Finite Group Databasebeta

← C2×#23749951 #34054577

Subgroups — C2×#23749951 #34054577

Order 19072.

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

normal subgroups only

This group has 468 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×#18011886C211yesmaximal, characteristic
2C2×#18011869C211yesmaximal, characteristic, complemented
3#23749951C218yesmaximal, direct product factor
4C2×#18011844C211yesmaximal, characteristic, complemented
5C2×#18011833C211yesmaximal, characteristic, complemented
6C2×#18011831C211yesmaximal, characteristic, complemented
7C2×#18011823C211yesmaximal, characteristic, complemented
8C2×#106×C149C211yesmaximal, characteristic, complemented
9C22×D596—21no—
10C22×D596C2211yescharacteristic
11C22×C4×D149C2211yescharacteristic
12C22×#11924746C2211yescharacteristic
13#18011886—22no—
14#18011886C2214yes—
15#18011869—22no—
16#18011869C2214yescomplemented
17C2×C4⋊Dic149C2211yescharacteristic
18C2×#14558713—21no—
19C2×#14558713—21no—
20C2×C4×Dic149—21no—
21#18011844C2214yescomplemented
22#18011833C2214yescomplemented
23#18011831C2214yescomplemented
24#18011823C2214yescomplemented
25C22×C8×C149C2211yescharacteristic
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#106×C149C2214yescomplemented
29C23×D149—21no—
30C23×D149D411yescharacteristic
31C2×D596—24no—
32C2×D596—21no—
33C2×D596—22no—
34C2×D596—22no—
35C2×D596—44no—
36C2×D596C2312yes—
37C22×Dic149—21no—
38C22×Dic149D411yescharacteristic
39C2×C4×D149—22no—
40C2×C4×D149—22no—
41C2×C4×D149D412yes—
42C2×C4×D149C2312yes—
43C2×#11924746—22no—
44C2×#11924746C2312yes—
45C4⋊Dic149—21no—
46C4⋊Dic149C2312yes—
47#14558713—24no—
48#14558713—24no—
49C4×Dic149—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×D149—22no—
62C22×D149—22no—
63C22×D149—42no—
64C22×D149—42no—
65C22×D149—42no—
66C22×D149C2×D412yes—
67D596—22no—
68D596—22no—
69D596—48no—
70D596—42no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—42no—
74C2×Dic149C2×D412yes—
75C4×D149—24no—
76C4×D149—22no—
77C4×D149—22no—
78#11924746—22no—
79C23×C149C2×D411yescharacteristic
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—42no—
83C2×C4×C149—42no—
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149#4112yes—
86C2×C4×C149#4112yes—
87C2×C4×C149C2411yescharacteristic
88C8×C149—22no—
89C22×C149#12312yes—
90C22×C149#13512yes—
91C22×C149AGL(1,ℤ/8)12yes—
92C22×C149C22×D411yescharacteristic
93C2×D149—22no—
94C2×D149—22no—
95C2×D149—22no—
96C2×D149—44no—
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—42no—
100C2×D149—84no—
101C4×C149—42no—
102C4×C149—42no—
103C4×C149#12312yes—
104C4×C149C2×#4111yescharacteristic
105C4×C149C2×#4111yescharacteristic
106Dic149—22no—
107Dic149—42no—
108C2×C149#48214yescomplemented
109C2×C149C2×#12311yescharacteristic
110C2×C149C2×#13511yescharacteristic
111C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
112D149—42no—
113D149—82no—
114C149C2×#48211yescharacteristic, complemented, Sylow
115C2×#482—1491nomaximal, Sylow
116C2×#121—1491no—
117C2×#117—1491no—
118#482—1498no—
119C2×#107—1491no—
120C2×#106D14911yescharacteristic, complemented
121C2×#102—1491no—
122C2×#102—1491no—
123C2×C22⋊C8—1491no—
124C22×D4—2981no—
125C22×D4—1491no—
126C23×C4—1491no—
127C22×C8—1491no—
128C22×C8C2×D14911yescharacteristic
129#121—2982no—
130#121—1494no—
131#117—2982no—
132#117—1494no—
133C2×C4⋊C4—1491no—
134C2×C4⋊C4C2×D14911yescharacteristic
135C2×C4⋊C4C2×D14911yescharacteristic
136C2×C22⋊C4—2981no—
137C2×C22⋊C4—2981no—
138C2×C42—2981no—
139#107—1494no—
140#106C2×D14914yescomplemented
141#102—1494no—
142#102—1494no—
143C22⋊C8—1494no—
144C24—2981no—
145C24—1491no—
146C2×D4—2984no—
147C2×D4—2981no—
148C2×D4—2982no—
149C2×D4—2982no—
150C2×D4—5964no—
151C2×D4—1492no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—2982no—
155C22×C4—2982no—
156C22×C4—2981no—
157C22×C4—1491no—
158C22×C4—1492no—
159C22×C4—1492no—
160C22×C4C22×D14911yescharacteristic
161C2×C8—22no—
162C2×C8—2982no—
163C2×C8—1492no—
164C2×C8C22×D14912yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—2981no—
168C4⋊C4—1492no—
169C4⋊C4C22×D14912yes—
170C4⋊C4C22×D14912yes—
171C22⋊C4—2984no—
172C22⋊C4—2984no—
173C42—2984no—
174C23—2982no—
175C23—2982no—
176C23—2982no—
177C23—2982no—
178C23—5962no—
179C23—5962no—
180C23—5962no—
181C23—1492no—
182C23D4×D14911yescharacteristic
183D4—2982no—
184D4—2982no—
185D4—5968no—
186D4—5962no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—2982no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—2984no—
195C2×C4—2982no—
196C2×C4—5962no—
197C2×C4—1492no—
198C2×C4D4×D14911yescharacteristic
199C2×C4#1455873612yes—
200C2×C4#1455873712yes—
201C2×C4C23×D14911yescharacteristic
202C8—22no—
203C8—2982no—
204C22—2982no—
205C22—2982no—
206C22—2982no—
207C22—5964no—
208C22—5962no—
209C22—5962no—
210C22—5962no—
211C22—11924no—
212C22#1801189612yes—
213C22#1801193212yes—
214C22#1801193812yes—
215C22C2×D4×D14911yescharacteristic
216C4—42no—
217C4—42no—
218C4—2982no—
219C4—5962no—
220C4#1801189612yes—
221C4C2×#1455873611yescharacteristic
222C4C2×#1455873711yescharacteristic
223C2—5962no—
224C2—11922no—
225C2#2374995114yesdirect product factor
226C2C2×#1801189611yescharacteristic
227C2C2×#1801193211yescharacteristic
228C2C2×#1801193811yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#106×C149C2
socleC23×C149C2×D4
prime radicalC2×#18011886C2
hypercenterC2×#106D149
hypocenterC149C2×#482
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#18011869C2semidirect
3. #23749951C2direct (N × H)
4. C2×#18011844C2semidirect
5. C2×#18011833C2semidirect
6. C2×#18011831C2semidirect
7. C2×#18011823C2semidirect
8. C2×#106×C149C2semidirect
16. #18011869C22semidirect
21. #18011844C22semidirect
22. #18011833C22semidirect
23. #18011831C22semidirect
24. #18011823C22semidirect
28. #106×C149C22semidirect
108. C2×C149#482semidirect
114. C149C2×#482semidirect
120. C2×#106D149semidirect
140. #106C2×D149semidirect
225. C2#23749951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180118862
C2×#180118692
#237499512
C2×#180118442
C2×#180118332
C2×#180118312
C2×#180118232
C2×#106×C1492
C2×#482149