Finite Group Databasebeta

← #34077158

Subgroups — #34077158

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×#18012728C211yesmaximal, characteristic, complemented
2C2×#18012725C211yesmaximal, characteristic, complemented
3#23752130C212yesmaximal, complemented
4#23752127C212yesmaximal, complemented
5#23752125C212yesmaximal, complemented
6#23752123C211yesmaximal, characteristic, complemented
7#23752122C211yesmaximal, characteristic, complemented
8#23752121C212yesmaximal, complemented
9#23752121C211yesmaximal, characteristic, complemented
10#23752076C211yesmaximal, characteristic, complemented
11#393×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×D604C2211yescharacteristic
14C22×D604C2212yes—
15C22×C22⋊D151C2211yescharacteristic
16C22×C22⋊D151C2212yes—
17#18012728—24no—
18#18012725—24no—
19C2×Dic151⋊C4C2212yes—
20C2×C22⋊Dic151C2211yescharacteristic
21C2×(C2×D151)⋊C4C2211yescharacteristic
22C2×(C2×D151)⋊C4C2211yescharacteristic
23C2×(C2×D151)⋊C4C2212yes—
24C2×(C2×D151)⋊C4C2212yes—
25C2×(C2×D151)⋊C4C2212yes—
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C2×C4×Dic151C2211yescharacteristic
29C151⋊#95C2211yescharacteristic
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×Q8×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37C23×D151C2311yescharacteristic
38C23×D151C2312yes—
39C2×Dic302—22no—
40C2×Dic302—42no—
41C2×D604—22no—
42C2×D604—42no—
43C2×D604—42no—
44C2×D604—42no—
45C2×D604—42no—
46C2×C22⋊D151—22no—
47C2×C22⋊D151—42no—
48C2×C22⋊D151—42no—
49C2×C22⋊D151—42no—
50C2×C22⋊D151—42no—
51C22×Dic151C2311yescharacteristic
52C22×Dic151C2312yes—
53C22×Dic151C2311yescharacteristic
54C22×Dic151C2311yescharacteristic
55Dic151⋊C4—42no—
56C22⋊Dic151—22no—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—24no—
59(C2×D151)⋊C4—24no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4—42no—
62(C2×D151)⋊C4—42no—
63(C2×D151)⋊C4—42no—
64C4×Dic151D414yescomplemented
65C24×C151C2311yescharacteristic
66C2×Q8×C151—22no—
67C2×Q8×C151—42no—
68C22×C4×C151C2311yescharacteristic
69C22×C4×C151C2312yes—
70C22×C4×C151C2312yes—
71C22×C4×C151C2311yescharacteristic
72C22⋊C4×C151—22no—
73C22⋊C4×C151—42no—
74C22×D151—21no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151—22no—
78C22×D151—22no—
79C22×D151—22no—
80C22×D151—22no—
81C22×D151—22no—
82C22×D151—22no—
83C22×D151—21no—
84C22×D151—21no—
85C22×D151—22no—
86Dic302—44no—
87D604—44no—
88D604—48no—
89C22⋊D151—44no—
90C22⋊D151—48no—
91C2×Dic151—21no—
92C2×Dic151—22no—
93C2×Dic151—21no—
94C2×Dic151—21no—
95C2×Dic151—22no—
96C2×Dic151—22no—
97C2×Dic151—22no—
98C2×Dic151—22no—
99C2×Dic151C2×D412yes—
100C2×Dic151C2×D412yes—
101C23×C151—21no—
102C23×C151—22no—
103C23×C151—21no—
104C23×C151—22no—
105C23×C151—21no—
106C23×C151C2411yescharacteristic
107Q8×C151—44no—
108C2×C4×C151—22no—
109C2×C4×C151—22no—
110C2×C4×C151—21no—
111C2×C4×C151—22no—
112C2×C4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151—22no—
116C2×C4×C151—22no—
117C2×C4×C151C2×D412yes—
118C22×C151—41no—
119C22×C151—41no—
120C22×C151—41no—
121C22×C151—42no—
122C22×C151—42no—
123C22×C151C22×D411yescharacteristic
124C22×C151H(5,𝔽2)12yes—
125C22×C151H(5,𝔽2)12yes—
126C22×C151H(5,𝔽2)11yescharacteristic
127C22×C1512−1+411yescharacteristic
128C2×D151—41no—
129C2×D151—42no—
130C2×D151—41no—
131C2×D151—42no—
132C2×D151—41no—
133C2×D151—42no—
134C2×D151—42no—
135C2×D151—42no—
136C2×D151—42no—
137C2×D151—42no—
138C2×D151—42no—
139C2×D151—42no—
140C4×C151—22no—
141C4×C151—42no—
142C4×C151—41no—
143C4×C151—42no—
144Dic151—22no—
145Dic151—22no—
146Dic151—41no—
147Dic151—42no—
148C2×C151—81no—
149C2×C151#53511yescharacteristic
150C2×C151#53511yescharacteristic
151C2×C151#53711yescharacteristic
152C2×C151H(3,𝔽4)12yes—
153C2×C151#56212yes—
154D151—81no—
155D151—82no—
156C151#281911yescharacteristic, complemented, Sylow
157#2819—1511nomaximal, Sylow
158C2×#124—1511no—
159C2×#124—1511no—
160#394—1512no—
161#394—1512no—
162#393—1511no—
163#393—1512no—
164#393D15111yescharacteristic, complemented
165#392—1512no—
166#392—1511no—
167#392—1511no—
168#382—1511no—
169C22×Q8—1511no—
170C22×Q8C2×D15111yescharacteristic
171C22×D4—1511no—
172C22×D4—1512no—
173C22×D4—1511no—
174C22×D4—1512no—
175#124—3024no—
176#124—3024no—
177C2×C4⋊C4—1512no—
178C2×C22⋊C4—1511no—
179C2×C22⋊C4—1512no—
180C2×C22⋊C4—1511no—
181C2×C22⋊C4—1512no—
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#95C2×D15111yescharacteristic
193#95C2×D15112yes—
194C24—1511no—
195C24—1512no—
196C24C22×D15111yescharacteristic
197C2×Q8—22no—
198C2×Q8—42no—
199C2×Q8—3022no—
200C2×Q8—6042no—
201C2×D4—3022no—
202C2×D4—3022no—
203C2×D4—6042no—
204C2×D4—6042no—
205C2×D4—6042no—
206C2×D4—6042no—
207C2×D4—6042no—
208C2×D4—6042no—
209C2×D4—6042no—
210C2×D4—6042no—
211C22×C4—1512no—
212C22×C4—1511no—
213C22×C4—1511no—
214C22×C4—1511no—
215C22×C4C22×D15112yes—
216C22×C4C22×D15112yes—
217C22×C4C22×D15111yescharacteristic
218C22×C4C22×D15111yescharacteristic
219C4⋊C4—6042no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—3022no—
223C22⋊C4—3024no—
224C22⋊C4—3024no—
225C22⋊C4—3022no—
226C22⋊C4—3022no—
227C22⋊C4—6042no—
228C22⋊C4—6042no—
229C22⋊C4—6042no—
230C42—1514no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—21no—
235C23—21no—
236C23—3022no—
237C23—3021no—
238C23—3022no—
239C23—3022no—
240C23—3022no—
241C23—3022no—
242C23—3022no—
243C23—3022no—
244C23—3021no—
245C23—3022no—
246C23—3021no—
247C23—3022no—
248C23C23×D15111yescharacteristic
249Q8—44no—
250Q8—6044no—
251D4—6044no—
252D4—6048no—
253D4—6044no—
254D4—6048no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—3021no—
265C2×C4—3022no—
266C2×C4—3021no—
267C2×C4—3021no—
268C2×C4—3022no—
269C2×C4—3022no—
270C2×C4—3022no—
271C2×C4—3022no—
272C2×C4—1512no—
273C2×C4—1512no—
274C2×C4D4×D15112yes—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—6042no—
281C22—6041no—
282C22—6041no—
283C22—6042no—
284C22—6042no—
285C22—6041no—
286C22—6042no—
287C22—6042no—
288C22—6042no—
289C22—6042no—
290C22—6042no—
291C22—6042no—
292C22C2×D4×D15111yescharacteristic
293C22#1801278412yes—
294C22#1801278512yes—
295C22#1801278511yescharacteristic
296C22#1801278711yescharacteristic
297C4—22no—
298C4—42no—
299C4—41no—
300C4—42no—
301C4—3022no—
302C4—3022no—
303C4—6041no—
304C4—6042no—
305C2—81no—
306C2—12082no—
307C2—12081no—
308C2#2375277711yescharacteristic
309C2#2375278011yescharacteristic
310C2#2375279211yescharacteristic
311C2#2375295412yes—
312C2#2375295812yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#393×C151C2
hypercenter#393D151
hypocenterC151#2819
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#18012728C2semidirect
2. C2×#18012725C2semidirect
3. #23752130C2semidirect
4. #23752127C2semidirect
5. #23752125C2semidirect
6. #23752123C2semidirect
7. #23752122C2semidirect
8. #23752121C2semidirect
9. #23752121C2semidirect
10. #23752076C2semidirect
11. #393×C151C2semidirect
64. C4×Dic151D4semidirect
156. C151#2819semidirect
164. #393D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127282
C2×#180127252
#237521302
#237521272
#237521252
#237521232
#237521222
#237521212
#237520762
#393×C1512
#2819151