Finite Group Databasebeta

← #34057088

Subgroups — #34057088

Order 19072.

366 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750322C212yesmaximal, complemented
2#23750026C211yesmaximal, characteristic, complemented
3#23749946C212yesmaximal, complemented
4#23749942C212yesmaximal, complemented
5#23749927C212yesmaximal, complemented
6#23749858C211yesmaximal, characteristic, complemented
7D8×Dic149C211yesmaximal, characteristic, complemented
8C8×C22⋊D149C211yesmaximal, characteristic, complemented
9#23749663C211yesmaximal, characteristic, complemented
10#107×D149C211yesmaximal, characteristic, complemented
11#466×C149C211yesmaximal, characteristic, complemented
12C2×C8×D149C2211yescharacteristic
13#18011904—22no—
14#18011902C2212yes—
15#18011892—22no—
16#18011882—22no—
17#18011882C2212yes—
18D4×Dic149C2212yes—
19C4×C22⋊D149C2211yescharacteristic
20#18011871—22no—
21#18011870C2212yes—
22C4⋊C4×D149C2212yes—
23#18011845C2211yescharacteristic
24#18011845C2211yescharacteristic
25#18011844C2212yes—
26#18011843C2212yes—
27#18011842C2212yes—
28#18011840C2211yescharacteristic
29#18011832C2212yes—
30#18011832C2212yes—
31C22⋊#11924746C2211yescharacteristic
32#18011823C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×D8×C149C2211yescharacteristic
35C22×C8×C149C2211yescharacteristic
36#121×C149C2212yes—
37#107×C149C2211yescharacteristic
38#102×C149C2212yes—
39C2×C22⋊D149—22no—
40C2×C22⋊D149D411yescharacteristic
41C22×Dic149—22no—
42C2×C4×D149—22no—
43C2×C4×D149C2311yescharacteristic
44C2×#11924746C2311yescharacteristic
45C2×#11924746C2311yescharacteristic
46C8×D149—22no—
47C4⋊Dic149—22no—
48C4⋊Dic149C2312yes—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51#14558715—22no—
52#14558715D411yescharacteristic
53C22⋊Dic149—22no—
54C22⋊Dic149—22no—
55C22⋊Dic149—22no—
56C22⋊Dic149D411yescharacteristic
57#14558713D411yescharacteristic
58C4×Dic149—22no—
59C4×Dic149C2311yescharacteristic
60C2×D4×C149—22no—
61C2×D4×C149C2312yes—
62C22×C4×C149C2311yescharacteristic
63D8×C149—22no—
64C2×C8×C149—22no—
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2311yescharacteristic
67C4⋊C4×C149C2312yes—
68C22⋊C4×C149—22no—
69C22×D149C2×D411yescharacteristic
70C22⋊D149—22no—
71C22⋊D149—44no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—82no—
75C2×Dic149C2×D411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C2×Dic149C2×D411yescharacteristic
78C4×D149—21no—
79C4×D149—21no—
80C4×D149—82no—
81#11924746—21no—
82#11924746—21no—
83C23×C149—22no—
84C23×C149C2×D411yescharacteristic
85D4×C149—22no—
86D4×C149—22no—
87D4×C149—82no—
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—22no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2411yescharacteristic
93C8×C149—21no—
94C8×C149#4112yes—
95C22×C149—21no—
96C22×C149—21no—
97C22×C149—21no—
98C22×C149—42no—
99C22×C149—42no—
100C22×C149—42no—
101C22×C149C22×D411yescharacteristic
102C2×D149—21no—
103C2×D149—21no—
104C2×D149#13512yes—
105C4×C149—21no—
106C4×C149—42no—
107C4×C149C2×#4111yescharacteristic
108C4×C1492−1+411yescharacteristic
109Dic149—21no—
110Dic149—21no—
111Dic149—21no—
112Dic149—42no—
113Dic149—42no—
114C2×C149—41no—
115C2×C149—82no—
116C2×C149#54711yescharacteristic
117C2×C149C2×#13511yescharacteristic
118C2×C149#57611yescharacteristic
119D149—22no—
120C149#333911yescharacteristic, complemented, Sylow
121#3339—1491nomaximal, Sylow
122#553—1492no—
123#499—1491no—
124#482—1492no—
125#481—1492no—
126#478—1492no—
127#466—1491no—
128#466D14911yescharacteristic, complemented
129C4×D8—1491no—
130C8×D4—1491no—
131#427—1491no—
132C2×#107—1491no—
133C2×D8C2×D14911yescharacteristic
134C22×C8—1491no—
135C22×C8C2×D14911yescharacteristic
136#126—2982no—
137#125—1492no—
138#123—2982no—
139#121—2982no—
140#121—1492no—
141#121C2×D14912yes—
142C4×D4—2982no—
143C4×D4—1492no—
144C4×D4—1491no—
145#117—1492no—
146C2×C4⋊C4—1492no—
147#107—1491no—
148#107—1491no—
149#107—1492no—
150#107C2×D14911yescharacteristic
151#106—1492no—
152#106—1492no—
153C4⋊C8—1491no—
154#102—1492no—
155#102—1492no—
156#102C2×D14912yes—
157C22⋊C8—1491no—
158C22⋊C8—1491no—
159C4×C8—1491no—
160C2×D4—22no—
161C2×D4—2982no—
162C2×D4—1491no—
163C2×D4C22×D14912yes—
164C22×C4—2982no—
165C22×C4—2982no—
166C22×C4—1491no—
167C22×C4C22×D14911yescharacteristic
168D8—22no—
169C2×C8—22no—
170C2×C8—2982no—
171C2×C8—1491no—
172C2×C8—1491no—
173C2×C8C22×D14911yescharacteristic
174C2×C8C22×D14911yescharacteristic
175C4⋊C4—2982no—
176C4⋊C4—2982no—
177C4⋊C4—2982no—
178C4⋊C4—1492no—
179C4⋊C4—1492no—
180C4⋊C4—1491no—
181C4⋊C4C22×D14912yes—
182C22⋊C4—22no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C22⋊C4—1491no—
187C22⋊C4—1491no—
188C42—2982no—
189C42—1491no—
190C23—22no—
191C23—1491no—
192C23D4×D14911yescharacteristic
193D4—22no—
194D4—22no—
195D4—82no—
196D4—2982no—
197D4—5964no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—2981no—
202C2×C4—2981no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—1491no—
206C2×C4—1491no—
207C2×C4—1491no—
208C2×C4—11922no—
209C2×C4—11922no—
210C2×C4D4×D14911yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—21no—
213C8—2981no—
214C8—2981no—
215C8#1455873512yes—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—2981no—
223C22—2981no—
224C22—1492no—
225C22C2×D4×D14911yescharacteristic
226C4—21no—
227C4—42no—
228C4—2981no—
229C4—2981no—
230C4—2981no—
231C4—5962no—
232C4—5962no—
233C4C2×#1455873511yescharacteristic
234C4#1801195811yescharacteristic
235C2—41no—
236C2—82no—
237C2—2982no—
238C2#2375027511yescharacteristic
239C2#135×D14911yescharacteristic
240C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149#3339
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23750322C2semidirect
2. #23750026C2semidirect
3. #23749946C2semidirect
4. #23749942C2semidirect
5. #23749927C2semidirect
6. #23749858C2semidirect
7. D8×Dic149C2semidirect
8. C8×C22⋊D149C2semidirect
9. #23749663C2semidirect
10. #107×D149C2semidirect
11. #466×C149C2semidirect
120. C149#3339semidirect
128. #466D149semidirect

Maximal subgroups

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

subgroupindex
#237503222
#237500262
#237499462
#237499422
#237499272
#237498582
D8×Dic1492
C8×C22⋊D1492
#237496632
#107×D1492
#466×C1492
#3339149