Finite Group Databasebeta

← #21456845

Subgroups — #21456845

Order 7808.

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

normal subgroups only

This group has 386 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#16840294C211yesmaximal, characteristic
3#16840153C212yesmaximal, complemented
4#16840129C212yesmaximal, complemented
5#16839973C211yesmaximal, characteristic, complemented
6#16839969C211yesmaximal, characteristic, complemented
7#16839967C211yesmaximal, characteristic, complemented
8#16839919C212yesmaximal, complemented
9#16839899C212yesmaximal
10#16839818C211yesmaximal, characteristic, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2212yes—
13C2×Dic244C2212yes—
14C2×#11758202C2212yes—
15C2×#11758200C2212yes—
16#14519777C2211yescharacteristic
17#14519776—21no—
18#14519776—21no—
19#14519775C2212yes—
20#14519770—21no—
21#14519768C2211yescharacteristic
22#14519764C2211yescharacteristic
23#14519759—21no—
24#14519757C2211yescharacteristic
25#14519748C2211yescharacteristic
26C4×Dic122C2211yescharacteristic
27C4×C22⋊D61—21no—
28#14519736—21no—
29C4⋊C4×D61—21no—
30C4⋊C4×D61—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37#14519687C2212yes—
38C2×SD16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61C2312yes—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47Q8×D61—42no—
48Q8×D61—42no—
49C2×C4×D61—22no—
50C2×C4×D61D411yescharacteristic
51C2×C4×D61D411yescharacteristic
52C2×C4×D61C2311yescharacteristic
53C2×Dic122—22no—
54C2×Dic122C2312yes—
55C2×Dic122C2311yescharacteristic
56SD16×C61—42no—
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—21no—
64C22⋊Dic61—21no—
65C22⋊Dic61—21no—
66#11758202—42no—
67#11758200—42no—
68#11758198—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2311yescharacteristic
74#11758196—21no—
75#11758196—22no—
76#11758196—22no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83Dic244—42no—
84C23×C61—21no—
85C22×D61C2×D411yescharacteristic
86Q8×C61—22no—
87Q8×C61—22no—
88D4×C61—21no—
89D4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—42no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—42no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103C4×D61—22no—
104C4×D61—22no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—44no—
108Dic122—21no—
109Dic122—22no—
110Dic122—22no—
111Dic122—21no—
112Dic122—44no—
113C8×C61—22no—
114#92418—22no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61C22×D411yescharacteristic
119C2×D61—21no—
120C2×D61—21no—
121C2×D61#13712yes—
122C4×C61—21no—
123C4×C61—42no—
124C4×C61—41no—
125C4×C61#13712yes—
126C4×C61H(5,𝔽2)11yescharacteristic
127C4×C61H(5,𝔽2)11yescharacteristic
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—42no—
132Dic61—41no—
133Dic61—41no—
134#3218—611nomaximal, Sylow
135C2×C61—81no—
136C2×C61#53511yescharacteristic
137C2×C61C2×#13711yescharacteristic
138C2×C61C2×#13711yescharacteristic
139D61—22no—
140C2×C4⋊Q8—611no—
141#529—611no—
142#497—612no—
143#491—612no—
144#462—611no—
145#462—611no—
146#461—611no—
147#461D6111yescharacteristic, complemented
148#451—612no—
149#448—612no—
150#432—611no—
151C61#321811yescharacteristic, complemented, Sylow
152C22×Q8—612no—
153C2×Q16—612no—
154C2×Q16—612no—
155C2×SD16—612no—
156C2×SD16C2×D6112yes—
157C4⋊Q8—612no—
158C4⋊Q8—611no—
159C4⋊Q8—1221no—
160C4⋊Q8—1221no—
161C4⋊Q8C2×D6111yescharacteristic
162#126—1221no—
163#125—611no—
164#124—611no—
165#123—1221no—
166C22⋊Q8—611no—
167#121—611no—
168C4×Q8—611no—
169C4×D4—1221no—
170C4×D4C2×D6111yescharacteristic
171#117—1221no—
172C2×C4⋊C4—1221no—
173C2×C4⋊C4—1221no—
174C2×C42—611no—
175C4⋊C8—611no—
176C4⋊C8C2×D6111yescharacteristic
177#103—612no—
178#103—612no—
179#103—612no—
180#103C2×D6112yes—
181C22⋊C8—612no—
182#97—612no—
183C2×Q8—612no—
184C2×Q8—611no—
185C2×Q8—1222no—
186C2×Q8—2442no—
187C2×Q8—2442no—
188C2×Q8C22×D6112yes—
189C2×D4—1221no—
190C2×D4C22×D6111yescharacteristic
191C22×C4—21no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1222no—
196Q16—2442no—
197Q16—2442no—
198SD16—42no—
199SD16—2442no—
200C2×C8—612no—
201C2×C8C22×D6112yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—611no—
205C4⋊C4—1222no—
206C4⋊C4—1222no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4C22×D6111yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42—1221no—
223C42C22×D6111yescharacteristic
224C23—21no—
225C23—611no—
226Q8—22no—
227Q8—22no—
228Q8—1221no—
229Q8—1222no—
230Q8—1222no—
231Q8—1221no—
232Q8—2444no—
233D4—21no—
234D4—21no—
235D4—2442no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—1222no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—2444no—
250C2×C4D4×D6111yescharacteristic
251C2×C4D4×D6111yescharacteristic
252C2×C4C23×D6111yescharacteristic
253C8—22no—
254C8—1222no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—612no—
259C22—1221no—
260C22—1221no—
261C22C2×D4×D6111yescharacteristic
262C4—21no—
263C4—41no—
264C4—42no—
265C4—1221no—
266C4—1221no—
267C4—1221no—
268C4—2441no—
269C4—2442no—
270C4—2441no—
271C4#1451980612yes—
272C4#1451982211yescharacteristic
273C4#1451982311yescharacteristic
274C2—81no—
275C2—1222no—
276C2#1684032811yescharacteristic
277C2#137×D6111yescharacteristic
278C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3218
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D61C2semidirect
3. #16840153C2semidirect
4. #16840129C2semidirect
5. #16839973C2semidirect
6. #16839969C2semidirect
7. #16839967C2semidirect
8. #16839919C2semidirect
10. #16839818C2semidirect
11. C61×#461C2semidirect
147. #461D61semidirect
151. C61#3218semidirect