Finite Group Databasebeta

← C2×#23749986 #34055021

Subgroups — C2×#23749986 #34055021

Order 19072.

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

normal subgroups only

This group has 436 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×#18011910C211yesmaximal, characteristic, complemented
2C2×#18011900C211yesmaximal, characteristic
3#23749986C218yesmaximal, direct product factor
4C2×#18011835C211yesmaximal, characteristic, complemented
5C2×#18011833C211yesmaximal, characteristic
6C2×#18011831C211yesmaximal, characteristic
7C2×#18011821C211yesmaximal, characteristic, complemented
8C2×#103×C149C211yesmaximal, characteristic, complemented
9C22×Dic298—21no—
10C22×D596C2211yescharacteristic
11C22×#11924746C2211yescharacteristic
12#18011910—22no—
13#18011910C2214yescomplemented
14#18011900—22no—
15#18011900C2214yes—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×#14558715—21no—
18C2×#14558713—21no—
19C2×#14558713—21no—
20C2×C4×Dic149C2211yescharacteristic
21#18011835C2214yescomplemented
22#18011833C2214yes—
23#18011831C2214yes—
24#18011821C2214yescomplemented
25C22×Q8×C149C2211yescharacteristic
26C22×C8×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#103×C149C2214yescomplemented
29C23×D149—21no—
30C2×Dic298—24no—
31C2×Dic298—44no—
32C2×D596—21no—
33C2×D596—22no—
34C2×D596—22no—
35C2×D596C2312yes—
36C22×Dic149—21no—
37C22×Dic149D411yescharacteristic
38C22×Dic149D411yescharacteristic
39C2×#11924746—22no—
40C2×#11924746C2312yes—
41C4⋊Dic149—21no—
42C4⋊Dic149C2312yes—
43#14558715—24no—
44#14558713—24no—
45#14558713—24no—
46C4×Dic149D412yes—
47C4×Dic149C2312yes—
48C2×Q8×C149—21no—
49C2×Q8×C149—22no—
50C2×Q8×C149—22no—
51C2×Q8×C149C2312yes—
52C22×C4×C149—21no—
53C22×C4×C149—21no—
54C22×C4×C149C2311yescharacteristic
55C2×C8×C149—22no—
56C2×C8×C149C2312yes—
57C4⋊C4×C149—21no—
58C4⋊C4×C149C2312yes—
59C22×D149—22no—
60C22×D149—42no—
61C22×D149—42no—
62C22×D149—42no—
63Dic298—48no—
64D596—22no—
65D596—22no—
66D596—42no—
67C2×Dic149—22no—
68C2×Dic149—22no—
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×C149—42no—
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149#4112yes—
84C2×C4×C149#4112yes—
85C2×C4×C149C2411yescharacteristic
86C8×C149—22no—
87C22×C149#12412yes—
88C22×C149AGL(1,ℤ/8)12yes—
89C22×C149#13712yes—
90C22×C149C22×D411yescharacteristic
91C2×D149—42no—
92C2×D149—42no—
93C2×D149—42no—
94C2×D149—84no—
95C4×C149—42no—
96C4×C149—42no—
97C4×C149#12412yes—
98C4×C149C2×#4111yescharacteristic
99C4×C149C2×#4111yescharacteristic
100Dic149—22no—
101Dic149—22no—
102Dic149—42no—
103C2×C149#48914yescomplemented
104C2×C149C2×#12411yescharacteristic
105C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
106C2×C149C2×#13711yescharacteristic
107D149—82no—
108C149C2×#48911yescharacteristic, complemented, Sylow
109C2×#489—1491nomaximal, Sylow
110C2×C4⋊Q8—1491no—
111C2×#124—1491no—
112#489—1498no—
113C2×#103—1491no—
114C2×#103D14911yescharacteristic, complemented
115C2×#102—1491no—
116C2×#102—1491no—
117C2×#97—1491no—
118C22×Q8—2981no—
119C22×Q8C2×D14911yescharacteristic
120C22×D4—1491no—
121C22×C8—1491no—
122C22×C8C2×D14911yescharacteristic
123C4⋊Q8—2982no—
124C4⋊Q8—1494no—
125#124—2982no—
126#124—1494no—
127C2×C4⋊C4—2981no—
128C2×C4⋊C4—1491no—
129C2×C4⋊C4C2×D14911yescharacteristic
130C2×C22⋊C4—2981no—
131C2×C22⋊C4—2981no—
132C2×C42—1491no—
133#103—1494no—
134#103C2×D14914yescomplemented
135#102—1494no—
136#102—1494no—
137#97—1494no—
138C24—2981no—
139C2×Q8—21no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—2984no—
143C2×Q8—5964no—
144C2×Q8C22×D14912yes—
145C2×D4—2981no—
146C2×D4—2982no—
147C2×D4—2982no—
148C2×D4—1492no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—2981no—
152C22×C4—1491no—
153C22×C4—1491no—
154C22×C4C22×D14911yescharacteristic
155C2×C8—22no—
156C2×C8—2982no—
157C2×C8—1492no—
158C2×C8C22×D14912yes—
159C4⋊C4—21no—
160C4⋊C4—2984no—
161C4⋊C4—2981no—
162C4⋊C4—1492no—
163C4⋊C4C22×D14912yes—
164C22⋊C4—2984no—
165C22⋊C4—2984no—
166C42—1492no—
167C42—1492no—
168C23—2982no—
169C23—5962no—
170C23—5962no—
171C23—5962no—
172C23D4×D14911yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—42no—
176Q8—5968no—
177D4—2982no—
178D4—2982no—
179D4—5962no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—5962no—
188C2×C4—1492no—
189C2×C4—1492no—
190C2×C4D4×D14911yescharacteristic
191C2×C4#1455873512yes—
192C2×C4#1455873612yes—
193C2×C4C23×D14911yescharacteristic
194C8—22no—
195C8—2982no—
196C22—5962no—
197C22—5962no—
198C22—5962no—
199C22—11924no—
200C22#1801189712yes—
201C22#1801193812yes—
202C22#1801194312yes—
203C22C2×D4×D14911yescharacteristic
204C4—42no—
205C4—42no—
206C4—2982no—
207C4—2982no—
208C4—5962no—
209C4#1801189712yes—
210C4C2×#1455873511yescharacteristic
211C4C2×#1455873611yescharacteristic
212C2—11922no—
213C2#2374998614yesdirect product factor
214C2C2×#1801189711yescharacteristic
215C2C2×#1801193811yescharacteristic
216C2C2×#1801194311yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#103×C149C2
socleC23×C149C2×D4
prime radicalC22×D596C22
hypercenterC2×#103D149
hypocenterC149C2×#489
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#18011910C2semidirect
3. #23749986C2direct (N × H)
4. C2×#18011835C2semidirect
7. C2×#18011821C2semidirect
8. C2×#103×C149C2semidirect
13. #18011910C22semidirect
21. #18011835C22semidirect
24. #18011821C22semidirect
28. #103×C149C22semidirect
103. C2×C149#489semidirect
108. C149C2×#489semidirect
114. C2×#103D149semidirect
134. #103C2×D149semidirect
213. C2#23749986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180119102
C2×#180119002
#237499862
C2×#180118352
C2×#180118332
C2×#180118312
C2×#180118212
C2×#103×C1492
C2×#489149