Finite Group Databasebeta

← #21457787

Subgroups — #21457787

Order 7808.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840417C211yesmaximal, characteristic, complemented
2#16840405C211yesmaximal, characteristic, complemented
3#16840121C211yesmaximal, characteristic, complemented
4#16840091C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840053C211yesmaximal, characteristic, complemented
7#16840012C211yesmaximal, characteristic, complemented
8#16839988C211yesmaximal, characteristic, complemented
9#16839906C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic, complemented
11#16839872C211yesmaximal, characteristic, complemented
12#16839832C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222—21no—
18C2×D4×D61C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic, complemented
21C2×C8×D61C2211yescharacteristic
22#14519777C2211yescharacteristic, complemented
23#14519759—21no—
24#14519759—21no—
25#14519759—21no—
26#14519756—21no—
27#14519753C2211yescharacteristic
28#14519750—21no—
29#14519748C2211yescharacteristic
30#14519748C2211yescharacteristic
31#14519748C2211yescharacteristic, complemented
32#14519747—21no—
33C4×D244C2211yescharacteristic
34C4×D244C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic, complemented
37C22⋊C4×D61—21no—
38#14519709C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519701C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519688C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic, complemented
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68#11758226—22no—
69#11758226—41no—
70D4×D61—22no—
71D4×D61—41no—
72#11758222—44no—
73C2×D244—21no—
74C2×D244D411yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61C2311yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83SD16×C61—41no—
84D8×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758199—22no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99#11758198D411yescharacteristic
100C4⋊Dic61—21no—
101C4⋊Dic61D411yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C8×D61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—81no—
118C22×D61C2×D411yescharacteristic
119C22×D61C2×D411yescharacteristic
120Q8×C61—21no—
121Q8×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—42no—
135C22⋊D61—81no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—22no—
142D244—21no—
143D244—42no—
144D244#4112yescomplemented
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—81no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—22no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—84no—
174C2×D61AGL(1,ℤ/8)12yes—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61C2×#4111yescharacteristic
180C4×C61H(5,𝔽2)11yescharacteristic
181Dic61—21no—
182Dic61—21no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186#3306—611nomaximal, Sylow
187C2×C61—81no—
188C2×C61—81no—
189C2×C61#54611yescharacteristic
190C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C61#57711yescharacteristic
192D61—22no—
193D61—41no—
194D61—42no—
195#547—611no—
196#546—611no—
197#489—611no—
198#483—611no—
199#481—611no—
200#476—611no—
201#469—611no—
202#465—611no—
203#463D6111yescharacteristic, complemented
204#449—611no—
205#447—611no—
206#442—611no—
207#435—611no—
208#417—611no—
209C2×#102—611no—
210C61#330611yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41—1221no—
213C22×D4—611no—
214C2×SD16C2×D6111yescharacteristic, complemented
215C2×D8—611no—
216C2×D8C2×D6111yescharacteristic
217C2×M16—611no—
218C22×C8—611no—
219C4⋊Q8—611no—
220#124C2×D6111yescharacteristic
221#123—1221no—
222#123—1221no—
223#123—1221no—
224C22⋊Q8—611no—
225C22⋊Q8—1221no—
226#121—611no—
227#121—611no—
228#121—611no—
229#121—1221no—
230#120—1221no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4C2×D6111yescharacteristic, complemented
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C22⋊C4—1221no—
237#106—611no—
238#106—611no—
239#106—611no—
240C4⋊C8C2×D6111yescharacteristic, complemented
241#103—611no—
242#103—611no—
243#103C2×D6111yescharacteristic, complemented
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102C2×D6111yescharacteristic
251C22⋊C8—611no—
252C22⋊C8—611no—
253#97—611no—
254C24—1221no—
255#41—1222no—
256#41—2444no—
257#41—2441no—
258C2×Q8—1221no—
259C2×Q8C22×D6111yescharacteristic
260C2×D4—611no—
261C2×D4—611no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1222no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—2441no—
269C2×D4C22×D6111yescharacteristic
270C2×D4C22×D6111yescharacteristic
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278SD16—41no—
279D8—41no—
280D8—1222no—
281M16—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—2441no—
285C2×C8C22×D6111yescharacteristic
286C2×C8C22×D6111yescharacteristic
287C4⋊C4—611no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22×D6111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—611no—
300C22⋊C4—611no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C42C22×D6111yescharacteristic
307C23—21no—
308C23—21no—
309C23—611no—
310C23—611no—
311C23—1221no—
312C23—4881no—
313C23—2442no—
314C23—2442no—
315Q8—21no—
316Q8—21no—
317Q8—2442no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—612no—
323D4—1222no—
324D4—1221no—
325D4—4881no—
326D4—2442no—
327D4—2442no—
328D4—2442no—
329D4—2442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—4881no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4D4×D6111yescharacteristic
347C2×C4D4×D6111yescharacteristic
348C2×C4C23×D6111yescharacteristic
349C8—21no—
350C8—21no—
351C8—1221no—
352C8—1221no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—612no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22—1221no—
364C22—1221no—
365C22—1222no—
366C22—4884no—
367C22—2441no—
368C22—2441no—
369C22C2×D4×D6111yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—1221no—
375C4—1221no—
376C4—2441no—
377C4—2441no—
378C4—2441no—
379C4#41×D6111yescharacteristic
380C4#1451982211yescharacteristic
381C2—81no—
382C2—81no—
383C2—1222no—
384C2—2441no—
385C2—2442no—
386C2#1684040911yescharacteristic
387C2AGL(1,ℤ/8)×D6111yescharacteristic
388C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3306
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840417C2semidirect
2. #16840405C2semidirect
3. #16840121C2semidirect
4. #16840091C2semidirect
5. #16840079C2semidirect
6. #16840053C2semidirect
7. #16840012C2semidirect
8. #16839988C2semidirect
9. #16839906C2semidirect
10. #16839894C2semidirect
11. #16839872C2semidirect
12. #16839832C2semidirect
13. #16839762C2semidirect
14. #102×D61C2semidirect
15. C61×#463C2semidirect
20. C2×#11758189C22semidirect
22. #14519777C22semidirect
31. #14519748C22semidirect
36. C4⋊C4×D61C22semidirect
38. #14519709C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519701C22semidirect
42. #14519701C22semidirect
47. #14519698C22semidirect
50. #14519689C22semidirect
51. #14519688C22semidirect
52. C2×SD16×C61C22semidirect
55. C4×D4×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #103×C61C22semidirect
144. D244#41semidirect
203. #463D61semidirect
210. C61#3306semidirect
214. C2×SD16C2×D61semidirect
233. C4×D4C2×D61semidirect
240. C4⋊C8C2×D61semidirect
243. #103C2×D61semidirect