal, Sylow
158C2×#124—1511no—
159C2×#124—1511no—
160#394—1512no—
161#394—1512no—
162#393—1512no—
163#393—1511no—
164#393—1511no—
165#392—1512no—
166#392—1511no—
167#392D15111yescharacteristic, complemented
168#382—1511no—
169C22×Q8—1511no—
170C22×Q8—1511no—
171C22×D4—1511no—
172C22×D4—1512no—
173C22×D4C2×D15111yescharacteristic
174C22×D4C2×D15112yes—
175#124—3024no—
176#124—3024no—
177C2×C4⋊C4—1512no—
178C2×C22⋊C4—1512no—
179C2×C22⋊C4—1512no—
180C2×C22⋊C4—1511no—
181C2×C22⋊C4—1511no—
182C2×C22⋊C4—1511no—
183C2×C22⋊C4—1512no—
184C2×C22⋊C4—1512no—
185C2×C22⋊C4—1512no—
186C2×C22⋊C4C2×D15111yescharacteristic
187C2×C22⋊C4C2×D15112yes—
188C2×C42—1511no—
189#95—1511no—
190#95—1512no—
191#95—1512no—
192#95—1512no—
193#95C2×D15111yescharacteristic
194C24—1511no—
195C24C22×D15111yescharacteristic
196C24C22×D15112yes—
197C2×Q8—3022no—
198C2×Q8—3022no—
199C2×Q8—6042no—
200C2×Q8—6042no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—3022no—
207C2×D4—6042no—
208C2×D4—6042no—
209C2×D4—6042no—
210C2×D4—6042no—
211C22×C4—1512no—
212C22×C4—1512no—
213C22×C4—1511no—
214C22×C4—1511no—
215C22×C4—1511no—
216C22×C4C22×D15112yes—
217C22×C4C22×D15111yescharacteristic
218C22×C4C22×D15111yescharacteristic
219C4⋊C4—6042no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—3022no—
223C22⋊C4—3022no—
224C22⋊C4—3024no—
225C22⋊C4—3024no—
226C22⋊C4—3022no—
227C22⋊C4—6042no—
228C22⋊C4—6042no—
229C22⋊C4—6042no—
230C42—1514no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—21no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—21no—
242C23—22no—
243C23—3021no—
244C23—3022no—
245C23—3022no—
246C23—3021no—
247C23—3021no—
248C23C23×D15111yescharacteristic
249Q8—6044no—
250Q8—6044no—
251D4—44no—
252D4—48no—
253D4—6044no—
254D4—6048no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—3021no—
262C2×C4—3022no—
263C2×C4—3021no—
264C2×C4—3021no—
265C2×C4—3022no—
266C2×C4—3022no—
267C2×C4—3022no—
268C2×C4—3022no—
269C2×C4—3022no—
270C2×C4—3022no—
271C2×C4—3022no—
272C2×C4—1512no—
273C2×C4—1512no—
274C2×C4D4×D15112yes—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—6041no—
288C22—6041no—
289C22—6041no—
290C22—6042no—
291C22—6042no—
292C22C2×D4×D15111yescharacteristic
293C22#1801278412yes—
294C22#1801278412yes—
295C22#1801278411yescharacteristic
296C22#1801278611yescharacteristic
297C4—22no—
298C4—41no—
299C4—42no—
300C4—3022no—
301C4—3022no—
302C4—6041no—
303C4—6042no—
304C4—6042no—
305C2—81no—
306C2—82no—
307C2—12081no—
308C2#2375277511yescharacteristic
309C2#2375277711yescharacteristic
310C2#2375279111yescharacteristic
311C2#2375295512yes—
312C2#2375295712yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#392×C151C2
hypercenter#392D151
hypocenterC151#2819
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#18012726C2semidirect
2. C2×#18012725C2semidirect
3. #23752127C2semidirect
4. #23752126C2semidirect
5. #23752125C2semidirect
6. #23752124C2semidirect
7. #23752124C2semidirect
8. #23752120C2semidirect
9. #23752120C2semidirect
10. #23752076C2semidirect
11. #392×C151C2semidirect
61. C4×Dic151D4semidirect
156. C151#2819semidirect
167. #392D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127262
C2×#180127252
#237521272
#237521262
#237521252
#237521242
#237521202
#237520762
#392×C1512
#2819151