Finite Group Databasebeta

← #21456846

Subgroups — #21456846

Order 7808.

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

normal subgroups only

This group has 386 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#16840154C212yesmaximal, complemented
3#16840130C212yesmaximal, complemented
4#16839969C212yesmaximal, complemented
5#16839964C212yesmaximal, complemented
6#16839918C212yesmaximal, complemented
7#16839901C212yesmaximal
8#16839819C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
10C2×#11758202C2214yes—
11C2×#11758201C2214yes—
12#14519771—21no—
13#14519769C2211yescharacteristic
14#14519765C2211yescharacteristic
15#14519760—21no—
16#14519756C2211yescharacteristic
17#14519751C2211yescharacteristic
18C4×Dic122C2211yescharacteristic
19C4×D244C2211yescharacteristic
20C4×C22⋊D61—21no—
21#14519734—21no—
22C4⋊#92418C2212yes—
23#14519701C2214yes—
24#14519701C2214yes—
25C22⋊#92418C2212yes—
26#14519688C2212yes—
27C22×Q8×C61C2212yes—
28C4⋊Q8×C61—21no—
29C4⋊Q8×C61—21no—
30C4⋊Q8×C61C2212yes—
31C4⋊Q8×C61C2212yes—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—21no—
34C2×C42×C61C2211yescharacteristic
35C2×Q8×C61—22no—
36C2×Q8×C61—44no—
37C2×Q8×C61C2314yes—
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×C61—22no—
50C42×C61D411yescharacteristic
51C42×C61D411yescharacteristic
52C42×C61C2311yescharacteristic
53C42×C61C2311yescharacteristic
54C22⋊Dic61—21no—
55#11758202—44no—
56#11758201—44no—
57#11758198—21no—
58#11758198—21no—
59#11758198—21no—
60#11758198—21no—
61C4⋊Dic61C2311yescharacteristic
62C4⋊Dic61C2311yescharacteristic
63#11758196—21no—
64#11758196—21no—
65#11758196—21no—
66#11758196—21no—
67C4×Dic61—21no—
68C2×#92418C2314yes—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71Q8×C61—24no—
72Q8×C61—24no—
73Q8×C61—44no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—24no—
78C2×C4×C61—44no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—42no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89D244—22no—
90C4×D61—42no—
91Dic122—22no—
92#92418—24no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61#13712yes—
96C22×C61C22×D411yescharacteristic
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—44no—
105C4×C61#13712yes—
106C4×C61H(5,𝔽2)12yes—
107Dic61—41no—
108Dic61—41no—
109Dic61—41no—
110#3218—611nomaximal, Sylow
111C2×C61—22no—
112C2×C61#53511yescharacteristic
113C2×C61C2×#13711yescharacteristic
114C2×C61C2×#13711yescharacteristic
115D61—81no—
116C2×C4⋊Q8D6111yescharacteristic, complemented
117#529—611no—
118#497—612no—
119#491—612no—
120#462—612no—
121#461—612no—
122#451—612no—
123#448—612no—
124#432—611no—
125C61#321811yescharacteristic, complemented, Sylow
126C22×Q8C2×D6112yes—
127C2×Q16—614no—
128C2×SD16—614no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8C2×D6112yes—
132C4⋊Q8C2×D6112yes—
133#126—1221no—
134#125—611no—
135#124—611no—
136#123—1221no—
137C22⋊Q8—611no—
138#121—611no—
139C4×Q8—611no—
140C4×D4—611no—
141C4×D4—1221no—
142#117—1221no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C42C2×D6111yescharacteristic
146C4⋊C8—612no—
147#103—614no—
148#103—614no—
149C22⋊C8—612no—
150#97—612no—
151C2×Q8—22no—
152C2×Q8—44no—
153C2×Q8—611no—
154C2×Q8C22×D6114yes—
155C2×D4—611no—
156C2×D4—1221no—
157C22×C4—22no—
158C22×C4—1221no—
159C22×C4C22⋊D6111yescharacteristic
160C22×C4C22⋊D6111yescharacteristic
161C22×C4C22×D6111yescharacteristic
162Q16—2444no—
163SD16—2444no—
164C2×C8—614no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—611no—
170C4⋊C4—611no—
171C4⋊C4—1221no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—1221no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C42—1221no—
181C42C22⋊D6111yescharacteristic
182C42C22⋊D6111yescharacteristic
183C42C22×D6111yescharacteristic
184C42C22×D6111yescharacteristic
185C23—1221no—
186C23C2×C22⋊D6111yescharacteristic
187Q8—24no—
188Q8—24no—
189Q8—44no—
190Q8—1222no—
191D4—1222no—
192D4—2442no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—44no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—2442no—
202C2×C4C2×C22⋊D6111yescharacteristic
203C2×C4C2×C22⋊D6111yescharacteristic
204C2×C4C2×C22⋊D6111yescharacteristic
205C2×C4C2×C22⋊D6111yescharacteristic
206C2×C4C2×C22⋊D6111yescharacteristic
207C2×C4C23×D6111yescharacteristic
208C8—1224no—
209C22—21no—
210C22—21no—
211C22—2441no—
212C22—2441no—
213C22—2441no—
214C22#1451980812yes—
215C22C22×C22⋊D6111yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—44no—
221C4—2441no—
222C4—2441no—
223C4—2441no—
224C4#1451980812yes—
225C4#1451982212yes—
226C2—22no—
227C2—4881no—
228C2#1684032911yescharacteristic
229C2C2×#1451980811yescharacteristic
230C2C2×#1451980811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4⋊Q8×C61C2
socleC22×C61C22×D4
hypercenterC2×C4⋊Q8D61
hypocenterC61#3218
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. #16840154C2semidirect
3. #16840130C2semidirect
4. #16839969C2semidirect
5. #16839964C2semidirect
6. #16839918C2semidirect
8. #16839819C2semidirect
9. C2×C4⋊Q8×C61C2semidirect
116. C2×C4⋊Q8D61semidirect
125. C61#3218semidirect