Finite Group Databasebeta

← C2×#16839944 #21455160

Subgroups — C2×#16839944 #21455160

Order 7808.

708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519825C211yesmaximal, characteristic
2C2×#14519808C212yesmaximal, complemented
3#16839944C218yesmaximal, direct product factor
4C2×#14519705C212yesmaximal, complemented
5C2×#14519696C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
7#14519825—22no—
8#14519825—24no—
9#14519825C2214yes—
10C2×#11758226—22no—
11C2×#11758222—22no—
12C2×#11758222C2212yes—
13C2×Q8×D61—22no—
14#14519808—24no—
15#14519808C2218yescomplemented
16C2×#11758202—22no—
17C2×#11758201—22no—
18C2×#11758194C2212yes—
19#14519705C2218yescomplemented
20#14519696C2214yescomplemented
21C22×Q8×C61C2211yescharacteristic
22C22×Q8×C61C2211yescharacteristic
23C4⋊Q8×C61—22no—
24C4⋊Q8×C61C2214yescomplemented
25C2×C4⋊C4×C61—22no—
26C2×C42×C61C2211yescharacteristic
27C2×Q8×C61—22no—
28C2×Q8×C61—22no—
29C2×Q8×C61—21no—
30C2×Q8×C61—22no—
31C2×Q8×C61—22no—
32C2×Q8×C61D412yes—
33C2×Q8×C61C2312yes—
34C2×Q8×C61C2312yes—
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61D412yes—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—22no—
40#11758226—28no—
41#11758226—28no—
42Q8×D61—28no—
43Q8×D61—28no—
44#11758222—28no—
45#11758222—28no—
46#11758222—22no—
47#11758222—22no—
48#11758222D414yes—
49#11758222C2314yes—
50C2×D244—22no—
51C2×D244D412yes—
52C2×C4×D61—24no—
53C2×C4×D61—22no—
54C2×Dic122—22no—
55C2×Dic122D412yes—
56C4⋊C4×C61—28no—
57C42×C61—21no—
58C42×C61C2312yes—
59#11758202—28no—
60#11758201—28no—
61#11758194—22no—
62#11758194C2314yes—
63C2×#92418—22no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66Q8×C61—24no—
67Q8×C61—24no—
68Q8×C61—24no—
69Q8×C61—42no—
70C2×C4×C61—24no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D414yes—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—24no—
83C22⋊D61—24no—
84C2×Dic61—22no—
85D244—28no—
86D244—22no—
87D244C2×D414yes—
88C4×D61—216no—
89C4×D61—24no—
90C4×D61—24no—
91Dic122—28no—
92Dic122—22no—
93Dic122C2×D414yes—
94#92418—24no—
95C22×C61—22no—
96C22×C61#12011yescharacteristic
97C22×C61#12011yescharacteristic
98C22×C61C22×D411yescharacteristic
99C2×D61—24no—
100C2×D61—44no—
101C4×C61—24no—
102C4×C61—24no—
103C4×C61—42no—
104C4×C61#12012yes—
105C4×C61C22×D412yes—
106Dic61—24no—
107C2×#456—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—21no—
110C2×C61#45612yescomplemented
111C2×C61C2×#12011yescharacteristic
112D61—44no—
113C2×2−1+4—611no—
114C2×#137—612no—
115C2×C4⋊Q8D6111yescharacteristic, complemented
116#456—618no—
117C2×#104—612no—
118C2×#101—611no—
119C61C2×#45611yescharacteristic, complemented, Sylow
1202−1+4—614no—
1212−1+4—1224no—
1222−1+4—1222no—
123C2×#41—612no—
124C2×#41—1222no—
125C2×#41—1222no—
126C22×Q8—1222no—
127C22×Q8C2×D6111yescharacteristic
128C22×Q8C2×D6111yescharacteristic
129#137—618no—
130#137—1224no—
131C2×Q16—1222no—
132C2×SD16—1222no—
133C2×M16—612no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D6114yescomplemented
136C2×C4⋊C4—22no—
137C2×C42C2×D6111yescharacteristic
138#104—618no—
139#101—614no—
140#41—614no—
141#41—614no—
142#41—1228no—
143#41—1228no—
144#41—1228no—
145#41—1222no—
146#41—1222no—
147#41—1228no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—612no—
154C2×Q8—1222no—
155C2×Q8—1228no—
156C2×Q8—1228no—
157C2×Q8C22⋊D6112yes—
158C2×Q8C22×D6112yes—
159C2×Q8C22×D6112yes—
160C2×D4—612no—
161C2×D4—1222no—
162C2×D4—1222no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—1224no—
166C22×C4—1222no—
167C22×C4C22⋊D6112yes—
168C22×C4C22×D6111yescharacteristic
169Q16—1228no—
170SD16—1228no—
171M16—614no—
172M16—1222no—
173C2×C8—1222no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D6112yes—
177C23—1222no—
178C23C2×C22⋊D6111yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—614no—
184Q8—1228no—
185Q8—1222no—
186D4—614no—
187D4—1228no—
188D4—1224no—
189D4—1224no—
190D4—1222no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—12216no—
199C2×C4—1222no—
200C2×C4—1224no—
201C2×C4—1224no—
202C2×C4D4×D6112yes—
203C2×C4D4×D6112yes—
204C2×C4C2×C22⋊D6114yes—
205C2×C4C2×C22⋊D6111yescharacteristic
206C2×C4C23×D6111yescharacteristic
207C8—1224no—
208C22—22no—
209C22—1224no—
210C22—2444no—
211C22#1451974511yescharacteristic
212C22#1451974511yescharacteristic
213C22C22×C22⋊D6111yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—1224no—
218C4#1451974512yes—
219C4C2×D4×D6112yes—
220C2—21no—
221C2—21no—
222C2—2444no—
223C2#1683994412yesdirect product factor
224C2C2×#1451974511yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4⋊Q8×C61C2
socleC22×C61#120
hypercenterC2×C4⋊Q8D61
hypocenterC61C2×#456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#14519808C2semidirect
3. #16839944C2direct (N × H)
4. C2×#14519705C2semidirect
5. C2×#14519696C2semidirect
6. C2×C4⋊Q8×C61C2semidirect
15. #14519808C22semidirect
19. #14519705C22semidirect
20. #14519696C22semidirect
24. C4⋊Q8×C61C22semidirect
110. C2×C61#456semidirect
115. C2×C4⋊Q8D61semidirect
119. C61C2×#456semidirect
135. C4⋊Q8C2×D61semidirect
223. C2#16839944direct (N × H)