Finite Group Databasebeta

← #21456007

Subgroups — #21456007

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#16840384C211yesmaximal, characteristic, complemented
2#16840234C211yesmaximal, characteristic, complemented
3#16840101C211yesmaximal, characteristic, complemented
4#16840089C211yesmaximal, characteristic, complemented
5#16840050C211yesmaximal, characteristic, complemented
6#16840041C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839911C211yesmaximal, characteristic, complemented
10#16839897C211yesmaximal, characteristic
11#16839875C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839824C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519776C2211yescharacteristic, complemented
21#14519771—21no—
22#14519766C2211yescharacteristic, complemented
23#14519765—21no—
24#14519762—21no—
25#14519755—21no—
26#14519753C2211yescharacteristic
27#14519752C2211yescharacteristic
28C4×D244C2211yescharacteristic
29C4×D244C2211yescharacteristic, complemented
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic
35#14519734C2211yescharacteristic
36C2×#11758198—21no—
37C22⋊C4×D61—21no—
38#14519710C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65D4×D61—22no—
66D4×D61—22no—
67C2×D244—21no—
68C2×D244C2311yescharacteristic
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75SD16×C61—22no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C42×C61—21no—
83C42×C61C2311yescharacteristic
84C22⋊Dic61—21no—
85#11758201—22no—
86#11758199—22no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96#11758198D411yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61—24no—
111C22×D61—21no—
112C22×D61—81no—
113C22×D61—81no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61#4112yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—81no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—24no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—81no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—21no—
136D244—81no—
137D244#4112yes—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—81no—
141C4×D61—81no—
142C4×D61—81no—
143Dic122—81no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—22no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—22no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—84no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61C2×#4111yescharacteristic
168C4×C61C2×#4111yescharacteristic
169Dic61—21no—
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174#3118—611nomaximal, Sylow
175C2×C61—42no—
176C2×C61#52511yescharacteristic
177C2×C61#57611yescharacteristic
178C2×C61#57711yescharacteristic
179D61—41no—
180D61—42no—
181D61—81no—
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#442—611no—
193#440D6111yescharacteristic, complemented
194C4×SD16—611no—
195C4×D8—611no—
196#433—611no—
197C61#311811yescharacteristic, complemented, Sylow
198C22×D4—611no—
199C2×SD16—611no—
200C2×SD16C2×D6111yescharacteristic
201C2×D8—611no—
202C2×D8—611no—
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×Q8C2×D6111yescharacteristic, complemented
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—1221no—
217C4×D4—1221no—
218C4×D4C2×D6111yescharacteristic
219#117—611no—
220#117—611no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223#107—611no—
224#107C2×D6111yescharacteristic, complemented
225#106—611no—
226#106—611no—
227C4⋊C8—611no—
228C4⋊C8—611no—
229#103—611no—
230#103C2×D6111yescharacteristic, complemented
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236#102C2×D6111yescharacteristic
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97C2×D6111yescharacteristic, complemented
240C4×C8—611no—
241C24—1221no—
242C2×Q8—1221no—
243C2×Q8C22×D6111yescharacteristic
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1222no—
249C2×D4—1222no—
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257SD16—22no—
258SD16—1222no—
259D8—1222no—
260D8—1222no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—611no—
276C22⋊C4—611no—
277C22⋊C4—1221no—
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—21no—
287C42—611no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—21no—
291C23—611no—
292C23—1224no—
293C23—1221no—
294C23—1221no—
295C23—4881no—
296C23—4881no—
297Q8—21no—
298Q8—21no—
299Q8—4881no—
300D4—21no—
301D4—612no—
302D4—1224no—
303D4—1221no—
304D4—1221no—
305D4—1221no—
306D4—4881no—
307D4#1175822212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
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—4881no—
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—1221no—
334C22—1222no—
335C22—1221no—
336C22—1221no—
337C22—4884no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1221no—
350C4—1221no—
351C4—1221no—
352C4—2441no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4C2×#1175822211yescharacteristic
356C2—42no—
357C2—4881no—
358C2—2441no—
359C2—2442no—
360C2#1684027111yescharacteristic
361C2#1684056611yescharacteristic
362C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16840384C2semidirect
2. #16840234C2semidirect
3. #16840101C2semidirect
4. #16840089C2semidirect
5. #16840050C2semidirect
6. #16840041C2semidirect
7. #16839980C2semidirect
8. #16839979C2semidirect
9. #16839911C2semidirect
11. #16839875C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758199C2semidirect
14. #16839824C2semidirect
15. C61×#440C2semidirect
20. #14519776C22semidirect
22. #14519766C22semidirect
29. C4×D244C22semidirect
38. #14519710C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519701C22semidirect
45. #14519699C22semidirect
48. #14519697C22semidirect
51. C4×#92418C22semidirect
53. C4×Q8×C61C22semidirect
55. #107×C61C22semidirect
56. #103×C61C22semidirect
58. #97×C61C22semidirect
193. #440D61semidirect
197. C61#3118semidirect
211. C4×Q8C2×D61semidirect
224. #107C2×D61semidirect
230. #103C2×D61semidirect
239. #97C2×D61semidirect