Finite Group Databasebeta

← #21456003

Subgroups — #21456003

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#16840383C211yesmaximal, characteristic, complemented
2#16840103C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840052C211yesmaximal, characteristic, complemented
5#16840042C211yesmaximal, characteristic, complemented
6#16839977C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839913C211yesmaximal, characteristic, complemented
9#16839896C211yesmaximal, characteristic
10#16839872C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12C4×#11758200C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#518C211yesmaximal, characteristic, complemented
16C2×#11758200C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519777C2211yescharacteristic, complemented
21#14519772—21no—
22#14519765C2211yescharacteristic, complemented
23#14519763—21no—
24#14519759—21no—
25#14519756C2211yescharacteristic
26#14519755—21no—
27#14519751C2211yescharacteristic
28C4×Dic122C2211yescharacteristic, complemented
29C4×D244C2211yescharacteristic, complemented
30#14519710C2211yescharacteristic, complemented
31#14519710C2211yescharacteristic, complemented
32#14519708C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35C4⋊#92418C2211yescharacteristic, complemented
36#14519700C2211yescharacteristic, complemented
37#14519700C2211yescharacteristic, complemented
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic, complemented
43#14519697C2211yescharacteristic, complemented
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic, complemented
47C4×#92418C2211yescharacteristic, complemented
48C22×D4×C61C2211yescharacteristic
49C4×D4×C61—21no—
50C4×D4×C61—21no—
51C4×D4×C61C2211yescharacteristic
52C4×D4×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#117×C61C2211yescharacteristic
56#117×C61C2211yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C24×C61—21no—
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×Dic122—21no—
74C2×Dic122C2311yescharacteristic
75C4⋊C4×C61D411yescharacteristic
76C4⋊C4×C61D411yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61D411yescharacteristic
85C22⋊C4×C61D411yescharacteristic
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90#11758200—22no—
91#11758200—22no—
92#11758199—22no—
93#11758199—22no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—24no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—81no—
112C23×C61—81no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115D4×C61—24no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61#4112yes—
119D4×C61#4112yes—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138D244—21no—
139D244—21no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—81no—
144#92418—21no—
145#92418—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—84no—
158C22×C61C22×D411yescharacteristic
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61C2×#4111yescharacteristic
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3118—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61—42no—
177C2×C61—42no—
178C2×C61#52511yescharacteristic
179C2×C61#57611yescharacteristic
180C2×C61#57711yescharacteristic
181D61—81no—
182#542—611no—
183#518D6111yescharacteristic, complemented
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#440—611no—
194C4×SD16—611no—
195C4×D8—611no—
196#433—611no—
197C61#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D6111yescharacteristic
199C2×SD16—611no—
200C2×SD16—611no—
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×Q8—611no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—611no—
215C4×D4C2×D6111yescharacteristic
216C4×D4C2×D6111yescharacteristic
217C4×D4C2×D6111yescharacteristic
218C4×D4C2×D6111yescharacteristic
219#117C2×D6111yescharacteristic
220#117C2×D6111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—611no—
224#107—611no—
225#106—611no—
226#106—611no—
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#102—611no—
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97—611no—
240C4×C8—611no—
241C24—21no—
242C2×Q8—611no—
243C2×Q8—1221no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4C22×D6111yescharacteristic
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4C22×D6111yescharacteristic
257SD16—1222no—
258SD16—1222no—
259D8—1222no—
260D8—1222no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4C22⋊D6111yescharacteristic
271C4⋊C4C22⋊D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4C22⋊D6111yescharacteristic
285C22⋊C4C22⋊D6111yescharacteristic
286C42—21no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C42C22×D6111yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—1221no—
296C23C2×C22⋊D6111yescharacteristic
297Q8—1221no—
298Q8—1221no—
299Q8—4881no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—1221no—
304D4—1221no—
305D4—4881no—
306D4#1175822212yes—
307D4#1175822212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—4881no—
320C2×C4C2×C22⋊D6111yescharacteristic
321C2×C4C2×C22⋊D6111yescharacteristic
322C2×C4C2×C22⋊D6111yescharacteristic
323C2×C4C2×C22⋊D6111yescharacteristic
324C2×C4C2×C22⋊D6111yescharacteristic
325C2×C4C23×D6111yescharacteristic
326C8—1221no—
327C8—1221no—
328C8—1221no—
329C8—1221no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C22×C22⋊D6111yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4C2×#1175822211yescharacteristic
355C4C2×#1175822211yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—4881no—
360C2#1684027311yescharacteristic
361C2#1684056511yescharacteristic
362C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#518C2
socleC22×C61C22×D4
hypercenter#518D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840103C2semidirect
3. #16840086C2semidirect
4. #16840052C2semidirect
5. #16840042C2semidirect
6. #16839977C2semidirect
7. #16839977C2semidirect
8. #16839913C2semidirect
10. #16839872C2semidirect
11. #16839862C2semidirect
12. C4×#11758200C2semidirect
13. C4×#11758199C2semidirect
14. #16839823C2semidirect
15. C61×#518C2semidirect
20. #14519777C22semidirect
22. #14519765C22semidirect
28. C4×Dic122C22semidirect
29. C4×D244C22semidirect
30. #14519710C22semidirect
31. #14519710C22semidirect
32. #14519708C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. C4⋊#92418C22semidirect
36. #14519700C22semidirect
37. #14519700C22semidirect
42. #14519697C22semidirect
43. #14519697C22semidirect
46. #14519688C22semidirect
47. C4×#92418C22semidirect
183. #518D61semidirect
197. C61#3118semidirect