Finite Group Databasebeta

← #21457672

Subgroups — #21457672

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840456C211yesmaximal, characteristic, complemented
2#16840409C211yesmaximal, characteristic, complemented
3#16840115C211yesmaximal, characteristic, complemented
4#16840099C211yesmaximal, characteristic, complemented
5#16840061C211yesmaximal, characteristic, complemented
6#16839996C211yesmaximal, characteristic, complemented
7#16839992C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic, complemented
9#16839909C211yesmaximal, characteristic, complemented
10#16839897C211yesmaximal, characteristic, complemented
11#16839844C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13#16839756C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic, complemented
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C22×#92418C2211yescharacteristic, complemented
22C2×C8×D61C2211yescharacteristic
23#14519771—21no—
24#14519768C2211yescharacteristic, complemented
25#14519764C2211yescharacteristic
26#14519759—21no—
27#14519759—21no—
28#14519757C2211yescharacteristic
29#14519752C2211yescharacteristic
30#14519751C2211yescharacteristic, complemented
31#14519750—21no—
32#14519748—21no—
33#14519745—21no—
34C4×D244—21no—
35#14519739C2211yescharacteristic
36#14519739C2211yescharacteristic, complemented
37C4×C22⋊D61C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39C22⋊C4×D61—21no—
40#14519710C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic, complemented
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61D411yescharacteristic
67D4×D61—22no—
68D4×D61—41no—
69#11758222—22no—
70#11758222—41no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758199—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108D488—22no—
109#11758190—41no—
110C8×D61—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—81no—
118C22×D61C2×D411yescharacteristic
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—81no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—22no—
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244—21no—
140D244—21no—
141D244—42no—
142D244#4112yes—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—42no—
146C4×D61—81no—
147C4×D61—81no—
148C4×D61—81no—
149Dic122—21no—
150Dic122—21no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—22no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—84no—
171C2×D61#13512yes—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61C2×#4111yescharacteristic
177C4×C61H(5,𝔽2)11yescharacteristic
178Dic61—21no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—41no—
183#3297—611nomaximal, Sylow
184C2×C61—41no—
185C2×C61—81no—
186C2×C61#54611yescharacteristic
187C2×C61C2×#13511yescharacteristic
188C2×C61#57611yescharacteristic
189D61—22no—
190D61—42no—
191D61—81no—
192#553—611no—
193#546—611no—
194#488—611no—
195#484—611no—
196#482D6111yescharacteristic, complemented
197#478—611no—
198#466—611no—
199#465—611no—
200#463—611no—
201#449—611no—
202#447—611no—
203C4×D8—611no—
204C8×D4—611no—
205#416—611no—
206C2×#102—611no—
207C61#329711yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C22×D4—611no—
210C2×SD16—611no—
211C2×D8—611no—
212C2×D8—611no—
213C22×C8—611no—
214C22×C8—611no—
215#126—1221no—
216#125—611no—
217#124—611no—
218#123—1221no—
219#123—1221no—
220C22⋊Q8—611no—
221#121—611no—
222#121—611no—
223#121—1221no—
224#121—1221no—
225#121C2×D6111yescharacteristic
226#120—1221no—
227C4×D4—611no—
228C4×D4—611no—
229C4×D4—611no—
230C4×D4—1221no—
231#117C2×D6111yescharacteristic, complemented
232C2×C4⋊C4—611no—
233C2×C22⋊C4—1221no—
234#107—611no—
235#107C2×D6111yescharacteristic, complemented
236#106C2×D6111yescharacteristic, complemented
237C4⋊C8—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102C2×D6111yescharacteristic
247#102C2×D6111yescharacteristic
248C22⋊C8—611no—
249C22⋊C8C2×D6111yescharacteristic, complemented
250C4×C8—611no—
251C24—1221no—
252#41—1222no—
253#41—2441no—
254C2×Q8—611no—
255C2×D4—21no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1222no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—2441no—
265C2×D4C22×D6111yescharacteristic
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4C22×D6111yescharacteristic
272SD16—2441no—
273D8—1222no—
274D8—2441no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8—2441no—
278C2×C8—2441no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4C22×D6111yescharacteristic
288C4⋊C4C22×D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—611no—
293C22⋊C4—611no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C42—21no—
302C42—611no—
303C23—21no—
304C23—611no—
305C23—1221no—
306C23—1221no—
307C23—4881no—
308C23—2442no—
309C23—2442no—
310C23D4×D6111yescharacteristic
311Q8—1221no—
312Q8—1221no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—612no—
317D4—1222no—
318D4—1221no—
319D4—1221no—
320D4—1221no—
321D4—4881no—
322D4—2442no—
323D4—2442no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—612no—
354C22—1221no—
355C22—1221no—
356C22—1222no—
357C22—4884no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22C2×D4×D6111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—1221no—
369C4—1221no—
370C4—1221no—
371C4—2441no—
372C4—2441no—
373C4#41×D6111yescharacteristic
374C4#1451982311yescharacteristic
375C2—41no—
376C2—81no—
377C2—1222no—
378C2—4881no—
379C2—2442no—
380C2#1684040411yescharacteristic
381C2#135×D6111yescharacteristic
382C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3297
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. #16840456C2semidirect
2. #16840409C2semidirect
3. #16840115C2semidirect
4. #16840099C2semidirect
5. #16840061C2semidirect
6. #16839996C2semidirect
7. #16839992C2semidirect
8. #16839976C2semidirect
9. #16839909C2semidirect
10. #16839897C2semidirect
11. #16839844C2semidirect
12. #16839825C2semidirect
13. #16839756C2semidirect
14. #102×D61C2semidirect
15. C61×#482C2semidirect
18. C2×#11758190C22semidirect
21. C22×#92418C22semidirect
24. #14519768C22semidirect
30. #14519751C22semidirect
36. #14519739C22semidirect
40. #14519710C22semidirect
41. #14519706C22semidirect
42. #14519702C22semidirect
43. #14519700C22semidirect
44. #14519700C22semidirect
49. #14519697C22semidirect
51. C8×Dic61C22semidirect
53. #117×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
58. C22⋊C8×C61C22semidirect
196. #482D61semidirect
207. C61#3297semidirect
231. #117C2×D61semidirect
235. #107C2×D61semidirect
236. #106C2×D61semidirect
249. C22⋊C8C2×D61semidirect