Finite Group Databasebeta

← C2×#16839560 #21447499

Subgroups — C2×#16839560 #21447499

Order 7808.

240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14519775C211yesmaximal, characteristic
2C2×#14519696C211yesmaximal, characteristic
3#16839560C214yesmaximal, direct product factor
4C2×#101×C61C211yesmaximal, characteristic
5C22×Dic122C411yescharacteristic
6C2×#11758194—21no—
7#14519775—21no—
8#14519775—21no—
9#14519775C412yes—
10#14519775C2212yes—
11C2×#11758196—21no—
12C2×#11758196—21no—
13C2×C4×Dic61C411yescharacteristic
14#14519696—21no—
15#14519696C2212yes—
16C22×Q8×C61C2211yescharacteristic
17C2×M16×C61—21no—
18#101×C61—21no—
19#101×C61C2212yes—
20C2×Q8×C61—41no—
21C2×Q8×C61—41no—
22C2×Q8×C61C2×C411yescharacteristic
23C2×Q8×C61D411yescharacteristic
24C2×Q8×C61D411yescharacteristic
25C2×Q8×C61C2311yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×Dic61—21no—
30C22×Dic61—21no—
31C2×Dic122—21no—
32C2×Dic122—41no—
33C2×Dic122—41no—
34C2×Dic122C2×C412yes—
35M16×C61—22no—
36M16×C61—41no—
37C2×C8×C61—41no—
38#11758196—22no—
39#11758196—22no—
40#11758196—22no—
41#11758196—22no—
42C4×Dic61—21no—
43C4×Dic61C2×C412yes—
44#11758194—22no—
45#11758194—41no—
46C2×#92418—41no—
47C23×C61C22⋊C411yescharacteristic
48Q8×C61—41no—
49Q8×C61—41no—
50Q8×C61—41no—
51Q8×C61—41no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—24no—
65C2×Dic61—22no—
66C2×Dic61—22no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69Dic122—42no—
70Dic122—42no—
71C8×C61—42no—
72#92418—42no—
73C22×C61—22no—
74C22×C61#9911yescharacteristic
75C22×C61#9911yescharacteristic
76C22×C61C2×C22⋊C411yescharacteristic
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—21no—
83Dic61—24no—
84Dic61—42no—
85C2×#356—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—21no—
88C2×C61#35612yescomplemented
89C2×C61C2×#9911yescharacteristic
90C2×C4⋊Q8—611no—
91C2×#101—611no—
92C2×#101D6111yescharacteristic
93#356—614no—
94C61C2×#35611yescharacteristic, complemented, Sylow
95C22×Q8—611no—
96C22×Q8C2×D6111yescharacteristic
97C2×M16—21no—
98C2×M16—1221no—
99C4⋊Q8—612no—
100C4⋊Q8—612no—
101C4⋊Q8—1221no—
102C4⋊Q8—1221no—
103C2×C4⋊C4—1221no—
104C2×C4⋊C4—1221no—
105C2×C42—611no—
106#101—21no—
107#101—612no—
108#101—1221no—
109#101C2×D6112yes—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8—612no—
113C2×Q8—1221no—
114C2×Q8—2441no—
115C2×Q8—2441no—
116C2×Q8C4×D6111yescharacteristic
117C2×Q8D24411yescharacteristic
118C2×Q8C22⋊D6111yescharacteristic
119C2×Q8C22×D6111yescharacteristic
120C22×C4—1221no—
121C22×C4—1221no—
122C22×C4C4×D6111yescharacteristic
123C22×C4D24411yescharacteristic
124C22×C4C22⋊D6111yescharacteristic
125M16—22no—
126M16—41no—
127M16—1222no—
128M16—2441no—
129C2×C8—41no—
130C2×C8—2441no—
131C4⋊C4—1222no—
132C4⋊C4—1222no—
133C4⋊C4—1222no—
134C4⋊C4—1222no—
135C42—612no—
136C42—1221no—
137C23#1175819811yescharacteristic
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—2442no—
143Q8—2442no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—1224no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4#1175819811yescharacteristic
156C2×C4#1175819811yescharacteristic
157C2×C4#1175819811yescharacteristic
158C2×C4C2×C4×D6111yescharacteristic
159C2×C4C2×D24411yescharacteristic
160C2×C4C2×C22⋊D6111yescharacteristic
161C8—42no—
162C8—2442no—
163C22—22no—
164C22#1451969111yescharacteristic
165C22#1451969111yescharacteristic
166C22C2×#1175819811yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—1224no—
174C4—2442no—
175C2—21no—
176C2—21no—
177C2#1683956012yesdirect product factor
178C2C2×#1451969111yescharacteristic
subgroupG/H
centerC22#14519691
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC2×#101×C61C2
socleC22×C61#99
hypercenterC2×#101D61
hypocenterC61C2×#356
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. #16839560C2direct (N × H)
88. C2×C61#356semidirect
94. C61C2×#356semidirect
177. C2#16839560direct (N × H)