Finite Group Databasebeta

← #21457173

Subgroups — #21457173

Order 7808.

360 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#16840299C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic, complemented
3#16840068C211yesmaximal, characteristic, complemented
4#16840061C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840002C211yesmaximal, characteristic, complemented
7#16839999C211yesmaximal, characteristic
8#16839994C211yesmaximal, characteristic, complemented
9#16839992C211yesmaximal, characteristic, complemented
10#16839987C211yesmaximal, characteristic, complemented
11#16839984C211yesmaximal, characteristic, complemented
12#16839980C211yesmaximal, characteristic, complemented
13#16839978C211yesmaximal, characteristic, complemented
14C4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#479C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519772—21no—
23#14519772—21no—
24#14519768C2211yescharacteristic
25#14519766C2211yescharacteristic
26#14519765C2211yescharacteristic
27#14519762—21no—
28#14519762—21no—
29#14519757C2211yescharacteristic
30#14519753C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519752C2211yescharacteristic
33#14519742C2211yescharacteristic
34C4×D244—21no—
35C4×D244C2211yescharacteristic
36#14519739—21no—
37#14519739C2211yescharacteristic
38#14519735—21no—
39#14519734—21no—
40C42×D61C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D244—21no—
61C2×D244—21no—
62C2×D244C2311yescharacteristic
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
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×C61—21no—
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C42×C61—21no—
79C42×C61C2311yescharacteristic
80#11758202—41no—
81#11758201—41no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98C4×Dic61—21no—
99C4×Dic61D411yescharacteristic
100C4×Dic61D411yescharacteristic
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104D488—41no—
105#11758190—41no—
106C8×D61—41no—
107C8×D61—41no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61C2×D411yescharacteristic
111Q8×C61—21no—
112Q8×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124C2×Dic61C2×D411yescharacteristic
125D244—21no—
126D244—21no—
127D244—21no—
128D244—21no—
129D244—42no—
130D244—42no—
131C4×D61—22no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—41no—
135C4×D61—42no—
136C4×D61—42no—
137Dic122—21no—
138Dic122—21no—
139C8×C61—21no—
140C8×C61—21no—
141#92418—21no—
142#92418—21no—
143C22×C61C22×D411yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—41no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61#13512yes—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61H(5,𝔽2)11yescharacteristic
160C4×C612−1+411yescharacteristic
161Dic61—21no—
162Dic61—21no—
163Dic61—21no—
164Dic61—41no—
165Dic61—41no—
166#3250—611nomaximal, Sylow
167C2×C61#53711yescharacteristic
168C2×C61C2×#13511yescharacteristic
169C2×C61#57511yescharacteristic
170D61—22no—
171D61—81no—
172D61—81no—
173#529—611no—
174#529—611no—
175#479—611no—
176#479D6111yescharacteristic, complemented
177#478—611no—
178#478—611no—
179#467—611no—
180#466—611no—
181#465—611no—
182#465—611no—
183#464—611no—
184#464—611no—
185#463—611no—
186#463—611no—
187C2×C4⋊C8—611no—
188C61#325011yescharacteristic, complemented, Sylow
189C2×Q16—611no—
190C2×SD16—611no—
191C2×SD16—611no—
192C2×D8—611no—
193C22×C8—611no—
194C22×C8—611no—
195#126—1221no—
196#126—1221no—
197#125—611no—
198#125C2×D6111yescharacteristic
199#124—611no—
200#124—611no—
201#123—1221no—
202#123—1221no—
203C22⋊Q8—611no—
204C22⋊Q8—611no—
205#121—611no—
206#121—611no—
207C4×Q8—611no—
208C4×Q8C2×D6111yescharacteristic
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#107C2×D6111yescharacteristic
218#106—611no—
219#106C2×D6111yescharacteristic
220C4⋊C8—611no—
221C4⋊C8—611no—
222C4⋊C8—611no—
223C4⋊C8C2×D6111yescharacteristic
224#103—611no—
225#103—611no—
226#103C2×D6111yescharacteristic
227#103C2×D6111yescharacteristic
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232C2×Q8—611no—
233C2×Q8C22×D6111yescharacteristic
234C2×D4—611no—
235C2×D4—611no—
236C2×D4—1221no—
237C2×D4—1221no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243Q16—2441no—
244SD16—2441no—
245SD16—2441no—
246D8—2441no—
247C2×C8—611no—
248C2×C8—611no—
249C2×C8—2441no—
250C2×C8—2441no—
251C2×C8C22×D6111yescharacteristic
252C2×C8C22×D6111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—611no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4C22×D6111yescharacteristic
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C22⋊C4—1221no—
266C22⋊C4—1221no—
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—21no—
276C42—611no—
277C42—611no—
278C42—611no—
279C42—1221no—
280C42C22×D6111yescharacteristic
281C23—611no—
282C23—1221no—
283C23—1221no—
284Q8—21no—
285Q8—21no—
286Q8—1221no—
287Q8—1221no—
288D4—1221no—
289D4—1221no—
290D4—1221no—
291D4—1221no—
292D4—2442no—
293D4—2442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1222no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—2441no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4D4×D6111yescharacteristic
310C2×C4D4×D6111yescharacteristic
311C2×C4C23×D6111yescharacteristic
312C8—21no—
313C8—21no—
314C8—1221no—
315C8—1221no—
316C22—612no—
317C22—1221no—
318C22—1221no—
319C22—2441no—
320C22—2441no—
321C22—2441no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22C2×D4×D6111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—1221no—
333C4—1221no—
334C4—1221no—
335C4—2441no—
336C4—2441no—
337C4#1451982311yescharacteristic
338C4#1451982511yescharacteristic
339C2—1222no—
340C2—4881no—
341C2—4881no—
342C2#1684034211yescharacteristic
343C2#135×D6111yescharacteristic
344C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3250
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #16840299C2semidirect
2. #16840297C2semidirect
3. #16840068C2semidirect
4. #16840061C2semidirect
5. #16840059C2semidirect
6. #16840002C2semidirect
8. #16839994C2semidirect
9. #16839992C2semidirect
10. #16839987C2semidirect
11. #16839984C2semidirect
12. #16839980C2semidirect
13. #16839978C2semidirect
14. C4⋊C8×D61C2semidirect
15. C61×#479C2semidirect
176. #479D61semidirect
188. C61#3250semidirect