Finite Group Databasebeta

← #34055856

Subgroups — #34055856

Order 19072.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#23750156C211yesmaximal, characteristic
2C2×#18011902C211yesmaximal, characteristic, complemented
3#23750026C212yesmaximal, complemented
4#23749978C212yesmaximal, complemented
5#23749961C211yesmaximal, characteristic, complemented
6#23749955C211yesmaximal, characteristic, complemented
7#23749941C211yesmaximal, characteristic
8#23749931C212yesmaximal, complemented
9#23749923C212yesmaximal, complemented
10#23749675C211yesmaximal, characteristic, complemented
11#480×C149C211yesmaximal, characteristic
12#18011904—21no—
13#18011902—21no—
14#18011902—21no—
15#18011902C2212yes—
16#18011902C2212yes—
17#18011902C2211yescharacteristic
18#18011898C2211yescharacteristic
19#18011892—21no—
20#18011890C2211yescharacteristic
21#18011876C2211yescharacteristic
22D4×Dic149—21no—
23D4×Dic149C2211yescharacteristic
24#18011867—21no—
25C2×C4⋊Dic149—21no—
26C2×C4⋊Dic149C2211yescharacteristic
27C2×#14558715—21no—
28C2×C4×Dic149C2211yescharacteristic
29#18011845C2212yes—
30#18011842C2212yes—
31#18011842C2212yes—
32#18011840C2212yes—
33#18011836C2212yes—
34#18011834C2212yes—
35#18011832C2212yes—
36C22⋊#11924746C2211yescharacteristic
37C8×Dic149C2212yes—
38#121×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yes—
41#102×C149C2212yes—
42C22⋊C8×C149C2211yescharacteristic
43C2×Dic298C2311yescharacteristic
44C22×Dic149—21no—
45C22×Dic149—21no—
46C22×Dic149D411yescharacteristic
47C22×Dic149D411yescharacteristic
48C2×#11924746C2312yes—
49C4⋊Dic149—21no—
50C4⋊Dic149—22no—
51C4⋊Dic149—22no—
52C4⋊Dic149—21no—
53C4⋊Dic149C2312yes—
54C4⋊Dic149C2311yescharacteristic
55#14558715—21no—
56#14558715—22no—
57#14558715—22no—
58#14558715—21no—
59#14558715—21no—
60C22⋊Dic149—21no—
61C22⋊Dic149—21no—
62C22⋊Dic149—21no—
63C22⋊Dic149—21no—
64C4×Dic149—21no—
65C4×Dic149D411yescharacteristic
66C4×Dic149D411yescharacteristic
67C4×Dic149C2311yescharacteristic
68C4×Dic149C2311yescharacteristic
69C2×D4×C149—21no—
70C2×D4×C149C2311yescharacteristic
71C22×C4×C149—21no—
72C22×C4×C149C2311yescharacteristic
73C2×C8×C149C2312yes—
74C4⋊C4×C149—21no—
75C4⋊C4×C149C2312yes—
76C4⋊C4×C149C2311yescharacteristic
77C22⋊C4×C149—21no—
78Dic298—22no—
79C2×Dic149—22no—
80C2×Dic149—21no—
81C2×Dic149—22no—
82C2×Dic149—21no—
83C2×Dic149—41no—
84C2×Dic149—42no—
85C2×Dic149—42no—
86C2×Dic149C2×D411yescharacteristic
87C2×Dic149C2×D411yescharacteristic
88C2×Dic149C2×D411yescharacteristic
89C2×Dic149C2×D411yescharacteristic
90#11924746—22no—
91C23×C149—21no—
92C23×C149C2×D411yescharacteristic
93D4×C149—22no—
94D4×C149—42no—
95C2×C4×C149—22no—
96C2×C4×C149—21no—
97C2×C4×C149—22no—
98C2×C4×C149—42no—
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2411yescharacteristic
101C8×C149—22no—
102C22×C149—21no—
103C22×C149—21no—
104C22×C149—41no—
105C22×C149—41no—
106C22×C149—41no—
107C22×C149#13512yes—
108C22×C149C22×D411yescharacteristic
109C4×C149—21no—
110C4×C149—42no—
111C4×C149—41no—
112C4×C1492−1+412yes—
113Dic149—21no—
114Dic149—21no—
115Dic149—21no—
116Dic149—21no—
117Dic149—41no—
118Dic149—41no—
119Dic149—42no—
120C2×C149—22no—
121C2×C149—81no—
122C2×C149#53611yescharacteristic
123C2×C149C2×#13511yescharacteristic
124C2×C149#57511yescharacteristic
125C149#323211yescharacteristic, complemented, Sylow
126#3232—1491nomaximal, Sylow
127#529—1491no—
128C2×#125—1491no—
129#499—1492no—
130#488—1492no—
131#484—1491no—
132#483—1491no—
133#481—1491no—
134#480D14911yescharacteristic
135#479—1492no—
136#478—1492no—
137#431—1491no—
138#126—2981no—
139#125—2981no—
140#125—2981no—
141#125—1492no—
142#125—1492no—
143#125—1491no—
144#124—1491no—
145#123—2981no—
146C22⋊Q8—1491no—
147#121C2×D14911yescharacteristic
148C4×Q8—1491no—
149C4×D4—2981no—
150C4×D4—1491no—
151#117—2981no—
152C2×C4⋊C4—2981no—
153C2×C4⋊C4—2981no—
154C2×C4⋊C4—1491no—
155C2×C4⋊C4C2×D14911yescharacteristic
156C2×C42—1491no—
157#107—1492no—
158#107C2×D14912yes—
159#106—1492no—
160#106—1492no—
161C4⋊C8—1492no—
162#103—1492no—
163#103—1492no—
164#102—1492no—
165#102C2×D14912yes—
166C22⋊C8—1491no—
167C22⋊C8C2×D14911yescharacteristic
168C4×C8—1492no—
169C2×Q8—1491no—
170C2×D4—21no—
171C2×D4C22×D14911yescharacteristic
172C22×C4—21no—
173C22×C4—2981no—
174C22×C4—2981no—
175C22×C4—1491no—
176C22×C4—1491no—
177C22×C4C22×D14911yescharacteristic
178C2×C8—1492no—
179C2×C8C22×D14912yes—
180C4⋊C4—21no—
181C4⋊C4—2982no—
182C4⋊C4—2982no—
183C4⋊C4—2982no—
184C4⋊C4—2982no—
185C4⋊C4—2981no—
186C4⋊C4—2981no—
187C4⋊C4—2981no—
188C4⋊C4—2981no—
189C4⋊C4—2981no—
190C4⋊C4—1492no—
191C4⋊C4—1491no—
192C4⋊C4C22×D14912yes—
193C4⋊C4C22×D14911yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—2981no—
196C22⋊C4—2981no—
197C22⋊C4—2981no—
198C22⋊C4—2981no—
199C42—2981no—
200C42—1491no—
201C42—1491no—
202C42—1491no—
203C42—1491no—
204C23—21no—
205C23D4×D14911yescharacteristic
206Q8—2982no—
207D4—22no—
208D4—42no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—2982no—
214C2×C4—2981no—
215C2×C4—2981no—
216C2×C4—2982no—
217C2×C4—5961no—
218C2×C4—5962no—
219C2×C4—5962no—
220C2×C4—1491no—
221C2×C4—1491no—
222C2×C4—1491no—
223C2×C4—1491no—
224C2×C4D4×D14911yescharacteristic
225C2×C4C23×D14911yescharacteristic
226C8—22no—
227C8—2982no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22#1801193012yes—
234C22C2×D4×D14911yescharacteristic
235C4—21no—
236C4—42no—
237C4—41no—
238C4—2981no—
239C4—2981no—
240C4—2981no—
241C4—2981no—
242C4—5961no—
243C4—5962no—
244C4—5961no—
245C4#1801195812yes—
246C2—22no—
247C2—81no—
248C2#2375019711yescharacteristic
249C2C2×#1801193011yescharacteristic
250C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#480×C149C2
socleC22×C149C22×D4
prime radical#121×C149C22
hypercenter#480D149
hypocenterC149#3232
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#18011902C2semidirect
3. #23750026C2semidirect
4. #23749978C2semidirect
5. #23749961C2semidirect
6. #23749955C2semidirect
8. #23749931C2semidirect
9. #23749923C2semidirect
10. #23749675C2semidirect
125. C149#3232semidirect

Maximal subgroups

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

subgroupindex
#237501562
C2×#180119022
#237500262
#237499782
#237499612
#237499552
#237499412
#237499312
#237499232
#237496752
#480×C1492
#3232149