Finite Group Databasebeta

← #21455874

Subgroups — #21455874

Order 7808.

434 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840307C211yesmaximal, characteristic, complemented
2#16840230C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840056C211yesmaximal, characteristic, complemented
5#16840051C211yesmaximal, characteristic, complemented
6#16839961C211yesmaximal, characteristic, complemented
7#16839956C211yesmaximal, characteristic, complemented
8#16839909C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839853C211yesmaximal, characteristic, complemented
11#16839849C211yesmaximal, characteristic, complemented
12#16839844C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839812C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224—21no—
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519763—21no—
25#14519751C2211yescharacteristic
26#14519749—21no—
27#14519742C2211yescharacteristic
28#14519742C2211yescharacteristic
29D4×Dic61C2211yescharacteristic
30#14519739C2211yescharacteristic
31#14519739C2211yescharacteristic
32#14519739C2211yescharacteristic
33#14519737—21no—
34#14519737—21no—
35#14519737—21no—
36#14519734—21no—
37C2×C4×Dic61C2211yescharacteristic
38C42×D61—21no—
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61D411yescharacteristic
68C22×Dic61D411yescharacteristic
69#11758224—44no—
70#11758222—22no—
71#11758222—22no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×Dic122—21no—
79C2×Dic122C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61—21no—
88C22⋊Dic61—21no—
89#11758200—22no—
90#11758199—22no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61D411yescharacteristic
102C4×Dic61D411yescharacteristic
103C4×Dic61C2311yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108#11758190—22no—
109C23×C61—21no—
110C23×C61C2×D411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113D4×C61—21no—
114D4×C61—21no—
115D4×C61—42no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2411yescharacteristic
123C22⋊D61—24no—
124C22⋊D61—42no—
125C22⋊D61—42no—
126C22⋊D61—42no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—21no—
131C2×Dic61—42no—
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136D244—21no—
137D244—21no—
138D244—21no—
139D244#4112yescomplemented
140C4×D61—24no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—42no—
144Dic122—21no—
145Dic122—42no—
146Dic122#4112yescomplemented
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—22no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61C2×#4111yescharacteristic
170Dic61—22no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61#13512yes—
175Dic61AGL(1,ℤ/8)12yes—
176#3106—611nomaximal, Sylow
177C2×C61—41no—
178C2×C61—81no—
179C2×C61#52511yescharacteristic
180C2×C61C2×#13511yescharacteristic
181C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
182D61—42no—
183D61—81no—
184#532—611no—
185C4×#41—611no—
186#482—611no—
187#482D6111yescharacteristic, complemented
188#477—611no—
189#476—611no—
190#460—611no—
191#459—611no—
192#449—611no—
193#449—611no—
194C4×SD16—611no—
195C4×SD16—611no—
196C4×D8—611no—
197C4×D8—611no—
198#431—611no—
199C61#310611yescharacteristic, complemented, Sylow
200C2×#41—611no—
201C2×#41—1221no—
202C2×SD16—611no—
203C2×SD16—611no—
204C2×D8—611no—
205C2×D8—611no—
206C4⋊Q8—611no—
207#127—611no—
208#124—1221no—
209#121—611no—
210#121—1221no—
211#121C2×D6111yescharacteristic
212C4×Q8—611no—
213C4×Q8—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—611no—
217C4×D4—611no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4—1221no—
221#117—1221no—
222#117C2×D6111yescharacteristic
223C2×C42—611no—
224C2×C42—1221no—
225#107—611no—
226#107C2×D6111yescharacteristic
227#106—611no—
228#106C2×D6111yescharacteristic
229C4⋊C8—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237#102C2×D6111yescharacteristic
238#102C2×D6111yescharacteristic
239C22⋊C8—611no—
240C22⋊C8C2×D6111yescharacteristic
241C4×C8—611no—
242C4×C8—611no—
243#41—1222no—
244#41—1222no—
245#41—2444no—
246C2×Q8—611no—
247C2×Q8—1221no—
248C2×D4—21no—
249C2×D4—611no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4C22×D6111yescharacteristic
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4C22×D6111yescharacteristic
264SD16—1222no—
265SD16—1222no—
266D8—1222no—
267D8—1222no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—611no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4C22×D6111yescharacteristic
277C4⋊C4C22×D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—21no—
287C42—611no—
288C42—611no—
289C42—611no—
290C42—611no—
291C42—1221no—
292C42—1221no—
293C23—21no—
294C23—1221no—
295C23—1221no—
296C23D4×D6111yescharacteristic
297Q8—612no—
298Q8—1221no—
299Q8—2442no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—612no—
304D4—1224no—
305D4—1221no—
306D4—1221no—
307D4—1221no—
308D4—2442no—
309D4—2442no—
310D4—2442no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—1224no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4D4×D6111yescharacteristic
330C2×C4C23×D6111yescharacteristic
331C8—21no—
332C8—21no—
333C8—1221no—
334C8—1221no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1222no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—612no—
353C4—612no—
354C4—1222no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4#41×D6111yescharacteristic
359C4#41×D6111yescharacteristic
360C2—41no—
361C2—81no—
362C2—4881no—
363C2—2442no—
364C2#1684027011yescharacteristic
365C2#135×D6111yescharacteristic
366C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3106
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840307C2semidirect
2. #16840230C2semidirect
3. #16840086C2semidirect
4. #16840056C2semidirect
5. #16840051C2semidirect
6. #16839961C2semidirect
7. #16839956C2semidirect
8. #16839909C2semidirect
9. #16839905C2semidirect
10. #16839853C2semidirect
11. #16839849C2semidirect
12. #16839844C2semidirect
13. #16839842C2semidirect
14. #16839812C2semidirect
15. C61×#482C2semidirect
139. D244#41semidirect
146. Dic122#41semidirect
187. #482D61semidirect
199. C61#3106semidirect