Finite Group Databasebeta

← #21455825

Subgroups — #21455825

Order 7808.

448 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840316C211yesmaximal, characteristic, complemented
2C4×D4×D61C211yesmaximal, characteristic
3#16840094C211yesmaximal, characteristic, complemented
4#16840091C211yesmaximal, characteristic, complemented
5#16840051C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16839966C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839914C211yesmaximal, characteristic
10#16839911C211yesmaximal, characteristic
11C4×#11758190C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758200C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic, complemented
15C4×SD16×C61C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C22×C4×D61—21no—
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21#14519776C2211yescharacteristic, complemented
22#14519775C2211yescharacteristic, complemented
23#14519767—21no—
24#14519757C2211yescharacteristic
25#14519755—21no—
26#14519753C2211yescharacteristic
27C4×Dic122—21no—
28C4×Dic122C2211yescharacteristic, complemented
29C4×D244C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519734—21no—
35C4⋊C4×D61C2211yescharacteristic
36C22⋊C4×D61—21no—
37C42×D61C2211yescharacteristic
38#14519709C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65D4×D61—22no—
66D4×D61—22no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—44no—
72C2×C4×D61D411yescharacteristic
73C2×C4×D61D411yescharacteristic
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77SD16×C61—22no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61—21no—
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87#11758201—22no—
88#11758200—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61D411yescharacteristic
104C4×Dic61D411yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108#11758190—22no—
109C23×C61—21no—
110C22×D61—24no—
111C22×D61—21no—
112C22×D61—42no—
113C22×D61—42no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61#4112yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—42no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—24no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—42no—
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134D244—21no—
135D244#4112yes—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—41no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61SD1614yescomplemented
143Dic122—21no—
144Dic122—21no—
145Dic122—42no—
146C8×C61—21no—
147C8×C61—21no—
148#92418—21no—
149#92418—21no—
150C22×C61—22no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61C22×D411yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—22no—
157C2×D61—48no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61C2×SD1612yes—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×SD1612yes—
166C4×C61C2×#4111yescharacteristic
167C4×C61C2×#4111yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61C2×SD1612yes—
174#3101—611nomaximal, Sylow
175C2×C61—42no—
176C2×C61#52511yescharacteristic
177C2×C61C22×SD1611yescharacteristic
178C2×C61#57511yescharacteristic
179D61—22no—
180D61—42no—
181#533—611no—
182C2×C4×D4—611no—
183#483—611no—
184#483—611no—
185#476—611no—
186#476—611no—
187#461—611no—
188#461—611no—
189#450—611no—
190#450—611no—
191C4×SD16—611no—
192C4×SD16—611no—
193C4×SD16—611no—
194C4×SD16D6111yescharacteristic, complemented
195#431—611no—
196C61#310111yescharacteristic, complemented, Sylow
197C22×D4—611no—
198C23×C4—1221no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16—611no—
202C2×SD16C2×D6111yescharacteristic
203C4⋊Q8—611no—
204C4⋊Q8—611no—
205#125—1221no—
206C22⋊Q8—611no—
207C22⋊Q8—611no—
208C22⋊Q8—1221no—
209C4×Q8—611no—
210C4×Q8—1221no—
211C4×Q8C2×D6111yescharacteristic, complemented
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—1221no—
216C4×D4—1221no—
217C4×D4C2×D6111yescharacteristic
218#117—1221no—
219C2×C4⋊C4—611no—
220C2×C22⋊C4—1221no—
221C2×C42—611no—
222#106—611no—
223#106—611no—
224#106—611no—
225#106C2×D6111yescharacteristic, complemented
226C4⋊C8—611no—
227C4⋊C8—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103C2×D6111yescharacteristic, complemented
232#102—611no—
233#102—611no—
234#102—611no—
235#102C2×D6111yescharacteristic
236C22⋊C8—611no—
237C22⋊C8—611no—
238C4×C8—611no—
239C4×C8C2×D6111yescharacteristic, complemented
240C24—1221no—
241C2×Q8—611no—
242C2×Q8—1221no—
243C2×Q8C22×D6111yescharacteristic
244C2×D4—611no—
245C2×D4—1221no—
246C2×D4—1222no—
247C2×D4—1222no—
248C2×D4C22×D6111yescharacteristic
249C22×C4—21no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—2444no—
258SD16—22no—
259SD16—1222no—
260SD16—1222no—
261SD16—1222no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8C22×D6111yescharacteristic
265C2×C8C22×D6111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4C22×D6111yescharacteristic
277C4⋊C4C22×D6111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C42—21no—
285C42—611no—
286C42—611no—
287C42—611no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—21no—
291C23—611no—
292C23—1224no—
293C23—1221no—
294C23—2442no—
295C23—2442no—
296Q8—21no—
297Q8—21no—
298Q8—1221no—
299Q8—1221no—
300Q8—2442no—
301D4—21no—
302D4—612no—
303D4—1224no—
304D4—1221no—
305D4#1175822212yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—611no—
311C2×C4—614no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—2441no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4D4×D6111yescharacteristic
325C2×C4D4×D6111yescharacteristic
326C2×C4C23×D6111yescharacteristic
327C8—21no—
328C8—21no—
329C8—1221no—
330C8—1221no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—612no—
335C22—1221no—
336C22—1221no—
337C22—1222no—
338C22—2448no—
339C22—2441no—
340C22—2441no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—612no—
347C4—1221no—
348C4—1221no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4SD16×D6112yes—
353C4#41×D6111yescharacteristic
354C4C2×#1175822211yescharacteristic
355C2—42no—
356C2—1222no—
357C2—2442no—
358C2#1684027111yescharacteristic
359C2C2×SD16×D6111yescharacteristic
360C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#3101
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840094C2semidirect
4. #16840091C2semidirect
5. #16840051C2semidirect
6. #16840050C2semidirect
7. #16839966C2semidirect
8. #16839965C2semidirect
11. C4×#11758190C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758200C2semidirect
14. #16839813C2semidirect
15. C4×SD16×C61C2semidirect
21. #14519776C22semidirect
22. #14519775C22semidirect
28. C4×Dic122C22semidirect
38. #14519709C22semidirect
39. #14519708C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519701C22semidirect
45. #14519700C22semidirect
51. C4×#92418C22semidirect
53. C4×Q8×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
58. C4×C8×C61C22semidirect
142. C4×D61SD16semidirect
194. C4×SD16D61semidirect
196. C61#3101semidirect
211. C4×Q8C2×D61semidirect
225. #106C2×D61semidirect
231. #103C2×D61semidirect
239. C4×C8C2×D61semidirect