Finite Group Databasebeta

← #21456961

Subgroups — #21456961

Order 7808.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840314C211yesmaximal, characteristic
2C2×#14519776C211yesmaximal, characteristic
3#16840159C212yesmaximal, complemented
4#16840111C212yesmaximal, complemented
5#16840093C211yesmaximal, characteristic
6#16840092C211yesmaximal, characteristic
7#16840090C211yesmaximal, characteristic
8#16840046C212yesmaximal, complemented
9#16840045C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic
11C61×#483C211yesmaximal, characteristic
12C22×Dic122—21no—
13#14519776—21no—
14#14519776—21no—
15#14519776C2212yes—
16#14519776C2212yes—
17#14519776C2211yescharacteristic
18#14519775C2211yescharacteristic
19#14519767—21no—
20#14519756C2211yescharacteristic
21#14519754—21no—
22Q8×Dic61C2211yescharacteristic
23#14519742—21no—
24#14519742C2211yescharacteristic
25#14519733—21no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—21no—
28C2×C4×Dic61C2211yescharacteristic
29#14519709C2212yes—
30#14519708C2212yes—
31#14519708C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yes—
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C22×Dic61—21no—
47C22×Dic61D411yescharacteristic
48C22×Dic61D411yescharacteristic
49C2×Dic122—22no—
50C2×Dic122—22no—
51C2×Dic122—21no—
52C2×Dic122—44no—
53C2×Dic122C2311yescharacteristic
54C2×C8×C61C2312yes—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C4⋊C4×C61C2311yescharacteristic
59C22⋊C4×C61—21no—
60C22⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C4⋊Dic61C2312yes—
64C4⋊Dic61C2311yescharacteristic
65#11758196—21no—
66#11758196—22no—
67#11758196—22no—
68#11758196—21no—
69#11758196—21no—
70#11758196—21no—
71#11758196—21no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C23×C61C2×D411yescharacteristic
80Q8×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—42no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—42no—
93C2×Dic61SD1614yes—
94C2×Dic61C2×D411yescharacteristic
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98Dic122—22no—
99Dic122—44no—
100Dic122—44no—
101Dic122—42no—
102C8×C61—22no—
103#92418—22no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61C2×SD1612yes—
107C22×C61C22×D411yescharacteristic
108C4×C61—21no—
109C4×C61—41no—
110C4×C61—42no—
111C4×C61—41no—
112C4×C612−1+412yes—
113Dic61—21no—
114Dic61—41no—
115Dic61—42no—
116Dic61—41no—
117Dic61C2×SD1612yes—
118Dic61C2×SD1612yes—
119Dic61#13712yes—
120#3229—611nomaximal, Sylow
121C2×C61—22no—
122C2×C61#53611yescharacteristic
123C2×C61C22×SD1611yescharacteristic
124C2×C61C2×#13711yescharacteristic
125#533—611no—
126C2×C4⋊Q8—611no—
127#498—612no—
128#487—612no—
129#483—611no—
130#483—611no—
131#483—611no—
132#483D6111yescharacteristic
133#475—612no—
134#475—612no—
135#431—611no—
136C61#322911yescharacteristic, complemented, Sylow
137C22×Q8—1221no—
138C4⋊Q8—612no—
139C4⋊Q8—612no—
140C4⋊Q8—611no—
141C4⋊Q8—611no—
142C4⋊Q8—1221no—
143C4⋊Q8—1221no—
144#125—1221no—
145C22⋊Q8—611no—
146C22⋊Q8—1221no—
147C22⋊Q8C2×D6111yescharacteristic
148C4×Q8—611no—
149C4×Q8—611no—
150C4×Q8—1221no—
151#117—1221no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4C2×D6111yescharacteristic
155C2×C42—611no—
156#106—612no—
157#106—612no—
158#106—612no—
159#106C2×D6112yes—
160C4⋊C8—612no—
161#103—612no—
162#103—612no—
163#103—612no—
164#103C2×D6112yes—
165C22⋊C8—611no—
166C22⋊C8C2×D6111yescharacteristic
167C4×C8—612no—
168C2×Q8—611no—
169C2×Q8—1221no—
170C2×Q8—1222no—
171C2×Q8—1222no—
172C2×Q8—2444no—
173C2×Q8C22×D6111yescharacteristic
174C22×C4—21no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1221no—
178C22×C4C22×D6111yescharacteristic
179C2×C8—612no—
180C2×C8C22×D6112yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—612no—
184C4⋊C4—611no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4C22×D6112yes—
195C4⋊C4C22×D6111yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—1221no—
198C42—611no—
199C42—611no—
200C42—611no—
201C42—611no—
202C42—1221no—
203C42—1221no—
204C23D4×D6111yescharacteristic
205Q8—22no—
206Q8—1222no—
207Q8—2442no—
208Q8—2444no—
209Q8—2444no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—614no—
219C2×C4—611no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—2442no—
225C2×C4D4×D6111yescharacteristic
226C2×C4C23×D6111yescharacteristic
227C8—22no—
228C8—1222no—
229C22—21no—
230C22—21no—
231C22SD16×D6112yes—
232C22C2×D4×D6111yescharacteristic
233C4—21no—
234C4—42no—
235C4—41no—
236C4—41no—
237C4—612no—
238C4—612no—
239C4—612no—
240C4—1221no—
241C4—2442no—
242C4—2441no—
243C4—2441no—
244C4#1451982412yes—
245C2—22no—
246C2#1684033411yescharacteristic
247C2C2×SD16×D6111yescharacteristic
248C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61#3229
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #16840159C2semidirect
4. #16840111C2semidirect
8. #16840046C2semidirect
9. #16840045C2semidirect
136. C61#3229semidirect