Finite Group Databasebeta

← #34055079

Subgroups — #34055079

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×#18011900C211yesmaximal, characteristic
3#23749986C214yesmaximal, complemented
4#23749981C214yesmaximal, complemented
5#23749634C211yesmaximal, characteristic, complemented
6#23749631C211yesmaximal, characteristic
7#23749629C211yesmaximal, characteristic
8M16×Dic149C211yesmaximal, characteristic, complemented
9#419×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C2×#14558720C2211yescharacteristic
12#18011910C2212yescomplemented
13#18011902C2212yescomplemented
14#18011900—22no—
15#18011900C2212yes—
16#18011900C2212yes—
17#18011888—22no—
18C4×Dic298—22no—
19#18011870C2211yescharacteristic
20C2×#14558713—22no—
21C2×C4×Dic149C2211yescharacteristic
22#18011835C2214yescomplemented
23#18011833C2214yes—
24#18011831C2214yes—
25#18011821C2212yescomplemented
26C8×Dic149C2212yescomplemented
27C22×Q8×C149C2211yescharacteristic
28C2×M16×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30#103×C149C2214yescomplemented
31C23×D149—21no—
32C2×Dic298—22no—
33C2×D596—21no—
34C2×D596—22no—
35C2×D596—22no—
36C2×D596C2312yes—
37C22×Dic149D412yes—
38#14558720—22no—
39C2×#11924746C2312yes—
40C4⋊Dic149—22no—
41C4⋊Dic149C2312yes—
42#14558715—22no—
43#14558715—22no—
44C22⋊Dic149—21no—
45#14558713—24no—
46#14558713—24no—
47C4×Dic149—21no—
48C4×Dic149D412yes—
49C4×Dic149C2311yescharacteristic
50C4×Dic149C2311yescharacteristic
51C2×Q8×C149—21no—
52C2×Q8×C149—22no—
53C2×Q8×C149—22no—
54C2×Q8×C149C2312yes—
55C22×C4×C149—21no—
56C22×C4×C149C2311yescharacteristic
57M16×C149—22no—
58C2×C8×C149C2312yes—
59C4⋊C4×C149C2312yes—
60C22⋊C4×C149—21no—
61C42×C149—21no—
62C22×D149—22no—
63C22×D149—44no—
64C22×D149—42no—
65Dic298—44no—
66D596—22no—
67D596—22no—
68D596—42no—
69C2×Dic149—22no—
70C2×Dic149—42no—
71C2×Dic149C2×D412yes—
72C2×Dic149C2×D412yes—
73#11924746—22no—
74C23×C149C2×D411yescharacteristic
75Q8×C149—22no—
76Q8×C149—22no—
77Q8×C149—42no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—42no—
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149#4112yes—
83C2×C4×C149#4112yes—
84C2×C4×C149C2411yescharacteristic
85C8×C149—22no—
86C22×C149—22no—
87C22×C149#12412yes—
88C22×C149C22×D411yescharacteristic
89C2×D149—42no—
90C2×D149—44no—
91C2×D149—84no—
92C4×C149—42no—
93C4×C149—42no—
94C4×C149#12412yes—
95C4×C149C2×#4111yescharacteristic
96C4×C149C2×#4111yescharacteristic
97Dic149—22no—
98Dic149—22no—
99Dic149—42no—
100C2×C149—22no—
101C2×C149C2×#12411yescharacteristic
102C2×C149#57512yes—
103D149—82no—
104C149#314011yescharacteristic, complemented, Sylow
105#3140—1491nomaximal, Sylow
106#533—1491no—
107C2×#124—1491no—
108#489—1494no—
109#488—1494no—
110#419—1491no—
111#419D14911yescharacteristic, complemented
112#418—1491no—
113#418—1491no—
114C4×M16—1491no—
115C22×Q8C2×D14911yescharacteristic
116C22×D4—1491no—
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#103C2×D14914yescomplemented
132#102—1494no—
133#102—1494no—
134#97—1492no—
135C4×C8—1492no—
136C24—2981no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—2982no—
141C2×Q8C22×D14912yes—
142C2×D4—2981no—
143C2×D4—2982no—
144C2×D4—2982no—
145C2×D4—1492no—
146C22×C4—21no—
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—2984no—
160C22⋊C4—2984no—
161C22⋊C4—2981no—
162C42—21no—
163C42—2981no—
164C42—1492no—
165C42—1491no—
166C42—1491no—
167C23—2982no—
168C23—5964no—
169C23—5962no—
170C23D4×D14911yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—42no—
174Q8—5964no—
175D4—2982no—
176D4—2982no—
177D4—5962no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—2982no—
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—5964no—
193C22—5962no—
194C22—11924no—
195C22#1801189712yes—
196C22C2×D4×D14911yescharacteristic
197C4—42no—
198C4—42no—
199C4—2982no—
200C4—2982no—
201C4—5962no—
202C4#1801189712yes—
203C4C2×#1455873511yescharacteristic
204C4C2×#1455873611yescharacteristic
205C2—22no—
206C2—11922no—
207C2C2×#1801189711yescharacteristic
208C2#2375042412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#419×C149C2
socleC22×C149C22×D4
prime radicalC22×D596C22
hypercenter#419D149
hypocenterC149#3140
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #23750178C2semidirect
3. #23749986C2semidirect
4. #23749981C2semidirect
5. #23749634C2semidirect
8. M16×Dic149C2semidirect
9. #419×C149C2semidirect
12. #18011910C22semidirect
13. #18011902C22semidirect
22. #18011835C22semidirect
25. #18011821C22semidirect
26. C8×Dic149C22semidirect
30. #103×C149C22semidirect
104. C149#3140semidirect
111. #419D149semidirect
131. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501782
C2×#180119002
#237499862
#237499812
#237496342
#237496312
#237496292
M16×Dic1492
#419×C1492
#3140149