Finite Group Databasebeta

← #34055927

Subgroups — #34055927

Order 19072.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750182C211yesmaximal, characteristic, complemented
2#23750035C211yesmaximal, characteristic, complemented
3#23750035C211yesmaximal, characteristic, complemented
4#23749984C211yesmaximal, characteristic, complemented
5#23749984C211yesmaximal, characteristic, complemented
6#23749963C212yesmaximal, complemented
7#23749946C212yesmaximal
8#23749932C212yesmaximal, complemented
9#23749925C212yesmaximal, complemented
10#23749682C211yesmaximal, characteristic, complemented
11#529×C149C211yesmaximal, characteristic
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011903C2212yes—
15#18011890—21no—
16#18011890—21no—
17C4×Dic298—21no—
18C4×Dic298—21no—
19#18011870C2212yes—
20#18011844C2212yes—
21#18011844C2212yes—
22#18011842C2212yes—
23#18011842C2212yes—
24C4⋊#11924746C2212yes—
25#18011835C2212yes—
26#18011835C2212yes—
27#18011832C2212yes—
28#18011832C2212yes—
29C22⋊#11924746C2212yes—
30#18011822C2211yescharacteristic
31#18011822C2211yescharacteristic
32#126×C149—21no—
33#125×C149C2211yescharacteristic
34#124×C149C2211yescharacteristic
35#123×C149—21no—
36C22⋊Q8×C149C2211yescharacteristic
37#121×C149C2211yescharacteristic
38C4×Q8×C149C2211yescharacteristic
39C4×D4×C149—21no—
40C4×D4×C149C2211yescharacteristic
41#117×C149—21no—
42C2×C42×C149C2211yescharacteristic
43C2×Dic298—21no—
44C2×Dic298—21no—
45C2×#11924746C2312yes—
46C2×#11924746C2312yes—
47C4⋊Dic149—21no—
48C4⋊Dic149—21no—
49C4⋊Dic149C2312yes—
50C4⋊Dic149C2312yes—
51#14558715—22no—
52#14558715—22no—
53C22⋊Dic149—22no—
54C4×Dic149—22no—
55C2×Q8×C149C2311yescharacteristic
56C2×D4×C149—21no—
57C2×D4×C149C2311yescharacteristic
58C22×C4×C149—21no—
59C22×C4×C149D411yescharacteristic
60C22×C4×C149D411yescharacteristic
61C22×C4×C149C2311yescharacteristic
62C4⋊C4×C149—21no—
63C4⋊C4×C149—21no—
64C4⋊C4×C149—21no—
65C4⋊C4×C149—21no—
66C4⋊C4×C149C2311yescharacteristic
67C4⋊C4×C149C2311yescharacteristic
68C22⋊C4×C149—21no—
69C22⋊C4×C149—21no—
70C22⋊C4×C149—21no—
71C22⋊C4×C149—21no—
72C22⋊C4×C149—21no—
73C42×C149—21no—
74C42×C149D411yescharacteristic
75C42×C149D411yescharacteristic
76C42×C149C2311yescharacteristic
77C42×C149C2311yescharacteristic
78Dic298—42no—
79Dic298—42no—
80C2×Dic149—22no—
81C2×Dic149—22no—
82#11924746—22no—
83#11924746—22no—
84C23×C149—21no—
85C23×C149C2×D411yescharacteristic
86Q8×C149—22no—
87D4×C149—22no—
88D4×C149—42no—
89C2×C4×C149—22no—
90C2×C4×C149—21no—
91C2×C4×C149—21no—
92C2×C4×C149—21no—
93C2×C4×C149—41no—
94C2×C4×C149—41no—
95C2×C4×C149—42no—
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2411yescharacteristic
102C22×C149—21no—
103C22×C149—21no—
104C22×C149—21no—
105C22×C149—41no—
106C22×C149—41no—
107C22×C149—41no—
108C22×C149C22×D411yescharacteristic
109C4×C149—21no—
110C4×C149—21no—
111C4×C149—21no—
112C4×C149—21no—
113C4×C149—21no—
114C4×C149—41no—
115C4×C149—41no—
116C4×C149—41no—
117C4×C1492−1+412yes—
118Dic149—42no—
119Dic149—42no—
120C2×C149—41no—
121C2×C149—81no—
122C2×C149#53611yescharacteristic
123C2×C149#57511yescharacteristic
124C2×C149#57511yescharacteristic
125C149#324011yescharacteristic, complemented, Sylow
126#3240—1491nomaximal, Sylow
127#533—1491no—
128#529D14911yescharacteristic
129#501—1491no—
130#501—1491no—
131#489—1491no—
132#489—1491no—
133#485—1492no—
134#482—1492no—
135#479—1492no—
136#478—1492no—
137#432—1491no—
138C4⋊Q8—1491no—
139C4⋊Q8—1491no—
140#126—21no—
141#125—1492no—
142#125C2×D14911yescharacteristic
143#124C2×D14911yescharacteristic
144#123—21no—
145C22⋊Q8—2981no—
146C22⋊Q8—2981no—
147C22⋊Q8C2×D14911yescharacteristic
148#121C2×D14911yescharacteristic
149C4×Q8—2981no—
150C4×Q8—2981no—
151C4×Q8C2×D14911yescharacteristic
152C4×D4—21no—
153C4×D4C2×D14911yescharacteristic
154#117—21no—
155#117—1492no—
156C2×C42C2×D14911yescharacteristic
157#107—1492no—
158#107—1492no—
159#106—1492no—
160#106—1492no—
161C4⋊C8—1492no—
162#103—1492no—
163#103—1492no—
164#102—1492no—
165#102—1492no—
166C22⋊C8—1492no—
167#97—1491no—
168#97—1491no—
169C2×Q8—2981no—
170C2×Q8—2981no—
171C2×Q8C22×D14911yescharacteristic
172C2×D4—21no—
173C2×D4C22×D14911yescharacteristic
174C22×C4—21no—
175C22×C4C22⋊D14911yescharacteristic
176C22×C4C22⋊D14911yescharacteristic
177C22×C4C22×D14911yescharacteristic
178C2×C8—1492no—
179C2×C8—1492no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—2982no—
185C4⋊C4—2982no—
186C4⋊C4—2981no—
187C4⋊C4—2981no—
188C4⋊C4—1492no—
189C4⋊C4—1492no—
190C4⋊C4C22×D14911yescharacteristic
191C4⋊C4C22×D14911yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—2982no—
198C42—21no—
199C42—2982no—
200C42C22⋊D14911yescharacteristic
201C42C22⋊D14911yescharacteristic
202C42C22×D14911yescharacteristic
203C42C22×D14911yescharacteristic
204C23—21no—
205C23C2×C22⋊D14911yescharacteristic
206Q8—22no—
207Q8—5962no—
208Q8—5962no—
209D4—22no—
210D4—42no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—2982no—
219C2×C4—2982no—
220C2×C4C2×C22⋊D14911yescharacteristic
221C2×C4C2×C22⋊D14911yescharacteristic
222C2×C4C2×C22⋊D14911yescharacteristic
223C2×C4C2×C22⋊D14911yescharacteristic
224C2×C4C2×C22⋊D14911yescharacteristic
225C2×C4C23×D14911yescharacteristic
226C8—2982no—
227C8—2982no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22C22×C22⋊D14911yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—41no—
243C4—5962no—
244C4—5962no—
245C4#1801195812yes—
246C2—41no—
247C2—81no—
248C2#2375019611yescharacteristic
249C2#2375042311yescharacteristic
250C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#529×C149C2
socleC22×C149C22×D4
prime radical#121×C149C22
hypercenter#529D149
hypocenterC149#3240
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #23750182C2semidirect
2. #23750035C2semidirect
3. #23750035C2semidirect
4. #23749984C2semidirect
5. #23749984C2semidirect
6. #23749963C2semidirect
8. #23749932C2semidirect
9. #23749925C2semidirect
10. #23749682C2semidirect
125. C149#3240semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237500352
#237499842
#237499632
#237499462
#237499322
#237499252
#237496822
#529×C1492
#3240149