Finite Group Databasebeta

← #21458011

Subgroups — #21458011

Order 7808.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840476C211yesmaximal, characteristic, complemented
2#16840422C211yesmaximal, characteristic, complemented
3#16840123C211yesmaximal, characteristic, complemented
4#16840100C211yesmaximal, characteristic, complemented
5#16840088C211yesmaximal, characteristic, complemented
6#16840046C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839899C211yesmaximal, characteristic, complemented
11#16839859C211yesmaximal, characteristic, complemented
12#16839833C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#16839759C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519766C2211yescharacteristic
23#14519764—21no—
24#14519763—21no—
25#14519763—21no—
26#14519755—21no—
27#14519752C2211yescharacteristic
28#14519750—21no—
29#14519749—21no—
30#14519748C2211yescharacteristic
31#14519742C2211yescharacteristic
32D4×Dic61C2211yescharacteristic
33#14519739—21no—
34C4×C22⋊D61C2211yescharacteristic
35#14519736C2211yescharacteristic
36#14519735C2211yescharacteristic
37#14519733—21no—
38#14519710C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C22×Dic61—21no—
67Q8×D61—22no—
68Q8×D61—41no—
69#11758222—22no—
70#11758222—41no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122C2311yescharacteristic
79SD16×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61D411yescharacteristic
92#11758200—22no—
93#11758199—41no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—81no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—41no—
128C22⋊D61—42no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139D244—42no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—42no—
143C4×D61—42no—
144Dic122—21no—
145Dic122—42no—
146Dic122—81no—
147Dic122#4112yes—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—22no—
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177#3321—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61—81no—
180C2×C61#54611yescharacteristic
181C2×C61#57511yescharacteristic
182C2×C61#57711yescharacteristic
183D61—41no—
184D61—81no—
185#555—611no—
186#548—611no—
187#489—611no—
188#485—611no—
189#482—611no—
190#475—611no—
191#469—611no—
192#465D6111yescharacteristic, complemented
193#463—611no—
194#449—611no—
195#448—611no—
196#440—611no—
197#435—611no—
198#419—611no—
199#416—611no—
200C61#332111yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C22×Q8—611no—
203C2×SD16—611no—
204C2×SD16C2×D6111yescharacteristic
205C2×D8—611no—
206C2×M16—611no—
207C22×C8C2×D6111yescharacteristic
208C4⋊Q8—611no—
209#124—611no—
210#124—1221no—
211#124—1221no—
212#124—1221no—
213C22⋊Q8—1221no—
214C22⋊Q8C2×D6111yescharacteristic
215#121—611no—
216#121—611no—
217#121—1221no—
218#121—1221no—
219#121C2×D6111yescharacteristic
220C4×Q8—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—1221no—
224#117—611no—
225#117—611no—
226#117—1221no—
227#107—611no—
228#106—611no—
229#106C2×D6111yescharacteristic
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103C2×D6111yescharacteristic
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241C22⋊C8—611no—
242C22⋊C8—611no—
243#97—611no—
244#41—1222no—
245#41—2441no—
246C2×Q8—611no—
247C2×Q8—1221no—
248C2×Q8—1221no—
249C2×Q8—1222no—
250C2×Q8—2441no—
251C2×Q8C22×D6111yescharacteristic
252C2×D4—21no—
253C2×D4—611no—
254C2×D4—611no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4C22×D6111yescharacteristic
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4C22×D6111yescharacteristic
264SD16—41no—
265SD16—1222no—
266D8—2441no—
267M16—2441no—
268C2×C8—41no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—611no—
284C22⋊C4—611no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C42—611no—
293C42—1221no—
294C42—1221no—
295C42—1221no—
296C23—21no—
297C23—611no—
298C23—1221no—
299C23D4×D6111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—612no—
303Q8—1221no—
304Q8—4881no—
305Q8—2442no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—1221no—
310D4—1221no—
311D4—4881no—
312D4—2442no—
313D4—2441no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4D4×D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—1221no—
336C8—1221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—1221no—
355C4—1221no—
356C4—1221no—
357C4—1222no—
358C4—2441no—
359C4—2441no—
360C4#41×D6111yescharacteristic
361C4#1451982211yescharacteristic
362C2—41no—
363C2—81no—
364C2—4881no—
365C2—2441no—
366C2#1684040111yescharacteristic
367C2#1684055911yescharacteristic
368C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3321
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #16840476C2semidirect
2. #16840422C2semidirect
3. #16840123C2semidirect
4. #16840100C2semidirect
5. #16840088C2semidirect
6. #16840046C2semidirect
7. #16840014C2semidirect
8. #16839979C2semidirect
9. #16839905C2semidirect
10. #16839899C2semidirect
11. #16839859C2semidirect
12. #16839833C2semidirect
13. #16839769C2semidirect
14. #16839759C2semidirect
15. C61×#465C2semidirect
192. #465D61semidirect
200. C61#3321semidirect