Finite Group Databasebeta

← C2×#23749968 #34054585

Subgroups — C2×#23749968 #34054585

Order 19072.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18011869C211yesmaximal, characteristic
3#23749968C218yesmaximal, direct product factor
4C2×#18011842C211yesmaximal, characteristic, complemented
5C2×#18011836C211yesmaximal, characteristic, complemented
6C2×#18011834C211yesmaximal, characteristic, complemented
7C2×#18011823C211yesmaximal, characteristic
8C2×#107×C149C211yesmaximal, characteristic, complemented
9C22×Dic298C2211yescharacteristic
10C22×C4×D149C2211yescharacteristic
11C22×#11924746C2211yescharacteristic
12#18011891—22no—
13#18011891C2214yes—
14#18011869—22no—
15#18011869C2214yes—
16C2×C4⋊Dic149—21no—
17C2×C4⋊Dic149C2211yescharacteristic
18C2×#14558713—21no—
19C2×#14558713—21no—
20C2×C4×Dic149—21no—
21#18011842C2214yescomplemented
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—22no—
38C2×C4×D149—22no—
39C2×C4×D149D412yes—
40C2×C4×D149C2312yes—
41C2×#11924746—22no—
42C2×#11924746C2312yes—
43C4⋊Dic149—24no—
44C4⋊Dic149—21no—
45C4⋊Dic149C2312yes—
46#14558713—24no—
47#14558713—24no—
48C4×Dic149—24no—
49C22×C4×C149—21no—
50C22×C4×C149—21no—
51C22×C4×C149C2311yescharacteristic
52C2×C8×C149—22no—
53C2×C8×C149C2312yes—
54C4⋊C4×C149—21no—
55C4⋊C4×C149—21no—
56C4⋊C4×C149C2312yes—
57C4⋊C4×C149C2312yes—
58C22×D149—22no—
59C22×D149—22no—
60C22×D149—22no—
61C22×D149C2×D412yes—
62Dic298—22no—
63Dic298—22no—
64Dic298—42no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—42no—
69C2×Dic149—42no—
70C2×Dic149C2×D412yes—
71C4×D149—24no—
72C4×D149—22no—
73C4×D149—22no—
74#11924746—22no—
75C23×C149C2×D411yescharacteristic
76C2×C4×C149—22no—
77C2×C4×C149—22no—
78C2×C4×C149—42no—
79C2×C4×C149—42no—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149#4112yes—
82C2×C4×C149#4112yes—
83C2×C4×C149C2411yescharacteristic
84C8×C149—22no—
85C22×C149#12312yes—
86C22×C149#13512yes—
87C22×C149#13712yes—
88C22×C149C22×D411yescharacteristic
89C2×D149—22no—
90C2×D149—22no—
91C2×D149—22no—
92C2×D149—44no—
93C4×C149—42no—
94C4×C149—42no—
95C4×C149#12312yes—
96C4×C149C2×#4111yescharacteristic
97C4×C149C2×#4111yescharacteristic
98Dic149—22no—
99Dic149—42no—
100Dic149—42no—
101C2×C149#48514yescomplemented
102C2×C149C2×#12311yescharacteristic
103C2×C149C2×#13511yescharacteristic
104C2×C149C2×#13711yescharacteristic
105D149—42no—
106C149C2×#48511yescharacteristic, complemented, Sylow
107C2×#485—1491nomaximal, Sylow
108C2×C22⋊Q8—1491no—
109C2×#117—1491no—
110#485—1498no—
111C2×#107D14911yescharacteristic, complemented
112C2×#106—1491no—
113C2×#103—1491no—
114C2×#103—1491no—
115C2×C22⋊C8—1491no—
116C22×Q8—1491no—
117C23×C4—1491no—
118C22×C8—1491no—
119C22×C8C2×D14911yescharacteristic
120C22⋊Q8—2982no—
121C22⋊Q8—1494no—
122#117—2982no—
123#117—1494no—
124C2×C4⋊C4—2981no—
125C2×C4⋊C4—1491no—
126C2×C4⋊C4C2×D14911yescharacteristic
127C2×C4⋊C4C2×D14911yescharacteristic
128C2×C22⋊C4—2981no—
129C2×C22⋊C4—2981no—
130C2×C42—2981no—
131#107C2×D14914yescomplemented
132#106—1494no—
133#103—1494no—
134#103—1494no—
135C22⋊C8—1494no—
136C24—1491no—
137C2×Q8—2981no—
138C2×Q8—2982no—
139C2×Q8—2982no—
140C2×Q8—1492no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—2982no—
144C22×C4—2982no—
145C22×C4—2981no—
146C22×C4—2981no—
147C22×C4—1491no—
148C22×C4—1492no—
149C22×C4—1492no—
150C22×C4C22×D14911yescharacteristic
151C2×C8—22no—
152C2×C8—2982no—
153C2×C8—1492no—
154C2×C8C22×D14912yes—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—2984no—
158C4⋊C4—2981no—
159C4⋊C4—1492no—
160C4⋊C4C22×D14912yes—
161C4⋊C4C22×D14912yes—
162C22⋊C4—2984no—
163C22⋊C4—2984no—
164C42—2984no—
165C23—2982no—
166C23—2982no—
167C23—2982no—
168C23—1492no—
169C23D4×D14911yescharacteristic
170Q8—2982no—
171Q8—2982no—
172Q8—5962no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—2982no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—2984no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—5962no—
184C2×C4—5962no—
185C2×C4—1492no—
186C2×C4D4×D14911yescharacteristic
187C2×C4#1455873612yes—
188C2×C4#1455873712yes—
189C2×C4C23×D14911yescharacteristic
190C8—22no—
191C8—2982no—
192C22—2982no—
193C22—2982no—
194C22—2982no—
195C22—5964no—
196C22#1801189612yes—
197C22#1801193012yes—
198C22#1801194312yes—
199C22C2×D4×D14911yescharacteristic
200C4—42no—
201C4—42no—
202C4—2982no—
203C4—5962no—
204C4—5962no—
205C4#1801189612yes—
206C4C2×#1455873611yescharacteristic
207C4C2×#1455873711yescharacteristic
208C2—5962no—
209C2#2374996814yesdirect product factor
210C2C2×#1801189611yescharacteristic
211C2C2×#1801193011yescharacteristic
212C2C2×#1801194311yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#107×C149C2
socleC23×C149C2×D4
prime radicalC23×D149D4
hypercenterC2×#107D149
hypocenterC149C2×#485
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. #23749968C2direct (N × H)
4. C2×#18011842C2semidirect
5. C2×#18011836C2semidirect
6. C2×#18011834C2semidirect
8. C2×#107×C149C2semidirect
21. #18011842C22semidirect
22. #18011836C22semidirect
23. #18011834C22semidirect
28. #107×C149C22semidirect
101. C2×C149#485semidirect
106. C149C2×#485semidirect
111. C2×#107D149semidirect
131. #107C2×D149semidirect
209. C2#23749968direct (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×#180118692
#237499682
C2×#180118422
C2×#180118362
C2×#180118342
C2×#180118232
C2×#107×C1492
C2×#485149