Finite Group Databasebeta

← #21455997

Subgroups — #21455997

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#16840236C211yesmaximal, characteristic, complemented
2#16840100C211yesmaximal, characteristic, complemented
3#16840083C211yesmaximal, characteristic, complemented
4#16840049C211yesmaximal, characteristic, complemented
5#16840039C211yesmaximal, characteristic, complemented
6#16839974C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839912C211yesmaximal, characteristic, complemented
9#16839895C211yesmaximal, characteristic
10#16839872C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#542C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C4×D244C2211yescharacteristic
22C4×D244C2211yescharacteristic
23C4×D244C2211yescharacteristic
24C4×D244C2211yescharacteristic
25#14519739—21no—
26#14519739—21no—
27#14519736C2211yescharacteristic
28C22⋊C4×D61—21no—
29C22⋊C4×D61—21no—
30#14519710C2211yescharacteristic, complemented
31#14519710C2211yescharacteristic, complemented
32#14519708C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35C4⋊#92418C2211yescharacteristic, complemented
36#14519701C2211yescharacteristic, complemented
37#14519701C2211yescharacteristic, complemented
38#14519698C2211yescharacteristic, complemented
39#14519698C2211yescharacteristic, complemented
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic, complemented
47C4×#92418C2211yescharacteristic, complemented
48C4⋊Q8×C61C2211yescharacteristic, complemented
49#126×C61—21no—
50#124×C61—21no—
51#124×C61C2211yescharacteristic, complemented
52#123×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic, complemented
58#117×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61C2311yescharacteristic
66C2×D244—21no—
67C2×D244—22no—
68C2×D244—22no—
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61D411yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61—21no—
90C42×C61C2311yescharacteristic
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93#11758201—22no—
94#11758201—22no—
95#11758199—22no—
96#11758199—22no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—24no—
113C22×D61—81no—
114C22×D61—81no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—81no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—81no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C2×Dic61—21no—
134C2×Dic61—21no—
135D244—24no—
136D244—21no—
137D244—21no—
138D244#4112yes—
139D244#4112yes—
140C4×D61—81no—
141C4×D61—81no—
142C4×D61—81no—
143C4×D61—81no—
144#92418—21no—
145#92418—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—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61C2×#4111yescharacteristic
171C4×C61C2×#4111yescharacteristic
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#542D6111yescharacteristic, complemented
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#433—611no—
197C61#311811yescharacteristic, complemented, Sylow
198C22×D4—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8C2×D6111yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C2×D6111yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D6111yescharacteristic
210#121C2×D6111yescharacteristic
211C4×Q8C2×D6111yescharacteristic, complemented
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—1221no—
217C4×D4—1221no—
218C4×D4C2×D6111yescharacteristic, complemented
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⋊C8—611no—
228C4⋊C8—611no—
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⋊C8—611no—
238C22⋊C8—611no—
239#97—611no—
240C4×C8—611no—
241C24—1221no—
242C2×Q8—21no—
243C2×Q8C22×D6111yescharacteristic
244C2×D4—21no—
245C2×D4—611no—
246C2×D4—611no—
247C2×D4—1222no—
248C2×D4—1222no—
249C2×D4—1221no—
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
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×C8—611no—
264C2×C8—611no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4C22⋊D6111yescharacteristic
271C4⋊C4C22⋊D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4C22⋊D6111yescharacteristic
285C22⋊C4C22⋊D6111yescharacteristic
286C42—21no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C42C22×D6111yescharacteristic
290C23—21no—
291C23—1224no—
292C23—1221no—
293C23—1221no—
294C23—4881no—
295C23—4881no—
296C23C2×C22⋊D6111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
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—81no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4C2×C22⋊D6111yescharacteristic
321C2×C4C2×C22⋊D6111yescharacteristic
322C2×C4C2×C22⋊D6111yescharacteristic
323C2×C4C2×C22⋊D6111yescharacteristic
324C2×C4C2×C22⋊D6111yescharacteristic
325C2×C4C23×D6111yescharacteristic
326C8—1221no—
327C8—1221no—
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—
343C22C22×C22⋊D6111yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—2441no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4#41×D6111yescharacteristic
356C2—41no—
357C2—81no—
358C2—2442no—
359C2—2442no—
360C2#1684026911yescharacteristic
361C2#1684056511yescharacteristic
362C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#542C2
socleC22×C61C22×D4
hypercenter#542D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #16840236C2semidirect
2. #16840100C2semidirect
3. #16840083C2semidirect
4. #16840049C2semidirect
5. #16840039C2semidirect
6. #16839974C2semidirect
7. #16839974C2semidirect
8. #16839912C2semidirect
10. #16839872C2semidirect
11. #16839860C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758199C2semidirect
14. #16839823C2semidirect
15. C61×#542C2semidirect
30. #14519710C22semidirect
31. #14519710C22semidirect
32. #14519708C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. C4⋊#92418C22semidirect
36. #14519701C22semidirect
37. #14519701C22semidirect
38. #14519698C22semidirect
39. #14519698C22semidirect
46. #14519688C22semidirect
47. C4×#92418C22semidirect
48. C4⋊Q8×C61C22semidirect
51. #124×C61C22semidirect
56. C4×Q8×C61C22semidirect
57. C4×D4×C61C22semidirect
182. #542D61semidirect
197. C61#3118semidirect
203. C4⋊Q8C2×D61semidirect
206. #124C2×D61semidirect
211. C4×Q8C2×D61semidirect
218. C4×D4C2×D61semidirect