Finite Group Databasebeta

← #21457784

Subgroups — #21457784

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#16840412C211yesmaximal, characteristic, complemented
2#16840406C211yesmaximal, characteristic, complemented
3#16840120C211yesmaximal, characteristic, complemented
4#16840093C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16840012C211yesmaximal, characteristic, complemented
8#16839989C211yesmaximal, characteristic, complemented
9#16839975C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11#16839874C211yesmaximal, characteristic, complemented
12#16839830C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14C2×#14519698C211yesmaximal, characteristic, complemented
15C61×#447C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×#11758224C2211yescharacteristic
18C2×#11758200C2211yescharacteristic, complemented
19C2×#11758189C2211yescharacteristic, complemented
20C22×#92418C2211yescharacteristic
21#14519776C2211yescharacteristic, complemented
22#14519764C2211yescharacteristic
23#14519759—21no—
24#14519758—21no—
25#14519758—21no—
26#14519756C2211yescharacteristic
27#14519754—21no—
28#14519749—21no—
29#14519748C2211yescharacteristic
30#14519748C2211yescharacteristic, complemented
31#14519746—21no—
32D4×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic, complemented
34C4×C22⋊D61C2211yescharacteristic
35C2×C4⋊Dic61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic, complemented
37C2×C22⋊Dic61—21no—
38#14519709C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C24×C61—21no—
60C2×D4×C61—22no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76#11758224—22no—
77#11758224—41no—
78#11758224—44no—
79C2×C4×D61—21no—
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122C2311yescharacteristic
83D8×C61—22no—
84D8×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊C4×C61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61D411yescharacteristic
97#11758200—41no—
98#11758198D411yescharacteristic
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418—41no—
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111#11758189—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—42no—
116C23×C61—42no—
117C23×C61—81no—
118C23×C61C2×D411yescharacteristic
119C22×D61C2×D411yescharacteristic
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—42no—
126D4×C61—42no—
127D4×C61#4112yescomplemented
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—22no—
134C22⋊D61—42no—
135C22⋊D61—42no—
136C22⋊D61—81no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—81no—
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—42no—
151Dic122—21no—
152Dic122—21no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—22no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—84no—
170C22×C61AGL(1,ℤ/8)12yes—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61C2×#4111yescharacteristic
178C4×C61H(5,𝔽2)11yescharacteristic
179Dic61—21no—
180Dic61—21no—
181Dic61—21no—
182Dic61—41no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186#3306—611nomaximal, Sylow
187C2×C61—22no—
188C2×C61—42no—
189C2×C61—81no—
190C2×C61—81no—
191C2×C61#54611yescharacteristic
192C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C61#57711yescharacteristic
194D61—41no—
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#463—611no—
204#449—611no—
205#447D6111yescharacteristic, complemented
206#442—611no—
207#435—611no—
208#417—611no—
209C2×#102—611no—
210C61#330611yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41—1221no—
213C22×D4C2×D6111yescharacteristic
214C2×SD16—611no—
215C2×D8C2×D6111yescharacteristic
216C2×D8C2×D6111yescharacteristic
217C2×M16—611no—
218C22×C8—611no—
219C4⋊Q8—611no—
220#124—611no—
221#123—1221no—
222#123—1221no—
223#123—1221no—
224C22⋊Q8—611no—
225C22⋊Q8—1221no—
226#121—611no—
227#121—611no—
228#121—1221no—
229#121C2×D6111yescharacteristic
230#120—1221no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C22⋊C4—1221no—
237#106—611no—
238#106—611no—
239#106—611no—
240C4⋊C8—611no—
241#103—611no—
242#103—611no—
243#103—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102C2×D6111yescharacteristic
250#102C2×D6111yescharacteristic
251C22⋊C8—611no—
252C22⋊C8C2×D6111yescharacteristic
253#97—611no—
254C24—21no—
255#41—1222no—
256#41—2441no—
257#41—2444no—
258C2×Q8—611no—
259C2×Q8—1221no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4C22×D6111yescharacteristic
269C2×D4C22×D6111yescharacteristic
270C2×D4C22×D6111yescharacteristic
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4C22×D6111yescharacteristic
278SD16—2441no—
279D8—22no—
280D8—41no—
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—611no—
298C22⋊C4—611no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C42—611no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—611no—
314C23D4×D6111yescharacteristic
315Q8—1221no—
316Q8—1221no—
317Q8—2442no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—1222no—
326D4—4881no—
327D4—2442no—
328D4—2442no—
329D4#1175822412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
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×C4—2442no—
347C2×C4D4×D6111yescharacteristic
348C2×C4C23×D6111yescharacteristic
349C8—21no—
350C8—21no—
351C8—1221no—
352C8—1221no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—1221no—
366C22—1221no—
367C22—1221no—
368C22#1451980112yes—
369C22C2×D4×D6111yescharacteristic
370C4—21no—
371C4—41no—
372C4—1221no—
373C4—1221no—
374C4—1221no—
375C4—2441no—
376C4—2441no—
377C4—2441no—
378C4—2441no—
379C4C2×#1175822411yescharacteristic
380C4#1451982211yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—2441no—
386C2#1684039911yescharacteristic
387C2C2×#1451980111yescharacteristic
388C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3306
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16840412C2semidirect
2. #16840406C2semidirect
3. #16840120C2semidirect
4. #16840093C2semidirect
5. #16840079C2semidirect
6. #16840050C2semidirect
7. #16840012C2semidirect
8. #16839989C2semidirect
9. #16839975C2semidirect
10. #16839904C2semidirect
11. #16839874C2semidirect
12. #16839830C2semidirect
13. #16839760C2semidirect
14. C2×#14519698C2semidirect
15. C61×#447C2semidirect
18. C2×#11758200C22semidirect
19. C2×#11758189C22semidirect
21. #14519776C22semidirect
30. #14519748C22semidirect
33. D4×Dic61C22semidirect
36. C4⋊C4×D61C22semidirect
38. #14519709C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519702C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
49. #14519698C22semidirect
50. #14519689C22semidirect
51. #14519687C22semidirect
127. D4×C61#41semidirect
205. #447D61semidirect
210. C61#3306semidirect
329. D4#11758224semidirect