Finite Group Databasebeta

← #21456784

Subgroups — #21456784

Order 7808.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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, complemented
2#16840144C212yesmaximal, complemented
3#16840116C212yesmaximal, complemented
4#16839981C212yesmaximal, complemented
5#16839974C212yesmaximal, complemented
6#16839918C211yesmaximal, characteristic, complemented
7#16839913C211yesmaximal, characteristic, complemented
8#16839901C211yesmaximal, characteristic, complemented
9#16839896C211yesmaximal, characteristic
10#16839815C211yesmaximal, characteristic, complemented
11C2×#124×C61C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yescomplemented
13C2×#11758200C2212yes—
14C2×#11758201C2212yescomplemented
15C2×#11758199C2212yes—
16#14519771—21no—
17#14519769C2211yescharacteristic, complemented
18#14519765C2211yescharacteristic, complemented
19#14519760—21no—
20#14519756C2211yescharacteristic
21#14519751C2211yescharacteristic
22C4×Dic122C2211yescharacteristic, complemented
23C4×D244C2211yescharacteristic, complemented
24C4×C22⋊D61—21no—
25#14519734—21no—
26C4⋊#92418C2212yescomplemented
27#14519701C2212yescomplemented
28#14519701C2212yescomplemented
29#14519698C2212yes—
30#14519698C2212yes—
31C22⋊#92418C2211yescharacteristic
32C22⋊#92418C2211yescharacteristic
33C4×#92418C2212yescomplemented
34C22×Q8×C61C2211yescharacteristic
35C22×D4×C61C2211yescharacteristic
36#124×C61—21no—
37#124×C61—21no—
38#124×C61C2212yes—
39#124×C61C2212yes—
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61—21no—
42C2×C42×C61C2211yescharacteristic
43C24×C61—21no—
44C2×Q8×C61—21no—
45C2×Q8×C61—42no—
46C2×Q8×C61C2312yes—
47C2×D4×C61—21no—
48C2×D4×C61—42no—
49C2×D4×C61C2312yes—
50C22×C4×C61—21no—
51C22×C4×C61D411yescharacteristic
52C22×C4×C61D411yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C2×C22⋊D61—21no—
55C2×D244C2311yescharacteristic
56C2×C4×D61—21no—
57C2×Dic122C2311yescharacteristic
58C22⋊C4×C61—22no—
59C22⋊C4×C61—22no—
60C22⋊C4×C61—22no—
61C22⋊C4×C61—22no—
62C42×C61D411yescharacteristic
63C42×C61D411yescharacteristic
64C42×C61C2311yescharacteristic
65C42×C61C2311yescharacteristic
66C22⋊Dic61—21no—
67#11758202—42no—
68#11758201—42no—
69#11758200—42no—
70#11758199—42no—
71#11758198—21no—
72#11758198—21no—
73#11758198—21no—
74#11758198—21no—
75C4⋊Dic61C2311yescharacteristic
76C4⋊Dic61C2311yescharacteristic
77#11758196—21no—
78#11758196—21no—
79#11758196—21no—
80#11758196—21no—
81C4×Dic61—21no—
82C2×#92418C2312yes—
83C2×#92418C2312yes—
84C23×C61—22no—
85C23×C61—42no—
86C23×C61—42no—
87C23×C61—42no—
88C23×C61C2×D411yescharacteristic
89C22×D61—21no—
90Q8×C61—22no—
91Q8×C61—22no—
92Q8×C61—42no—
93D4×C61—22no—
94D4×C61—22no—
95D4×C61—42no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2×D411yescharacteristic
106C2×C4×C61C2411yescharacteristic
107C22⋊D61—42no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111D244—22no—
112C4×D61—42no—
113Dic122—22no—
114#92418—22no—
115#92418—22no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—84no—
122C22×C61#13512yes—
123C22×C61C22×D411yescharacteristic
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—41no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—42no—
133C4×C61H(5,𝔽2)12yes—
134Dic61—41no—
135Dic61—41no—
136Dic61—41no—
137#3211—611nomaximal, Sylow
138C2×C61—22no—
139C2×C61—82no—
140C2×C61#53511yescharacteristic
141C2×C61C2×#13511yescharacteristic
142C2×C61#57511yescharacteristic
143D61—81no—
144#529—611no—
145C2×#124D6111yescharacteristic, complemented
146#495—612no—
147#488—612no—
148#464—612no—
149#463—612no—
150#451—611no—
151#450—611no—
152#448—611no—
153#447—611no—
154#431—611no—
155C61#321111yescharacteristic, complemented, Sylow
156C22×Q8C2×D6111yescharacteristic
157C22×D4C2×D6111yescharacteristic
158C2×Q16—612no—
159C2×SD16—612no—
160C2×SD16—612no—
161C2×D8—612no—
162#126—1221no—
163#125—611no—
164#124—21no—
165#124—21no—
166#124—611no—
167#124C2×D6112yes—
168#124C2×D6112yes—
169#123—1221no—
170C22⋊Q8—611no—
171#121—611no—
172C4×Q8—611no—
173C4×D4—611no—
174C4×D4—1221no—
175#117—1221no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42C2×D6111yescharacteristic
179C4⋊C8—612no—
180#103—612no—
181#103—612no—
182#102—612no—
183#102—612no—
184C22⋊C8—611no—
185C22⋊C8—611no—
186C4×C8—612no—
187C24—21no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—611no—
191C2×Q8C22×D6112yes—
192C2×D4—21no—
193C2×D4—42no—
194C2×D4—611no—
195C2×D4—1221no—
196C2×D4C22×D6112yes—
197C22×C4—21no—
198C22×C4—1221no—
199C22×C4C22⋊D6111yescharacteristic
200C22×C4C22⋊D6111yescharacteristic
201C22×C4C22×D6111yescharacteristic
202Q16—2442no—
203SD16—2442no—
204SD16—2442no—
205D8—2442no—
206C2×C8—612no—
207C2×C8—612no—
208C4⋊C4—611no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C22⋊C4—1221no—
221C22⋊C4—1221no—
222C22⋊C4—1221no—
223C42—1221no—
224C42C22⋊D6111yescharacteristic
225C42C22⋊D6111yescharacteristic
226C42C22×D6111yescharacteristic
227C42C22×D6111yescharacteristic
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—1221no—
233C23C2×C22⋊D6111yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—1222no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—1222no—
242D4—2442no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—2442no—
252C2×C4C2×C22⋊D6111yescharacteristic
253C2×C4C2×C22⋊D6111yescharacteristic
254C2×C4C2×C22⋊D6111yescharacteristic
255C2×C4C2×C22⋊D6111yescharacteristic
256C2×C4C2×C22⋊D6111yescharacteristic
257C2×C4C23×D6111yescharacteristic
258C8—1222no—
259C8—1222no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—2441no—
267C22—2441no—
268C22—2441no—
269C22#1451979712yes—
270C22C22×C22⋊D6111yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—2441no—
278C4—2441no—
279C4—2441no—
280C4#1451982212yes—
281C2—22no—
282C2—82no—
283C2—4881no—
284C2#1684032911yescharacteristic
285C2C2×#1451979711yescharacteristic
286C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#124×C61C2
socleC22×C61C22×D4
hypercenterC2×#124D61
hypocenterC61#3211
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #16840296C2semidirect
2. #16840144C2semidirect
3. #16840116C2semidirect
4. #16839981C2semidirect
5. #16839974C2semidirect
6. #16839918C2semidirect
7. #16839913C2semidirect
8. #16839901C2semidirect
10. #16839815C2semidirect
11. C2×#124×C61C2semidirect
12. C2×#11758202C22semidirect
14. C2×#11758201C22semidirect
17. #14519769C22semidirect
18. #14519765C22semidirect
22. C4×Dic122C22semidirect
23. C4×D244C22semidirect
26. C4⋊#92418C22semidirect
27. #14519701C22semidirect
28. #14519701C22semidirect
33. C4×#92418C22semidirect
145. C2×#124D61semidirect
155. C61#3211semidirect