Finite Group Databasebeta

← #21457883

Subgroups — #21457883

Order 7808.

380 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#16840480C211yesmaximal, characteristic, complemented
2#16840422C211yesmaximal, characteristic
3#16840123C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic, complemented
5#16840056C211yesmaximal, characteristic, complemented
6#16840009C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839987C211yesmaximal, characteristic, complemented
9#16839926C211yesmaximal, characteristic, complemented
10#16839919C211yesmaximal, characteristic, complemented
11#16839868C211yesmaximal, characteristic, complemented
12#16839830C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#16839756C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519776C2211yescharacteristic
24#14519771—21no—
25#14519770—21no—
26#14519766C2211yescharacteristic
27#14519763—21no—
28#14519763—21no—
29#14519757C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519755—21no—
32#14519752C2211yescharacteristic
33#14519750—21no—
34C4×Dic122—21no—
35#14519742C2211yescharacteristic
36#14519742C2211yescharacteristic
37#14519739—21no—
38C4×C22⋊D61C2211yescharacteristic
39#14519735C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×C22⋊D61D411yescharacteristic
63Q8×D61—22no—
64Q8×D61—41no—
65#11758222—22no—
66#11758222—41no—
67C2×D244—21no—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122C2311yescharacteristic
75C2×Dic122C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C42×C61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61D411yescharacteristic
87#11758202—41no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108Dic244—22no—
109#11758190—41no—
110#11758189—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—41no—
125C22⋊D61—42no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—21no—
133D244—21no—
134D244—42no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—42no—
138C4×D61—42no—
139Dic122—21no—
140Dic122—21no—
141Dic122—21no—
142Dic122—42no—
143Dic122—42no—
144Dic122#4112yes—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C61H(5,𝔽2)11yescharacteristic
166Dic61—22no—
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172#3313—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61#54611yescharacteristic
175C2×C61#57511yescharacteristic
176C2×C61#57811yescharacteristic
177D61—41no—
178D61—81no—
179#556—611no—
180#548—611no—
181#489—611no—
182#485D6111yescharacteristic, complemented
183#482—611no—
184#477—611no—
185#468—611no—
186#467—611no—
187#464—611no—
188#452—611no—
189#451—611no—
190#441—611no—
191#435—611no—
192#419—611no—
193#416—611no—
194C61#331311yescharacteristic, complemented, Sylow
195C2×#41—611no—
196C22×Q8—611no—
197C2×Q16—611no—
198C2×Q16—611no—
199C2×SD16—611no—
200C2×M16—611no—
201C22×C8—611no—
202C4⋊Q8—611no—
203#126—1221no—
204#126—1221no—
205#124—611no—
206#124—1221no—
207#124—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—611no—
210C22⋊Q8—1221no—
211C22⋊Q8C2×D6111yescharacteristic
212#121—611no—
213#121—1221no—
214C4×Q8—611no—
215C4×Q8—611no—
216C4×Q8—1221no—
217C4×D4—611no—
218C4×D4—1221no—
219#117—611no—
220#117C2×D6111yescharacteristic
221#107—611no—
222#107C2×D6111yescharacteristic
223#106C2×D6111yescharacteristic
224C4⋊C8—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#103C2×D6111yescharacteristic
232#102—611no—
233#102—611no—
234#102—611no—
235C22⋊C8—611no—
236C22⋊C8C2×D6111yescharacteristic
237#97—611no—
238#41—1222no—
239#41—2441no—
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—1222no—
245C2×Q8—2441no—
246C2×Q8C22×D6111yescharacteristic
247C2×D4—611no—
248C2×D4—611no—
249C2×D4—1221no—
250C2×D4—1221no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4C22×D6111yescharacteristic
255Q16—1222no—
256Q16—2441no—
257SD16—2441no—
258M16—2441no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—2441no—
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—611no—
278C22⋊C4—611no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C42—21no—
286C42—611no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C23—611no—
291C23—1221no—
292C23D4×D6111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—612no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299Q8—2442no—
300Q8—2442no—
301D4—1221no—
302D4—1221no—
303D4—2442no—
304D4—2441no—
305D4—2442no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4D4×D6111yescharacteristic
323C2×C4C23×D6111yescharacteristic
324C8—21no—
325C8—21no—
326C8—1221no—
327C8—1221no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—1221no—
332C22—1221no—
333C22—1221no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1221no—
344C4—1221no—
345C4—1221no—
346C4—1222no—
347C4—2441no—
348C4—2441no—
349C4#41×D6111yescharacteristic
350C4#1451982311yescharacteristic
351C2—41no—
352C2—4881no—
353C2—2441no—
354C2#1684040411yescharacteristic
355C2#1684055911yescharacteristic
356C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3313
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16840480C2semidirect
3. #16840123C2semidirect
4. #16840088C2semidirect
5. #16840056C2semidirect
6. #16840009C2semidirect
7. #16840001C2semidirect
8. #16839987C2semidirect
9. #16839926C2semidirect
10. #16839919C2semidirect
11. #16839868C2semidirect
12. #16839830C2semidirect
13. #16839769C2semidirect
14. #16839756C2semidirect
15. C61×#485C2semidirect
182. #485D61semidirect
194. C61#3313semidirect