Finite Group Databasebeta

← #21455736

Subgroups — #21455736

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840274C211yesmaximal, characteristic
2#117×D61C211yesmaximal, characteristic, complemented
3#16840106C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840099C211yesmaximal, characteristic, complemented
6#16840094C211yesmaximal, characteristic, complemented
7#16840089C211yesmaximal, characteristic, complemented
8#16840088C211yesmaximal, characteristic, complemented
9#16840082C211yesmaximal, characteristic, complemented
10#16840077C211yesmaximal, characteristic, complemented
11#16839798C211yesmaximal, characteristic, complemented
12#16839759C211yesmaximal, characteristic, complemented
13#16839756C211yesmaximal, characteristic, complemented
14C2×#14519689C211yesmaximal, characteristic, complemented
15C61×#427C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519761—21no—
20#14519757C2211yescharacteristic
21#14519757C2211yescharacteristic
22#14519752C2211yescharacteristic
23#14519752C2211yescharacteristic
24#14519747—21no—
25C4×D244—21no—
26C4×D244—21no—
27#14519736C2211yescharacteristic
28#14519735C2211yescharacteristic
29#14519735C2211yescharacteristic
30#14519734—21no—
31#14519733—21no—
32C4⋊C4×D61C2211yescharacteristic
33C4⋊C4×D61C2211yescharacteristic
34C22⋊C4×D61—21no—
35C42×D61—21no—
36#14519710C2211yescharacteristic, complemented
37#14519710C2211yescharacteristic, complemented
38#14519708C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519702C2211yescharacteristic, complemented
41#14519702C2211yescharacteristic, complemented
42#14519700C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic, complemented
46#14519697C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C22×C8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#117×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic, complemented
56#107×C61C2211yescharacteristic, complemented
57#106×C61C2211yescharacteristic, complemented
58#106×C61C2211yescharacteristic, complemented
59C23×D61D411yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C22×Dic61D411yescharacteristic
63#11758222—22no—
64#11758222—22no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61D411yescharacteristic
74C2×C4×D61D411yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78C2×C8×C61—22no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C2×#92418—22no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61C2×D411yescharacteristic
109C22×D61—22no—
110C22×D61—22no—
111C22×D61—21no—
112C22×D61—41no—
113C22×D61C2×D411yescharacteristic
114C22×D61C2×D411yescharacteristic
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61#4112yes—
121C2×C4×C61#4112yes—
122C2×C4×C61C2411yescharacteristic
123C22⋊D61—42no—
124C2×Dic61—22no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244—21no—
132D244—42no—
133D244—42no—
134C4×D61—22no—
135C4×D61—22no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61—42no—
143Dic122—21no—
144Dic122—21no—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61#12312yes—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—44no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61#13512yes—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61#12312yes—
168C4×C61C2×#4111yescharacteristic
169C4×C61C2×#4111yescharacteristic
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175#3091—611nomaximal, Sylow
176C2×C61—22no—
177C2×C61C2×#12311yescharacteristic
178C2×C61C2×#13511yescharacteristic
179C2×C61#57511yescharacteristic
180D61—22no—
181D61—41no—
182D61—81no—
183#525—611no—
184C2×#117—611no—
185#485—611no—
186#485—611no—
187#484—611no—
188#483—611no—
189#482—611no—
190#482—611no—
191#481—611no—
192#480—611no—
193#427—611no—
194#427D6111yescharacteristic, complemented
195#416—611no—
196#416—611no—
197C2×C22⋊C8—611no—
198C61#309111yescharacteristic, complemented, Sylow
199C2×#41—611no—
200C23×C4—611no—
201C22×C8—611no—
202C22×C8C2×D6111yescharacteristic
203#123—1221no—
204C22⋊Q8—611no—
205C22⋊Q8—611no—
206#121—611no—
207#121—611no—
208#120—1221no—
209C4×D4—1221no—
210C4×D4—1221no—
211#117—611no—
212#117—611no—
213#117—611no—
214#117—1221no—
215#117—1221no—
216#117C2×D6111yescharacteristic
217#117C2×D6111yescharacteristic
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C22⋊C4—1221no—
221C2×C42—1221no—
222#107—611no—
223#107—611no—
224#107C2×D6111yescharacteristic, complemented
225#107C2×D6111yescharacteristic, complemented
226#106—611no—
227#106—611no—
228#106C2×D6111yescharacteristic, complemented
229#106C2×D6111yescharacteristic, complemented
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237#102—611no—
238C22⋊C8—611no—
239C22⋊C8—611no—
240C22⋊C8—611no—
241C22⋊C8—611no—
242C24—611no—
243#41—1222no—
244#41—1222no—
245C2×Q8—611no—
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1221no—
260C22×C4C22×D6111yescharacteristic
261C2×C8—22no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—1222no—
265C2×C8C22×D6111yescharacteristic
266C2×C8C22×D6111yescharacteristic
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—21no—
287C42—21no—
288C42—1221no—
289C42—1221no—
290C42—1221no—
291C23—611no—
292C23—611no—
293C23—1222no—
294C23—1222no—
295C23—1221no—
296C23—2441no—
297C23D4×D6111yescharacteristic
298Q8—1221no—
299Q8—1221no—
300D4—1221no—
301D4—1221no—
302D4—2442no—
303D4—2442no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—1222no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4#1175822212yes—
325C2×C4D4×D6111yescharacteristic
326C2×C4#1175822612yes—
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—612no—
335C22—1221no—
336C22—1221no—
337C22—1221no—
338C22—1221no—
339C22—1221no—
340C22—2444no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22#1451976212yes—
345C22C2×D4×D6111yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—1221no—
351C4—1221no—
352C4—2441no—
353C4—2441no—
354C4—2441no—
355C4#1451976212yes—
356C4C2×#1175822211yescharacteristic
357C4C2×#1175822611yescharacteristic
358C2—22no—
359C2—1222no—
360C2—4881no—
361C2—2441no—
362C2C2×#1451976211yescharacteristic
363C2#135×D6111yescharacteristic
364C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#427C2
socleC22×C61C22×D4
hypercenter#427D61
hypocenterC61#3091
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D61C2semidirect
3. #16840106C2semidirect
4. #16840105C2semidirect
5. #16840099C2semidirect
6. #16840094C2semidirect
7. #16840089C2semidirect
8. #16840088C2semidirect
9. #16840082C2semidirect
10. #16840077C2semidirect
11. #16839798C2semidirect
12. #16839759C2semidirect
13. #16839756C2semidirect
14. C2×#14519689C2semidirect
15. C61×#427C2semidirect
36. #14519710C22semidirect
37. #14519710C22semidirect
38. #14519708C22semidirect
39. #14519708C22semidirect
40. #14519702C22semidirect
41. #14519702C22semidirect
42. #14519700C22semidirect
43. #14519700C22semidirect
44. #14519699C22semidirect
45. #14519699C22semidirect
46. #14519697C22semidirect
47. #14519697C22semidirect
55. #107×C61C22semidirect
56. #107×C61C22semidirect
57. #106×C61C22semidirect
58. #106×C61C22semidirect
194. #427D61semidirect
198. C61#3091semidirect
224. #107C2×D61semidirect
225. #107C2×D61semidirect
228. #106C2×D61semidirect
229. #106C2×D61semidirect