Finite Group Databasebeta

← #21457776

Subgroups — #21457776

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#16840413C211yesmaximal, characteristic, complemented
2#16840406C211yesmaximal, characteristic, complemented
3#16840120C211yesmaximal, characteristic, complemented
4#16840092C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839976C211yesmaximal, characteristic, complemented
10#16839908C211yesmaximal, characteristic, complemented
11#16839896C211yesmaximal, characteristic, complemented
12#16839871C211yesmaximal, characteristic, complemented
13#16839833C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C2×#102×C61C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758224C2211yescharacteristic
18C2×#11758190C2211yescharacteristic, complemented
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758189C2211yescharacteristic, complemented
22#14519776C2211yescharacteristic, complemented
23#14519764C2211yescharacteristic
24#14519762—21no—
25#14519760—21no—
26#14519758—21no—
27#14519756C2211yescharacteristic
28#14519755—21no—
29#14519752C2211yescharacteristic, complemented
30#14519751C2211yescharacteristic
31#14519749—21no—
32#14519748C2211yescharacteristic
33#14519746—21no—
34D4×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic, complemented
36C4×C22⋊D61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic, complemented
38C2×C22⋊Dic61—21no—
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#102×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C24×C61—21no—
60C2×D4×C61—22no—
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73#11758224—22no—
74#11758224—41no—
75#11758222—44no—
76C2×D244—21no—
77C2×D244C2311yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122C2311yescharacteristic
83C2×C8×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61—21no—
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61D411yescharacteristic
95#11758199—22no—
96#11758199—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198D411yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190—41no—
111#11758189—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—42no—
115C23×C61—42no—
116C23×C61—81no—
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
119C22×D61C2×D411yescharacteristic
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—42no—
124D4×C61#4112yescomplemented
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—42no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—22no—
133C22⋊D61—42no—
134C22⋊D61—42no—
135C22⋊D61—81no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61—81no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146D244—42no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—42no—
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—84no—
167C22×C61AGL(1,ℤ/8)12yes—
168C22×C61C22×D411yescharacteristic
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61C2×#4111yescharacteristic
179C4×C61H(5,𝔽2)11yescharacteristic
180Dic61—21no—
181Dic61—21no—
182Dic61—21no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186#3306—611nomaximal, Sylow
187C2×C61—22no—
188C2×C61—42no—
189C2×C61—81no—
190C2×C61#54611yescharacteristic
191C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C61#57711yescharacteristic
193D61—41no—
194D61—81no—
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#447—611no—
206#442—611no—
207#435—611no—
208#417—611no—
209C2×#102D6111yescharacteristic, complemented
210C61#330611yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41—1221no—
213C22×D4C2×D6111yescharacteristic
214C2×SD16—611no—
215C2×D8—611no—
216C2×D8—611no—
217C2×M16—611no—
218C22×C8C2×D6111yescharacteristic
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—611no—
229#121—1221no—
230#120—1221no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4C2×D6111yescharacteristic
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#102C2×D6111yescharacteristic
248#102C2×D6111yescharacteristic
249#102C2×D6111yescharacteristic
250#102C2×D6111yescharacteristic
251C22⋊C8—611no—
252C22⋊C8—611no—
253#97—611no—
254C24—21no—
255#41—1222no—
256#41—2444no—
257#41—2441no—
258C2×Q8—611no—
259C2×Q8—1221no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4C22×D6111yescharacteristic
270C2×D4C22×D6111yescharacteristic
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4C22×D6111yescharacteristic
278SD16—2441no—
279D8—1222no—
280D8—2441no—
281M16—2441no—
282C2×C8—41no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8C22×D6111yescharacteristic
286C2×C8C22×D6111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4C22×D6111yescharacteristic
295C4⋊C4C22×D6111yescharacteristic
296C22⋊C4—611no—
297C22⋊C4—611no—
298C22⋊C4—1221no—
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—42no—
310C23—42no—
311C23—81no—
312C23—611no—
313C23—1221no—
314C23D4×D6111yescharacteristic
315Q8—1221no—
316Q8—1221no—
317Q8—2442no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—1222no—
323D4—1221no—
324D4—1221no—
325D4—4881no—
326D4—2442no—
327D4—2442no—
328D4—2442no—
329D4#1175822212yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
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—84no—
362C22—1221no—
363C22—1221no—
364C22—1221no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1451980112yes—
369C22C2×D4×D6111yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—1221no—
374C4—1221no—
375C4—1221no—
376C4—2441no—
377C4—2441no—
378C4—2441no—
379C4C2×#1175822211yescharacteristic
380C4#1451982211yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—4881no—
385C2—2441no—
386C2#1684040211yescharacteristic
387C2C2×#1451980111yescharacteristic
388C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#102×C61C2
socleC22×C61C22×D4
hypercenterC2×#102D61
hypocenterC61#3306
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #16840413C2semidirect
2. #16840406C2semidirect
3. #16840120C2semidirect
4. #16840092C2semidirect
5. #16840079C2semidirect
6. #16840050C2semidirect
7. #16840014C2semidirect
8. #16839991C2semidirect
9. #16839976C2semidirect
10. #16839908C2semidirect
11. #16839896C2semidirect
12. #16839871C2semidirect
13. #16839833C2semidirect
14. #16839760C2semidirect
15. C2×#102×C61C2semidirect
18. C2×#11758190C22semidirect
21. C2×#11758189C22semidirect
22. #14519776C22semidirect
29. #14519752C22semidirect
35. #14519739C22semidirect
37. C4⋊C4×D61C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519708C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
45. #14519700C22semidirect
46. #14519699C22semidirect
50. #14519689C22semidirect
51. #14519687C22semidirect
124. D4×C61#41semidirect
209. C2×#102D61semidirect
210. C61#3306semidirect
329. D4#11758222semidirect