Finite Group Databasebeta

← #21455643

Subgroups — #21455643

Order 7808.

398 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#16840389C211yesmaximal, characteristic, complemented
2#16840234C211yesmaximal, characteristic
3#16840065C211yesmaximal, characteristic, complemented
4#16840063C211yesmaximal, characteristic, complemented
5#16840062C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16840050C211yesmaximal, characteristic, complemented
8#16840049C211yesmaximal, characteristic, complemented
9#16840041C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic, complemented
11#16839799C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic
14#102×D61C211yesmaximal, characteristic
15C61×#474C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758189C2211yescharacteristic
18C2×C8×D61C2211yescharacteristic
19#14519776C2211yescharacteristic, complemented
20#14519775—21no—
21#14519769C2211yescharacteristic, complemented
22#14519768C2211yescharacteristic, complemented
23#14519767—21no—
24#14519755—21no—
25#14519753—21no—
26C4×D244C2211yescharacteristic
27D4×Dic61C2211yescharacteristic
28#14519739C2211yescharacteristic
29C4×C22⋊D61—21no—
30#14519737—21no—
31#14519735C2211yescharacteristic
32#14519735C2211yescharacteristic
33#14519734C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
35C2×#11758198—21no—
36C22⋊C4×D61—21no—
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43C4⋊#92418C2211yescharacteristic, complemented
44#14519706C2211yescharacteristic, complemented
45#14519706C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic, complemented
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#107×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65D4×D61—22no—
66D4×D61Q814yescomplemented
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×Dic122—21no—
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C42×C61C2311yescharacteristic
81C22⋊Dic61—21no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198D411yescharacteristic
87#11758198D411yescharacteristic
88C4⋊Dic61—21no—
89C4⋊Dic61C2311yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196D411yescharacteristic
98#11758196D411yescharacteristic
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104#11758189—22no—
105C8×D61—22no—
106C23×C61—21no—
107C22×D61—21no—
108C22×D61—24no—
109C22×D61—81no—
110C22×D61—81no—
111C22×D61C2×D411yescharacteristic
112Q8×C61—81no—
113D4×C61—21no—
114D4×C61C2×Q812yes—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—81no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—24no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—81no—
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244C2×Q812yes—
132C4×D61—81no—
133C4×D61—81no—
134C4×D61—81no—
135C4×D61C2×Q812yes—
136C4×D61#4112yes—
137Dic122—81no—
138C8×C61—21no—
139C8×C61—21no—
140#92418—21no—
141#92418—21no—
142C22×C61—22no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61C22×D411yescharacteristic
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—22no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—84no—
152C2×D61C22⋊Q812yes—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61C22×Q811yescharacteristic
159C4×C61C2×#4111yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—41no—
163Dic61—41no—
164Dic61—41no—
165Dic61C22⋊Q812yes—
166#3081—611nomaximal, Sylow
167C2×C61—42no—
168C2×C61C2×C22⋊Q811yescharacteristic
169C2×C61#57611yescharacteristic
170C2×C61#57711yescharacteristic
171D61—22no—
172D61—42no—
173#544—611no—
174#518—611no—
175#478—611no—
176#478—611no—
177#478—611no—
178#478—611no—
179#476—611no—
180#476—611no—
181#474—611no—
182#474D6111yescharacteristic, complemented
183#428—611no—
184#427—611no—
185#424—611no—
186#418—611no—
187C2×#102—611no—
188C61#308111yescharacteristic, complemented, Sylow
189C22×D4—611no—
190C2×M16—611no—
191C22×C8—611no—
192C4⋊Q8—611no—
193C4⋊Q8—1221no—
194C4⋊Q8C2×D6111yescharacteristic, complemented
195#125—611no—
196#125—611no—
197#125—1221no—
198C22⋊Q8—1221no—
199C22⋊Q8—1221no—
200C4×D4—611no—
201C4×D4—611no—
202C4×D4—611no—
203C4×D4—1221no—
204C4×D4—1221no—
205C4×D4C2×D6111yescharacteristic
206#117—611no—
207#117—611no—
208#117—611no—
209C2×C4⋊C4—611no—
210C2×C22⋊C4—1221no—
211C2×C22⋊C4—1221no—
212#107—611no—
213#107—611no—
214#107C2×D6111yescharacteristic, complemented
215#107C2×D6111yescharacteristic, complemented
216#106—611no—
217#106—611no—
218#106—611no—
219#106—611no—
220C4⋊C8—611no—
221C4⋊C8—611no—
222C4⋊C8—611no—
223C4⋊C8C2×D6111yescharacteristic, complemented
224#102—611no—
225#102—611no—
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230#102C2×D6111yescharacteristic
231#102C2×D6111yescharacteristic
232C24—1221no—
233C2×Q8—21no—
234C2×Q8—1221no—
235C2×D4—614no—
236C2×D4—611no—
237C2×D4—1222no—
238C2×D4—1221no—
239C2×D4C22×D6111yescharacteristic
240C22×C4—21no—
241C22×C4—611no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246M16—1222no—
247C2×C8—611no—
248C2×C8—611no—
249C2×C8—1222no—
250C2×C8C22×D6111yescharacteristic
251C2×C8C22×D6111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—611no—
254C4⋊C4—611no—
255C4⋊C4—611no—
256C4⋊C4—611no—
257C4⋊C4—611no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4C22×D6111yescharacteristic
265C4⋊C4C22×D6111yescharacteristic
266C4⋊C4C22×D6111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—611no—
269C22⋊C4—611no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C42—611no—
276C42—1221no—
277C42—1221no—
278C42C22×D6111yescharacteristic
279C23—21no—
280C23—611no—
281C23—1224no—
282C23—1221no—
283C23—4881no—
284C23—4881no—
285Q8—81no—
286Q8—4881no—
287D4—21no—
288D4—612no—
289D4—1224no—
290D4—1221no—
291D4Q8×D6112yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—611no—
297C2×C4—612no—
298C2×C4—612no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—4881no—
305C2×C4—4881no—
306C2×C4—4881no—
307C2×C4—4881no—
308C2×C4D4×D6111yescharacteristic
309C2×C4D4×D6111yescharacteristic
310C2×C4C23×D6111yescharacteristic
311C8—21no—
312C8—21no—
313C8—1221no—
314C8—1221no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—612no—
319C22—1221no—
320C22—1221no—
321C22—1222no—
322C22—4884no—
323C22—2441no—
324C22—2441no—
325C22C2×D4×D6111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—612no—
332C4—1221no—
333C4—1221no—
334C4—2441no—
335C4—2441no—
336C4—2441no—
337C4C2×Q8×D6111yescharacteristic
338C4#41×D6111yescharacteristic
339C2—42no—
340C2—1222no—
341C2—2442no—
342C2C22⋊Q8×D6111yescharacteristic
343C2#1684056311yescharacteristic
344C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3081
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16840389C2semidirect
3. #16840065C2semidirect
4. #16840063C2semidirect
5. #16840062C2semidirect
6. #16840060C2semidirect
7. #16840050C2semidirect
8. #16840049C2semidirect
9. #16840041C2semidirect
10. #16839803C2semidirect
11. #16839799C2semidirect
12. #16839787C2semidirect
15. C61×#474C2semidirect
19. #14519776C22semidirect
21. #14519769C22semidirect
22. #14519768C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519708C22semidirect
42. #14519708C22semidirect
43. C4⋊#92418C22semidirect
44. #14519706C22semidirect
45. #14519706C22semidirect
52. C4⋊Q8×C61C22semidirect
54. #107×C61C22semidirect
55. #107×C61C22semidirect
56. C4⋊C8×C61C22semidirect
66. D4×D61Q8semidirect
182. #474D61semidirect
188. C61#3081semidirect
194. C4⋊Q8C2×D61semidirect
214. #107C2×D61semidirect
215. #107C2×D61semidirect
223. C4⋊C8C2×D61semidirect