Finite Group Databasebeta

← C2×#23749919 #34054461

Subgroups — C2×#23749919 #34054461

Order 19072.

416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 157 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
2C2×#18011876C211yesmaximal, characteristic
3#23749919C218yesmaximal, direct product factor
4C2×#18011844C211yesmaximal, characteristic
5C2×#18011840C211yesmaximal, characteristic
6C2×#18011836C211yesmaximal, characteristic
7C2×#18011834C211yesmaximal, characteristic
8C2×#107×C149C211yesmaximal, characteristic
9C22×Dic298—21no—
10C22×Dic298C2211yescharacteristic
11C22×#11924746C2211yescharacteristic
12#18011910—22no—
13#18011910C2214yes—
14#18011876—22no—
15#18011876C2214yes—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×#14558715—21no—
18C2×#14558715—21no—
19C2×C4×Dic149—21no—
20C2×C4×Dic149C2211yescharacteristic
21#18011844C2214yes—
22#18011840C2214yes—
23#18011836C2214yes—
24#18011834C2214yes—
25C22×C8×C149C2211yescharacteristic
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#107×C149C2214yes—
29C2×Dic298—24no—
30C2×Dic298—21no—
31C2×Dic298—22no—
32C2×Dic298—44no—
33C2×Dic298Q814yescomplemented
34C2×Dic298C2312yes—
35C22×Dic149—21no—
36C22×Dic149—21no—
37C22×Dic149D411yescharacteristic
38C22×Dic149D411yescharacteristic
39C2×#11924746—22no—
40C2×#11924746C2312yes—
41C4⋊Dic149—21no—
42C4⋊Dic149C2312yes—
43#14558715—24no—
44#14558715—24no—
45C4×Dic149—24no—
46C4×Dic149D412yes—
47C4×Dic149C2312yes—
48C22×C4×C149—21no—
49C22×C4×C149—21no—
50C22×C4×C149C2311yescharacteristic
51C2×C8×C149—22no—
52C2×C8×C149C2312yes—
53C4⋊C4×C149—21no—
54C4⋊C4×C149—21no—
55C4⋊C4×C149C2312yes—
56C4⋊C4×C149C2312yes—
57Dic298—24no—
58Dic298—22no—
59Dic298—48no—
60Dic298C2×Q814yescomplemented
61C2×Dic149—24no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—42no—
66C2×Dic149Q1614yes—
67C2×Dic149C2×D412yes—
68C2×Dic149C2×D412yes—
69#11924746—22no—
70C23×C149C2×D411yescharacteristic
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—42no—
74C2×C4×C149—42no—
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2×Q812yes—
77C2×C4×C149#4112yes—
78C2×C4×C149C2411yescharacteristic
79C8×C149—22no—
80C22×C149C22⋊Q812yes—
81C22×C149C2×Q1612yes—
82C22×C149AGL(1,ℤ/8)12yes—
83C22×C149C22×D411yescharacteristic
84C4×C149—42no—
85C4×C149—42no—
86C4×C149C22⋊Q812yes—
87C4×C149C22×Q811yescharacteristic
88C4×C149C2×#4111yescharacteristic
89Dic149—24no—
90Dic149—22no—
91Dic149—42no—
92Dic149C2×Q1614yes—
93C2×C149#47714yescomplemented
94C2×C149C2×C22⋊Q811yescharacteristic
95C2×C149C22×Q1611yescharacteristic
96C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
97C149C2×#47711yescharacteristic, complemented, Sylow
98C2×#477—1491nomaximal, Sylow
99C2×C4⋊Q8—1491no—
100C2×C4×Q8—1491no—
101#477—1498no—
102C2×#107—1491no—
103C2×#107D14911yescharacteristic
104C2×C4⋊C8—1491no—
105C2×#103—1491no—
106C2×#103—1491no—
107C22×Q8—2981no—
108C22×Q8—1491no—
109C22×C8—1491no—
110C22×C8C2×D14911yescharacteristic
111C4⋊Q8—2982no—
112C4⋊Q8—1494no—
113C4×Q8—2982no—
114C4×Q8—1494no—
115C2×C4⋊C4—2981no—
116C2×C4⋊C4—2981no—
117C2×C4⋊C4—1491no—
118C2×C4⋊C4C2×D14911yescharacteristic
119C2×C4⋊C4C2×D14911yescharacteristic
120C2×C42—2981no—
121C2×C42—1491no—
122#107—1494no—
123#107C2×D14914yes—
124C4⋊C8—1494no—
125#103—1494no—
126#103—1494no—
127C2×Q8—2984no—
128C2×Q8—2981no—
129C2×Q8—2982no—
130C2×Q8—5964no—
131C2×Q8—1494no—
132C2×Q8—1492no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—2981no—
136C22×C4—2981no—
137C22×C4—1491no—
138C22×C4—1491no—
139C22×C4C22×D14911yescharacteristic
140C2×C8—22no—
141C2×C8—2982no—
142C2×C8—1492no—
143C2×C8C22×D14912yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—2984no—
147C4⋊C4—2984no—
148C4⋊C4—2981no—
149C4⋊C4—1492no—
150C4⋊C4C22×D14912yes—
151C4⋊C4C22×D14912yes—
152C42—2984no—
153C42—1492no—
154C42—1492no—
155C23D4×D14911yescharacteristic
156Q8—2982no—
157Q8—2984no—
158Q8—5968no—
159Q8—1494no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2984no—
167C2×C4—2982no—
168C2×C4—5962no—
169C2×C4—1492no—
170C2×C4—1494no—
171C2×C4—1492no—
172C2×C4D4×D14911yescharacteristic
173C2×C4Q8×D14912yes—
174C2×C4#1455873612yes—
175C2×C4C23×D14911yescharacteristic
176C8—22no—
177C8—2982no—
178C22#1801188912yes—
179C22Q16×D14912yes—
180C22#1801193512yes—
181C22C2×D4×D14911yescharacteristic
182C4—42no—
183C4—42no—
184C4—2982no—
185C4—2984no—
186C4—5962no—
187C4—1494no—
188C4#1801188912yes—
189C4C2×Q8×D14911yescharacteristic
190C4C2×#1455873611yescharacteristic
191C2#2374991914yesdirect product factor
192C2C2×#1801188911yescharacteristic
193C2C2×Q16×D14911yescharacteristic
194C2C2×#1801193511yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#107×C149C2
socle, prime radicalC23×C149C2×D4
hypercenterC2×#107D149
hypocenterC149C2×#477
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. #23749919C2direct (N × H)
33. C2×Dic298Q8semidirect
60. Dic298C2×Q8semidirect
93. C2×C149#477semidirect
97. C149C2×#477semidirect
191. C2#23749919direct (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×#180118762
#237499192
C2×#180118442
C2×#180118402
C2×#180118362
C2×#180118342
C2×#107×C1492
C2×#477149