Finite Group Databasebeta

← #21455473

Subgroups — #21455473

Order 7808.

460 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C22×#11758202C211yesmaximal, characteristic, complemented
2C2×#14519785C211yesmaximal, characteristic
3#16840338C211yesmaximal, characteristic
4#16840336C211yesmaximal, characteristic
5#16840019C214yesmaximal, complemented
6#16840002C214yesmaximal, complemented
7#16839798C211yesmaximal, characteristic, complemented
8#16839772C211yesmaximal, characteristic, complemented
9C61×#419C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12C2×#11758202—24no—
13C2×#11758202C2212yes—
14C2×#11758202C2212yes—
15#14519785—24no—
16C2×#11758189C2212yes—
17C22×#92418C2211yescharacteristic
18C2×C8×D61C2212yes—
19#14519777—21no—
20#14519775—21no—
21#14519766—21no—
22#14519765—21no—
23#14519761—22no—
24#14519760—22no—
25#14519757C2214yes—
26#14519753C2214yes—
27#14519736C2211yescharacteristic
28#14519710C2212yes—
29#14519708C2212yes—
30#14519702C2214yes—
31C22×Q8×C61C2211yescharacteristic
32C2×M16×C61C2211yescharacteristic
33#117×C61C2211yescharacteristic
34#103×C61C2214yes—
35C2×Q8×C61—21no—
36C2×Q8×C61—22no—
37C2×Q8×C61—22no—
38C2×Q8×C61C2312yes—
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61D412yes—
42C22×Dic61—21no—
43#11758222—22no—
44#11758222—22no—
45C2×D244D411yescharacteristic
46C2×C4×D61C2312yes—
47C2×Dic122—22no—
48C2×Dic122—22no—
49C2×Dic122—21no—
50C2×Dic122D411yescharacteristic
51C2×Dic122C2312yes—
52M16×C61—22no—
53C2×C8×C61C2312yes—
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—21no—
56C42×C61—21no—
57C22⋊Dic61—21no—
58#11758202—24no—
59#11758202—24no—
60#11758198—24no—
61#11758198—24no—
62C4⋊Dic61—24no—
63C4⋊Dic61C2312yes—
64#11758196—24no—
65C4×Dic61—21no—
66C2×#92418D414yes—
67C2×#92418C2311yescharacteristic
68C2×#92418C2311yescharacteristic
69#11758189—24no—
70C8×D61—24no—
71C23×C61C2×D411yescharacteristic
72C22×D61C2×D412yes—
73Q8×C61—22no—
74Q8×C61—22no—
75Q8×C61—42no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—42no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D412yes—
81C2×C4×C61#4112yes—
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—24no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—42no—
87C2×Dic61C2×D412yes—
88D244—22no—
89C4×D61—22no—
90C4×D61—22no—
91Dic122—22no—
92Dic122—22no—
93Dic122—22no—
94Dic122—42no—
95C8×C61—22no—
96#92418C2×D412yes—
97#92418C2×D412yes—
98C22×C61—22no—
99C22×C61#12112yes—
100C22×C61C22×D411yescharacteristic
101C2×D61—22no—
102C2×D61—24no—
103C4×C61—42no—
104C4×C61—42no—
105C4×C61#12112yes—
106C4×C61C22×D411yescharacteristic
107C4×C61C2×#4111yescharacteristic
108Dic61—22no—
109Dic61—42no—
110Dic61—42no—
111#3059—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61C2×#12111yescharacteristic
114C2×C61#57812yes—
115D61—42no—
116C22×Q16—611no—
117C2×#131—611no—
118#536—611no—
119#536—611no—
120#470—614no—
121#467—614no—
122#427—611no—
123#419—611no—
124#419D6111yescharacteristic, complemented
125C61#305911yescharacteristic, complemented, Sylow
126C2×#41—611no—
127C22×Q8—611no—
128C22×Q8C2×D6111yescharacteristic
129C2×Q16—612no—
130C2×Q16—612no—
131C2×Q16—1224no—
132#131—1224no—
133C2×M16—612no—
134C2×M16C2×D6111yescharacteristic
135C22×C8—611no—
136C22×C8—612no—
137C4⋊Q8—1221no—
138C4⋊Q8—1221no—
139#124—1221no—
140#124—1221no—
141#123—1222no—
142#123—1222no—
143C22⋊Q8—614no—
144C22⋊Q8—614no—
145#117—611no—
146#117C2×D6111yescharacteristic
147#107—612no—
148#106—612no—
149#103—614no—
150#103C2×D6114yes—
151#41—1222no—
152#41—1222no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—611no—
157C2×Q8—612no—
158C2×Q8—1221no—
159C2×Q8—1222no—
160C2×Q8—1222no—
161C2×Q8C22×D6112yes—
162C2×D4—612no—
163C2×D4—611no—
164C22×C4—21no—
165C22×C4—612no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168Q16—1224no—
169Q16—1224no—
170M16—22no—
171M16—1224no—
172C2×C8—614no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—1224no—
176C2×C8C22×D6112yes—
177C4⋊C4—612no—
178C4⋊C4—1224no—
179C4⋊C4—1224no—
180C4⋊C4C22×D6112yes—
181C22⋊C4—21no—
182C22⋊C4—1224no—
183C22⋊C4—1224no—
184C22⋊C4—1221no—
185C42—21no—
186C42—1221no—
187C23—612no—
188C23D4×D6111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—1222no—
193Q8—1222no—
194Q8—1222no—
195Q8—2442no—
196D4—1224no—
197D4—1222no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—612no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—2442no—
207C2×C4#1175822212yes—
208C2×C4D4×D6112yes—
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—612no—
213C8—612no—
214C22—22no—
215C22—1222no—
216C22—1224no—
217C22#1451975012yes—
218C22C2×D4×D6111yescharacteristic
219C4—42no—
220C4—42no—
221C4—1222no—
222C4—2442no—
223C4—2442no—
224C4#1451975012yes—
225C4C2×D4×D6111yescharacteristic
226C4C2×#1175822211yescharacteristic
227C2—22no—
228C2—2442no—
229C2C2×#1451975011yescharacteristic
230C2#1684057812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#419C2
socleC22×C61C22×D4
hypercenter#419D61
hypocenterC61#3059
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#11758202C2semidirect
5. #16840019C2semidirect
6. #16840002C2semidirect
7. #16839798C2semidirect
8. #16839772C2semidirect
9. C61×#419C2semidirect
124. #419D61semidirect
125. C61#3059semidirect