Finite Group Databasebeta

← C2×#16839945 #21455161

Subgroups — C2×#16839945 #21455161

Order 7808.

708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519807C212yesmaximal, complemented
2C2×#14519775C211yesmaximal, characteristic, complemented
3#16839945C218yesmaximal, direct product factor
4C2×#14519704C212yesmaximal, complemented
5C2×#14519696C211yesmaximal, characteristic, complemented
6C2×2−1+4×C61C211yesmaximal, characteristic
7C22×Dic122C2211yescharacteristic
8#14519807—24no—
9#14519807C2218yescomplemented
10C2×#11758202—22no—
11C2×#11758200—22no—
12C2×#11758194C2212yes—
13#14519775—22no—
14#14519775C2214yescomplemented
15C2×#11758196—22no—
16C2×C4×Dic61C2211yescharacteristic
17#14519704C2218yescomplemented
18#14519696C2214yescomplemented
192−1+4×C61—24no—
202−1+4×C61—22no—
212−1+4×C61C2214yes—
22C2×#41×C61—22no—
23C2×#41×C61—22no—
24C2×#41×C61C2212yes—
25C22×Q8×C61—22no—
26C22×Q8×C61C2211yescharacteristic
27#41×C61—28no—
28#41×C61—28no—
29#41×C61—28no—
30#41×C61—28no—
31#41×C61—22no—
32#41×C61—22no—
33#41×C61D414yes—
34#41×C61C2314yes—
35C2×Q8×C61—22no—
36C2×Q8×C61—28no—
37C2×Q8×C61—28no—
38C2×Q8×C61—22no—
39C2×Q8×C61—22no—
40C2×Q8×C61D412yes—
41C2×Q8×C61D412yes—
42C2×Q8×C61C2312yes—
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61D412yes—
46C22×C4×C61—24no—
47C22×C4×C61—22no—
48C22×C4×C61D412yes—
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—21no—
51C22×Dic61—21no—
52C2×Dic122—22no—
53C2×Dic122—22no—
54C2×Dic122—21no—
55C2×Dic122C2312yes—
56#11758202—28no—
57#11758200—28no—
58#11758196—28no—
59C4×Dic61—21no—
60C4×Dic61C2312yes—
61#11758194—22no—
62#11758194C2314yes—
63C2×#92418—22no—
64C23×C61—22no—
65C23×C61C2×D411yescharacteristic
66Q8×C61—28no—
67Q8×C61—22no—
68Q8×C61—24no—
69Q8×C61—24no—
70Q8×C61C2×D414yes—
71D4×C61—28no—
72D4×C61—24no—
73D4×C61—24no—
74D4×C61—22no—
75D4×C61C2×D414yes—
76C2×C4×C61—216no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—24no—
81C2×C4×C61—24no—
82C2×C4×C61C2×D414yes—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D412yes—
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—24no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92Dic122—24no—
93Dic122—42no—
94#92418—24no—
95C22×C61—22no—
96C22×C61—24no—
97C22×C61—44no—
98C22×C61#12011yescharacteristic
99C22×C61#12011yescharacteristic
100C22×C61C22×D411yescharacteristic
101C4×C61—24no—
102C4×C61—24no—
103C4×C61#12012yes—
104C4×C61C22×D412yes—
105Dic61—24no—
106Dic61—42no—
107C2×#456—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—21no—
110C2×C61—44no—
111C2×C61#45612yescomplemented
112C2×C61C2×#12011yescharacteristic
113C2×2−1+4D6111yescharacteristic
114C2×#137—612no—
115C2×C4⋊Q8—611no—
116#456—618no—
117C2×#104—612no—
118C2×#101—611no—
119C61C2×#45611yescharacteristic, complemented, Sylow
1202−1+4—24no—
1212−1+4—22no—
1222−1+4C2×D6114yes—
123C2×#41—22no—
124C2×#41—22no—
125C2×#41C2×D6112yes—
126C22×Q8—22no—
127C22×Q8—611no—
128C22×Q8C2×D6111yescharacteristic
129#137—618no—
130#137—1224no—
131C2×Q16—1222no—
132C2×SD16—1222no—
133C2×M16—612no—
134C4⋊Q8—614no—
135C4⋊Q8—1222no—
136C2×C4⋊C4—1222no—
137C2×C42—611no—
138#104—618no—
139#101—614no—
140#41—28no—
141#41—28no—
142#41—28no—
143#41—28no—
144#41—22no—
145#41—22no—
146#41C22⋊D6114yes—
147#41C22×D6114yes—
148C2×Q8—22no—
149C2×Q8—28no—
150C2×Q8—28no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—612no—
154C2×Q8—1221no—
155C2×Q8—1222no—
156C2×Q8—1222no—
157C2×Q8C22⋊D6112yes—
158C2×Q8C22⋊D6112yes—
159C2×Q8C22×D6112yes—
160C2×D4—22no—
161C2×D4—22no—
162C2×D4C22⋊D6112yes—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—1221no—
166C22×C4—1221no—
167C22×C4C22⋊D6112yes—
168C22×C4C22×D6111yescharacteristic
169Q16—1228no—
170SD16—1228no—
171M16—614no—
172M16—1222no—
173C2×C8—1222no—
174C4⋊C4—1228no—
175C42—612no—
176C42—1221no—
177C23—22no—
178C23C2×C22⋊D6111yescharacteristic
179Q8—28no—
180Q8—24no—
181Q8—22no—
182Q8—24no—
183Q8—1224no—
184Q8—2442no—
185Q8C2×C22⋊D6114yes—
186D4—28no—
187D4—24no—
188D4—24no—
189D4—22no—
190D4C2×C22⋊D6114yes—
191C2×C4—216no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—1224no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—2441no—
201C2×C4—2441no—
202C2×C4C2×C22⋊D6114yes—
203C2×C4C2×C22⋊D6112yes—
204C2×C4C2×C22⋊D6112yes—
205C2×C4C2×C22⋊D6111yescharacteristic
206C2×C4C23×D6111yescharacteristic
207C8—1224no—
208C22—22no—
209C22—24no—
210C22—44no—
211C22#1451974611yescharacteristic
212C22#1451974611yescharacteristic
213C22C22×C22⋊D6111yescharacteristic
214C4—24no—
215C4—24no—
216C4—1224no—
217C4—2442no—
218C4#1451974612yes—
219C4C22×C22⋊D6112yes—
220C2—21no—
221C2—21no—
222C2—44no—
223C2#1683994512yesdirect product factor
224C2C2×#1451974611yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×2−1+4×C61C2
socleC22×C61#120
hypercenterC2×2−1+4D61
hypocenterC61C2×#456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C2×#14519775C2semidirect
3. #16839945C2direct (N × H)
4. C2×#14519704C2semidirect
5. C2×#14519696C2semidirect
9. #14519807C22semidirect
14. #14519775C22semidirect
17. #14519704C22semidirect
18. #14519696C22semidirect
111. C2×C61#456semidirect
119. C61C2×#456semidirect
223. C2#16839945direct (N × H)