Finite Group Databasebeta

← #21456005

Subgroups — #21456005

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#16840383C211yesmaximal, characteristic, complemented
2#16840236C211yesmaximal, characteristic, complemented
3#16840104C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840053C211yesmaximal, characteristic, complemented
6#16840043C211yesmaximal, characteristic, complemented
7#16839978C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839915C211yesmaximal, characteristic, complemented
10#16839898C211yesmaximal, characteristic
11#16839875C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13C4×#11758190C211yesmaximal, characteristic, complemented
14C4×D488C211yesmaximal, characteristic, complemented
15C61×#433C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21#14519777C2211yescharacteristic, complemented
22#14519772—21no—
23#14519765C2211yescharacteristic, complemented
24#14519763—21no—
25#14519759—21no—
26#14519756C2211yescharacteristic
27#14519755—21no—
28#14519751C2211yescharacteristic
29C4×Dic122C2211yescharacteristic, complemented
30C4×D244C2211yescharacteristic
31C4×D244C2211yescharacteristic
32C4×D244C2211yescharacteristic
33C4×D244C2211yescharacteristic
34C4×D244C2211yescharacteristic, complemented
35#14519739—21no—
36#14519739—21no—
37#14519736C2211yescharacteristic
38C22⋊C4×D61—21no—
39C22⋊C4×D61—21no—
40#14519711C2211yescharacteristic, complemented
41#14519711C2211yescharacteristic, complemented
42#14519709C2211yescharacteristic, complemented
43#14519709C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519702C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52#117×C61C2211yescharacteristic
53C4⋊C8×C61C2211yescharacteristic, complemented
54C4⋊C8×C61C2211yescharacteristic, complemented
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×D244—21no—
63C2×D244—22no—
64C2×D244—22no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
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
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61D411yescharacteristic
80C4⋊C4×C61D411yescharacteristic
81C22⋊C4×C61D411yescharacteristic
82C22⋊C4×C61D411yescharacteristic
83C42×C61C2311yescharacteristic
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104D488—22no—
105D488—22no—
106#11758190—22no—
107#11758190—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—24no—
112C22×D61—21no—
113C22×D61—81no—
114C22×D61—81no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2411yescharacteristic
123C22⋊D61—81no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129D244—24no—
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244#4112yes—
135D244#4112yes—
136C4×D61—81no—
137C4×D61—81no—
138C4×D61—81no—
139C4×D61—81no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—81no—
144C8×C61—21no—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—84no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61C2×#4111yescharacteristic
168C4×C61C2×#4111yescharacteristic
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3118—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61#52511yescharacteristic
177C2×C61#57611yescharacteristic
178C2×C61#57711yescharacteristic
179D61—42no—
180D61—42no—
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#450—611no—
191#447—611no—
192#442—611no—
193#440—611no—
194C4×SD16—611no—
195C4×D8—611no—
196#433D6111yescharacteristic, complemented
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#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#117C2×D6111yescharacteristic
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223#107—611no—
224#107—611no—
225#106—611no—
226#106—611no—
227C4⋊C8C2×D6111yescharacteristic, complemented
228C4⋊C8C2×D6111yescharacteristic, complemented
229#103—611no—
230#103—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237C22⋊C8C2×D6111yescharacteristic
238C22⋊C8C2×D6111yescharacteristic
239#97C2×D6111yescharacteristic, complemented
240C4×C8C2×D6111yescharacteristic, complemented
241C24—1221no—
242C2×Q8—611no—
243C2×Q8—1221no—
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—611no—
247C2×D4—1222no—
248C2×D4—1222no—
249C2×D4—1221no—
250C2×D4—1221no—
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×C8C22×D6111yescharacteristic
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4D24411yescharacteristic
273C4⋊C4D24411yescharacteristic
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4D24411yescharacteristic
285C22⋊C4D24411yescharacteristic
286C42—1221no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C42C22×D6111yescharacteristic
290C23—1224no—
291C23—1221no—
292C23—1221no—
293C23—1221no—
294C23—4881no—
295C23—4881no—
296C23C2×D24411yescharacteristic
297Q8—1221no—
298Q8—1221no—
299Q8—4881no—
300D4—612no—
301D4—612no—
302D4—1224no—
303D4—1221no—
304D4—1221no—
305D4—1221no—
306D4—1221no—
307D4—4881no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4C2×D24411yescharacteristic
321C2×C4C2×D24411yescharacteristic
322C2×C4C2×D24411yescharacteristic
323C2×C4C2×D24411yescharacteristic
324C2×C4C2×D24411yescharacteristic
325C2×C4C23×D6111yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—1222no—
334C22—1222no—
335C22—4884no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C22×D24411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4#41×D6111yescharacteristic
356C2—41no—
357C2—4881no—
358C2—2442no—
359C2—2442no—
360C2#1684027411yescharacteristic
361C2#1684056711yescharacteristic
362C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840236C2semidirect
3. #16840104C2semidirect
4. #16840087C2semidirect
5. #16840053C2semidirect
6. #16840043C2semidirect
7. #16839978C2semidirect
8. #16839978C2semidirect
9. #16839915C2semidirect
11. #16839875C2semidirect
12. #16839864C2semidirect
13. C4×#11758190C2semidirect
14. C4×D488C2semidirect
15. C61×#433C2semidirect
21. #14519777C22semidirect
23. #14519765C22semidirect
29. C4×Dic122C22semidirect
34. C4×D244C22semidirect
40. #14519711C22semidirect
41. #14519711C22semidirect
42. #14519709C22semidirect
43. #14519709C22semidirect
44. #14519702C22semidirect
45. #14519702C22semidirect
50. #14519699C22semidirect
51. #14519699C22semidirect
53. C4⋊C8×C61C22semidirect
54. C4⋊C8×C61C22semidirect
57. #97×C61C22semidirect
58. C4×C8×C61C22semidirect
196. #433D61semidirect
197. C61#3118semidirect
227. C4⋊C8C2×D61semidirect
228. C4⋊C8C2×D61semidirect
239. #97C2×D61semidirect
240. C4×C8C2×D61semidirect