Finite Group Databasebeta

← C2×#23749962 #34054598

Subgroups — C2×#23749962 #34054598

Order 19072.

460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#18011891C211yesmaximal, characteristic
2C2×C4⋊C4×D149C211yesmaximal, characteristic
3#23749962C218yesmaximal, direct product factor
4C2×#18011844C211yesmaximal, characteristic, complemented
5C2×#18011836C211yesmaximal, characteristic, complemented
6C2×#18011834C211yesmaximal, characteristic, complemented
7C2×#18011823C211yesmaximal, characteristic
8C2×#107×C149C211yesmaximal, characteristic, complemented
9C22×Dic298C2211yescharacteristic
10C22×C4×D149—21no—
11C22×C4×D149C2211yescharacteristic
12C22×#11924746C2211yescharacteristic
13#18011891—22no—
14#18011891C2214yes—
15C2×C4⋊Dic149—21no—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×#14558715—21no—
18C4⋊C4×D149—22no—
19C4⋊C4×D149C2214yes—
20C2×#14558713—21no—
21#18011844C2214yescomplemented
22#18011836C2214yescomplemented
23#18011834C2214yescomplemented
24#18011823C2214yes—
25C22×C8×C149C2211yescharacteristic
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#107×C149C2214yescomplemented
29C23×D149D411yescharacteristic
30C2×Dic298—21no—
31C2×Dic298—22no—
32C2×Dic298—22no—
33C2×Dic298C2312yes—
34C22×Dic149—21no—
35C22×Dic149—21no—
36C22×Dic149D411yescharacteristic
37C2×C4×D149—24no—
38C2×C4×D149—22no—
39C2×C4×D149—22no—
40C2×C4×D149—44no—
41C2×C4×D149D412yes—
42C2×C4×D149C2312yes—
43C2×#11924746—22no—
44C2×#11924746C2312yes—
45C4⋊Dic149—24no—
46C4⋊Dic149—21no—
47C4⋊Dic149C2312yes—
48#14558715—24no—
49#14558713—24no—
50C22×C4×C149—21no—
51C22×C4×C149—21no—
52C22×C4×C149C2311yescharacteristic
53C2×C8×C149—22no—
54C2×C8×C149C2312yes—
55C4⋊C4×C149—21no—
56C4⋊C4×C149—21no—
57C4⋊C4×C149C2312yes—
58C4⋊C4×C149C2312yes—
59C22×D149—22no—
60C22×D149—22no—
61C22×D149Q1614yes—
62C22×D149C2×D412yes—
63Dic298—22no—
64Dic298—22no—
65Dic298—42no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—42no—
70C2×Dic149—42no—
71C2×Dic149C2×D412yes—
72C4×D149—24no—
73C4×D149—22no—
74C4×D149—22no—
75C4×D149—48no—
76#11924746—22no—
77C23×C149C2×D411yescharacteristic
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—42no—
81C2×C4×C149—42no—
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149#4112yes—
84C2×C4×C149#4112yes—
85C2×C4×C149C2411yescharacteristic
86C8×C149—22no—
87C22×C149#12312yes—
88C22×C149C2×Q1612yes—
89C22×C149AGL(1,ℤ/8)12yes—
90C22×C149C22×D411yescharacteristic
91C2×D149—22no—
92C2×D149—22no—
93C2×D149—28no—
94C2×D149C2×Q1614yes—
95C4×C149—42no—
96C4×C149—42no—
97C4×C149#12312yes—
98C4×C149C2×#4111yescharacteristic
99C4×C149C2×#4111yescharacteristic
100Dic149—22no—
101Dic149—42no—
102Dic149—42no—
103C2×C149#48414yescomplemented
104C2×C149C2×#12311yescharacteristic
105C2×C149C22×Q1611yescharacteristic
106C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
107D149—24no—
108C149C2×#48411yescharacteristic, complemented, Sylow
109C2×#484—1491nomaximal, Sylow
110C2×C22⋊Q8—1491no—
111C22×C4⋊C4—1491no—
112#484—1498no—
113C2×#107—1491no—
114C2×#107D14911yescharacteristic, complemented
115C2×#103—1491no—
116C2×#103—1491no—
117C2×C22⋊C8—1491no—
118C22×Q8—1491no—
119C23×C4—2981no—
120C23×C4—1491no—
121C22×C8—1491no—
122C22×C8C2×D14911yescharacteristic
123C22⋊Q8—2982no—
124C22⋊Q8—1494no—
125C2×C4⋊C4—2982no—
126C2×C4⋊C4—2981no—
127C2×C4⋊C4—2981no—
128C2×C4⋊C4—1491no—
129C2×C4⋊C4—1494no—
130C2×C4⋊C4C2×D14911yescharacteristic
131C2×C4⋊C4C2×D14911yescharacteristic
132C2×C22⋊C4—2981no—
133#107—1494no—
134#107C2×D14914yescomplemented
135#103—1494no—
136#103—1494no—
137C22⋊C8—1494no—
138C24—1491no—
139C2×Q8—2981no—
140C2×Q8—2982no—
141C2×Q8—2982no—
142C2×Q8—1492no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2984no—
146C22×C4—2982no—
147C22×C4—2982no—
148C22×C4—2981no—
149C22×C4—2981no—
150C22×C4—5964no—
151C22×C4—1491no—
152C22×C4—1492no—
153C22×C4—1492no—
154C22×C4C22×D14911yescharacteristic
155C2×C8—22no—
156C2×C8—2982no—
157C2×C8—1492no—
158C2×C8C22×D14912yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2984no—
162C4⋊C4—2984no—
163C4⋊C4—2981no—
164C4⋊C4—1492no—
165C4⋊C4C22×D14912yes—
166C4⋊C4C22×D14912yes—
167C22⋊C4—2984no—
168C23—2982no—
169C23—2982no—
170C23—1494no—
171C23—1492no—
172C23D4×D14911yescharacteristic
173Q8—2982no—
174Q8—2982no—
175Q8—5962no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—2984no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—5968no—
187C2×C4—5962no—
188C2×C4—5962no—
189C2×C4—1492no—
190C2×C4D4×D14911yescharacteristic
191C2×C4#1455873612yes—
192C2×C4#1455873712yes—
193C2×C4C23×D14911yescharacteristic
194C8—22no—
195C8—2982no—
196C22—2982no—
197C22—2988no—
198C22—2982no—
199C22—1494no—
200C22#1801189612yes—
201C22Q16×D14912yes—
202C22#1801193512yes—
203C22C2×D4×D14911yescharacteristic
204C4—42no—
205C4—42no—
206C4—2982no—
207C4—5962no—
208C4—5962no—
209C4#1801189612yes—
210C4C2×#1455873611yescharacteristic
211C4C2×#1455873711yescharacteristic
212C2—2984no—
213C2#2374996214yesdirect product factor
214C2C2×#1801189611yescharacteristic
215C2C2×Q16×D14911yescharacteristic
216C2C2×#1801193511yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#107×C149C2
socleC23×C149C2×D4
prime radicalC23×D149D4
hypercenterC2×#107D149
hypocenterC149C2×#484
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #23749962C2direct (N × H)
4. C2×#18011844C2semidirect
5. C2×#18011836C2semidirect
6. C2×#18011834C2semidirect
8. C2×#107×C149C2semidirect
21. #18011844C22semidirect
22. #18011836C22semidirect
23. #18011834C22semidirect
28. #107×C149C22semidirect
103. C2×C149#484semidirect
108. C149C2×#484semidirect
114. C2×#107D149semidirect
134. #107C2×D149semidirect
213. C2#23749962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180118912
C2×C4⋊C4×D1492
#237499622
C2×#180118442
C2×#180118362
C2×#180118342
C2×#180118232
C2×#107×C1492
C2×#484149