Finite Group Databasebeta

← #21458364

Subgroups — #21458364

Order 7808.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic
2#16840168C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840090C211yesmaximal, characteristic, complemented
5#16840086C211yesmaximal, characteristic, complemented
6#16840086C211yesmaximal, characteristic, complemented
7#16840069C211yesmaximal, characteristic, complemented
8#16840049C211yesmaximal, characteristic, complemented
9#16840010C211yesmaximal, characteristic, complemented
10#16839993C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839805C211yesmaximal, characteristic, complemented
14#16839798C211yesmaximal, characteristic, complemented
15C61×#556C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519772—21no—
20#14519769C2211yescharacteristic
21#14519759—21no—
22#14519751C2211yescharacteristic
23#14519751C2211yescharacteristic
24#14519749—21no—
25C4×D244C2211yescharacteristic
26#14519737—21no—
27#14519736C2211yescharacteristic
28C2×C4⋊Dic61C2211yescharacteristic
29#14519710C2211yescharacteristic
30#14519710C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519708C2211yescharacteristic
34#14519708C2211yescharacteristic
35#14519708C2211yescharacteristic
36#14519708C2211yescharacteristic
37#14519708C2211yescharacteristic
38C4⋊#92418C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519701C2211yescharacteristic
41#14519701C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C4⋊Q8×C61C2211yescharacteristic
49#126×C61—21no—
50#126×C61—21no—
51#124×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53C22⋊Q8×C61C2211yescharacteristic
54C4×Q8×C61—21no—
55C4×Q8×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57#117×C61C2211yescharacteristic
58#117×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61D411yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61D411yescharacteristic
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C22⋊C4×C61—21no—
78C22⋊C4×C61—21no—
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61D411yescharacteristic
82C22⋊C4×C61D411yescharacteristic
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88#11758201—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98C4×Dic61—21no—
99#11758194—22no—
100C2×#92418—22no—
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C23×C61C2×D411yescharacteristic
106C23×C61C2×D411yescharacteristic
107C22×D61—21no—
108Q8×C61—21no—
109Q8×C61—21no—
110Q8×C61—42no—
111D4×C61—41no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—81no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—81no—
131D244—21no—
132D244—21no—
133C4×D61—81no—
134#92418—21no—
135#92418—21no—
136#92418—21no—
137#92418#4112yes—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61C22×D411yescharacteristic
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—41no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61C2×#4111yescharacteristic
157C4×C612−1+411yescharacteristic
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161#3350—611nomaximal, Sylow
162C2×C61—41no—
163C2×C61—41no—
164C2×C61#54711yescharacteristic
165C2×C61#57511yescharacteristic
166C2×C61#57711yescharacteristic
167D61—81no—
168#556D6111yescharacteristic, complemented
169#553—611no—
170#501—611no—
171#485—611no—
172#483—611no—
173#482—611no—
174#482—611no—
175#479—611no—
176#476—611no—
177#468—611no—
178#465—611no—
179#440—611no—
180#435—611no—
181#428—611no—
182#427—611no—
183C61#335011yescharacteristic, complemented, Sylow
184C2×SD16—611no—
185C2×M16—611no—
186C22×C8—611no—
187C4⋊Q8C2×D6111yescharacteristic
188#126—21no—
189#126—21no—
190#126—1221no—
191#125—611no—
192#124—21no—
193#123—1221no—
194C22⋊Q8C2×D6111yescharacteristic
195C22⋊Q8C2×D6111yescharacteristic
196#121—611no—
197#121—611no—
198#121—1221no—
199C4×Q8—21no—
200C4×Q8C2×D6111yescharacteristic
201C4×D4—611no—
202C4×D4—1221no—
203C4×D4C2×D6111yescharacteristic
204#117—611no—
205#117C2×D6111yescharacteristic
206#117C2×D6111yescharacteristic
207C2×C4⋊C4—611no—
208#107—611no—
209#107—611no—
210#107—611no—
211#107—611no—
212#106—611no—
213#106—611no—
214#106—611no—
215#106—611no—
216#106—611no—
217C4⋊C8—611no—
218#103—611no—
219#103—611no—
220#103—611no—
221#102—611no—
222#102—611no—
223#102—611no—
224C22⋊C8—611no—
225C22⋊C8—611no—
226#97—611no—
227C2×Q8—21no—
228C2×Q8C22×D6111yescharacteristic
229C2×D4—611no—
230C2×D4—1221no—
231C2×D4—1221no—
232C2×D4C22⋊D6111yescharacteristic
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4C22×D6111yescharacteristic
236C22×C4C22×D6111yescharacteristic
237SD16—1222no—
238M16—1222no—
239C2×C8—611no—
240C2×C8—611no—
241C2×C8—611no—
242C2×C8—611no—
243C2×C8—1222no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—611no—
249C4⋊C4—611no—
250C4⋊C4—611no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4C22⋊D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C4⋊C4C22×D6111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4C22⋊D6111yescharacteristic
267C22⋊C4C22⋊D6111yescharacteristic
268C42—21no—
269C42—21no—
270C42—21no—
271C42—1221no—
272C42C22×D6111yescharacteristic
273C23—1221no—
274C23C2×C22⋊D6111yescharacteristic
275C23C2×C22⋊D6111yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—42no—
279D4—41no—
280D4—1221no—
281D4—1221no—
282D4—4881no—
283D4—2442no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—4881no—
296C2×C4—4881no—
297C2×C4C2×C22⋊D6111yescharacteristic
298C2×C4C2×C22⋊D6111yescharacteristic
299C2×C4C2×C22⋊D6111yescharacteristic
300C2×C4C2×C22⋊D6111yescharacteristic
301C2×C4C23×D6111yescharacteristic
302C8—612no—
303C8—1221no—
304C8—1221no—
305C8—1221no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—2441no—
313C22—2441no—
314C22—2441no—
315C22C22×C22⋊D6111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2441no—
325C4—2441no—
326C4—2441no—
327C4#41×D6111yescharacteristic
328C4#1451982411yescharacteristic
329C2—41no—
330C2—41no—
331C2—4881no—
332C2#1684041111yescharacteristic
333C2#1684056011yescharacteristic
334C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#556C2
socleC22×C61C22×D4
hypercenter#556D61
hypocenterC61#3350
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #16840168C2semidirect
3. #16840100C2semidirect
4. #16840090C2semidirect
5. #16840086C2semidirect
6. #16840086C2semidirect
7. #16840069C2semidirect
8. #16840049C2semidirect
9. #16840010C2semidirect
10. #16839993C2semidirect
11. #16839860C2semidirect
12. #16839834C2semidirect
13. #16839805C2semidirect
14. #16839798C2semidirect
15. C61×#556C2semidirect
168. #556D61semidirect
183. C61#3350semidirect