Finite Group Databasebeta

← C2×#17988383 #22611608

Subgroups — C2×#17988383 #22611608

Order 9344.

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

normal subgroups only

This group has 260 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×#14556580C211yesmaximal, characteristic
2C2×#14556510C211yesmaximal, characteristic, complemented
3#17988383C214yesmaximal, direct product factor
4C2×#101×C73C211yesmaximal, characteristic, complemented
5C22×D292C411yescharacteristic
6C2×#11924012—21no—
7#14556580—21no—
8#14556580—21no—
9#14556580C412yes—
10#14556580C2212yes—
11C2×#11924005—21no—
12C2×#11924005—21no—
13C2×C4×Dic73C411yescharacteristic
14#14556510—21no—
15#14556510C2212yescomplemented
16C22×Q8×C73C2211yescharacteristic
17C2×M16×C73—21no—
18#101×C73—21no—
19#101×C73C2212yescomplemented
20C23×D73—21no—
21C2×D292—21no—
22C2×D292—41no—
23C2×D292—41no—
24C2×D292C2×C412yes—
25C22×Dic73—21no—
26#11924012—22no—
27#11924012—41no—
28C2×#10596831—41no—
29#11924005—22no—
30#11924005—22no—
31#11924005—22no—
32#11924005—22no—
33C4×Dic73—21no—
34C4×Dic73C2×C412yes—
35C2×Q8×C73—41no—
36C2×Q8×C73—41no—
37C2×Q8×C73C2×C411yescharacteristic
38C2×Q8×C73D411yescharacteristic
39C2×Q8×C73D411yescharacteristic
40C2×Q8×C73C2311yescharacteristic
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C22×C4×C73D411yescharacteristic
44M16×C73—22no—
45M16×C73—41no—
46C2×C8×C73—41no—
47C23×C73C22⋊C411yescharacteristic
48C22×D73—22no—
49C22×D73—44no—
50C22×D73—41no—
51C22×D73—41no—
52Q8×C73—41no—
53Q8×C73—41no—
54Q8×C73—41no—
55Q8×C73—41no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73C22⋊C411yescharacteristic
63C2×C4×C73C22⋊C411yescharacteristic
64C2×C4×C73C22⋊C411yescharacteristic
65C2×C4×C73C22×C411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×Dic73—22no—
69C2×Dic73—42no—
70D292—42no—
71D292—42no—
72C8×C73—42no—
73#10596831—42no—
74C22×C73—22no—
75C22×C73#9911yescharacteristic
76C22×C73#9911yescharacteristic
77C22×C73C2×C22⋊C411yescharacteristic
78C2×D73—44no—
79C2×D73—42no—
80C2×D73—82no—
81C2×D73—82no—
82C4×C73—21no—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—21no—
86C4×C73—21no—
87C4×C73—21no—
88Dic73—42no—
89C2×C73—21no—
90C2×C73—21no—
91C2×C73#35512yescomplemented
92C2×C73C2×#9911yescharacteristic
93D73—82no—
94C2×#355—731nomaximal, Sylow
95C73C2×#35511yescharacteristic, complemented, Sylow
96C2×#124—731no—
97C2×#101—731no—
98C2×#101D7311yescharacteristic, complemented
99#355—734no—
100C22×Q8C2×D7311yescharacteristic
101C22×D4—731no—
102C2×M16—21no—
103C2×M16—1461no—
104#124—732no—
105#124—732no—
106#124—1461no—
107#124—1461no—
108C2×C22⋊C4—1461no—
109C2×C22⋊C4—1461no—
110C2×C42—731no—
111#101—21no—
112#101—732no—
113#101—1461no—
114#101C2×D7312yescomplemented
115C24—1461no—
116C2×Q8—41no—
117C2×Q8—41no—
118C2×Q8C4×D7311yescharacteristic
119C2×Q8D29211yescharacteristic
120C2×Q8C22⋊D7311yescharacteristic
121C2×Q8C22×D7311yescharacteristic
122C2×D4—2921no—
123C2×D4—2921no—
124C2×D4—732no—
125C2×D4—1461no—
126C22×C4—1461no—
127C22×C4C4×D7311yescharacteristic
128C22×C4D29211yescharacteristic
129C22×C4C22⋊D7311yescharacteristic
130M16—22no—
131M16—41no—
132M16—2921no—
133M16—1462no—
134C2×C8—41no—
135C2×C8—2921no—
136C22⋊C4—1462no—
137C22⋊C4—1462no—
138C22⋊C4—1462no—
139C22⋊C4—1462no—
140C42—732no—
141C42—1461no—
142C23—2924no—
143C23—2921no—
144C23—2921no—
145C23—1462no—
146C23#1192400511yescharacteristic
147Q8—41no—
148Q8—41no—
149Q8—41no—
150Q8—41no—
151D4—2922no—
152D4—2922no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—2922no—
160C2×C4—1462no—
161C2×C4#1192400511yescharacteristic
162C2×C4#1192400511yescharacteristic
163C2×C4#1192400511yescharacteristic
164C2×C4C2×C4×D7311yescharacteristic
165C2×C4C2×C22⋊D7311yescharacteristic
166C2×C4C2×D29211yescharacteristic
167C8—42no—
168C8—2922no—
169C22—22no—
170C22—2924no—
171C22—2922no—
172C22—5842no—
173C22—5842no—
174C22#1455650511yescharacteristic
175C22#1455650511yescharacteristic
176C22C2×#1192400511yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—2922no—
184C2—21no—
185C2—21no—
186C2—5842no—
187C2#1798838312yesdirect product factor
188C2C2×#1455650511yescharacteristic
subgroupG/H
centerC22#14556505
commutatorC2×C4×C73C22×C4
FrattiniC2×Q8C22×D73
FittingC2×#101×C73C2
socleC22×C73#99
hypercenterC2×#101D73
hypocenterC73C2×#355
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14556510C2semidirect
3. #17988383C2direct (N × H)
4. C2×#101×C73C2semidirect
15. #14556510C22semidirect
19. #101×C73C22semidirect
91. C2×C73#355semidirect
95. C73C2×#355semidirect
98. C2×#101D73semidirect
114. #101C2×D73semidirect
187. C2#17988383direct (N × H)