Finite Group Databasebeta

← #21456004

Subgroups — #21456004

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#16840385C211yesmaximal, characteristic, complemented
2#16840237C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840050C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16839979C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839896C211yesmaximal, characteristic
10#16839871C211yesmaximal, characteristic, complemented
11#16839863C211yesmaximal, characteristic, complemented
12SD16×Dic61C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758199C2211yescharacteristic
17C2×#11758199C2211yescharacteristic
18#14519776C2211yescharacteristic, complemented
19#14519772—21no—
20#14519766C2211yescharacteristic, complemented
21#14519763—21no—
22#14519759—21no—
23#14519757—21no—
24#14519751C2211yescharacteristic
25Q8×Dic61C2211yescharacteristic, complemented
26D4×Dic61—21no—
27D4×Dic61—21no—
28D4×Dic61C2211yescharacteristic
29D4×Dic61C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic, complemented
33#14519736C2211yescharacteristic
34#14519736C2211yescharacteristic
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C24×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×Dic122—21no—
75SD16×C61—22no—
76SD16×C61—22no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C22⋊Dic61—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⋊Dic61—21no—
96C4⋊Dic61D411yescharacteristic
97C4⋊Dic61D411yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—24no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—81no—
112C23×C61—81no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—24no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61#4112yes—
121D4×C61#4112yes—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—81no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140D244—21no—
141D244—21no—
142C4×D61—81no—
143Dic122—81no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—84no—
158C22×C61C22×D411yescharacteristic
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×#4111yescharacteristic
166C4×C61C2×#4111yescharacteristic
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3118—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61—42no—
177C2×C61—42no—
178C2×C61#52511yescharacteristic
179C2×C61#57611yescharacteristic
180C2×C61#57711yescharacteristic
181D61—81no—
182#542—611no—
183#518—611no—
184#485—611no—
185#482—611no—
186#476—611no—
187#474—611no—
188#463—611no—
189#463—611no—
190#450D6111yescharacteristic, complemented
191#447—611no—
192#442—611no—
193#440—611no—
194C4×SD16—611no—
195C4×D8—611no—
196#433—611no—
197C61#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D6111yescharacteristic
199C2×SD16C2×D6111yescharacteristic
200C2×SD16C2×D6111yescharacteristic
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8—611no—
204#126—1221no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208C22⋊Q8—1221no—
209C22⋊Q8C2×D6111yescharacteristic
210#121—611no—
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#117—611no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223#107—611no—
224#107—611no—
225#106—611no—
226#106—611no—
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
236#102C2×D6111yescharacteristic
237C22⋊C8—611no—
238C22⋊C8C2×D6111yescharacteristic
239#97—611no—
240C4×C8—611no—
241C24—21no—
242C2×Q8—1221no—
243C2×Q8C22×D6111yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4C22×D6111yescharacteristic
250C2×D4C22×D6111yescharacteristic
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4C22×D6111yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—1222no—
260D8—1222no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C22×D6111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—611no—
276C22⋊C4—611no—
277C22⋊C4—1221no—
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—611no—
287C42—611no—
288C42—1221no—
289C42—1221no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—1221no—
296C23D4×D6111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—4881no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—1221no—
304D4—1221no—
305D4—4881no—
306D4#1175822412yes—
307D4#1175822412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—1221no—
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—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—1221no—
348C4—1221no—
349C4—1221no—
350C4—1221no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4C2×#1175822411yescharacteristic
355C4C2×#1175822411yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—4881no—
360C2#1684026811yescharacteristic
361C2#1684056611yescharacteristic
362C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840385C2semidirect
2. #16840237C2semidirect
3. #16840100C2semidirect
4. #16840087C2semidirect
5. #16840050C2semidirect
6. #16840040C2semidirect
7. #16839979C2semidirect
8. #16839979C2semidirect
10. #16839871C2semidirect
11. #16839863C2semidirect
12. SD16×Dic61C2semidirect
13. #16839842C2semidirect
14. #16839820C2semidirect
15. C61×#450C2semidirect
18. #14519776C22semidirect
20. #14519766C22semidirect
25. Q8×Dic61C22semidirect
32. #14519739C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519701C22semidirect
44. #14519701C22semidirect
45. #14519699C22semidirect
46. #14519699C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
190. #450D61semidirect
197. C61#3118semidirect