Finite Group Databasebeta

← #21458013

Subgroups — #21458013

Order 7808.

414 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#16840464C211yesmaximal, characteristic, complemented
2#16840400C211yesmaximal, characteristic, complemented
3#16840118C211yesmaximal, characteristic, complemented
4#16840102C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16840013C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839979C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic, complemented
11D8×Dic61C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839763C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758199C2211yescharacteristic
18C2×#11758194C2211yescharacteristic, complemented
19C2×#11758189C2211yescharacteristic
20#14519770—21no—
21#14519768C2211yescharacteristic, complemented
22#14519766C2211yescharacteristic
23#14519761—21no—
24#14519760—21no—
25#14519753C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519749—21no—
28#14519749—21no—
29#14519748C2211yescharacteristic
30#14519745—21no—
31D4×Dic61—21no—
32D4×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic, complemented
34C4×C22⋊D61C2211yescharacteristic
35#14519735C2211yescharacteristic
36C2×C4⋊Dic61C2211yescharacteristic, complemented
37C2×#11758198—21no—
38#14519711C2211yescharacteristic, complemented
39#14519711C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic, complemented
52C2×#41×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60#41×C61—22no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76D4×D61—22no—
77D4×D61—41no—
78C2×D244C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80SD16×C61—41no—
81D8×C61—22no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61D411yescharacteristic
90#11758199—41no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107#11758194—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—81no—
118C22×D61C2×D411yescharacteristic
119Q8×C61—21no—
120Q8×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—42no—
125D4×C61—42no—
126D4×C61#4112yes—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—41no—
135C22⋊D61—42no—
136C22⋊D61—81no—
137C22⋊D61—81no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—21no—
148D244—21no—
149C4×D61—21no—
150C4×D61—21no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—22no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
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—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—84no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61C2×#4111yescharacteristic
176C4×C61H(5,𝔽2)11yescharacteristic
177Dic61—21no—
178Dic61—21no—
179Dic61—21no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3322—611nomaximal, Sylow
184C2×C61—42no—
185C2×C61—41no—
186C2×C61—81no—
187C2×C61#54611yescharacteristic
188C2×C61#57511yescharacteristic
189C2×C61#57611yescharacteristic
190D61—41no—
191D61—81no—
192#553—611no—
193#546—611no—
194#488—611no—
195#485—611no—
196#480—611no—
197#478—611no—
198#469—611no—
199#468—611no—
200#463—611no—
201#449D6111yescharacteristic, complemented
202#447—611no—
203C4×D8—611no—
204#436—611no—
205#418—611no—
206#417—611no—
207C61#332211yescharacteristic, complemented, Sylow
208C2×#41C2×D6111yescharacteristic
209C22×D4—611no—
210C2×SD16C2×D6111yescharacteristic, complemented
211C2×D8—611no—
212C2×D8C2×D6111yescharacteristic
213C2×M16—611no—
214C2×M16—611no—
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—1221no—
224#121—1221no—
225#121C2×D6111yescharacteristic, complemented
226#120—1221no—
227C4×D4—611no—
228C4×D4—611no—
229C4×D4—611no—
230C4×D4—1221no—
231#117—611no—
232C2×C4⋊C4—611no—
233C2×C22⋊C4—1221no—
234#107—611no—
235#107—611no—
236#106—611no—
237C4⋊C8—611no—
238#103—611no—
239#103—611no—
240#103C2×D6111yescharacteristic, complemented
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102C2×D6111yescharacteristic
248C22⋊C8—611no—
249C22⋊C8C2×D6111yescharacteristic, complemented
250C4×C8—611no—
251C24—1221no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1222no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—2441no—
264C2×D4C22×D6111yescharacteristic
265C2×D4C22×D6111yescharacteristic
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4C22×D6111yescharacteristic
272SD16—41no—
273D8—22no—
274D8—2441no—
275M16—2441no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
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⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—611no—
292C22⋊C4—611no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C42—611no—
302C42—1221no—
303C23—21no—
304C23—21no—
305C23—611no—
306C23—1221no—
307C23—4881no—
308C23—2442no—
309C23—2442no—
310C23D4×D6111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—42no—
318D4—1221no—
319D4—1221no—
320D4—4881no—
321D4—4881no—
322D4—2441no—
323D4—2442no—
324D4#1175822412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—4884no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22C2×D4×D6111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—1221no—
368C4—1221no—
369C4—1221no—
370C4—2441no—
371C4—2441no—
372C4—2441no—
373C4C2×#1175822411yescharacteristic
374C4#1451982211yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—4881no—
379C2—2441no—
380C2#1684039911yescharacteristic
381C2#1684055811yescharacteristic
382C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3322
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16840464C2semidirect
2. #16840400C2semidirect
3. #16840118C2semidirect
4. #16840102C2semidirect
5. #16840076C2semidirect
6. #16840060C2semidirect
7. #16840013C2semidirect
8. #16840005C2semidirect
9. #16839979C2semidirect
10. #16839894C2semidirect
11. D8×Dic61C2semidirect
12. #16839837C2semidirect
13. #16839765C2semidirect
14. #16839763C2semidirect
15. C61×#449C2semidirect
18. C2×#11758194C22semidirect
21. #14519768C22semidirect
33. D4×Dic61C22semidirect
36. C2×C4⋊Dic61C22semidirect
38. #14519711C22semidirect
39. #14519711C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519701C22semidirect
43. #14519701C22semidirect
48. #14519698C22semidirect
51. C8×Dic61C22semidirect
53. C2×SD16×C61C22semidirect
55. #121×C61C22semidirect
56. #103×C61C22semidirect
58. C22⋊C8×C61C22semidirect
201. #449D61semidirect
207. C61#3322semidirect
210. C2×SD16C2×D61semidirect
225. #121C2×D61semidirect
240. #103C2×D61semidirect
249. C22⋊C8C2×D61semidirect