Finite Group Databasebeta

← #21457016

Subgroups — #21457016

Order 7808.

366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840317C211yesmaximal, characteristic, complemented
2#16840309C211yesmaximal, characteristic
3#16840170C212yesmaximal, complemented
4#16840125C212yesmaximal, complemented
5#16840089C212yesmaximal, complemented
6#16840085C212yesmaximal, complemented
7#16840053C211yesmaximal, characteristic, complemented
8#16840052C211yesmaximal, characteristic, complemented
9#16840039C211yesmaximal, characteristic, complemented
10#16839818C211yesmaximal, characteristic, complemented
11C61×#474C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13#14519777C2211yescharacteristic
14#14519776C2211yescharacteristic
15#14519773C2211yescharacteristic
16#14519768C2212yes—
17#14519763—21no—
18#14519757—21no—
19#14519753—21no—
20#14519752C2211yescharacteristic
21#14519750—21no—
22#14519748C2211yescharacteristic
23Q8×Dic61—21no—
24#14519742—21no—
25C4×D244C2211yescharacteristic
26C4×C22⋊D61—21no—
27#14519735C2212yes—
28C42×D61C2211yescharacteristic
29#14519710C2212yes—
30#14519709C2212yes—
31#14519708C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519699C2212yes—
34#14519698C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37#14519687C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×Q8×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49#11758222—44no—
50C2×D244—21no—
51C2×D244C2311yescharacteristic
52C2×C4×D61—21no—
53C2×C4×D61D411yescharacteristic
54C2×C4×D61D411yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×Dic122—21no—
57C2×Dic122—21no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2312yes—
61C4⋊C4×C61C2311yescharacteristic
62C22⋊C4×C61—21no—
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758198—22no—
66#11758198—21no—
67#11758198—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61—22no—
70C4⋊Dic61C2312yes—
71C4⋊Dic61C2311yescharacteristic
72#11758196—21no—
73#11758196—22no—
74C4×Dic61—22no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C23×C61—21no—
80C22×D61—21no—
81C22×D61C2×D411yescharacteristic
82Q8×C61—42no—
83D4×C61—21no—
84D4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—42no—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2411yescharacteristic
91C22⋊D61—42no—
92C22⋊D61—42no—
93C22⋊D61—42no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99D244—21no—
100D244—21no—
101D244—42no—
102C4×D61—22no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—41no—
106C4×D61—42no—
107Dic122—42no—
108Dic122—42no—
109C8×C61—22no—
110#92418—22no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61C22×D411yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61—21no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—41no—
121C4×C61—21no—
122C4×C61—41no—
123C4×C61—42no—
124C4×C61AGL(1,ℤ/8)12yes—
125C4×C612−1+411yescharacteristic
126C4×C612−1+411yescharacteristic
127Dic61—21no—
128Dic61—21no—
129Dic61—21no—
130Dic61—41no—
131Dic61—42no—
132#3235—611nomaximal, Sylow
133C2×C61—81no—
134C2×C61#53611yescharacteristic
135C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C61#57511yescharacteristic
137D61—41no—
138D61—81no—
139#533—611no—
140#532—611no—
141#501—612no—
142#490—612no—
143#482—612no—
144#482—612no—
145#476—611no—
146#476—611no—
147#474—611no—
148#474D6111yescharacteristic, complemented
149#432—611no—
150C61#323511yescharacteristic, complemented, Sylow
151C2×#41—1221no—
152C4⋊Q8—611no—
153C4⋊Q8—611no—
154C4⋊Q8C2×D6111yescharacteristic
155#127—611no—
156#125—612no—
157#124—1221no—
158C22⋊Q8—1221no—
159C22⋊Q8—1221no—
160#121—611no—
161#121—611no—
162#121—1221no—
163C4×Q8—1221no—
164C4×Q8—1221no—
165C4×D4—611no—
166C4×D4—1221no—
167C4×D4C2×D6111yescharacteristic
168#117—612no—
169C2×C42—611no—
170#107—612no—
171#107C2×D6112yes—
172#106—612no—
173#106—612no—
174C4⋊C8—611no—
175C4⋊C8C2×D6111yescharacteristic
176#102—612no—
177#102—612no—
178#102—612no—
179#102C2×D6112yes—
180C22⋊C8—612no—
181#97—612no—
182#41—2444no—
183C2×Q8—21no—
184C2×Q8—1221no—
185C2×Q8—1221no—
186C2×D4—611no—
187C2×D4—1221no—
188C2×D4—1221no—
189C2×D4—1221no—
190C2×D4—1221no—
191C2×D4C22×D6111yescharacteristic
192C22×C4—21no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—1221no—
197C2×C8—612no—
198C2×C8C22×D6112yes—
199C4⋊C4—21no—
200C4⋊C4—612no—
201C4⋊C4—611no—
202C4⋊C4—1221no—
203C4⋊C4—1222no—
204C4⋊C4—1222no—
205C4⋊C4—1221no—
206C4⋊C4C22×D6112yes—
207C4⋊C4C22×D6111yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—1221no—
210C22⋊C4—1222no—
211C22⋊C4—1221no—
212C22⋊C4—1221no—
213C42—611no—
214C42—611no—
215C42—611no—
216C42—1222no—
217C42C22×D6111yescharacteristic
218C23—21no—
219C23—611no—
220C23—1221no—
221Q8—42no—
222Q8—2442no—
223Q8—2442no—
224D4—21no—
225D4—21no—
226D4—1221no—
227D4—1221no—
228D4—2442no—
229D4—2442no—
230D4—2442no—
231D4—2442no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—2441no—
244C2×C4—2442no—
245C2×C4D4×D6111yescharacteristic
246C2×C4D4×D6111yescharacteristic
247C2×C4C23×D6111yescharacteristic
248C8—22no—
249C8—1222no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—1221no—
254C22—1221no—
255C22—1221no—
256C22—2441no—
257C22—2441no—
258C22—2441no—
259C22C2×D4×D6111yescharacteristic
260C4—21no—
261C4—41no—
262C4—42no—
263C4—1221no—
264C4—1221no—
265C4—1221no—
266C4—2441no—
267C4—2442no—
268C4#1451980112yes—
269C4#1451982411yescharacteristic
270C4#1451982511yescharacteristic
271C2—81no—
272C2—4881no—
273C2—2441no—
274C2#1684033511yescharacteristic
275C2C2×#1451980111yescharacteristic
276C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3235
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840170C2semidirect
4. #16840125C2semidirect
5. #16840089C2semidirect
6. #16840085C2semidirect
7. #16840053C2semidirect
8. #16840052C2semidirect
9. #16840039C2semidirect
10. #16839818C2semidirect
11. C61×#474C2semidirect
148. #474D61semidirect
150. C61#3235semidirect