Finite Group Databasebeta

← #21456118

Subgroups — #21456118

Order 7808.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840370C211yesmaximal, characteristic
2#16840238C211yesmaximal, characteristic
3#16840106C211yesmaximal, characteristic
4#16840101C211yesmaximal, characteristic
5#16840072C211yesmaximal, characteristic, complemented
6#16840067C211yesmaximal, characteristic, complemented
7#16839971C211yesmaximal, characteristic, complemented
8#16839970C211yesmaximal, characteristic, complemented
9#16839919C211yesmaximal, characteristic
10#16839916C211yesmaximal, characteristic
11#16839870C211yesmaximal, characteristic, complemented
12C4×#11758202C211yesmaximal, characteristic, complemented
13C4×#11758202C211yesmaximal, characteristic, complemented
14#16839824C211yesmaximal, characteristic
15C61×#441C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20#14519775C2211yescharacteristic
21#14519772—21no—
22#14519771—21no—
23#14519769—21no—
24#14519768C2211yescharacteristic
25#14519767—21no—
26#14519757C2211yescharacteristic
27#14519753C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic
29C4×Dic122—21no—
30C4×Dic122C2211yescharacteristic
31C4×Dic122C2211yescharacteristic
32#14519742—21no—
33#14519742C2211yescharacteristic
34#14519735—21no—
35#14519735C2211yescharacteristic
36#14519734—21no—
37#14519734C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61Q8×D61—22no—
62Q8×D61—22no—
63C2×C4×D61—21no—
64C2×C4×D61C2311yescharacteristic
65C2×Dic122—21no—
66C2×Dic122C2311yescharacteristic
67C2×Dic122C2311yescharacteristic
68Q16×C61—22no—
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61C2311yescharacteristic
74C4⋊C4×C61C2311yescharacteristic
75C42×C61—21no—
76C42×C61—21no—
77C42×C61C2311yescharacteristic
78#11758202—22no—
79#11758202—22no—
80#11758198—21no—
81#11758198—21no—
82#11758198—21no—
83#11758198D411yescharacteristic
84#11758198D411yescharacteristic
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61C2311yescharacteristic
89C4⋊Dic61C2311yescharacteristic
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196D411yescharacteristic
98#11758196D411yescharacteristic
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107Dic244—22no—
108C22×D61C2×D411yescharacteristic
109Q8×C61—21no—
110Q8×C61—21no—
111Q8×C61—21no—
112Q8×C61#4112yes—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127C4×D61—24no—
128C4×D61—21no—
129C4×D61—21no—
130Dic122—24no—
131Dic122—21no—
132Dic122—21no—
133Dic122—21no—
134Dic122#4112yes—
135C8×C61—21no—
136C8×C61—21no—
137#92418—21no—
138#92418—21no—
139C22×C61C22×D411yescharacteristic
140C2×D61—21no—
141C2×D61—21no—
142C2×D61—21no—
143C4×C61—22no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61C2×#4111yescharacteristic
150C4×C61C2×#4111yescharacteristic
151Dic61—21no—
152Dic61—22no—
153Dic61—21no—
154Dic61—21no—
155Dic61—41no—
156Dic61—41no—
157Dic61—41no—
158#3127—611nomaximal, Sylow
159C2×C61#52511yescharacteristic
160C2×C61#57811yescharacteristic
161C2×C61#57811yescharacteristic
162D61—41no—
163#541—611no—
164#519—611no—
165#485—611no—
166#485—611no—
167#479—611no—
168#479—611no—
169#462—611no—
170#462—611no—
171#451—611no—
172#451—611no—
173#441—611no—
174#441D6111yescharacteristic, complemented
175C4×Q16—611no—
176C4×Q16—611no—
177#433—611no—
178C61#312711yescharacteristic, complemented, Sylow
179C22×Q8—611no—
180C2×Q16—611no—
181C2×Q16—611no—
182C2×Q16—611no—
183C2×Q16C2×D6111yescharacteristic
184C4⋊Q8—611no—
185#126—1221no—
186#126—1221no—
187#125—611no—
188#125—1221no—
189#125—1221no—
190C22⋊Q8—611no—
191C22⋊Q8—611no—
192C4×Q8—611no—
193C4×Q8—611no—
194C4×Q8—611no—
195C4×Q8—611no—
196C4×Q8—1221no—
197C4×Q8—1221no—
198C4×Q8C2×D6111yescharacteristic
199C4×Q8C2×D6111yescharacteristic
200#117—611no—
201#117—611no—
202#117—1221no—
203#117—1221no—
204#107—611no—
205#107—611no—
206#106—611no—
207#106C2×D6111yescharacteristic
208C4⋊C8—611no—
209C4⋊C8—611no—
210#103—611no—
211#103—611no—
212#103—611no—
213#103—611no—
214#103—611no—
215#103—611no—
216#103C2×D6111yescharacteristic
217#103C2×D6111yescharacteristic
218C22⋊C8—611no—
219C22⋊C8—611no—
220#97C2×D6111yescharacteristic
221C4×C8—611no—
222C2×Q8—611no—
223C2×Q8—611no—
224C2×Q8—1221no—
225C2×Q8—1222no—
226C2×Q8—1222no—
227C2×Q8C22×D6111yescharacteristic
228C2×Q8C22×D6111yescharacteristic
229C22×C4—611no—
230C22×C4—1221no—
231Q16—22no—
232Q16—1222no—
233Q16—1222no—
234Q16—1222no—
235C2×C8—611no—
236C2×C8—611no—
237C2×C8C22×D6111yescharacteristic
238C2×C8C22×D6111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—611no—
242C4⋊C4—611no—
243C4⋊C4—611no—
244C4⋊C4—611no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C22⋊C4—611no—
258C22⋊C4—611no—
259C22⋊C4—1221no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C42—21no—
263C42—21no—
264C42—611no—
265C42—1221no—
266C42—1221no—
267C42—1221no—
268C42—1221no—
269C42—1221no—
270C42C22×D6111yescharacteristic
271C23—611no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—612no—
276Q8—1224no—
277Q8—1221no—
278Q8—1221no—
279Q8—1221no—
280Q8#1175822212yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—1224no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4D4×D6111yescharacteristic
296C2×C4D4×D6111yescharacteristic
297C2×C4C23×D6111yescharacteristic
298C8—21no—
299C8—21no—
300C8—1221no—
301C8—1221no—
302C22—1221no—
303C22—1221no—
304C22—1221no—
305C22C2×D4×D6111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—1221no—
313C4—1222no—
314C4—1221no—
315C4—1221no—
316C4—2441no—
317C4—2441no—
318C4—2441no—
319C4#41×D6111yescharacteristic
320C4C2×#1175822211yescharacteristic
321C2—2441no—
322C2#1684027111yescharacteristic
323C2#1684057811yescharacteristic
324C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3127
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
5. #16840072C2semidirect
6. #16840067C2semidirect
7. #16839971C2semidirect
8. #16839970C2semidirect
11. #16839870C2semidirect
12. C4×#11758202C2semidirect
13. C4×#11758202C2semidirect
15. C61×#441C2semidirect
174. #441D61semidirect
178. C61#3127semidirect