Finite Group Databasebeta

← #21458587

Subgroups — #21458587

Order 7808.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840497C211yesmaximal, characteristic
2#16840128C211yesmaximal, characteristic
3#16840124C211yesmaximal, characteristic, complemented
4#16840119C211yesmaximal, characteristic, complemented
5#16840066C211yesmaximal, characteristic, complemented
6#16840059C211yesmaximal, characteristic, complemented
7#16840049C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839984C211yesmaximal, characteristic, complemented
10#16839962C211yesmaximal, characteristic
11#16839893C211yesmaximal, characteristic, complemented
12#16839867C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic, complemented
14C4×#11758201C211yesmaximal, characteristic, complemented
15C61×#557C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19#14519774C2211yescharacteristic
20#14519766—21no—
21#14519765C2211yescharacteristic
22#14519765C2211yescharacteristic
23#14519762—21no—
24#14519762—21no—
25C4×Dic122C2211yescharacteristic
26C4×D244C2211yescharacteristic
27C4×D244C2211yescharacteristic
28#14519739—21no—
29#14519710C2211yescharacteristic
30#14519708C2211yescharacteristic
31#14519708C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic
33C4⋊#92418C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519697C2211yescharacteristic
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45#14519688C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48C4⋊Q8×C61—21no—
49C4⋊Q8×C61C2211yescharacteristic
50#125×C61—21no—
51#125×C61—21no—
52#125×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54C4×Q8×C61—21no—
55C4×Q8×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic
58C4×Q8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61D411yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D244—21no—
63C2×D244—21no—
64C2×D244C2311yescharacteristic
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×Dic122C2311yescharacteristic
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61D411yescharacteristic
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61D411yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C42×C61C2311yescharacteristic
87C42×C61C2311yescharacteristic
88C42×C61C2311yescharacteristic
89#11758202—22no—
90#11758201—22no—
91#11758201—22no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100C4×Dic61—21no—
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C22×D61—21no—
106C22×D61—21no—
107Q8×C61—21no—
108Q8×C61—41no—
109Q8×C61—42no—
110Q8×C61#4112yes—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C2×Dic61—21no—
123C2×Dic61—21no—
124D244—21no—
125D244—21no—
126D244—21no—
127D244—21no—
128D244—42no—
129D244—81no—
130C4×D61—81no—
131C4×D61—81no—
132Dic122—21no—
133Dic122—21no—
134#92418—21no—
135#92418—21no—
136#92418—21no—
137#92418—21no—
138C22×C61C22×D411yescharacteristic
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—41no—
145C4×C61—22no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61C2×#4111yescharacteristic
156C4×C612−1+411yescharacteristic
157Dic61—41no—
158Dic61—41no—
159#3371—611nomaximal, Sylow
160C2×C61#54811yescharacteristic
161C2×C61#57511yescharacteristic
162C2×C61#57711yescharacteristic
163D61—81no—
164D61—81no—
165#559—611no—
166#557D6111yescharacteristic, complemented
167#490—611no—
168#489—611no—
169#488—611no—
170#479—611no—
171#478—611no—
172#476—611no—
173#464—611no—
174#464—611no—
175#460—611no—
176#446—611no—
177#441—611no—
178#440—611no—
179C4×SD16—611no—
180C61#337111yescharacteristic, complemented, Sylow
181C2×Q16—611no—
182C2×SD16—611no—
183C2×SD16—611no—
184C4⋊Q8—21no—
185C4⋊Q8C2×D6111yescharacteristic
186#127—611no—
187#125—21no—
188#125—21no—
189#125C2×D6111yescharacteristic
190#125C2×D6111yescharacteristic
191#124—611no—
192#124—611no—
193#124—1221no—
194#123—1221no—
195#123—1221no—
196C4×Q8—21no—
197C4×Q8—611no—
198C4×Q8C2×D6111yescharacteristic
199C4×Q8C2×D6111yescharacteristic
200C4×Q8C2×D6111yescharacteristic
201C4×Q8C2×D6111yescharacteristic
202C4×D4—611no—
203C4×D4—611no—
204C4×D4—1221no—
205#107—611no—
206#106—611no—
207#106—611no—
208C4⋊C8—611no—
209C4⋊C8—611no—
210C4⋊C8—611no—
211#103—611no—
212#103—611no—
213#103—611no—
214#103—611no—
215#102—611no—
216#102—611no—
217#102—611no—
218#102—611no—
219#102—611no—
220#102—611no—
221#97—611no—
222#97—611no—
223C4×C8—611no—
224C2×Q8—21no—
225C2×Q8—611no—
226C2×Q8C22⋊D6111yescharacteristic
227C2×Q8C22×D6111yescharacteristic
228C2×D4—611no—
229C2×D4—611no—
230C2×D4—1221no—
231C2×D4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234Q16—1222no—
235SD16—1222no—
236SD16—1222no—
237C2×C8—611no—
238C2×C8—611no—
239C2×C8—611no—
240C2×C8—611no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—611no—
250C4⋊C4—1221no—
251C4⋊C4C22⋊D6111yescharacteristic
252C4⋊C4C22⋊D6111yescharacteristic
253C4⋊C4C22⋊D6111yescharacteristic
254C4⋊C4C22×D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C22⋊C4—1221no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—1221no—
267C42C22×D6111yescharacteristic
268C42C22×D6111yescharacteristic
269C42C22×D6111yescharacteristic
270C23—1221no—
271C23—1221no—
272Q8—21no—
273Q8—41no—
274Q8—42no—
275Q8—1221no—
276Q8—1221no—
277Q8#1175822612yes—
278D4—1221no—
279D4—1221no—
280D4—1221no—
281D4—1221no—
282D4—4881no—
283D4—2442no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—4881no—
291C2×C4—4881no—
292C2×C4C2×C22⋊D6111yescharacteristic
293C2×C4C2×C22⋊D6111yescharacteristic
294C2×C4C2×C22⋊D6111yescharacteristic
295C2×C4C2×C22⋊D6111yescharacteristic
296C2×C4C2×C22⋊D6111yescharacteristic
297C2×C4C2×C22⋊D6111yescharacteristic
298C2×C4C23×D6111yescharacteristic
299C8—1221no—
300C8—1221no—
301C8—1221no—
302C8—1221no—
303C22—2441no—
304C22—2441no—
305C22—2441no—
306C22—2441no—
307C22—2441no—
308C22—2441no—
309C22C22×C22⋊D6111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2441no—
321C4—2441no—
322C4C2×#1175822611yescharacteristic
323C4#1451982511yescharacteristic
324C2—4881no—
325C2—4881no—
326C2#1684042311yescharacteristic
327C2#1684056011yescharacteristic
328C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#557C2
socleC22×C61C22×D4
hypercenter#557D61
hypocenterC61#3371
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
3. #16840124C2semidirect
4. #16840119C2semidirect
5. #16840066C2semidirect
6. #16840059C2semidirect
7. #16840049C2semidirect
8. #16839984C2semidirect
9. #16839984C2semidirect
11. #16839893C2semidirect
12. #16839867C2semidirect
13. #16839860C2semidirect
14. C4×#11758201C2semidirect
15. C61×#557C2semidirect
166. #557D61semidirect
180. C61#3371semidirect