Finite Group Databasebeta

← #21456547

Subgroups — #21456547

Order 7808.

370 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#16840297C211yesmaximal, characteristic, complemented
2#16840291C211yesmaximal, characteristic, complemented
3#16840161C211yesmaximal, characteristic, complemented
4#16840144C211yesmaximal, characteristic, complemented
5#16840117C211yesmaximal, characteristic, complemented
6#16840019C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic
8#16840011C211yesmaximal, characteristic, complemented
9#16840007C211yesmaximal, characteristic, complemented
10#16839871C211yesmaximal, characteristic, complemented
11#16839866C211yesmaximal, characteristic, complemented
12#16839865C211yesmaximal, characteristic, complemented
13#16839859C211yesmaximal, characteristic, complemented
14C4×#11758189C211yesmaximal, characteristic, complemented
15C61×#488C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22#14519772—21no—
23#14519770—21no—
24#14519769C2211yescharacteristic
25#14519765C2211yescharacteristic
26#14519762—21no—
27#14519759—21no—
28#14519757C2211yescharacteristic
29#14519753C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519748C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33#14519742C2211yescharacteristic
34D4×Dic61C2211yescharacteristic
35#14519739—21no—
36#14519739C2211yescharacteristic
37#14519737—21no—
38#14519735—21no—
39#14519733—21no—
40C42×D61C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519708C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519687C2211yescharacteristic
50#14519687C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52#125×C61C2211yescharacteristic
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63C2×D244—21no—
64C2×D244C2311yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61D411yescharacteristic
67C2×C4×D61D411yescharacteristic
68C2×C4×D61C2311yescharacteristic
69C2×Dic122C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C22⋊C4×C61—21no—
77C22⋊C4×C61—21no—
78C42×C61C2311yescharacteristic
79C22⋊Dic61—21no—
80C22⋊Dic61—21no—
81#11758202—22no—
82#11758201—22no—
83#11758200—22no—
84#11758199—22no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61D411yescharacteristic
102C4×Dic61D411yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107#11758189—22no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61C2×D411yescharacteristic
111Q8×C61—21no—
112Q8×C61—21no—
113D4×C61—21no—
114D4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C22⋊D61—42no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—42no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129D244—21no—
130D244—21no—
131D244—42no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—41no—
135C4×D61—41no—
136C4×D61—42no—
137Dic122—21no—
138Dic122—21no—
139C8×C61—21no—
140C8×C61—21no—
141#92418#4112yes—
142#92418#4112yes—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61C22×D411yescharacteristic
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61C2×#4111yescharacteristic
159C4×C61C2×#4111yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166#3183—611nomaximal, Sylow
167C2×C61—81no—
168C2×C61#53211yescharacteristic
169C2×C61#57511yescharacteristic
170C2×C61#57511yescharacteristic
171D61—41no—
172D61—81no—
173#529—611no—
174#529—611no—
175#499—611no—
176#495—611no—
177#488—611no—
178#488D6111yescharacteristic, complemented
179#470—611no—
180#469—611no—
181#468—611no—
182#468—611no—
183#442—611no—
184#441—611no—
185#440—611no—
186#440—611no—
187C4×M16—611no—
188C61#318311yescharacteristic, complemented, Sylow
189C2×Q16—611no—
190C2×SD16—611no—
191C2×SD16—611no—
192C2×D8—611no—
193C2×M16—611no—
194C2×M16—611no—
195#126—1221no—
196#126—1221no—
197#125—611no—
198#125C2×D6111yescharacteristic
199#124—611no—
200#124C2×D6111yescharacteristic
201#123—1221no—
202#123—1221no—
203C22⋊Q8—611no—
204C22⋊Q8—611no—
205#121—611no—
206#121—611no—
207C4×Q8—611no—
208C4×Q8—611no—
209C4×D4—611no—
210C4×D4—611no—
211C4×D4—1221no—
212C4×D4—1221no—
213#117—1221no—
214#117—1221no—
215C2×C42—611no—
216#107—611no—
217#107—611no—
218#106—611no—
219#106—611no—
220#103—611no—
221#103—611no—
222#103C2×D6111yescharacteristic
223#103C2×D6111yescharacteristic
224#102—611no—
225#102—611no—
226#102C2×D6111yescharacteristic
227#102C2×D6111yescharacteristic
228#97—611no—
229#97—611no—
230C4×C8—611no—
231C4×C8C2×D6111yescharacteristic
232C2×Q8—611no—
233C2×Q8C22×D6111yescharacteristic
234C2×D4—611no—
235C2×D4—1221no—
236C2×D4—1221no—
237C2×D4C22×D6111yescharacteristic
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243Q16—1222no—
244SD16—1222no—
245SD16—1222no—
246D8—1222no—
247M16—1222no—
248M16—1222no—
249C2×C8—611no—
250C2×C8—611no—
251C2×C8C22×D6111yescharacteristic
252C2×C8C22×D6111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—611no—
256C4⋊C4—611no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
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—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C42—611no—
276C42—611no—
277C42—611no—
278C42—1221no—
279C42—1221no—
280C42C22×D6111yescharacteristic
281C23—21no—
282C23—611no—
283C23—1221no—
284Q8—21no—
285Q8—21no—
286Q8—1221no—
287Q8—1221no—
288D4—21no—
289D4—21no—
290D4—1221no—
291D4—1221no—
292D4—2442no—
293D4—2442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4D4×D6111yescharacteristic
310C2×C4D4×D6111yescharacteristic
311C2×C4C23×D6111yescharacteristic
312C8—21no—
313C8—21no—
314C8—612no—
315C8—612no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—1221no—
320C22—1221no—
321C22—1221no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22C2×D4×D6111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1221no—
332C4—1221no—
333C4—1221no—
334C4—2441no—
335C4—2441no—
336C4—2441no—
337C4#41×D6111yescharacteristic
338C4#41×D6111yescharacteristic
339C2—81no—
340C2—4881no—
341C2—2441no—
342C2#1684031111yescharacteristic
343C2#1684055911yescharacteristic
344C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3183
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16840297C2semidirect
2. #16840291C2semidirect
3. #16840161C2semidirect
4. #16840144C2semidirect
5. #16840117C2semidirect
6. #16840019C2semidirect
8. #16840011C2semidirect
9. #16840007C2semidirect
10. #16839871C2semidirect
11. #16839866C2semidirect
12. #16839865C2semidirect
13. #16839859C2semidirect
14. C4×#11758189C2semidirect
15. C61×#488C2semidirect
178. #488D61semidirect
188. C61#3183semidirect