Finite Group Databasebeta

← #21457782

Subgroups — #21457782

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#16840416C211yesmaximal, characteristic, complemented
2#16840408C211yesmaximal, characteristic, complemented
3#16840122C211yesmaximal, characteristic, complemented
4#16840093C211yesmaximal, characteristic, complemented
5#16840081C211yesmaximal, characteristic, complemented
6#16840053C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839978C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic, complemented
11#16839898C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic, complemented
13#16839764C211yesmaximal, characteristic, complemented
14C2×#14519699C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224—21no—
18C22×D244C2211yescharacteristic
19C2×#11758190C2211yescharacteristic, complemented
20C2×D488C2211yescharacteristic
21C2×D488C2211yescharacteristic
22#14519777C2211yescharacteristic, complemented
23#14519765C2211yescharacteristic
24#14519762—21no—
25#14519761—21no—
26#14519761—21no—
27#14519757—21no—
28#14519756C2211yescharacteristic
29#14519751C2211yescharacteristic
30#14519751C2211yescharacteristic
31#14519751C2211yescharacteristic, complemented
32#14519750—21no—
33#14519745—21no—
34C4×D244C2211yescharacteristic
35C4×D244C2211yescharacteristic, complemented
36C2×C4⋊Dic61C2211yescharacteristic
37C2×C4⋊Dic61C2211yescharacteristic, complemented
38C22⋊C4×D61—21no—
39#14519709C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic, complemented
52C2×M16×C61C2211yescharacteristic, complemented
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic, complemented
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61D411yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758224—44no—
70#11758222—22no—
71#11758222—41no—
72C2×D244—22no—
73C2×D244—21no—
74C2×D244—41no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×D244C2311yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×Dic122—21no—
82C2×Dic122C2311yescharacteristic
83M16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61D411yescharacteristic
90C22⋊C4×C61D411yescharacteristic
91C22⋊C4×C61D411yescharacteristic
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107C4⋊Dic61C2311yescharacteristic
108#11758196—21no—
109D488—22no—
110D488—41no—
111#11758190—41no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—81no—
120D4×C61—22no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—42no—
147D244#4112yescomplemented
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—81no—
151Dic122—21no—
152Dic122—21no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156C8×C61—21no—
157C8×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61AGL(1,ℤ/8)12yes—
164C22×C61C22×D411yescharacteristic
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—84no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61C2×#4111yescharacteristic
180C4×C61H(5,𝔽2)11yescharacteristic
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186#3306—611nomaximal, Sylow
187C2×C61—22no—
188C2×C61—41no—
189C2×C61#54611yescharacteristic
190C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C61#57711yescharacteristic
192D61—42no—
193D61—81no—
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#435D6111yescharacteristic, complemented
208#417—611no—
209C2×#102—611no—
210C61#330611yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41—1221no—
213C22×D4—611no—
214C2×SD16—611no—
215C2×D8—611no—
216C2×D8—611no—
217C2×M16C2×D6111yescharacteristic, complemented
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×D4C2×D6111yescharacteristic
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#103—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251C22⋊C8C2×D6111yescharacteristic
252C22⋊C8C2×D6111yescharacteristic, complemented
253#97C2×D6111yescharacteristic, complemented
254C24—1221no—
255#41—1222no—
256#41—2441no—
257#41—2444no—
258C2×Q8—611no—
259C2×Q8—1221no—
260C2×D4—611no—
261C2×D4—611no—
262C2×D4—611no—
263C2×D4—1222no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—2441no—
270C2×D4D24411yescharacteristic
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4C22×D6111yescharacteristic
277C22×C4C22×D6111yescharacteristic
278SD16—2441no—
279D8—1222no—
280D8—2441no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D6111yescharacteristic
284C2×C8C22×D6111yescharacteristic
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⋊C4D24411yescharacteristic
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4D24411yescharacteristic
305C22⋊C4D24411yescharacteristic
306C42C22×D6111yescharacteristic
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—4881no—
311C23—2442no—
312C23—2442no—
313C23C2×D24411yescharacteristic
314C23C2×D24411yescharacteristic
315Q8—1221no—
316Q8—1221no—
317Q8—2442no—
318D4—22no—
319D4—612no—
320D4—1221no—
321D4—1221no—
322D4—1221no—
323D4—1221no—
324D4—1221no—
325D4—4881no—
326D4—2442no—
327D4—2442no—
328D4—2442no—
329D4—2442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4C2×D24411yescharacteristic
345C2×C4C2×D24411yescharacteristic
346C2×C4C2×D24411yescharacteristic
347C2×C4C2×D24411yescharacteristic
348C2×C4C23×D6111yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—1222no—
359C22—4884no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1451980512yes—
369C22C22×D24411yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—2441no—
375C4—2441no—
376C4—2441no—
377C4—2441no—
378C4—2441no—
379C4#41×D6111yescharacteristic
380C4#1451982211yescharacteristic
381C2—22no—
382C2—41no—
383C2—4881no—
384C2—4881no—
385C2—2442no—
386C2#1684040711yescharacteristic
387C2C2×#1451980511yescharacteristic
388C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3306
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16840416C2semidirect
2. #16840408C2semidirect
3. #16840122C2semidirect
4. #16840093C2semidirect
5. #16840081C2semidirect
6. #16840053C2semidirect
7. #16840015C2semidirect
8. #16839991C2semidirect
9. #16839978C2semidirect
10. #16839909C2semidirect
11. #16839898C2semidirect
12. #16839875C2semidirect
13. #16839764C2semidirect
14. C2×#14519699C2semidirect
15. C61×#435C2semidirect
19. C2×#11758190C22semidirect
22. #14519777C22semidirect
31. #14519751C22semidirect
35. C4×D244C22semidirect
37. C2×C4⋊Dic61C22semidirect
39. #14519709C22semidirect
40. #14519709C22semidirect
41. #14519709C22semidirect
42. #14519702C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
51. #14519699C22semidirect
52. C2×M16×C61C22semidirect
55. C4⋊C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. #97×C61C22semidirect
147. D244#41semidirect
207. #435D61semidirect
210. C61#3306semidirect
217. C2×M16C2×D61semidirect
240. C4⋊C8C2×D61semidirect
252. C22⋊C8C2×D61semidirect
253. #97C2×D61semidirect