Finite Group Databasebeta

← #34055336

Subgroups — #34055336

Order 19072.

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

normal subgroups only

This group has 386 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#23750228C212yesmaximal, complemented
2#23750025C211yesmaximal, characteristic, complemented
3#23750000C211yesmaximal, characteristic, complemented
4#23749988C212yesmaximal, complemented
5#23749878C211yesmaximal, characteristic, complemented
6#23749859C212yesmaximal, complemented
7#23749737C211yesmaximal, characteristic, complemented
8#23749736C211yesmaximal, characteristic, complemented
9#23749705C212yesmaximal, complemented
10#23749583C211yesmaximal, characteristic, complemented
11#469×C149C211yesmaximal, characteristic, complemented
12C2×D1192C2211yescharacteristic
13C2×#14558721C2212yes—
14C22×#11924746C2211yescharacteristic
15#18011907C2212yes—
16#18011902C2212yes—
17#18011895—22no—
18#18011893—22no—
19#18011885C2212yes—
20#18011883—22no—
21#18011882—22no—
22D4×Dic149C2212yes—
23#18011873C2212yes—
24#18011870C2211yescharacteristic
25#18011844C2212yes—
26#18011843C2211yescharacteristic
27#18011833C2212yes—
28#18011832C2212yes—
29#18011831C2212yes—
30#18011821C2211yescharacteristic
31#18011821C2211yescharacteristic
32C8×Dic149C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×D8×C149C2211yescharacteristic
35C2×M16×C149C2211yescharacteristic
36#121×C149C2212yes—
37#106×C149C2211yescharacteristic
38#102×C149C2212yes—
39C2×D596C2312yes—
40C2×C22⋊D149—22no—
41C2×C22⋊D149—22no—
42C2×C22⋊D149—22no—
43C22×Dic149—22no—
44C2×C4×D149—22no—
45D1192—22no—
46#14558721—24no—
47C2×#11924746—22no—
48C2×#11924746C2311yescharacteristic
49C2×#11924746C2311yescharacteristic
50C4⋊Dic149—22no—
51C4⋊Dic149D412yes—
52C4⋊Dic149C2312yes—
53#14558715—22no—
54C22⋊Dic149—22no—
55C22⋊Dic149D412yes—
56#14558713—22no—
57#14558713—22no—
58C4×Dic149C2311yescharacteristic
59C4×Dic149C2311yescharacteristic
60C2×D4×C149—22no—
61C2×D4×C149C2312yes—
62C22×C4×C149C2311yescharacteristic
63D8×C149—22no—
64M16×C149—22no—
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2311yescharacteristic
67C4⋊C4×C149C2312yes—
68C22⋊C4×C149—22no—
69C22×D149—22no—
70D596—22no—
71D596—22no—
72C22⋊D149—82no—
73C22⋊D149—82no—
74C22⋊D149—82no—
75C2×Dic149—22no—
76C2×Dic149—82no—
77C2×Dic149C2×D412yes—
78C2×Dic149C2×D412yes—
79C4×D149—82no—
80#11924746—21no—
81#11924746#4112yes—
82C23×C149—22no—
83C23×C149C2×D411yescharacteristic
84D4×C149—22no—
85D4×C149—22no—
86D4×C149—82no—
87C2×C4×C149—21no—
88C2×C4×C149—21no—
89C2×C4×C149—22no—
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2411yescharacteristic
92C8×C149—21no—
93C8×C149#4112yes—
94C22×C149—21no—
95C22×C149—22no—
96C22×C149—42no—
97C22×C149—42no—
98C22×C149—42no—
99C22×C149C22×D411yescharacteristic
100C2×D149—42no—
101C2×D149—42no—
102C2×D149—42no—
103C4×C149—21no—
104C4×C149—42no—
105C4×C149C2×#4111yescharacteristic
106C4×C149C2×#4111yescharacteristic
107Dic149—22no—
108Dic149—22no—
109Dic149—42no—
110C2×C149—41no—
111C2×C149—82no—
112C2×C149#53211yescharacteristic
113C2×C149#57612yes—
114D149—82no—
115C149#317611yescharacteristic, complemented, Sylow
116#3176—1491nomaximal, Sylow
117#540—1492no—
118#499—1491no—
119#493—1491no—
120#490—1492no—
121#469—1491no—
122#469D14911yescharacteristic, complemented
123#466—1492no—
124#442—1491no—
125#442—1491no—
126C4×D8—1492no—
127#405—1491no—
128C2×D8—1492no—
129C2×D8—1491no—
130C2×D8C2×D14911yescharacteristic
131C2×M16C2×D14911yescharacteristic
132C22×C8—1491no—
133#127—1492no—
134#125—1492no—
135#123—2982no—
136#123—2982no—
137#121—2982no—
138#121—2982no—
139#121—1492no—
140#121C2×D14912yes—
141C4×D4—1492no—
142C4×D4—1492no—
143#117—1491no—
144#107—1492no—
145#106—1491no—
146#106C2×D14911yescharacteristic
147#102—1492no—
148#102—1492no—
149#102—1492no—
150#102C2×D14912yes—
151#97—1491no—
152#97—1491no—
153C4×C8—1491no—
154C4×C8—1491no—
155C2×D4—22no—
156C2×D4—2982no—
157C2×D4—2982no—
158C2×D4—2982no—
159C2×D4—1492no—
160C2×D4C22×D14912yes—
161C22×C4—2982no—
162C22×C4—2982no—
163C22×C4C22×D14911yescharacteristic
164D8—22no—
165D8—2984no—
166D8—2982no—
167M16—22no—
168C2×C8—2982no—
169C2×C8—1491no—
170C2×C8—1491no—
171C2×C8C22×D14911yescharacteristic
172C2×C8C22×D14911yescharacteristic
173C4⋊C4—2982no—
174C4⋊C4—2982no—
175C4⋊C4—1492no—
176C4⋊C4—1492no—
177C4⋊C4C22×D14912yes—
178C22⋊C4—22no—
179C22⋊C4—2982no—
180C22⋊C4—2982no—
181C22⋊C4—2982no—
182C22⋊C4—1492no—
183C42—1491no—
184C42—1491no—
185C23—22no—
186C23—2982no—
187C23D4×D14911yescharacteristic
188D4—22no—
189D4—22no—
190D4—82no—
191D4—2982no—
192D4—2982no—
193D4—11922no—
194D4—11922no—
195D4—11922no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—2982no—
200C2×C4—1492no—
201C2×C4—1492no—
202C2×C4—11922no—
203C2×C4—11922no—
204C2×C4D4×D14911yescharacteristic
205C2×C4C23×D14911yescharacteristic
206C8—21no—
207C8—2981no—
208C8—1492no—
209C8#1455873512yes—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—5962no—
216C22—5962no—
217C22—5962no—
218C22C2×D4×D14911yescharacteristic
219C4—21no—
220C4—42no—
221C4—2982no—
222C4—2982no—
223C4—5962no—
224C4#41×D14911yescharacteristic
225C4C2×#1455873511yescharacteristic
226C2—41no—
227C2—82no—
228C2—11922no—
229C2#2375017011yescharacteristic
230C2#2375042912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3176
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23750228C2semidirect
2. #23750025C2semidirect
3. #23750000C2semidirect
4. #23749988C2semidirect
5. #23749878C2semidirect
6. #23749859C2semidirect
7. #23749737C2semidirect
8. #23749736C2semidirect
9. #23749705C2semidirect
10. #23749583C2semidirect
11. #469×C149C2semidirect
115. C149#3176semidirect
122. #469D149semidirect

Maximal subgroups

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

subgroupindex
#237502282
#237500252
#237500002
#237499882
#237498782
#237498592
#237497372
#237497362
#237497052
#237495832
#469×C1492
#3176149