Finite Group Databasebeta

← #21456851

Subgroups — #21456851

Order 7808.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840310C211yesmaximal, characteristic, complemented
2#16840291C211yesmaximal, characteristic, complemented
3#16840157C211yesmaximal, characteristic, complemented
4#16840131C211yesmaximal, characteristic, complemented
5#16840126C211yesmaximal, characteristic, complemented
6#16839982C212yesmaximal, complemented
7#16839975C212yesmaximal, complemented
8#16839921C212yesmaximal, complemented
9#16839904C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#496C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yes—
13C2×#11758202C2212yes—
14C2×#11758200C2212yes—
15#14519777C2211yescharacteristic
16#14519770—21no—
17#14519769C2211yescharacteristic
18#14519764C2212yes—
19#14519759—21no—
20#14519753C2211yescharacteristic
21#14519748—21no—
22#14519748—21no—
23#14519748C2211yescharacteristic
24Q8×Dic61C2211yescharacteristic
25D4×Dic61—21no—
26D4×Dic61—21no—
27D4×Dic61C2211yescharacteristic
28#14519737—21no—
29#14519733—21no—
30C42×D61C2211yescharacteristic
31#14519706C2212yes—
32#14519702C2212yes—
33#14519702C2212yes—
34#14519698C2212yes—
35#14519698C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic
38C2×SD16×C61C2212yes—
39C2×D8×C61C2212yes—
40#127×C61C2211yescharacteristic
41#124×C61C2211yescharacteristic
42#97×C61C2211yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61C2312yes—
47C2×D4×C61C2311yescharacteristic
48C2×C22⋊D61—22no—
49C2×C22⋊D61—21no—
50C22×Dic61—22no—
51C22×Dic61—21no—
52#11758224—42no—
53#11758224—42no—
54C2×C4×D61D411yescharacteristic
55C2×C4×D61D411yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×Dic122C2312yes—
58SD16×C61—42no—
59D8×C61—42no—
60C2×C8×C61C2312yes—
61C22⋊C4×C61—21no—
62C22⋊C4×C61—21no—
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65C22⋊Dic61—22no—
66C22⋊Dic61—22no—
67C22⋊Dic61—21no—
68#11758202—42no—
69#11758200—42no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61C2311yescharacteristic
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80C4×Dic61D411yescharacteristic
81C4×Dic61D411yescharacteristic
82C4×Dic61C2311yescharacteristic
83C2×#92418C2312yes—
84C23×C61—21no—
85C23×C61—22no—
86C22×D61C2×D411yescharacteristic
87Q8×C61—22no—
88D4×C61—22no—
89D4×C61—22no—
90D4×C61—22no—
91D4×C61—42no—
92D4×C61—42no—
93C2×C4×C61—21no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—44no—
98C22⋊D61—42no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—44no—
103C2×Dic61—42no—
104C2×Dic61C2×D411yescharacteristic
105C2×Dic61C2×D411yescharacteristic
106C2×Dic61C2×D411yescharacteristic
107C4×D61—22no—
108C4×D61—41no—
109C4×D61—41no—
110Dic122—22no—
111Dic122—22no—
112C8×C61—22no—
113#92418—22no—
114C22×C61—42no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61C22×D411yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61H(5,𝔽2)12yes—
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—42no—
132Dic61—41no—
133Dic61—41no—
134#3219—611nomaximal, Sylow
135C2×C61—82no—
136C2×C61—81no—
137C2×C61#53511yescharacteristic
138C2×C61#57511yescharacteristic
139C2×C61#57511yescharacteristic
140D61—41no—
141#532—611no—
142#529—611no—
143#497—611no—
144#496D6111yescharacteristic, complemented
145#491—611no—
146#490—611no—
147#464—612no—
148#463—612no—
149#452—612no—
150#449—612no—
151#432—611no—
152C61#321911yescharacteristic, complemented, Sylow
153C2×#41—612no—
154C2×Q16—612no—
155C2×SD16—612no—
156C2×SD16C2×D6112yes—
157C2×D8C2×D6112yes—
158C4⋊Q8—611no—
159#127C2×D6111yescharacteristic
160#126—1221no—
161#125—611no—
162#124—612no—
163#124C2×D6111yescharacteristic
164#123—1221no—
165C22⋊Q8—611no—
166#121—611no—
167#121—1221no—
168#121—1221no—
169C4×Q8—611no—
170C4×D4—611no—
171C4×D4—1221no—
172C4×D4—1221no—
173C4×D4—1221no—
174#117—1221no—
175C2×C42—611no—
176C4⋊C8—612no—
177#103—612no—
178#103—612no—
179#102—612no—
180#102—612no—
181C22⋊C8—612no—
182#97—611no—
183#97C2×D6111yescharacteristic
184#41—2442no—
185#41—2442no—
186C2×Q8—612no—
187C2×Q8C22×D6111yescharacteristic
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—1221no—
191C2×D4—1222no—
192C2×D4C22×D6112yes—
193C2×D4C22×D6111yescharacteristic
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1221no—
198C22×C4—1222no—
199Q16—2442no—
200SD16—42no—
201SD16—2442no—
202D8—42no—
203C2×C8—612no—
204C2×C8C22×D6112yes—
205C4⋊C4—611no—
206C4⋊C4—611no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C22⋊C4—1222no—
219C22⋊C4—1222no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42—1221no—
224C42C22×D6111yescharacteristic
225C23—21no—
226C23—22no—
227C23—611no—
228Q8—22no—
229Q8—1222no—
230Q8—1222no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—42no—
235D4—42no—
236D4—2442no—
237D4—2444no—
238C2×C4—21no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—1222no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1222no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2442no—
249C2×C4—2444no—
250C2×C4D4×D6111yescharacteristic
251C2×C4D4×D6111yescharacteristic
252C2×C4C23×D6111yescharacteristic
253C8—22no—
254C8—1222no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—1221no—
262C22—1221no—
263C22—1221no—
264C22C2×D4×D6111yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—1221no—
269C4—1221no—
270C4—1221no—
271C4—2441no—
272C4—2441no—
273C4—2442no—
274C4#1451982212yes—
275C2—81no—
276C2—82no—
277C2—2441no—
278C2#1684032511yescharacteristic
279C2#1684055811yescharacteristic
280C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3219
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840310C2semidirect
2. #16840291C2semidirect
3. #16840157C2semidirect
4. #16840131C2semidirect
5. #16840126C2semidirect
6. #16839982C2semidirect
7. #16839975C2semidirect
8. #16839921C2semidirect
9. #16839904C2semidirect
10. #16839817C2semidirect
11. C61×#496C2semidirect
144. #496D61semidirect
152. C61#3219semidirect