Finite Group Databasebeta

← #21458034

Subgroups — #21458034

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#16840450C211yesmaximal, characteristic, complemented
2#16840405C211yesmaximal, characteristic
3#16840101C211yesmaximal, characteristic, complemented
4#16840079C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840019C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic, complemented
8#16839981C211yesmaximal, characteristic, complemented
9#16839927C211yesmaximal, characteristic, complemented
10#16839914C211yesmaximal, characteristic, complemented
11C4×#11758190C211yesmaximal, characteristic, complemented
12#16839841C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#488C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758202C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22C2×#11758189C2211yescharacteristic, complemented
23#14519772—21no—
24#14519768—21no—
25#14519762—21no—
26#14519759—21no—
27#14519757C2211yescharacteristic
28#14519757C2211yescharacteristic, complemented
29#14519753C2211yescharacteristic
30#14519750—21no—
31#14519748C2211yescharacteristic
32#14519747—21no—
33C4×Dic122C2211yescharacteristic, complemented
34C4×D244C2211yescharacteristic
35C4×D244C2211yescharacteristic
36#14519735—21no—
37#14519735C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic, complemented
39C22⋊C4×D61—21no—
40#14519710C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43C4⋊#92418C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic, complemented
52#125×C61C2211yescharacteristic, complemented
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic, complemented
55#103×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64#11758226—22no—
65#11758226—41no—
66D4×D61—22no—
67D4×D61—41no—
68C2×D244—21no—
69C2×D244D411yescharacteristic
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C2311yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87#11758202—41no—
88#11758200—41no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198D411yescharacteristic
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108#11758190—22no—
109#11758189—41no—
110#11758189—41no—
111C23×C61—21no—
112C22×D61—21no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61—81no—
116C22×D61C2×D411yescharacteristic
117C22×D61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—42no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—21no—
136D244—41no—
137D244—42no—
138D244#4112yes—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—42no—
144C4×D61—42no—
145C4×D61—81no—
146Dic122—21no—
147Dic122—21no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—22no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—84no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61C2×#4111yescharacteristic
172C4×C61H(5,𝔽2)11yescharacteristic
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3323—611nomaximal, Sylow
179C2×C61—81no—
180C2×C61#54611yescharacteristic
181C2×C61#57511yescharacteristic
182C2×C61#57711yescharacteristic
183D61—41no—
184D61—41no—
185D61—42no—
186#552—611no—
187#546—611no—
188#488D6111yescharacteristic, complemented
189#485—611no—
190#481—611no—
191#478—611no—
192#470—611no—
193#468—611no—
194#464—611no—
195#452—611no—
196#450—611no—
197C4×SD16—611no—
198#436—611no—
199#418—611no—
200#417—611no—
201C61#332311yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C22×D4—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×M16—611no—
208C2×M16—611no—
209#126—1221no—
210#125—1221no—
211#125C2×D6111yescharacteristic, complemented
212#124C2×D6111yescharacteristic
213#123—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×D4—611no—
223C4×D4—611no—
224#117—611no—
225#117—1221no—
226C2×C4⋊C4—611no—
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—
244C4×C8C2×D6111yescharacteristic, complemented
245C24—1221no—
246#41—1222no—
247#41—2441no—
248C2×Q8—611no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—611no—
251C2×D4—611no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1222no—
255C2×D4—1221no—
256C2×D4—2441no—
257C2×D4C22×D6111yescharacteristic
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263Q16—2441no—
264SD16—1222no—
265SD16—2441no—
266M16—2441no—
267M16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4C22×D6111yescharacteristic
283C4⋊C4C22×D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—611no—
287C22⋊C4—611no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—1221no—
295C42—1221no—
296C42C22×D6111yescharacteristic
297C23—21no—
298C23—611no—
299C23—611no—
300C23—1221no—
301C23—4881no—
302C23—2442no—
303C23—2442no—
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—612no—
311D4—1221no—
312D4—4881no—
313D4—2441no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—4881no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4D4×D6111yescharacteristic
332C2×C4D4×D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—1221no—
337C8—1221no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—1221no—
347C22—1222no—
348C22—4884no—
349C22—2441no—
350C22—2441no—
351C22C2×D4×D6111yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1221no—
358C4—1221no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4#41×D6111yescharacteristic
363C4#1451982311yescharacteristic
364C2—81no—
365C2—2441no—
366C2—2441no—
367C2—2442no—
368C2#1684040511yescharacteristic
369C2#1684055911yescharacteristic
370C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16840450C2semidirect
3. #16840101C2semidirect
4. #16840079C2semidirect
5. #16840059C2semidirect
6. #16840019C2semidirect
7. #16840007C2semidirect
8. #16839981C2semidirect
9. #16839927C2semidirect
10. #16839914C2semidirect
11. C4×#11758190C2semidirect
12. #16839841C2semidirect
13. #16839765C2semidirect
14. #16839762C2semidirect
15. C61×#488C2semidirect
18. C2×#11758202C22semidirect
22. C2×#11758189C22semidirect
28. #14519757C22semidirect
33. C4×Dic122C22semidirect
38. C4⋊C4×D61C22semidirect
40. #14519710C22semidirect
41. #14519709C22semidirect
42. #14519708C22semidirect
43. C4⋊#92418C22semidirect
44. #14519702C22semidirect
45. #14519701C22semidirect
51. #14519689C22semidirect
52. #125×C61C22semidirect
54. #103×C61C22semidirect
55. #103×C61C22semidirect
58. C4×C8×C61C22semidirect
188. #488D61semidirect
201. C61#3323semidirect
211. #125C2×D61semidirect
234. #103C2×D61semidirect
235. #103C2×D61semidirect
244. C4×C8C2×D61semidirect