Finite Group Databasebeta

← #21457044

Subgroups — #21457044

Order 7808.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2#16840299C211yesmaximal, characteristic
3#16840170C212yesmaximal, complemented
4#16840123C212yesmaximal, complemented
5#16840091C212yesmaximal, complemented
6#16840077C212yesmaximal
7#16840057C211yesmaximal, characteristic, complemented
8#16840053C211yesmaximal, characteristic, complemented
9#16840049C211yesmaximal, characteristic, complemented
10#16839818C211yesmaximal, characteristic, complemented
11C61×#477C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13#14519777C2211yescharacteristic
14#14519776—21no—
15#14519776C2212yes—
16#14519775—21no—
17#14519772—21no—
18#14519768C2211yescharacteristic
19#14519766C2211yescharacteristic
20#14519762—21no—
21#14519753C2211yescharacteristic
22#14519752C2211yescharacteristic
23C4×D244—21no—
24C4×D244C2211yescharacteristic
25#14519734—21no—
26C4⋊C4×D61—21no—
27C4⋊C4×D61C2212yes—
28C42×D61C2211yescharacteristic
29#14519710C2212yes—
30#14519709C2212yes—
31#14519708C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519701C2212yes—
34#14519699C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37#14519687C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45Q8×D61—44no—
46C2×D244—21no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—21no—
50C2×C4×D61D411yescharacteristic
51C2×C4×D61D411yescharacteristic
52C2×C4×D61C2311yescharacteristic
53C2×Dic122—21no—
54C2×Dic122—22no—
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2312yes—
59C4⋊C4×C61C2311yescharacteristic
60C42×C61—21no—
61C42×C61C2311yescharacteristic
62#11758198—21no—
63#11758198—21no—
64#11758198—21no—
65#11758198—21no—
66#11758198—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61C2312yes—
70C4⋊Dic61C2311yescharacteristic
71#11758196—22no—
72#11758196—22no—
73#11758196—21no—
74#11758196—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C22×D61—21no—
80C22×D61C2×D411yescharacteristic
81Q8×C61—21no—
82Q8×C61—21no—
83Q8×C61—42no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2411yescharacteristic
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61C2×D411yescharacteristic
93C2×Dic61C2×D411yescharacteristic
94C2×Dic61C2×D411yescharacteristic
95D244—21no—
96D244—21no—
97D244—42no—
98C4×D61—22no—
99C4×D61—22no—
100C4×D61—21no—
101C4×D61—21no—
102C4×D61—44no—
103C4×D61—42no—
104Dic122—44no—
105Dic122—42no—
106C8×C61—22no—
107#92418—22no—
108C22×C61C22×D411yescharacteristic
109C2×D61—21no—
110C2×D61—21no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61AGL(1,ℤ/8)12yes—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61—42no—
118C4×C61—41no—
119C4×C61#13712yes—
120C4×C612−1+411yescharacteristic
121C4×C612−1+411yescharacteristic
122Dic61—21no—
123Dic61—21no—
124Dic61—21no—
125Dic61—42no—
126Dic61—41no—
127#3238—611nomaximal, Sylow
128C2×C61#53611yescharacteristic
129C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C61C2×#13711yescharacteristic
131D61—22no—
132D61—81no—
133C2×C4⋊Q8—611no—
134#529—611no—
135#501—612no—
136#489—612no—
137#483—612no—
138#480—612no—
139#477—611no—
140#477D6111yescharacteristic, complemented
141#476—611no—
142#476—611no—
143#432—611no—
144C61#323811yescharacteristic, complemented, Sylow
145C22×Q8—1221no—
146C4⋊Q8—612no—
147C4⋊Q8—611no—
148C4⋊Q8—1221no—
149C4⋊Q8—1221no—
150C4⋊Q8C2×D6111yescharacteristic
151#126—1221no—
152#125—611no—
153#124—611no—
154#123—1221no—
155C22⋊Q8—611no—
156#121—611no—
157C4×Q8C2×D6111yescharacteristic
158C4×D4—611no—
159C4×D4—1221no—
160#117—1221no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—1221no—
163C2×C42—611no—
164#107—612no—
165#107C2×D6112yes—
166#106—612no—
167#106—612no—
168C4⋊C8—611no—
169C4⋊C8C2×D6111yescharacteristic
170#103—612no—
171#103C2×D6112yes—
172#102—612no—
173#102—612no—
174C22⋊C8—612no—
175#97—612no—
176C2×Q8—21no—
177C2×Q8—1222no—
178C2×Q8—1221no—
179C2×Q8—2444no—
180C2×Q8C22×D6111yescharacteristic
181C2×D4—611no—
182C2×D4—1221no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—1222no—
187C22×C4—1221no—
188C2×C8—612no—
189C2×C8C22×D6112yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—612no—
193C4⋊C4—611no—
194C4⋊C4—1222no—
195C4⋊C4—1222no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C4⋊C4—1221no—
200C4⋊C4C22×D6112yes—
201C4⋊C4C22×D6111yescharacteristic
202C22⋊C4—1221no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C22⋊C4—1221no—
207C42—21no—
208C42—611no—
209C42—611no—
210C42—611no—
211C42C22×D6111yescharacteristic
212C23—611no—
213C23—1221no—
214Q8—21no—
215Q8—21no—
216Q8—42no—
217Q8—2442no—
218Q8—2444no—
219D4—1221no—
220D4—1221no—
221D4—2442no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1222no—
234C2×C4—2444no—
235C2×C4—2442no—
236C2×C4D4×D6111yescharacteristic
237C2×C4D4×D6111yescharacteristic
238C2×C4C23×D6111yescharacteristic
239C8—22no—
240C8—1222no—
241C22—612no—
242C22—1221no—
243C22—1221no—
244C22—2441no—
245C22—2441no—
246C22—2441no—
247C22C2×D4×D6111yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—41no—
252C4—1221no—
253C4—1221no—
254C4—1221no—
255C4—2442no—
256C4—2441no—
257C4#1451980912yes—
258C4#1451982411yescharacteristic
259C4#1451982511yescharacteristic
260C2—1222no—
261C2—4881no—
262C2#1684033511yescharacteristic
263C2AGL(1,ℤ/8)×D6111yescharacteristic
264C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#477C2
socleC22×C61C22×D4
hypercenter#477D61
hypocenterC61#3238
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D61C2semidirect
3. #16840170C2semidirect
4. #16840123C2semidirect
5. #16840091C2semidirect
7. #16840057C2semidirect
8. #16840053C2semidirect
9. #16840049C2semidirect
10. #16839818C2semidirect
11. C61×#477C2semidirect
140. #477D61semidirect
144. C61#3238semidirect