Finite Group Databasebeta

← C2×#17988866 #22619675

Subgroups — C2×#17988866 #22619675

Order 9344.

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

normal subgroups only

This group has 480 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×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556553C211yesmaximal, characteristic
3#17988866C218yesmaximal, direct product factor
4C2×#14556524C211yesmaximal, characteristic, complemented
5C2×#14556520C211yesmaximal, characteristic, complemented
6C2×#14556513C211yesmaximal, characteristic
7C2×#14556511C211yesmaximal, characteristic
8C2×#107×C73C211yesmaximal, characteristic, complemented
9C22×Dic146—21no—
10C22×D292C2211yescharacteristic
11C22×C4×D73—21no—
12C22×#10596831C2211yescharacteristic
13#14556590—22no—
14#14556590C2214yescomplemented
15#14556553—22no—
16#14556553C2214yes—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007—21no—
19C2×#11924005—21no—
20C2×C4×Dic73C2211yescharacteristic
21#14556524C2214yescomplemented
22#14556520C2214yescomplemented
23#14556513C2214yes—
24#14556511C2214yes—
25C22×C8×C73C2211yescharacteristic
26C2×C4⋊C4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28#107×C73C2214yescomplemented
29C23×D73—21no—
30C2×Dic146—24no—
31C2×Dic146—44no—
32C2×D292—21no—
33C2×D292—22no—
34C2×D292Q814yescomplemented
35C2×D292C2312yes—
36C22×Dic73—21no—
37C22×Dic73D411yescharacteristic
38C22×Dic73D411yescharacteristic
39C2×C4×D73—24no—
40C2×C4×D73—44no—
41C2×#10596831—22no—
42C2×#10596831C2312yes—
43C4⋊Dic73—21no—
44C4⋊Dic73C2312yes—
45#11924007—24no—
46#11924005—24no—
47C4×Dic73D412yes—
48C4×Dic73C2312yes—
49C22×C4×C73—21no—
50C22×C4×C73—21no—
51C22×C4×C73C2311yescharacteristic
52C2×C8×C73—22no—
53C2×C8×C73C2312yes—
54C4⋊C4×C73—21no—
55C4⋊C4×C73—21no—
56C4⋊C4×C73C2312yes—
57C4⋊C4×C73C2312yes—
58C23×C73C2×D411yescharacteristic
59C22×D73—24no—
60C22×D73—22no—
61C22×D73—42no—
62C22×D73—42no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—42no—
66C2×C4×C73—42no—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×Q812yes—
69C2×C4×C73#4112yes—
70C2×C4×C73C2411yescharacteristic
71C2×Dic73—22no—
72C2×Dic73—22no—
73C2×Dic73—42no—
74C2×Dic73D814yes—
75C2×Dic73C2×D412yes—
76C2×Dic73C2×D412yes—
77D292—24no—
78D292—22no—
79D292C2×Q814yescomplemented
80C4×D73—48no—
81Dic146—48no—
82C8×C73—22no—
83#10596831—22no—
84C22×C73C22⋊Q812yes—
85C22×C73C2×D812yes—
86C22×C73#13712yes—
87C22×C73C22×D411yescharacteristic
88C2×D73—24no—
89C2×D73—42no—
90C2×D73—42no—
91C2×D73—48no—
92C4×C73—42no—
93C4×C73—42no—
94C4×C73C22⋊Q812yes—
95C4×C73C22×Q811yescharacteristic
96C4×C73C2×#4111yescharacteristic
97Dic73—22no—
98Dic73—42no—
99Dic73C2×D814yes—
100C2×C73#47414yescomplemented
101C2×C73C2×C22⋊Q811yescharacteristic
102C2×C73C22×D811yescharacteristic
103C2×C73C2×#13711yescharacteristic
104D73—44no—
105C2×#474—731nomaximal, Sylow
106C73C2×#47411yescharacteristic, complemented, Sylow
107C2×C4⋊Q8—731no—
108C2×C4×D4—731no—
109#474—738no—
110C2×#107—731no—
111C2×#107D7311yescharacteristic, complemented
112C2×C4⋊C8—731no—
113C2×#102—731no—
114C2×#102—731no—
115C22×Q8—1461no—
116C22×D4—731no—
117C23×C4—1461no—
118C22×C8—731no—
119C22×C8C2×D7311yescharacteristic
120C4⋊Q8—734no—
121C4⋊Q8—1462no—
122C4×D4—734no—
123C4×D4—1462no—
124C2×C4⋊C4—731no—
125C2×C4⋊C4—1461no—
126C2×C4⋊C4C2×D7311yescharacteristic
127C2×C4⋊C4C2×D7311yescharacteristic
128C2×C22⋊C4—1461no—
129C2×C42—731no—
130#107—734no—
131#107C2×D7314yescomplemented
132C4⋊C8—734no—
133#102—734no—
134#102—734no—
135C24—1461no—
136C2×Q8—2924no—
137C2×Q8—1464no—
138C2×D4—734no—
139C2×D4—732no—
140C2×D4—1461no—
141C2×D4—1462no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—2924no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—1464no—
148C22×C4—1461no—
149C22×C4C22×D7311yescharacteristic
150C2×C8—22no—
151C2×C8—732no—
152C2×C8—1462no—
153C2×C8C22×D7312yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—732no—
157C4⋊C4—1464no—
158C4⋊C4—1461no—
159C4⋊C4C22×D7312yes—
160C4⋊C4C22×D7312yes—
161C22⋊C4—1464no—
162C42—732no—
163C42—732no—
164C23—2922no—
165C23—2922no—
166C23—1464no—
167C23—1462no—
168C23D4×D7311yescharacteristic
169Q8—2928no—
170D4—734no—
171D4—1464no—
172D4—1462no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—2928no—
178C2×C4—2922no—
179C2×C4—734no—
180C2×C4—732no—
181C2×C4—732no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4D4×D7311yescharacteristic
185C2×C4Q8×D7312yes—
186C2×C4#1192402812yes—
187C2×C4C23×D7311yescharacteristic
188C8—22no—
189C8—1462no—
190C22—2928no—
191C22—2922no—
192C22—2922no—
193C22—1464no—
194C22#1455656912yes—
195C22D8×D7312yes—
196C22#1455662312yes—
197C22C2×D4×D7311yescharacteristic
198C4—42no—
199C4—42no—
200C4—2922no—
201C4—734no—
202C4—1462no—
203C4#1455656912yes—
204C4C2×Q8×D7311yescharacteristic
205C4C2×#1192402811yescharacteristic
206C2—2924no—
207C2#1798886614yesdirect product factor
208C2C2×#1455656911yescharacteristic
209C2C2×D8×D7311yescharacteristic
210C2C2×#1455662311yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#107×C73C2
socleC23×C73C2×D4
hypercenterC2×#107D73
hypocenterC73C2×#474
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
3. #17988866C2direct (N × H)
4. C2×#14556524C2semidirect
5. C2×#14556520C2semidirect
8. C2×#107×C73C2semidirect
14. #14556590C22semidirect
21. #14556524C22semidirect
22. #14556520C22semidirect
28. #107×C73C22semidirect
34. C2×D292Q8semidirect
79. D292C2×Q8semidirect
100. C2×C73#474semidirect
106. C73C2×#474semidirect
111. C2×#107D73semidirect
131. #107C2×D73semidirect
207. C2#17988866direct (N × H)