Finite Group Databasebeta

← #34055075

Subgroups — #34055075

Order 19072.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 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
1#23750178C211yesmaximal, characteristic, complemented
2C2×#18011898C211yesmaximal, characteristic
3#23749983C214yesmaximal, complemented
4#23749978C214yesmaximal, complemented
5#23749635C211yesmaximal, characteristic, complemented
6#23749633C211yesmaximal, characteristic, complemented
7#23749630C211yesmaximal, characteristic
8M16×Dic149C211yesmaximal, characteristic, complemented
9#418×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11C2×#14558720C2211yescharacteristic
12#18011910C2212yescomplemented
13#18011902C2212yescomplemented
14#18011898—22no—
15#18011898C2212yes—
16#18011898C2212yes—
17#18011888—22no—
18C4×Dic298—22no—
19#18011870C2211yescharacteristic
20C2×C22⋊Dic149—22no—
21C2×C4×Dic149C2211yescharacteristic
22#18011836C2214yescomplemented
23#18011834C2214yescomplemented
24#18011832C2214yes—
25#18011821C2212yescomplemented
26C8×Dic149C2212yescomplemented
27C22×D4×C149C2211yescharacteristic
28C2×M16×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30#102×C149C2214yes—
31C2×Dic298—22no—
32C2×Dic298—21no—
33C2×Dic298—22no—
34C2×Dic298—22no—
35C2×Dic298C2312yes—
36C22×Dic149—21no—
37C22×Dic149D412yes—
38#14558720—22no—
39C2×#11924746C2312yes—
40C4⋊Dic149—22no—
41C4⋊Dic149C2312yes—
42#14558715—22no—
43#14558715—22no—
44C22⋊Dic149—24no—
45C22⋊Dic149—24no—
46C22⋊Dic149—21no—
47C4×Dic149—21no—
48C4×Dic149D412yes—
49C4×Dic149C2311yescharacteristic
50C4×Dic149C2311yescharacteristic
51C24×C149—21no—
52C2×D4×C149—21no—
53C2×D4×C149—22no—
54C2×D4×C149—22no—
55C2×D4×C149C2312yes—
56C22×C4×C149C2311yescharacteristic
57M16×C149—22no—
58C2×C8×C149C2312yes—
59C4⋊C4×C149C2312yes—
60C22⋊C4×C149—21no—
61C42×C149—21no—
62Dic298—22no—
63Dic298—22no—
64Dic298—44no—
65Dic298—42no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—42no—
69C2×Dic149—42no—
70C2×Dic149C2×D412yes—
71C2×Dic149C2×D412yes—
72#11924746—22no—
73C23×C149—22no—
74C23×C149—44no—
75C23×C149—42no—
76C23×C149C2×D411yescharacteristic
77D4×C149—22no—
78D4×C149—22no—
79D4×C149—42no—
80C2×C4×C149—22no—
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149#4112yes—
83C2×C4×C149#4112yes—
84C2×C4×C149C2411yescharacteristic
85C8×C149—22no—
86C22×C149—22no—
87C22×C149—42no—
88C22×C149—44no—
89C22×C149—84no—
90C22×C149#12412yes—
91C22×C149C22×D411yescharacteristic
92C4×C149—42no—
93C4×C149#12412yes—
94C4×C149C2×#4111yescharacteristic
95C4×C149C2×#4111yescharacteristic
96Dic149—22no—
97Dic149—22no—
98Dic149—42no—
99Dic149—42no—
100C2×C149—22no—
101C2×C149—82no—
102C2×C149C2×#12411yescharacteristic
103C2×C149#57512yes—
104C149#314011yescharacteristic, complemented, Sylow
105#3140—1491nomaximal, Sylow
106#533—1491no—
107C2×#124—1491no—
108#489—1494no—
109#488—1494no—
110#419—1491no—
111#419—1491no—
112#418—1491no—
113#418D14911yescharacteristic
114C4×M16—1491no—
115C22×Q8—1491no—
116C22×D4C2×D14911yescharacteristic
117C2×M16—1491no—
118C2×M16C2×D14911yescharacteristic
119C4⋊Q8—1492no—
120#125—1492no—
121#124—2982no—
122#124—1492no—
123#124—1492no—
124C22⋊Q8—2982no—
125C4×Q8—2982no—
126#117—1491no—
127#117C2×D14911yescharacteristic
128C2×C22⋊C4—2982no—
129C2×C42—1491no—
130#103—1494no—
131#103—1494no—
132#102—1494no—
133#102C2×D14914yes—
134#97—1492no—
135C4×C8—1492no—
136C24—21no—
137C2×Q8—2982no—
138C2×Q8—2981no—
139C2×Q8—2982no—
140C2×Q8—2982no—
141C2×Q8—1492no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22×D14912yes—
146C22×C4—2981no—
147C22×C4—1492no—
148C22×C4C22×D14911yescharacteristic
149M16—22no—
150M16—2982no—
151C2×C8—1492no—
152C2×C8C22×D14912yes—
153C4⋊C4—2982no—
154C4⋊C4—2982no—
155C4⋊C4—2982no—
156C4⋊C4—1492no—
157C4⋊C4C22×D14912yes—
158C22⋊C4—21no—
159C22⋊C4—2981no—
160C22⋊C4—2984no—
161C22⋊C4—2984no—
162C42—21no—
163C42—2981no—
164C42—1492no—
165C42—1491no—
166C42—1491no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D14911yescharacteristic
171Q8—2982no—
172Q8—2982no—
173Q8—5964no—
174Q8—5962no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—5962no—
182C2×C4—5962no—
183C2×C4—1492no—
184C2×C4—1492no—
185C2×C4D4×D14911yescharacteristic
186C2×C4#1455873512yes—
187C2×C4#1455873612yes—
188C2×C4C23×D14911yescharacteristic
189C8—22no—
190C8—2982no—
191C22—22no—
192C22—44no—
193C22—42no—
194C22—84no—
195C22#1801189712yes—
196C22C2×D4×D14911yescharacteristic
197C4—42no—
198C4—2982no—
199C4—2982no—
200C4—5962no—
201C4—5962no—
202C4#1801189712yes—
203C4C2×#1455873511yescharacteristic
204C4C2×#1455873611yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#1801189711yescharacteristic
208C2#2375042112yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#418×C149C2
socleC22×C149C22×D4
prime radicalC22×D4×C149C22
hypercenter#418D149
hypocenterC149#3140
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #23750178C2semidirect
3. #23749983C2semidirect
4. #23749978C2semidirect
5. #23749635C2semidirect
6. #23749633C2semidirect
8. M16×Dic149C2semidirect
12. #18011910C22semidirect
13. #18011902C22semidirect
22. #18011836C22semidirect
23. #18011834C22semidirect
25. #18011821C22semidirect
26. C8×Dic149C22semidirect
104. C149#3140semidirect

Maximal subgroups

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

subgroupindex
#237501782
C2×#180118982
#237499832
#237499782
#237496352
#237496332
#237496302
M16×Dic1492
#418×C1492
#3140149