Finite Group Databasebeta

← #21457851

Subgroups — #21457851

Order 7808.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840480C211yesmaximal, characteristic, complemented
2#16840400C211yesmaximal, characteristic
3#16840123C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840086C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16840019C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839987C211yesmaximal, characteristic, complemented
10#16839924C211yesmaximal, characteristic, complemented
11#16839914C211yesmaximal, characteristic, complemented
12#16839859C211yesmaximal, characteristic, complemented
13#16839833C211yesmaximal, characteristic, complemented
14#16839765C211yesmaximal, characteristic, complemented
15C61×#416C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758202C2211yescharacteristic, complemented
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21#14519776C2211yescharacteristic, complemented
22#14519771—21no—
23#14519770—21no—
24#14519766C2211yescharacteristic
25#14519763—21no—
26#14519760—21no—
27#14519757C2211yescharacteristic
28#14519756C2211yescharacteristic, complemented
29#14519753C2211yescharacteristic
30#14519751C2211yescharacteristic
31#14519749—21no—
32#14519745—21no—
33C4×Dic122—21no—
34#14519742C2211yescharacteristic, complemented
35D4×Dic61C2211yescharacteristic
36C4×C22⋊D61C2211yescharacteristic
37#14519735C2211yescharacteristic
38C2×#11758198—21no—
39#14519710C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic, complemented
52C2×#41×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic, complemented
54#117×C61C2211yescharacteristic, complemented
55#103×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60#41×C61—22no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71D4×D61—22no—
72D4×D61—41no—
73C2×D244C2311yescharacteristic
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77C2×C8×C61—41no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C42×C61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61D411yescharacteristic
87#11758202—41no—
88#11758200—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758190—41no—
110#11758189—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—81no—
117C22×D61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122D4×C61#4112yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—41no—
132C22⋊D61—42no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—81no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143C4×D61—21no—
144C4×D61—21no—
145Dic122—21no—
146Dic122—21no—
147Dic122—42no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—22no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—84no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61C2×#4111yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3311—611nomaximal, Sylow
179C2×C61—42no—
180C2×C61—41no—
181C2×C61#54611yescharacteristic
182C2×C61#57511yescharacteristic
183C2×C61#57711yescharacteristic
184D61—41no—
185D61—81no—
186#556—611no—
187#546—611no—
188#489—611no—
189#485—611no—
190#482—611no—
191#476—611no—
192#470—611no—
193#465—611no—
194#464—611no—
195#452—611no—
196#450—611no—
197#440—611no—
198#435—611no—
199#418—611no—
200#416D6111yescharacteristic, complemented
201C61#331111yescharacteristic, complemented, Sylow
202C2×#41C2×D6111yescharacteristic
203C22×D4—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×M16—611no—
208C22×C8C2×D6111yescharacteristic, complemented
209C4⋊Q8—611no—
210#126—1221no—
211#126—1221no—
212#124—611no—
213#124—1221no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8—611no—
217C22⋊Q8—611no—
218#121—611no—
219#121—1221no—
220#120—1221no—
221C4×Q8—611no—
222C4×Q8—1221no—
223C4×D4—611no—
224C4×D4—611no—
225#117—611no—
226#117C2×D6111yescharacteristic, complemented
227C2×C22⋊C4—1221no—
228#107—611no—
229#106—611no—
230#106—611no—
231C4⋊C8—611no—
232#103—611no—
233#103—611no—
234#103C2×D6111yescharacteristic, complemented
235#103C2×D6111yescharacteristic, complemented
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241#102C2×D6111yescharacteristic
242C22⋊C8—611no—
243C22⋊C8—611no—
244#97—611no—
245C24—1221no—
246#41—22no—
247#41—41no—
248C2×Q8—611no—
249C2×Q8—1221no—
250C2×Q8C22×D6111yescharacteristic
251C2×D4—21no—
252C2×D4—611no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1222no—
256C2×D4—1221no—
257C2×D4—2441no—
258C2×D4C22×D6111yescharacteristic
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4C22×D6111yescharacteristic
263Q16—2441no—
264SD16—1222no—
265SD16—2441no—
266M16—2441no—
267C2×C8—41no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4C22×D6111yescharacteristic
281C4⋊C4C22×D6111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—611no—
284C22⋊C4—611no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—21no—
294C42—611no—
295C42—1221no—
296C42—1221no—
297C23—21no—
298C23—611no—
299C23—1221no—
300C23—4881no—
301C23—2442no—
302C23—2442no—
303C23D4×D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308Q8—2442no—
309D4—21no—
310D4—42no—
311D4—1221no—
312D4—1221no—
313D4—4881no—
314D4—2441no—
315D4—2442no—
316D4#1175822212yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4881no—
332C2×C4D4×D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—1221no—
345C22—1221no—
346C22—1221no—
347C22—4884no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22C2×D4×D6111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1221no—
357C4—1221no—
358C4—1221no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4C2×#1175822211yescharacteristic
363C4#1451982211yescharacteristic
364C2—41no—
365C2—42no—
366C2—4881no—
367C2—2441no—
368C2#1684040211yescharacteristic
369C2#1684055911yescharacteristic
370C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#416C2
socleC22×C61C22×D4
hypercenter#416D61
hypocenterC61#3311
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #16840480C2semidirect
3. #16840123C2semidirect
4. #16840101C2semidirect
5. #16840086C2semidirect
6. #16840050C2semidirect
7. #16840019C2semidirect
8. #16839991C2semidirect
9. #16839987C2semidirect
10. #16839924C2semidirect
11. #16839914C2semidirect
12. #16839859C2semidirect
13. #16839833C2semidirect
14. #16839765C2semidirect
15. C61×#416C2semidirect
17. C2×#11758202C22semidirect
21. #14519776C22semidirect
28. #14519756C22semidirect
34. #14519742C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519708C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519701C22semidirect
49. C22⋊#92418C22semidirect
51. #14519687C22semidirect
53. C22×C8×C61C22semidirect
54. #117×C61C22semidirect
55. #103×C61C22semidirect
56. #103×C61C22semidirect
200. #416D61semidirect
201. C61#3311semidirect
208. C22×C8C2×D61semidirect
226. #117C2×D61semidirect
234. #103C2×D61semidirect
235. #103C2×D61semidirect