Finite Group Databasebeta

← #21456001

Subgroups — #21456001

Order 7808.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840377C211yesmaximal, characteristic, complemented
2#16840234C211yesmaximal, characteristic, complemented
3#16840106C211yesmaximal, characteristic, complemented
4#16840084C211yesmaximal, characteristic, complemented
5#16840051C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16839976C211yesmaximal, characteristic, complemented
8#16839975C211yesmaximal, characteristic, complemented
9#16839914C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic
11#16839864C211yesmaximal, characteristic, complemented
12C4×#11758200C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839824C211yesmaximal, characteristic, complemented
15C61×#442C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519776C2211yescharacteristic, complemented
21#14519770—21no—
22#14519764C2211yescharacteristic, complemented
23#14519763—21no—
24#14519760—21no—
25#14519757C2211yescharacteristic
26#14519756—21no—
27#14519748C2211yescharacteristic
28C4×Dic122C2211yescharacteristic, complemented
29C4×D244C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic
35#14519734C2211yescharacteristic
36C2×#11758198—21no—
37C22⋊C4×D61—21no—
38#14519711C2211yescharacteristic, complemented
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67D4×D61—22no—
68D4×D61—22no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61C2311yescharacteristic
73C2×Dic122—21no—
74C2×Dic122C2311yescharacteristic
75D8×C61—22no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C42×C61C2311yescharacteristic
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87#11758200—22no—
88#11758199—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94#11758198D411yescharacteristic
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107#11758190—22no—
108C23×C61—21no—
109C23×C61—21no—
110C22×D61—21no—
111C22×D61—24no—
112C22×D61—81no—
113C22×D61—81no—
114C22×D61C2×D411yescharacteristic
115D4×C61—21no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61#4112yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—24no—
127C22⋊D61—81no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—81no—
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—21no—
136D244#4112yes—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—81no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—81no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—22no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—22no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—84no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61C2×#4111yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3118—611nomaximal, Sylow
175C2×C61—42no—
176C2×C61—81no—
177C2×C61#52511yescharacteristic
178C2×C61#57611yescharacteristic
179C2×C61#57711yescharacteristic
180D61—41no—
181D61—42no—
182#542—611no—
183#518—611no—
184#485—611no—
185#482—611no—
186#476—611no—
187#474—611no—
188#463—611no—
189#463—611no—
190#450—611no—
191#447—611no—
192#442D6111yescharacteristic, complemented
193#440—611no—
194C4×SD16—611no—
195C4×D8—611no—
196#433—611no—
197C61#311811yescharacteristic, complemented, Sylow
198C22×D4—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×D8—611no—
202C2×D8C2×D6111yescharacteristic
203C4⋊Q8—611no—
204#126—1221no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—1221no—
210#121—611no—
211C4×Q8—611no—
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—1221no—
216C4×D4—1221no—
217C4×D4C2×D6111yescharacteristic
218C4×D4C2×D6111yescharacteristic, complemented
219#117—611no—
220#117—611no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223#107—611no—
224#107—611no—
225#106—611no—
226#106C2×D6111yescharacteristic, complemented
227C4⋊C8—611no—
228C4⋊C8—611no—
229#103—611no—
230#103—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102C2×D6111yescharacteristic
236#102C2×D6111yescharacteristic, complemented
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97C2×D6111yescharacteristic, complemented
240C4×C8—611no—
241C24—1221no—
242C2×Q8—611no—
243C2×Q8—1221no—
244C2×D4—611no—
245C2×D4—1221no—
246C2×D4—1222no—
247C2×D4—1222no—
248C2×D4—1221no—
249C2×D4C22×D6111yescharacteristic
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257SD16—1222no—
258SD16—1222no—
259D8—22no—
260D8—1222no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—611no—
277C22⋊C4—611no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—611no—
287C42—1221no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—21no—
291C23—21no—
292C23—611no—
293C23—1224no—
294C23—1221no—
295C23—4881no—
296C23—4881no—
297Q8—1221no—
298Q8—1221no—
299Q8—4881no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—612no—
304D4—1224no—
305D4—1221no—
306D4—4881no—
307D4#1175822212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4D4×D6111yescharacteristic
324C2×C4D4×D6111yescharacteristic
325C2×C4C23×D6111yescharacteristic
326C8—21no—
327C8—21no—
328C8—1221no—
329C8—1221no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—1221no—
337C22—1222no—
338C22—1221no—
339C22—1221no—
340C22—4884no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—1221no—
349C4—1221no—
350C4—1221no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4C2×#1175822211yescharacteristic
356C2—42no—
357C2—81no—
358C2—2441no—
359C2—2442no—
360C2#1684027111yescharacteristic
361C2#1684056611yescharacteristic
362C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16840377C2semidirect
2. #16840234C2semidirect
3. #16840106C2semidirect
4. #16840084C2semidirect
5. #16840051C2semidirect
6. #16840040C2semidirect
7. #16839976C2semidirect
8. #16839975C2semidirect
9. #16839914C2semidirect
11. #16839864C2semidirect
12. C4×#11758200C2semidirect
13. C4×#11758199C2semidirect
14. #16839824C2semidirect
15. C61×#442C2semidirect
20. #14519776C22semidirect
22. #14519764C22semidirect
28. C4×Dic122C22semidirect
38. #14519711C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
47. #14519698C22semidirect
51. C4×#92418C22semidirect
54. C4×D4×C61C22semidirect
55. #106×C61C22semidirect
57. #102×C61C22semidirect
58. #97×C61C22semidirect
192. #442D61semidirect
197. C61#3118semidirect
218. C4×D4C2×D61semidirect
226. #106C2×D61semidirect
236. #102C2×D61semidirect
239. #97C2×D61semidirect