Finite Group Databasebeta

← #21456779

Subgroups — #21456779

Order 7808.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840291C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic, complemented
3#16840144C211yesmaximal, characteristic, complemented
4#16840117C211yesmaximal, characteristic, complemented
5#16840116C211yesmaximal, characteristic, complemented
6#16839986C211yesmaximal, characteristic, complemented
7#16839982C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839975C211yesmaximal, characteristic, complemented
10#16839916C211yesmaximal, characteristic, complemented
11#16839911C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839894C211yesmaximal, characteristic
14#16839813C211yesmaximal, characteristic, complemented
15C61×#495C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758202C2211yescharacteristic, complemented
19C2×#11758200C2211yescharacteristic, complemented
20C2×#11758201C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22#14519770—21no—
23#14519769C2211yescharacteristic, complemented
24#14519766C2211yescharacteristic
25#14519765C2211yescharacteristic
26#14519764C2211yescharacteristic
27#14519763—21no—
28#14519763—21no—
29#14519759—21no—
30#14519753C2211yescharacteristic
31#14519748C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic, complemented
33D4×Dic61C2211yescharacteristic, complemented
34#14519737—21no—
35#14519733—21no—
36C22⋊C4×D61—21no—
37C22⋊C4×D61—21no—
38C42×D61C2211yescharacteristic
39#14519706C2211yescharacteristic, complemented
40#14519706C2211yescharacteristic, complemented
41#14519702C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67Q8×D61—41no—
68Q8×D61—41no—
69D4×D61—41no—
70D4×D61—41no—
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61D411yescharacteristic
74C2×C4×D61D411yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78Q16×C61—41no—
79SD16×C61—41no—
80SD16×C61—41no—
81D8×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93#11758202—41no—
94#11758201—41no—
95#11758200—41no—
96#11758199—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61D411yescharacteristic
110C4×Dic61D411yescharacteristic
111C4×Dic61C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61—21no—
116C22×D61—21no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61C2×D411yescharacteristic
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—42no—
135C22⋊D61—42no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143D244—21no—
144D244—21no—
145C4×D61—22no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—41no—
149C4×D61—42no—
150Dic122—21no—
151Dic122—21no—
152Dic122—42no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61C22×D411yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—84no—
170C2×D61#13512yes—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61H(5,𝔽2)11yescharacteristic
176C4×C61H(5,𝔽2)11yescharacteristic
177Dic61—21no—
178Dic61—21no—
179Dic61—21no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3211—611nomaximal, Sylow
184C2×C61—81no—
185C2×C61—81no—
186C2×C61#53511yescharacteristic
187C2×C61C2×#13511yescharacteristic
188C2×C61#57511yescharacteristic
189D61—22no—
190D61—81no—
191#529—611no—
192C2×#124—611no—
193#495—611no—
194#495D6111yescharacteristic, complemented
195#488—611no—
196#488—611no—
197#464—611no—
198#464—611no—
199#463—611no—
200#463—611no—
201#451—611no—
202#450—611no—
203#448—611no—
204#447—611no—
205#431—611no—
206C61#321111yescharacteristic, complemented, Sylow
207C22×Q8—611no—
208C22×D4—611no—
209C2×Q16—611no—
210C2×Q16C2×D6111yescharacteristic, complemented
211C2×SD16—611no—
212C2×SD16—611no—
213C2×SD16C2×D6111yescharacteristic
214C2×SD16C2×D6111yescharacteristic, complemented
215C2×D8—611no—
216C2×D8C2×D6111yescharacteristic
217#126—1221no—
218#125—611no—
219#124—611no—
220#124—611no—
221#124—611no—
222#124—1221no—
223#124—1221no—
224#124C2×D6111yescharacteristic
225#124C2×D6111yescharacteristic, complemented
226#123—1221no—
227C22⋊Q8—611no—
228#121—611no—
229C4×Q8—611no—
230C4×D4—611no—
231C4×D4—1221no—
232#117—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C42—611no—
236C4⋊C8—611no—
237C4⋊C8—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#103—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246C22⋊C8—611no—
247C22⋊C8—611no—
248C4×C8—611no—
249C4×C8C2×D6111yescharacteristic, complemented
250C24—1221no—
251C2×Q8—611no—
252C2×Q8—1221no—
253C2×Q8—2441no—
254C2×Q8—2441no—
255C2×Q8C22×D6111yescharacteristic
256C2×Q8C22×D6111yescharacteristic
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—2441no—
261C2×D4—2441no—
262C2×D4C22×D6111yescharacteristic
263C2×D4C22×D6111yescharacteristic
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269Q16—41no—
270Q16—2441no—
271SD16—41no—
272SD16—41no—
273SD16—2441no—
274SD16—2441no—
275D8—41no—
276D8—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C42—611no—
301C42—611no—
302C42—611no—
303C42—1221no—
304C42C22×D6111yescharacteristic
305C23—21no—
306C23—21no—
307C23—611no—
308C23—1221no—
309C23—2442no—
310C23—2442no—
311C23—2442no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—1221no—
317Q8—1221no—
318Q8—2442no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—1221no—
324D4—1221no—
325D4—2442no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1222no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—2441no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4D4×D6111yescharacteristic
342C2×C4D4×D6111yescharacteristic
343C2×C4C23×D6111yescharacteristic
344C8—21no—
345C8—21no—
346C8—1221no—
347C8—1221no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—612no—
355C22—1221no—
356C22—1221no—
357C22—4884no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22C2×D4×D6111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—1221no—
367C4—1221no—
368C4—1221no—
369C4—2441no—
370C4—2441no—
371C4—2441no—
372C4#1451982211yescharacteristic
373C4#1451982211yescharacteristic
374C2—81no—
375C2—81no—
376C2—1222no—
377C2—4881no—
378C2#1684032511yescharacteristic
379C2#135×D6111yescharacteristic
380C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC22×C61C22×D4
hypercenter#495D61
hypocenterC61#3211
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #16840291C2semidirect
2. #124×D61C2semidirect
3. #16840144C2semidirect
4. #16840117C2semidirect
5. #16840116C2semidirect
6. #16839986C2semidirect
7. #16839982C2semidirect
8. #16839979C2semidirect
9. #16839975C2semidirect
10. #16839916C2semidirect
11. #16839911C2semidirect
12. #16839899C2semidirect
14. #16839813C2semidirect
15. C61×#495C2semidirect
18. C2×#11758202C22semidirect
19. C2×#11758200C22semidirect
23. #14519769C22semidirect
32. Q8×Dic61C22semidirect
33. D4×Dic61C22semidirect
39. #14519706C22semidirect
40. #14519706C22semidirect
41. #14519702C22semidirect
42. #14519702C22semidirect
43. #14519701C22semidirect
44. #14519701C22semidirect
51. C4×#92418C22semidirect
52. C2×Q16×C61C22semidirect
54. C2×SD16×C61C22semidirect
57. #124×C61C22semidirect
58. C4×C8×C61C22semidirect
194. #495D61semidirect
206. C61#3211semidirect
210. C2×Q16C2×D61semidirect
214. C2×SD16C2×D61semidirect
225. #124C2×D61semidirect
249. C4×C8C2×D61semidirect