Finite Group Databasebeta

← #21457671

Subgroups — #21457671

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic, complemented
2#16840408C211yesmaximal, characteristic, complemented
3#16840117C211yesmaximal, characteristic, complemented
4#16840098C211yesmaximal, characteristic, complemented
5#16840087C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16839998C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839978C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic, complemented
11#16839898C211yesmaximal, characteristic, complemented
12C4×D488C211yesmaximal, characteristic, complemented
13#16839759C211yesmaximal, characteristic, complemented
14C2×#14519699C211yesmaximal, characteristic, complemented
15C8×D4×C61C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×#11758190C2211yescharacteristic, complemented
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21#14519772—21no—
22#14519769C2211yescharacteristic, complemented
23#14519765C2211yescharacteristic
24#14519762—21no—
25#14519759—21no—
26#14519756C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519751C2211yescharacteristic, complemented
30#14519750—21no—
31#14519749—21no—
32#14519745—21no—
33C4×D244C2211yescharacteristic
34C4×D244C2211yescharacteristic, complemented
35#14519737—21no—
36#14519736C2211yescharacteristic, complemented
37C2×C4⋊Dic61C2211yescharacteristic
38C22⋊C4×D61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519711C2211yescharacteristic, 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
52C22×C8×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic, complemented
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic, complemented
58C4×C8×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—
68#11758222—22no—
69#11758222—41no—
70C2×D244—22no—
71C2×D244—21no—
72C2×D244—41no—
73C2×D244C2311yescharacteristic
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×Dic122C2311yescharacteristic
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61D411yescharacteristic
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61C2311yescharacteristic
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108D488—22no—
109D488—41no—
110#11758190—41no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—81no—
119D4×C61—22no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—42no—
130C22⋊D61—42no—
131C22⋊D61—81no—
132C22⋊D61—81no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—81no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—42no—
145D244#4112yes—
146C4×D61—42no—
147C4×D61—81no—
148C4×D61—81no—
149Dic122—21no—
150Dic122—21no—
151C8×C61—21no—
152C8×C61—21no—
153C8×C61—21no—
154C8×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#13512yes—
161C22×C61C22×D411yescharacteristic
162C2×D61—22no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—84no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61C2×#4111yescharacteristic
177C4×C61H(5,𝔽2)11yescharacteristic
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3297—611nomaximal, Sylow
184C2×C61—22no—
185C2×C61—41no—
186C2×C61#54611yescharacteristic
187C2×C61C2×#13511yescharacteristic
188C2×C61#57611yescharacteristic
189D61—42no—
190D61—81no—
191D61—81no—
192#553—611no—
193#546—611no—
194#488—611no—
195#484—611no—
196#482—611no—
197#478—611no—
198#466—611no—
199#465—611no—
200#463—611no—
201#449—611no—
202#447—611no—
203C4×D8—611no—
204C8×D4D6111yescharacteristic, complemented
205#416—611no—
206C2×#102—611no—
207C61#329711yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C22×D4—611no—
210C2×SD16—611no—
211C2×D8—611no—
212C2×D8—611no—
213C22×C8C2×D6111yescharacteristic
214C22×C8C2×D6111yescharacteristic, complemented
215#126—1221no—
216#125—611no—
217#124—611no—
218#123—1221no—
219#123—1221no—
220C22⋊Q8—611no—
221#121—611no—
222#121—611no—
223#121—611no—
224#121—1221no—
225#121—1221no—
226#120—1221no—
227C4×D4—611no—
228C4×D4—611no—
229C4×D4—1221no—
230C4×D4C2×D6111yescharacteristic
231#117—611no—
232C2×C4⋊C4—611no—
233C2×C22⋊C4—1221no—
234#107—611no—
235#107—611no—
236#106—611no—
237C4⋊C8C2×D6111yescharacteristic, complemented
238#103—611no—
239#103—611no—
240#103—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248C22⋊C8C2×D6111yescharacteristic
249C22⋊C8C2×D6111yescharacteristic, complemented
250C4×C8C2×D6111yescharacteristic, complemented
251C24—1221no—
252#41—1222no—
253#41—2441no—
254C2×Q8—611no—
255C2×D4—611no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1222no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—2441no—
265C2×D4D24411yescharacteristic
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272SD16—2441no—
273D8—1222no—
274D8—2441no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4D24411yescharacteristic
290C22⋊C4—1221no—
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⋊C4D24411yescharacteristic
300C22⋊C4D24411yescharacteristic
301C42—1221no—
302C42C22×D6111yescharacteristic
303C23—1221no—
304C23—1221no—
305C23—1221no—
306C23—4881no—
307C23—2442no—
308C23—2442no—
309C23C2×D24411yescharacteristic
310C23C2×D24411yescharacteristic
311Q8—1221no—
312Q8—1221no—
313D4—22no—
314D4—612no—
315D4—1221no—
316D4—1221no—
317D4—1221no—
318D4—1221no—
319D4—1221no—
320D4—4881no—
321D4—4881no—
322D4—2442no—
323D4—2442no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4C2×D24411yescharacteristic
339C2×C4C2×D24411yescharacteristic
340C2×C4C2×D24411yescharacteristic
341C2×C4C2×D24411yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—1222no—
353C22—4884no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22#1451979912yes—
363C22C22×D24411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4—2441no—
372C4—2441no—
373C4#41×D6111yescharacteristic
374C4#1451982211yescharacteristic
375C2—22no—
376C2—41no—
377C2—4881no—
378C2—4881no—
379C2—2442no—
380C2#1684040711yescharacteristic
381C2C2×#1451979911yescharacteristic
382C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC8×D4×C61C2
socleC22×C61C22×D4
hypercenterC8×D4D61
hypocenterC61#3297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #16840458C2semidirect
2. #16840408C2semidirect
3. #16840117C2semidirect
4. #16840098C2semidirect
5. #16840087C2semidirect
6. #16840063C2semidirect
7. #16839998C2semidirect
8. #16839991C2semidirect
9. #16839978C2semidirect
10. #16839909C2semidirect
11. #16839898C2semidirect
12. C4×D488C2semidirect
13. #16839759C2semidirect
14. C2×#14519699C2semidirect
15. C8×D4×C61C2semidirect
18. C2×#11758190C22semidirect
22. #14519769C22semidirect
29. #14519751C22semidirect
34. C4×D244C22semidirect
36. #14519736C22semidirect
39. #14519711C22semidirect
40. #14519711C22semidirect
41. #14519709C22semidirect
42. #14519702C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
51. #14519699C22semidirect
53. C22×C8×C61C22semidirect
55. C4⋊C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. C4×C8×C61C22semidirect
204. C8×D4D61semidirect
207. C61#3297semidirect
214. C22×C8C2×D61semidirect
237. C4⋊C8C2×D61semidirect
249. C22⋊C8C2×D61semidirect
250. C4×C8C2×D61semidirect