Finite Group Databasebeta

← #21457198

Subgroups — #21457198

Order 7808.

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

normal subgroups only

This group has 430 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
1#16840310C211yesmaximal, characteristic, complemented
2#16840309C211yesmaximal, characteristic, complemented
3#16840053C211yesmaximal, characteristic, complemented
4#16840052C211yesmaximal, characteristic, complemented
5#16840050C212yesmaximal, complemented
6#16840014C212yesmaximal, complemented
7#16840012C212yesmaximal, complemented
8#16839955C212yesmaximal, complemented
9#16839954C211yesmaximal, characteristic, complemented
10#16839784C211yesmaximal, characteristic, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13C2×#11758224—21no—
14C2×#11758199C2212yes—
15C2×#11758189C2212yes—
16#14519777C2211yescharacteristic
17#14519776C2211yescharacteristic
18#14519773C2211yescharacteristic
19#14519764—21no—
20#14519763—21no—
21#14519752C2211yescharacteristic
22#14519750—21no—
23#14519748—21no—
24#14519748C2211yescharacteristic
25#14519748C2212yes—
26C4×D244C2211yescharacteristic
27D4×Dic61—21no—
28D4×Dic61C2212yes—
29C4×C22⋊D61—21no—
30C42×D61C2211yescharacteristic
31#14519709C2212yes—
32#14519708C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519699C2212yes—
36#14519698C2212yes—
37#14519698C2212yes—
38C2×D8×C61C2212yes—
39#127×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×D4×C61—21no—
44C2×D4×C61—21no—
45C2×D4×C61C2312yes—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—21no—
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52C22×Dic61—22no—
53#11758224—44no—
54#11758222—44no—
55C2×D244—21no—
56C2×D244C2311yescharacteristic
57C2×C4×D61—21no—
58C2×C4×D61D411yescharacteristic
59C2×C4×D61D411yescharacteristic
60C2×C4×D61C2311yescharacteristic
61C2×Dic122—21no—
62C2×Dic122—21no—
63D8×C61—42no—
64C2×C8×C61C2312yes—
65C4⋊C4×C61C2311yescharacteristic
66C22⋊C4×C61—21no—
67C42×C61C2311yescharacteristic
68C22⋊Dic61—21no—
69C22⋊Dic61—22no—
70C22⋊Dic61—22no—
71#11758199—42no—
72#11758198—21no—
73#11758198—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2311yescharacteristic
76C4⋊Dic61C2312yes—
77#11758196—21no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82#11758189—42no—
83C23×C61—22no—
84C23×C61—21no—
85C22×D61—21no—
86C22×D61C2×D411yescharacteristic
87D4×C61—22no—
88D4×C61—21no—
89D4×C61—22no—
90D4×C61—21no—
91D4×C61—42no—
92D4×C61—42no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—42no—
99C22⋊D61—42no—
100C22⋊D61—44no—
101C22⋊D61—42no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—44no—
105C2×Dic61C2×D411yescharacteristic
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108D244—21no—
109D244—21no—
110D244—42no—
111C4×D61—22no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—22no—
115C4×D61—42no—
116Dic122—42no—
117Dic122—42no—
118C8×C61—22no—
119#92418—22no—
120C22×C61—42no—
121C22×C61—41no—
122C22×C61—42no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61C22×D411yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C4×C61—21no—
134C4×C61—41no—
135C4×C61AGL(1,ℤ/8)12yes—
136C4×C61H(5,𝔽2)11yescharacteristic
137C4×C612−1+411yescharacteristic
138Dic61—21no—
139Dic61—21no—
140Dic61—41no—
141Dic61—42no—
142Dic61AGL(1,ℤ/8)12yes—
143#3253—611nomaximal, Sylow
144C2×C61—82no—
145C2×C61—81no—
146C2×C61#53711yescharacteristic
147C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
149D61—41no—
150D61—81no—
151#532—611no—
152#532—611no—
153#476—611no—
154#476—611no—
155#476—612no—
156#469—612no—
157#469—612no—
158#459—612no—
159#459—611no—
160#459D6111yescharacteristic, complemented
161#423—611no—
162C61#325311yescharacteristic, complemented, Sylow
163C2×#41—1221no—
164C2×#41—1221no—
165C2×D8—612no—
166C2×D8C2×D6112yes—
167C2×M16—612no—
168C4⋊Q8—611no—
169C4⋊Q8—611no—
170#127—611no—
171#127C2×D6111yescharacteristic
172#124—1221no—
173#124—1221no—
174#121—611no—
175#121—612no—
176#121—611no—
177#121—1221no—
178#121—1221no—
179C4×D4—612no—
180C4×D4—611no—
181C4×D4—1221no—
182C4×D4—1221no—
183C4×D4C2×D6111yescharacteristic
184C2×C42—611no—
185#106—612no—
186#106—612no—
187C4⋊C8—612no—
188C4⋊C8—611no—
189C4⋊C8C2×D6111yescharacteristic
190#102—612no—
191#102—612no—
192#102—612no—
193#102C2×D6112yes—
194#41—2444no—
195#41—2444no—
196C2×Q8—1221no—
197C2×Q8—1221no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—611no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4—1221no—
204C2×D4—1221no—
205C2×D4—1222no—
206C2×D4C22×D6111yescharacteristic
207C2×D4C22×D6112yes—
208C22×C4—21no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1222no—
213C22×C4—1221no—
214D8—42no—
215D8—2442no—
216M16—2442no—
217C2×C8—612no—
218C2×C8C22×D6112yes—
219C4⋊C4—611no—
220C4⋊C4—612no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4C22×D6111yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—1221no—
226C22⋊C4—1222no—
227C22⋊C4—1221no—
228C22⋊C4—1222no—
229C22⋊C4—1221no—
230C42—611no—
231C42—611no—
232C42—611no—
233C42C22×D6111yescharacteristic
234C23—21no—
235C23—22no—
236C23—611no—
237C23—1221no—
238Q8—2442no—
239Q8—2442no—
240D4—21no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—42no—
245D4—42no—
246D4—1221no—
247D4—1221no—
248D4—2442no—
249D4—2442no—
250D4—2442no—
251D4—2444no—
252D4—2442no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—1222no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—2444no—
265C2×C4—2442no—
266C2×C4D4×D6111yescharacteristic
267C2×C4D4×D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—22no—
270C8—1222no—
271C22—42no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—41no—
276C22—42no—
277C22—1221no—
278C22—1221no—
279C22—1221no—
280C22—2441no—
281C22—2441no—
282C22—2441no—
283C22C2×D4×D6111yescharacteristic
284C4—21no—
285C4—41no—
286C4—612no—
287C4—1221no—
288C4—1221no—
289C4—2442no—
290C4—2441no—
291C4#1451980112yes—
292C4#1451982211yescharacteristic
293C4#1451982411yescharacteristic
294C2—82no—
295C2—81no—
296C2—4881no—
297C2—2441no—
298C2#1684034111yescharacteristic
299C2AGL(1,ℤ/8)×D6111yescharacteristic
300C2C2×#1451980111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3253
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840310C2semidirect
2. #16840309C2semidirect
3. #16840053C2semidirect
4. #16840052C2semidirect
5. #16840050C2semidirect
6. #16840014C2semidirect
7. #16840012C2semidirect
8. #16839955C2semidirect
9. #16839954C2semidirect
10. #16839784C2semidirect
11. C61×#459C2semidirect
160. #459D61semidirect
162. C61#3253semidirect