Finite Group Databasebeta

← #21457049

Subgroups — #21457049

Order 7808.

362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#16840296C211yesmaximal, characteristic
2#16840168C212yesmaximal, complemented
3#16840124C212yesmaximal, complemented
4#16840097C212yesmaximal, complemented
5#16840080C212yesmaximal
6#16840044C212yesmaximal, complemented
7#16840039C212yesmaximal, complemented
8#16839819C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
10#14519771—21no—
11#14519769C2211yescharacteristic
12#14519765C2211yescharacteristic
13#14519760—21no—
14#14519756C2211yescharacteristic
15#14519751C2211yescharacteristic
16C4×Dic122C2211yescharacteristic
17C4×D244C2211yescharacteristic
18C4×C22⋊D61—21no—
19#14519734—21no—
20#14519710C2214yes—
21#14519708C2214yes—
22C4⋊#92418C2212yes—
23#14519700C2214yes—
24#14519697C2214yes—
25C22⋊#92418C2212yes—
26#14519688C2212yes—
27C22×Q8×C61—21no—
28C4⋊Q8×C61—21no—
29C4⋊Q8×C61—21no—
30C4⋊Q8×C61C2212yes—
31C4⋊Q8×C61C2212yes—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61C2212yes—
34C2×C42×C61C2211yescharacteristic
35C2×Q8×C61—22no—
36C2×Q8×C61—22no—
37C2×Q8×C61—44no—
38C22×C4×C61—22no—
39C22×C4×C61D411yescharacteristic
40C22×C4×C61D411yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—21no—
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122C2311yescharacteristic
46C4⋊C4×C61—22no—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61C2314yes—
50C42×C61D411yescharacteristic
51C42×C61D411yescharacteristic
52C42×C61C2311yescharacteristic
53C42×C61C2311yescharacteristic
54C22⋊Dic61—21no—
55#11758198—21no—
56#11758198—21no—
57#11758198—21no—
58#11758198—21no—
59C4⋊Dic61C2311yescharacteristic
60C4⋊Dic61C2311yescharacteristic
61#11758196—21no—
62#11758196—21no—
63#11758196—21no—
64#11758196—21no—
65C4×Dic61—21no—
66C2×#92418C2314yes—
67C23×C61C2×D411yescharacteristic
68C22×D61—21no—
69Q8×C61—44no—
70Q8×C61—44no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—24no—
75C2×C4×C61—44no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—42no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86D244—22no—
87C4×D61—42no—
88Dic122—22no—
89#92418—24no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61#13712yes—
93C22×C61C22×D411yescharacteristic
94C2×D61—41no—
95C2×D61—41no—
96C2×D61—41no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—44no—
102C4×C61AGL(1,ℤ/8)12yes—
103C4×C612−1+412yes—
104Dic61—41no—
105Dic61—41no—
106Dic61—41no—
107#3239—611nomaximal, Sylow
108C2×C61—22no—
109C2×C61#53611yescharacteristic
110C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C61C2×#13711yescharacteristic
112D61—81no—
113C2×C4⋊Q8D6111yescharacteristic, complemented
114#529—611no—
115#501—612no—
116#489—612no—
117#484—612no—
118#481—612no—
119#475—612no—
120#474—612no—
121#432—611no—
122C61#323911yescharacteristic, complemented, Sylow
123C22×Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8C2×D6112yes—
127C4⋊Q8C2×D6112yes—
128#126—1221no—
129#125—611no—
130#124—611no—
131#123—1221no—
132C22⋊Q8—611no—
133#121—611no—
134C4×Q8—611no—
135C4×D4—611no—
136C4×D4—1221no—
137#117—1221no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C2×D6112yes—
140C2×C42C2×D6111yescharacteristic
141#107—614no—
142#106—614no—
143C4⋊C8—612no—
144#103—614no—
145#102—614no—
146C22⋊C8—612no—
147#97—612no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—44no—
151C2×Q8—611no—
152C2×D4—611no—
153C2×D4—1221no—
154C22×C4—22no—
155C22×C4—1221no—
156C22×C4C22⋊D6111yescharacteristic
157C22×C4C22⋊D6111yescharacteristic
158C22×C4C22×D6111yescharacteristic
159C2×C8—614no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—611no—
164C4⋊C4—611no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4C22×D6114yes—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C22⋊C4—1221no—
175C42—1221no—
176C42C22⋊D6111yescharacteristic
177C42C22⋊D6111yescharacteristic
178C42C22×D6111yescharacteristic
179C42C22×D6111yescharacteristic
180C23—1221no—
181C23C2×C22⋊D6111yescharacteristic
182Q8—44no—
183Q8—44no—
184Q8—1222no—
185D4—1222no—
186D4—2442no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—44no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—2442no—
196C2×C4C2×C22⋊D6111yescharacteristic
197C2×C4C2×C22⋊D6111yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C2×C4C2×C22⋊D6111yescharacteristic
200C2×C4C2×C22⋊D6111yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—1224no—
203C22—21no—
204C22—21no—
205C22—2441no—
206C22—2441no—
207C22—2441no—
208C22#1451980812yes—
209C22C22×C22⋊D6111yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—44no—
215C4—2441no—
216C4—2441no—
217C4—2441no—
218C4#1451980312yes—
219C4#1451982512yes—
220C2—22no—
221C2—4881no—
222C2#1684033611yescharacteristic
223C2C2×#1451980311yescharacteristic
224C2C2×#1451980811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4⋊Q8×C61C2
socleC22×C61C22×D4
hypercenterC2×C4⋊Q8D61
hypocenterC61#3239
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16840168C2semidirect
3. #16840124C2semidirect
4. #16840097C2semidirect
6. #16840044C2semidirect
7. #16840039C2semidirect
8. #16839819C2semidirect
9. C2×C4⋊Q8×C61C2semidirect
113. C2×C4⋊Q8D61semidirect
122. C61#3239semidirect