Finite Group Databasebeta

← C2×#19098912 #23773709

Subgroups — C2×#19098912 #23773709

Order 10112.

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

normal subgroups only

This group has 424 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×#14579160C211yesmaximal, characteristic
2C2×#14579159C211yesmaximal, characteristic
3#19098912C218yesmaximal, direct product factor
4C2×#14579086C211yesmaximal, characteristic
5C2×#14579085C211yesmaximal, characteristic
6C2×#14579084C211yesmaximal, characteristic
7C2×C8×Dic79C211yesmaximal, characteristic
8C2×#103×C79C211yesmaximal, characteristic
9C22×Dic158—21no—
10C22×Dic158C2211yescharacteristic
11C22×C79⋊C8C2211yescharacteristic
12#14579160—22no—
13#14579160C2214yes—
14#14579159—22no—
15#14579159C2214yes—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4—21no—
18C2×Dic79⋊C4—21no—
19C2×Dic79⋊C4—21no—
20C2×C4×Dic79C2211yescharacteristic
21#14579086C2214yes—
22#14579085C2214yes—
23#14579084C2214yes—
24C8×Dic79C2214yes—
25C22×Q8×C79C2211yescharacteristic
26C22×C8×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28#103×C79C2214yes—
29C2×Dic158—24no—
30C2×Dic158—21no—
31C2×Dic158—22no—
32C2×Dic158—22no—
33C2×Dic158—44no—
34C2×Dic158C2312yes—
35C22×Dic79—21no—
36C22×Dic79—21no—
37C22×Dic79D411yescharacteristic
38C22×Dic79D411yescharacteristic
39C2×C79⋊C8—22no—
40C2×C79⋊C8C2312yes—
41C4⋊Dic79—21no—
42C4⋊Dic79C2312yes—
43Dic79⋊C4—24no—
44Dic79⋊C4—24no—
45Dic79⋊C4—24no—
46C4×Dic79D412yes—
47C4×Dic79C2312yes—
48C2×Q8×C79—21no—
49C2×Q8×C79—22no—
50C2×Q8×C79—22no—
51C2×Q8×C79C2312yes—
52C22×C4×C79—21no—
53C22×C4×C79—21no—
54C22×C4×C79C2311yescharacteristic
55C2×C8×C79—22no—
56C2×C8×C79C2312yes—
57C4⋊C4×C79—21no—
58C4⋊C4×C79C2312yes—
59C23×C79C2×D411yescharacteristic
60Q8×C79—22no—
61Q8×C79—22no—
62Q8×C79—42no—
63C2×C4×C79—22no—
64C2×C4×C79—22no—
65C2×C4×C79—42no—
66C2×C4×C79—42no—
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79#4112yes—
69C2×C4×C79#4112yes—
70C2×C4×C79C2411yescharacteristic
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—42no—
74C2×Dic79—42no—
75C2×Dic79SD1614yes—
76C2×Dic79Q1614yes—
77C2×Dic79C2×D412yes—
78C2×Dic79C2×D412yes—
79Dic158—22no—
80Dic158—22no—
81Dic158—42no—
82Dic158—48no—
83C8×C79—22no—
84C79⋊C8—22no—
85C22×C79#12412yes—
86C22×C79C2×SD1612yes—
87C22×C79C2×Q1612yes—
88C22×C79C22×D411yescharacteristic
89C4×C79—42no—
90C4×C79—42no—
91C4×C79#12412yes—
92C4×C79C2×#4111yescharacteristic
93C4×C79C2×#4111yescharacteristic
94Dic79—42no—
95Dic79—42no—
96Dic79C2×SD1614yes—
97Dic79C2×Q1614yes—
98C2×C79#48714yescomplemented
99C2×C79C2×#12411yescharacteristic
100C2×C79C22×SD1611yescharacteristic
101C2×C79C22×Q1611yescharacteristic
102C2×#487—791nomaximal, Sylow
103C79C2×#48711yescharacteristic, complemented, Sylow
104C2×C4⋊Q8—791no—
105C2×C4⋊Q8—791no—
106#487—798no—
107C2×#103—791no—
108C2×#103—791no—
109C2×#103—791no—
110C2×#103D7911yescharacteristic
111C2×C4×C8—791no—
112C22×Q8—791no—
113C22×Q8—1581no—
114C22×Q8C2×D7911yescharacteristic
115C22×C8—791no—
116C22×C8C2×D7911yescharacteristic
117C4⋊Q8—794no—
118C4⋊Q8—794no—
119C4⋊Q8—1582no—
120C4⋊Q8—1582no—
121C2×C4⋊C4—791no—
122C2×C4⋊C4—1581no—
123C2×C4⋊C4—1581no—
124C2×C4⋊C4—1581no—
125C2×C4⋊C4C2×D7911yescharacteristic
126C2×C42—791no—
127#103—794no—
128#103—794no—
129#103—794no—
130#103C2×D7914yes—
131C4×C8—794no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—3164no—
136C2×Q8—792no—
137C2×Q8—1584no—
138C2×Q8—1582no—
139C2×Q8—1582no—
140C2×Q8—1581no—
141C2×Q8C22×D7912yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—791no—
145C22×C4—791no—
146C22×C4—1581no—
147C22×C4—1581no—
148C22×C4C22×D7911yescharacteristic
149C2×C8—22no—
150C2×C8—792no—
151C2×C8—1582no—
152C2×C8C22×D7912yes—
153C4⋊C4—21no—
154C4⋊C4—792no—
155C4⋊C4—1584no—
156C4⋊C4—1584no—
157C4⋊C4—1584no—
158C4⋊C4—1581no—
159C4⋊C4C22×D7912yes—
160C42—792no—
161C42—792no—
162C23D4×D7911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—42no—
166Q8—3168no—
167Q8—3162no—
168Q8—1582no—
169Q8—1582no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—3162no—
175C2×C4—3162no—
176C2×C4—794no—
177C2×C4—794no—
178C2×C4—792no—
179C2×C4—792no—
180C2×C4—1582no—
181C2×C4—1582no—
182C2×C4D4×D7911yescharacteristic
183C2×C4#1192962312yes—
184C2×C4#1192962412yes—
185C2×C4C23×D7911yescharacteristic
186C8—22no—
187C8—1582no—
188C22#1457914712yes—
189C22SD16×D7912yes—
190C22Q16×D7912yes—
191C22C2×D4×D7911yescharacteristic
192C4—42no—
193C4—42no—
194C4—3162no—
195C4—3162no—
196C4—794no—
197C4—794no—
198C4#1457914712yes—
199C4C2×#1192962311yescharacteristic
200C4C2×#1192962411yescharacteristic
201C2#1909891214yesdirect product factor
202C2C2×#1457914711yescharacteristic
203C2C2×SD16×D7911yescharacteristic
204C2C2×Q16×D7911yescharacteristic
subgroupG/H
centerC23D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#103×C79C2
socle, prime radicalC23×C79C2×D4
hypercenterC2×#103D79
hypocenterC79C2×#487
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #19098912C2direct (N × H)
98. C2×C79#487semidirect
103. C79C2×#487semidirect
201. C2#19098912direct (N × H)