Finite Group Databasebeta

← C2×#17988385 #22611611

Subgroups — C2×#17988385 #22611611

Order 9344.

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×#14556589C211yesmaximal, characteristic
2C2×#14556510C211yesmaximal, characteristic
3#17988385C214yesmaximal, direct product factor
4C2×#101×C73C211yesmaximal, characteristic
5C22×Dic146C411yescharacteristic
6C2×#11924012—21no—
7#14556589—21no—
8#14556589—21no—
9#14556589C412yes—
10#14556589C2212yes—
11C2×#11924007—21no—
12C2×#11924007—21no—
13C2×C4×Dic73C411yescharacteristic
14#14556510—21no—
15#14556510C2212yes—
16C22×Q8×C73C2211yescharacteristic
17C2×M16×C73—21no—
18#101×C73—21no—
19#101×C73C2212yes—
20C2×Dic146—21no—
21C2×Dic146—41no—
22C2×Dic146—41no—
23C2×Dic146C2×C412yes—
24C22×Dic73—21no—
25C22×Dic73—21no—
26#11924012—22no—
27#11924012—41no—
28C2×#10596831—41no—
29#11924007—22no—
30#11924007—22no—
31#11924007—22no—
32#11924007—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
48Q8×C73—41no—
49Q8×C73—41no—
50Q8×C73—41no—
51Q8×C73—41no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22×C411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×D411yescharacteristic
64C2×Dic73—24no—
65C2×Dic73—22no—
66C2×Dic73—22no—
67C2×Dic73—41no—
68C2×Dic73—41no—
69Dic146—42no—
70Dic146—42no—
71C8×C73—42no—
72#10596831—42no—
73C22×C73—22no—
74C22×C73#9911yescharacteristic
75C22×C73#9911yescharacteristic
76C22×C73C2×C22⋊C411yescharacteristic
77C4×C73—21no—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—21no—
82C4×C73—21no—
83Dic73—24no—
84Dic73—42no—
85C2×C73—21no—
86C2×C73—21no—
87C2×C73#35612yescomplemented
88C2×C73C2×#9911yescharacteristic
89C2×#356—731nomaximal, Sylow
90C73C2×#35611yescharacteristic, complemented, Sylow
91C2×C4⋊Q8—731no—
92C2×#101—731no—
93C2×#101D7311yescharacteristic
94#356—734no—
95C22×Q8—731no—
96C22×Q8C2×D7311yescharacteristic
97C2×M16—21no—
98C2×M16—1461no—
99C4⋊Q8—732no—
100C4⋊Q8—732no—
101C4⋊Q8—1461no—
102C4⋊Q8—1461no—
103C2×C4⋊C4—1461no—
104C2×C4⋊C4—1461no—
105C2×C42—731no—
106#101—21no—
107#101—732no—
108#101—1461no—
109#101C2×D7312yes—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8—2921no—
113C2×Q8—2921no—
114C2×Q8—732no—
115C2×Q8—1461no—
116C2×Q8C4×D7311yescharacteristic
117C2×Q8D29211yescharacteristic
118C2×Q8C22⋊D7311yescharacteristic
119C2×Q8C22×D7311yescharacteristic
120C22×C4—1461no—
121C22×C4—1461no—
122C22×C4C4×D7311yescharacteristic
123C22×C4D29211yescharacteristic
124C22×C4C22⋊D7311yescharacteristic
125M16—22no—
126M16—41no—
127M16—2921no—
128M16—1462no—
129C2×C8—41no—
130C2×C8—2921no—
131C4⋊C4—1462no—
132C4⋊C4—1462no—
133C4⋊C4—1462no—
134C4⋊C4—1462no—
135C42—732no—
136C42—1461no—
137C23#1192400511yescharacteristic
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—2922no—
143Q8—2922no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—2921no—
151C2×C4—2921no—
152C2×C4—1462no—
153C2×C4—1464no—
154C2×C4—1462no—
155C2×C4#1192400511yescharacteristic
156C2×C4#1192400511yescharacteristic
157C2×C4#1192400511yescharacteristic
158C2×C4C2×C4×D7311yescharacteristic
159C2×C4C2×C22⋊D7311yescharacteristic
160C2×C4C2×D29211yescharacteristic
161C8—42no—
162C8—2922no—
163C22—22no—
164C22#1455650511yescharacteristic
165C22#1455650511yescharacteristic
166C22C2×#1192400511yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—2922no—
174C4—1464no—
175C2—21no—
176C2—21no—
177C2#1798838512yesdirect product factor
178C2C2×#1455650511yescharacteristic
subgroupG/H
centerC22#14556505
commutatorC2×C4×C73C22×C4
FrattiniC2×Q8C22×D73
FittingC2×#101×C73C2
socleC22×C73#99
hypercenterC2×#101D73
hypocenterC73C2×#356
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
3. #17988385C2direct (N × H)
87. C2×C73#356semidirect
90. C73C2×#356semidirect
177. C2#17988385direct (N × H)