Finite Group Databasebeta

← #21457708

Subgroups — #21457708

Order 7808.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840452C211yesmaximal, characteristic, complemented
2#16840421C211yesmaximal, characteristic
3#16840117C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840070C211yesmaximal, characteristic, complemented
7#16840003C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839985C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839920C211yesmaximal, characteristic, complemented
12C4×Dic244C211yesmaximal, characteristic, complemented
13#16839759C211yesmaximal, characteristic, complemented
14C2×#14519702C211yesmaximal, characteristic, complemented
15C8×D4×C61C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×Dic244C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21#14519770—21no—
22#14519769C2211yescharacteristic
23#14519767—21no—
24#14519765C2211yescharacteristic
25#14519763—21no—
26#14519758—21no—
27#14519756C2211yescharacteristic
28#14519756C2211yescharacteristic
29#14519756C2211yescharacteristic
30#14519755—21no—
31#14519751C2211yescharacteristic
32#14519749—21no—
33C4×Dic122C2211yescharacteristic
34C4×Dic122C2211yescharacteristic
35#14519737—21no—
36#14519736C2211yescharacteristic
37#14519733—21no—
38C2×C4⋊Dic61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C22×C8×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×D4×C61D411yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66#11758222—22no—
67#11758222—41no—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×Dic122—22no—
71C2×Dic122—21no—
72C2×Dic122—41no—
73C2×Dic122C2311yescharacteristic
74C2×Dic122C2311yescharacteristic
75C2×Dic122C2311yescharacteristic
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61D411yescharacteristic
83C22⋊C4×C61D411yescharacteristic
84C22⋊C4×C61D411yescharacteristic
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108Dic244—22no—
109Dic244—41no—
110#11758190—41no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114D4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—42no—
125C22⋊D61—42no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135D244—21no—
136D244—21no—
137C4×D61—42no—
138Dic122—21no—
139Dic122—21no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—42no—
144Dic122#4112yes—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—21no—
148C8×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61#13512yes—
155C22×C61C22×D411yescharacteristic
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61C2×#4111yescharacteristic
164C4×C61H(5,𝔽2)11yescharacteristic
165Dic61—22no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3300—611nomaximal, Sylow
173C2×C61—22no—
174C2×C61—41no—
175C2×C61#54611yescharacteristic
176C2×C61C2×#13511yescharacteristic
177C2×C61#57811yescharacteristic
178D61—81no—
179#552—611no—
180#548—611no—
181#488—611no—
182#485—611no—
183#480—611no—
184#479—611no—
185#467—611no—
186#465—611no—
187#464—611no—
188#452—611no—
189#451—611no—
190C4×Q16—611no—
191C8×D4D6111yescharacteristic, complemented
192#416—611no—
193C2×#103—611no—
194C61#330011yescharacteristic, complemented, Sylow
195C2×#41—611no—
196C22×Q8—611no—
197C2×Q16—611no—
198C2×Q16—611no—
199C2×SD16—611no—
200C22×C8C2×D6111yescharacteristic
201C22×C8C2×D6111yescharacteristic
202#126—1221no—
203#125—611no—
204#125—1221no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212#121—611no—
213#121—1221no—
214C4×Q8—611no—
215C4×Q8—611no—
216C4×D4—1221no—
217C4×D4C2×D6111yescharacteristic
218#117—611no—
219#117—1221no—
220C2×C4⋊C4—611no—
221#107—611no—
222#107—611no—
223#106—611no—
224C4⋊C8C2×D6111yescharacteristic
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235C22⋊C8C2×D6111yescharacteristic
236C22⋊C8C2×D6111yescharacteristic
237C4×C8C2×D6111yescharacteristic
238#41—1222no—
239#41—2441no—
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—611no—
243C2×Q8—1222no—
244C2×Q8—1221no—
245C2×Q8—2441no—
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4D24411yescharacteristic
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255Q16—1222no—
256Q16—2441no—
257SD16—2441no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4D24411yescharacteristic
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4D24411yescharacteristic
285C22⋊C4D24411yescharacteristic
286C42—1221no—
287C42—1221no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—1221no—
291C23C2×D24411yescharacteristic
292C23C2×D24411yescharacteristic
293Q8—612no—
294Q8—1221no—
295Q8—1221no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299Q8—2442no—
300D4—22no—
301D4—1221no—
302D4—1221no—
303D4—2442no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4C2×D24411yescharacteristic
320C2×C4C2×D24411yescharacteristic
321C2×C4C2×D24411yescharacteristic
322C2×C4C2×D24411yescharacteristic
323C2×C4C23×D6111yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22#1451979912yes—
337C22C22×D24411yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—1222no—
343C4—2441no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4#41×D6111yescharacteristic
350C4#1451982211yescharacteristic
351C2—22no—
352C2—41no—
353C2—4881no—
354C2#1684040711yescharacteristic
355C2C2×#1451979911yescharacteristic
356C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC8×D4×C61C2
socleC22×C61C22×D4
hypercenterC8×D4D61
hypocenterC61#3300
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #16840452C2semidirect
3. #16840117C2semidirect
4. #16840104C2semidirect
5. #16840076C2semidirect
6. #16840070C2semidirect
7. #16840003C2semidirect
8. #16839991C2semidirect
9. #16839985C2semidirect
10. #16839926C2semidirect
11. #16839920C2semidirect
12. C4×Dic244C2semidirect
13. #16839759C2semidirect
14. C2×#14519702C2semidirect
15. C8×D4×C61C2semidirect
191. C8×D4D61semidirect
194. C61#3300semidirect