Finite Group Databasebeta

← #21456383

Subgroups — #21456383

Order 7808.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840296C211yesmaximal, characteristic, complemented
2#16840161C211yesmaximal, characteristic, complemented
3#16840144C211yesmaximal, characteristic, complemented
4#16840119C211yesmaximal, characteristic, complemented
5#16840116C211yesmaximal, characteristic, complemented
6#16840001C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic
8#16839993C211yesmaximal, characteristic, complemented
9#16839989C211yesmaximal, characteristic, complemented
10C4×#11758202C211yesmaximal, characteristic, complemented
11C4×#11758201C211yesmaximal, characteristic, complemented
12C4×#11758200C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14C2×C4×#92418C211yesmaximal, characteristic, complemented
15C61×#529C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C22×#92418C2211yescharacteristic
21C22×#92418C2211yescharacteristic
22#14519771—21no—
23#14519769C2211yescharacteristic
24#14519765C2211yescharacteristic
25#14519760—21no—
26#14519756C2211yescharacteristic
27#14519751C2211yescharacteristic
28C4×Dic122C2211yescharacteristic
29C4×D244C2211yescharacteristic
30C4×C22⋊D61—21no—
31#14519734—21no—
32#14519710C2211yescharacteristic
33#14519710C2211yescharacteristic
34#14519708C2211yescharacteristic
35#14519708C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C4×#92418C2211yescharacteristic
45C4×#92418C2211yescharacteristic
46C4×#92418C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48#126×C61—21no—
49#125×C61C2211yescharacteristic
50#124×C61C2211yescharacteristic
51#123×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55C4×D4×C61—21no—
56C4×D4×C61C2211yescharacteristic
57#117×C61—21no—
58C2×C42×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61D411yescharacteristic
64C22×C4×C61D411yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×Dic122C2311yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C22⋊C4×C61—21no—
77C22⋊C4×C61—21no—
78C22⋊C4×C61—21no—
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C42×C61—21no—
82C42×C61D411yescharacteristic
83C42×C61D411yescharacteristic
84C42×C61C2311yescharacteristic
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87#11758202—22no—
88#11758201—22no—
89#11758200—22no—
90#11758199—22no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C2×#92418—22no—
103C2×#92418—22no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111Q8×C61—21no—
112Q8×C61—21no—
113D4×C61—21no—
114D4×C61—21no—
115D4×C61—42no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—42no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134D244—21no—
135D244—21no—
136C4×D61—42no—
137Dic122—21no—
138Dic122—21no—
139#92418—21no—
140#92418—21no—
141#92418#4112yes—
142#92418#4112yes—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61#13512yes—
149C22×C61C22×D411yescharacteristic
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61#13512yes—
161C4×C61C2×#4111yescharacteristic
162C4×C61C2×#4111yescharacteristic
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166#3168—611nomaximal, Sylow
167C2×C61—22no—
168C2×C61—81no—
169C2×C61#53211yescharacteristic
170C2×C61C2×#13511yescharacteristic
171C2×C61C2×#13511yescharacteristic
172D61—81no—
173#529—611no—
174#529D6111yescharacteristic, complemented
175#499—611no—
176#495—611no—
177#488—611no—
178#488—611no—
179#467—611no—
180#466—611no—
181#465—611no—
182#465—611no—
183C4×Q16—611no—
184C4×SD16—611no—
185C4×SD16—611no—
186C4×D8—611no—
187C2×C4×C8—611no—
188C61#316811yescharacteristic, complemented, Sylow
189C2×Q16—611no—
190C2×SD16—611no—
191C2×SD16—611no—
192C2×D8—611no—
193C22×C8—611no—
194C22×C8—611no—
195#126—21no—
196#126—1221no—
197#125—611no—
198#125C2×D6111yescharacteristic
199#124—611no—
200#124C2×D6111yescharacteristic
201#123—21no—
202#123—1221no—
203C22⋊Q8—611no—
204C22⋊Q8C2×D6111yescharacteristic
205#121—611no—
206#121C2×D6111yescharacteristic
207C4×Q8—611no—
208C4×Q8C2×D6111yescharacteristic
209C4×D4—21no—
210C4×D4—611no—
211C4×D4—1221no—
212C4×D4C2×D6111yescharacteristic
213#117—21no—
214#117—1221no—
215C2×C42C2×D6111yescharacteristic
216#107—611no—
217#107—611no—
218#106—611no—
219#106—611no—
220#103—611no—
221#103—611no—
222#103—611no—
223#103—611no—
224#102—611no—
225#102—611no—
226#102—611no—
227#102—611no—
228C4×C8—611no—
229C4×C8—611no—
230C4×C8—611no—
231C4×C8—611no—
232C2×Q8—611no—
233C2×Q8C22×D6111yescharacteristic
234C2×D4—21no—
235C2×D4—611no—
236C2×D4—1221no—
237C2×D4C22×D6111yescharacteristic
238C22×C4—21no—
239C22×C4—1221no—
240C22×C4C22⋊D6111yescharacteristic
241C22×C4C22⋊D6111yescharacteristic
242C22×C4C22×D6111yescharacteristic
243Q16—1222no—
244SD16—1222no—
245SD16—1222no—
246D8—1222no—
247C2×C8—611no—
248C2×C8—611no—
249C2×C8—611no—
250C2×C8—611no—
251C2×C8—1222no—
252C2×C8—1222no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C42—21no—
276C42—1221no—
277C42C22⋊D6111yescharacteristic
278C42C22⋊D6111yescharacteristic
279C42C22×D6111yescharacteristic
280C42C22×D6111yescharacteristic
281C23—21no—
282C23—1221no—
283C23C2×C22⋊D6111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—1221no—
287Q8—1221no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—1221no—
292D4—1221no—
293D4—2442no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—2442no—
306C2×C4C2×C22⋊D6111yescharacteristic
307C2×C4C2×C22⋊D6111yescharacteristic
308C2×C4C2×C22⋊D6111yescharacteristic
309C2×C4C2×C22⋊D6111yescharacteristic
310C2×C4C2×C22⋊D6111yescharacteristic
311C2×C4C23×D6111yescharacteristic
312C8—612no—
313C8—612no—
314C8—1221no—
315C8—1221no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—2441no—
322C22—2441no—
323C22—2441no—
324C22#1451979712yes—
325C22C22×C22⋊D6111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—2441no—
334C4—2441no—
335C4—2441no—
336C4#1451979712yes—
337C4#41×D6111yescharacteristic
338C4#41×D6111yescharacteristic
339C2—22no—
340C2—81no—
341C2—4881no—
342C2#1684030811yescharacteristic
343C2C2×#1451979711yescharacteristic
344C2C2×#1451979711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#529C2
socleC22×C61C22×D4
hypercenter#529D61
hypocenterC61#3168
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #16840296C2semidirect
2. #16840161C2semidirect
3. #16840144C2semidirect
4. #16840119C2semidirect
5. #16840116C2semidirect
6. #16840001C2semidirect
8. #16839993C2semidirect
9. #16839989C2semidirect
10. C4×#11758202C2semidirect
11. C4×#11758201C2semidirect
12. C4×#11758200C2semidirect
13. C4×#11758199C2semidirect
14. C2×C4×#92418C2semidirect
15. C61×#529C2semidirect
174. #529D61semidirect
188. C61#3168semidirect