Finite Group Databasebeta

← #21455998

Subgroups — #21455998

Order 7808.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840379C211yesmaximal, characteristic, complemented
2#16840236C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840051C211yesmaximal, characteristic, complemented
5#16840041C211yesmaximal, characteristic, complemented
6#16839976C211yesmaximal, characteristic, complemented
7#16839976C211yesmaximal, characteristic, complemented
8#16839915C211yesmaximal, characteristic, complemented
9#16839895C211yesmaximal, characteristic
10#16839871C211yesmaximal, characteristic, complemented
11#16839861C211yesmaximal, characteristic, complemented
12#16839849C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519776C2211yescharacteristic, complemented
22#14519770—21no—
23#14519764—21no—
24#14519764C2211yescharacteristic, complemented
25#14519758—21no—
26#14519756C2211yescharacteristic
27#14519754—21no—
28#14519742C2211yescharacteristic, complemented
29C4×D244—21no—
30C4×D244—21no—
31D4×Dic61C2211yescharacteristic, complemented
32#14519739C2211yescharacteristic
33#14519739C2211yescharacteristic
34#14519739C2211yescharacteristic
35#14519739C2211yescharacteristic
36#14519736C2211yescharacteristic
37C22⋊C4×D61—21no—
38C22⋊C4×D61—21no—
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×Dic61—21no—
64C2×D244—21no—
65C2×D244—22no—
66C2×D244—22no—
67C2×D244C2311yescharacteristic
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×Dic122—21no—
74C2×Dic122C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C42×C61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61D411yescharacteristic
88C22⋊Dic61D411yescharacteristic
89#11758199—22no—
90#11758199—22no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61D411yescharacteristic
96C4⋊Dic61D411yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758190—22no—
107#11758190—22no—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—24no—
113C22×D61—81no—
114C22×D61—81no—
115D4×C61—21no—
116D4×C61—21no—
117D4×C61—81no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—81no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—24no—
133D244—21no—
134D244—21no—
135D244#4112yes—
136D244#4112yes—
137C4×D61—81no—
138C4×D61—81no—
139C4×D61—81no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—81no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—22no—
156C2×D61—22no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—84no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61C2×#4111yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174#3118—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61—81no—
177C2×C61#52511yescharacteristic
178C2×C61#57611yescharacteristic
179C2×C61#57711yescharacteristic
180D61—42no—
181D61—42no—
182#542—611no—
183#518—611no—
184#485—611no—
185#482D6111yescharacteristic, complemented
186#476—611no—
187#474—611no—
188#463—611no—
189#463—611no—
190#450—611no—
191#447—611no—
192#442—611no—
193#440—611no—
194C4×SD16—611no—
195C4×D8—611no—
196#433—611no—
197C61#311811yescharacteristic, complemented, Sylow
198C22×D4—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8—611no—
204#126—1221no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—1221no—
210#121C2×D6111yescharacteristic
211C4×Q8—611no—
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—611no—
217C4×D4—1221no—
218C4×D4—1221no—
219#117—611no—
220#117C2×D6111yescharacteristic
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223#107—611no—
224#107C2×D6111yescharacteristic, complemented
225#106—611no—
226#106C2×D6111yescharacteristic, complemented
227C4⋊C8—611no—
228C4⋊C8—611no—
229#103—611no—
230#103—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102C2×D6111yescharacteristic, complemented
236#102C2×D6111yescharacteristic, complemented
237C22⋊C8—611no—
238C22⋊C8C2×D6111yescharacteristic
239#97—611no—
240C4×C8—611no—
241C24—1221no—
242C2×Q8—611no—
243C2×Q8—1221no—
244C2×D4—21no—
245C2×D4—611no—
246C2×D4—611no—
247C2×D4—1222no—
248C2×D4—1222no—
249C2×D4—1221no—
250C2×D4C22×D6111yescharacteristic
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4C22×D6111yescharacteristic
257SD16—1222no—
258SD16—1222no—
259D8—1222no—
260D8—1222no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4C22×D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—611no—
277C22⋊C4—611no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—21no—
287C42—611no—
288C42—611no—
289C42—1221no—
290C23—21no—
291C23—1224no—
292C23—1221no—
293C23—1221no—
294C23—4881no—
295C23—4881no—
296C23D4×D6111yescharacteristic
297Q8—1221no—
298Q8—1221no—
299Q8—4881no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—612no—
304D4—612no—
305D4—1224no—
306D4—1221no—
307D4—1221no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4D4×D6111yescharacteristic
325C2×C4C23×D6111yescharacteristic
326C8—21no—
327C8—21no—
328C8—1221no—
329C8—1221no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—1222no—
337C22—1222no—
338C22—4884no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—1221no—
349C4—1221no—
350C4—1221no—
351C4—1221no—
352C4—2441no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4#41×D6111yescharacteristic
356C2—41no—
357C2—81no—
358C2—2442no—
359C2—2442no—
360C2#1684027011yescharacteristic
361C2#1684056611yescharacteristic
362C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840379C2semidirect
2. #16840236C2semidirect
3. #16840103C2semidirect
4. #16840051C2semidirect
5. #16840041C2semidirect
6. #16839976C2semidirect
7. #16839976C2semidirect
8. #16839915C2semidirect
10. #16839871C2semidirect
11. #16839861C2semidirect
12. #16839849C2semidirect
13. #16839842C2semidirect
14. #16839820C2semidirect
15. C61×#482C2semidirect
21. #14519776C22semidirect
24. #14519764C22semidirect
28. #14519742C22semidirect
31. D4×Dic61C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519700C22semidirect
44. #14519700C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
185. #482D61semidirect
197. C61#3118semidirect
224. #107C2×D61semidirect
226. #106C2×D61semidirect
235. #102C2×D61semidirect
236. #102C2×D61semidirect