Finite Group Databasebeta

← #21458507

Subgroups — #21458507

Order 7808.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840489C211yesmaximal, characteristic, complemented
2#16840484C211yesmaximal, characteristic
3#16840119C211yesmaximal, characteristic
4#16840118C211yesmaximal, characteristic
5#16840111C211yesmaximal, characteristic, complemented
6#16840072C211yesmaximal, characteristic, complemented
7#16840041C211yesmaximal, characteristic
8#16839987C211yesmaximal, characteristic
9#16839985C211yesmaximal, characteristic
10#16839971C211yesmaximal, characteristic, complemented
11#16839886C211yesmaximal, characteristic, complemented
12#16839856C211yesmaximal, characteristic, complemented
13C4×#11758202C211yesmaximal, characteristic, complemented
14#16839849C211yesmaximal, characteristic
15C61×#479C211yesmaximal, characteristic, complemented
16C2×Dic244C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19#14519776—21no—
20#14519776C2211yescharacteristic
21#14519775C2211yescharacteristic
22#14519772—21no—
23#14519771—21no—
24#14519768C2211yescharacteristic
25#14519767—21no—
26#14519767—21no—
27#14519766C2211yescharacteristic
28#14519765C2211yescharacteristic
29#14519755—21no—
30C4×Dic122C2211yescharacteristic
31C4×Dic122C2211yescharacteristic
32#14519742—21no—
33#14519742C2211yescharacteristic
34#14519742C2211yescharacteristic
35#14519742C2211yescharacteristic
36#14519739C2211yescharacteristic
37#14519734—21no—
38#14519710C2211yescharacteristic
39#14519706C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C4×#92418C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D244C2311yescharacteristic
61C2×C4×D61—21no—
62C2×Dic122—21no—
63C2×Dic122D411yescharacteristic
64C2×Dic122C2311yescharacteristic
65C2×Dic122C2311yescharacteristic
66C2×C8×C61C2311yescharacteristic
67C2×C8×C61C2311yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61C2311yescharacteristic
72C4⋊C4×C61C2311yescharacteristic
73C4⋊C4×C61C2311yescharacteristic
74C42×C61—21no—
75C42×C61C2311yescharacteristic
76#11758202—22no—
77#11758198—21no—
78#11758198—21no—
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61D411yescharacteristic
84C4⋊Dic61C2311yescharacteristic
85#11758196—21no—
86#11758196—21no—
87#11758196—21no—
88#11758196—21no—
89#11758196—21no—
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196D411yescharacteristic
94#11758196D411yescharacteristic
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61C2311yescharacteristic
100C4×Dic61C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103Dic244—22no—
104#11758190—22no—
105C22×D61—21no—
106Q8×C61—21no—
107Q8×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2411yescharacteristic
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61C2×D411yescharacteristic
119C2×Dic61C2×D411yescharacteristic
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122D244—21no—
123D244—21no—
124C4×D61—42no—
125Dic122—21no—
126Dic122—22no—
127Dic122—21no—
128Dic122—21no—
129Dic122—42no—
130Dic122#4112yes—
131C8×C61—21no—
132C8×C61—21no—
133#92418—21no—
134#92418—21no—
135C22×C61C22×D411yescharacteristic
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—41no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61C2×#4111yescharacteristic
146C4×C612−1+411yescharacteristic
147Dic61—22no—
148Dic61—21no—
149Dic61—21no—
150Dic61—21no—
151Dic61—41no—
152Dic61—41no—
153Dic61#13512yes—
154#3364—611nomaximal, Sylow
155C2×C61#54811yescharacteristic
156C2×C61C2×#13511yescharacteristic
157C2×C61#57811yescharacteristic
158D61—81no—
159#557—611no—
160#556—611no—
161#488—611no—
162#488—611no—
163#487—611no—
164#479—611no—
165#479D6111yescharacteristic, complemented
166#474—611no—
167#464—611no—
168#464—611no—
169#462—611no—
170C8×Q8—611no—
171C4×Q16—611no—
172C4×Q16—611no—
173C4×SD16—611no—
174C61#336411yescharacteristic, complemented, Sylow
175C2×Q16—611no—
176C2×Q16—611no—
177C2×SD16—611no—
178C4⋊Q8—611no—
179C4⋊Q8—611no—
180C4⋊Q8—1221no—
181#126—1221no—
182#126—1221no—
183#125—611no—
184#125—1221no—
185#125—1221no—
186#125C2×D6111yescharacteristic
187#124—611no—
188#124—611no—
189C22⋊Q8—1221no—
190C4×Q8—611no—
191C4×Q8—611no—
192C4×Q8—611no—
193C4×Q8—611no—
194C4×Q8—611no—
195C4×Q8—1221no—
196C4×Q8C2×D6111yescharacteristic
197C4×D4—611no—
198#117—1221no—
199#107—611no—
200#107C2×D6111yescharacteristic
201#106C2×D6111yescharacteristic
202C4⋊C8—611no—
203C4⋊C8—611no—
204C4⋊C8C2×D6111yescharacteristic
205#103—611no—
206#103—611no—
207#103—611no—
208#103—611no—
209#103—611no—
210#103C2×D6111yescharacteristic
211#103C2×D6111yescharacteristic
212#102—611no—
213#102—611no—
214#102—611no—
215C4×C8—611no—
216C4×C8—611no—
217C4×C8—611no—
218C2×Q8—611no—
219C2×Q8—611no—
220C2×Q8—611no—
221C2×Q8—1221no—
222C2×Q8C22×D6111yescharacteristic
223C2×D4—611no—
224C22×C4—1221no—
225Q16—1222no—
226Q16—1222no—
227SD16—1222no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8C22×D6111yescharacteristic
231C2×C8C22×D6111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—611no—
236C4⋊C4—611no—
237C4⋊C4—611no—
238C4⋊C4—611no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4C22×D6111yescharacteristic
249C4⋊C4C22×D6111yescharacteristic
250C4⋊C4C22×D6111yescharacteristic
251C22⋊C4—1221no—
252C22⋊C4—1221no—
253C22⋊C4—1221no—
254C22⋊C4—1221no—
255C22⋊C4—1221no—
256C42—21no—
257C42—611no—
258C42—611no—
259C42—1221no—
260C42—1221no—
261C42—1221no—
262C42—1221no—
263C42C22×D6111yescharacteristic
264C23—1221no—
265Q8—21no—
266Q8—21no—
267Q8—612no—
268Q8—1222no—
269Q8—1221no—
270Q8—1221no—
271Q8—1221no—
272Q8—2442no—
273D4—1221no—
274D4—1221no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—611no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—2442no—
287C2×C4D4×D6111yescharacteristic
288C2×C4D4×D6111yescharacteristic
289C2×C4C23×D6111yescharacteristic
290C8—21no—
291C8—21no—
292C8—1221no—
293C8—1221no—
294C22—2441no—
295C22—2441no—
296C22—2441no—
297C22C2×D4×D6111yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—612no—
305C4—1221no—
306C4—1221no—
307C4—1221no—
308C4—1222no—
309C4—2441no—
310C4—2441no—
311C4#41×D6111yescharacteristic
312C4#1451982511yescharacteristic
313C2—4881no—
314C2#1684042211yescharacteristic
315C2#135×D6111yescharacteristic
316C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3364
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #16840489C2semidirect
5. #16840111C2semidirect
6. #16840072C2semidirect
10. #16839971C2semidirect
11. #16839886C2semidirect
12. #16839856C2semidirect
13. C4×#11758202C2semidirect
15. C61×#479C2semidirect
165. #479D61semidirect
174. C61#3364semidirect