Finite Group Databasebeta

← #21458661

Subgroups — #21458661

Order 7808.

332 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#16840485C211yesmaximal, characteristic
2#16840132C211yesmaximal, characteristic, complemented
3#16840124C211yesmaximal, characteristic
4#16840119C211yesmaximal, characteristic
5#16840066C211yesmaximal, characteristic, complemented
6#16840059C211yesmaximal, characteristic
7#16840054C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic
9#16839984C211yesmaximal, characteristic
10#16839972C211yesmaximal, characteristic, complemented
11#16839893C211yesmaximal, characteristic, complemented
12#16839867C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic
14C4×#11758202C211yesmaximal, characteristic, complemented
15C61×#557C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519772—21no—
21#14519772—21no—
22#14519765C2211yescharacteristic
23#14519765C2211yescharacteristic
24#14519753—21no—
25C4×Dic122C2211yescharacteristic
26C4×Dic122C2211yescharacteristic
27C4×D244C2211yescharacteristic
28#14519735—21no—
29#14519710C2211yescharacteristic
30#14519710C2211yescharacteristic
31#14519708C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic
33C4⋊#92418C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45#14519688C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48C4⋊Q8×C61—21no—
49C4⋊Q8×C61C2211yescharacteristic
50#125×C61—21no—
51#125×C61—21no—
52#125×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54C4×Q8×C61—21no—
55C4×Q8×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic
58C4×Q8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61D411yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D244C2311yescharacteristic
63C2×C4×D61—21no—
64C2×Dic122C2311yescharacteristic
65C2×Dic122C2311yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61D411yescharacteristic
75C4⋊C4×C61D411yescharacteristic
76C4⋊C4×C61D411yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C42×C61—21no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61C2311yescharacteristic
84C42×C61C2311yescharacteristic
85C42×C61C2311yescharacteristic
86#11758202—22no—
87#11758202—22no—
88#11758201—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C22×D61—21no—
106Q8×C61—21no—
107Q8×C61—41no—
108Q8×C61—42no—
109Q8×C61#4112yes—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124D244—21no—
125D244—21no—
126C4×D61—42no—
127Dic122—21no—
128Dic122—21no—
129Dic122—21no—
130Dic122—21no—
131#92418—21no—
132#92418—21no—
133#92418—21no—
134#92418—21no—
135C22×C61C22×D411yescharacteristic
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—41no—
139C4×C61—22no—
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61C2×#4111yescharacteristic
150C4×C612−1+411yescharacteristic
151Dic61—41no—
152Dic61—41no—
153Dic61—41no—
154#3377—611nomaximal, Sylow
155C2×C61#54811yescharacteristic
156C2×C61#57511yescharacteristic
157C2×C61#57811yescharacteristic
158D61—81no—
159#557D6111yescharacteristic, complemented
160#556—611no—
161#491—611no—
162#489—611no—
163#488—611no—
164#479—611no—
165#478—611no—
166#477—611no—
167#464—611no—
168#464—611no—
169#462—611no—
170#446—611no—
171#441—611no—
172#440—611no—
173C4×Q16—611no—
174C61#337711yescharacteristic, complemented, Sylow
175C2×Q16—611no—
176C2×Q16—611no—
177C2×SD16—611no—
178C4⋊Q8—21no—
179C4⋊Q8—611no—
180C4⋊Q8C2×D6111yescharacteristic
181#126—1221no—
182#126—1221no—
183#125—21no—
184#125—21no—
185#125C2×D6111yescharacteristic
186#125C2×D6111yescharacteristic
187#124—611no—
188#124—611no—
189C22⋊Q8—1221no—
190C4×Q8—21no—
191C4×Q8—611no—
192C4×Q8—611no—
193C4×Q8C2×D6111yescharacteristic
194C4×Q8C2×D6111yescharacteristic
195C4×Q8C2×D6111yescharacteristic
196C4×Q8C2×D6111yescharacteristic
197C4×D4—611no—
198#117—1221no—
199#107—611no—
200#107—611no—
201#106—611no—
202C4⋊C8—611no—
203C4⋊C8—611no—
204C4⋊C8—611no—
205#103—611no—
206#103—611no—
207#103—611no—
208#103—611no—
209#103—611no—
210#103—611no—
211#103—611no—
212#102—611no—
213#102—611no—
214#102—611no—
215#97—611no—
216#97—611no—
217C4×C8—611no—
218C2×Q8—21no—
219C2×Q8—611no—
220C2×Q8—611no—
221C2×Q8C22⋊D6111yescharacteristic
222C2×Q8C22×D6111yescharacteristic
223C2×D4—611no—
224C22×C4—1221no—
225Q16—1222no—
226Q16—1222no—
227SD16—1222no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8—611no—
231C2×C8—611no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—611no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4C22⋊D6111yescharacteristic
246C4⋊C4C22⋊D6111yescharacteristic
247C4⋊C4C22⋊D6111yescharacteristic
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—21no—
258C42—21no—
259C42—1221no—
260C42—1221no—
261C42C22×D6111yescharacteristic
262C42C22×D6111yescharacteristic
263C42C22×D6111yescharacteristic
264C23—1221no—
265Q8—21no—
266Q8—41no—
267Q8—42no—
268Q8—1221no—
269Q8—1221no—
270Q8—1221no—
271Q8—1221no—
272Q8#1175822612yes—
273D4—1221no—
274D4—1221no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—2442no—
283C2×C4C2×C22⋊D6111yescharacteristic
284C2×C4C2×C22⋊D6111yescharacteristic
285C2×C4C2×C22⋊D6111yescharacteristic
286C2×C4C2×C22⋊D6111yescharacteristic
287C2×C4C2×C22⋊D6111yescharacteristic
288C2×C4C2×C22⋊D6111yescharacteristic
289C2×C4C23×D6111yescharacteristic
290C8—1221no—
291C8—1221no—
292C8—1221no—
293C8—1221no—
294C22—2441no—
295C22—2441no—
296C22—2441no—
297C22C22×C22⋊D6111yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—2441no—
309C4—2441no—
310C4—2441no—
311C4C2×#1175822611yescharacteristic
312C4#1451982511yescharacteristic
313C2—4881no—
314C2#1684042311yescharacteristic
315C2#1684056011yescharacteristic
316C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#557C2
socleC22×C61C22×D4
hypercenter#557D61
hypocenterC61#3377
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
2. #16840132C2semidirect
5. #16840066C2semidirect
7. #16840054C2semidirect
10. #16839972C2semidirect
11. #16839893C2semidirect
12. #16839867C2semidirect
14. C4×#11758202C2semidirect
15. C61×#557C2semidirect
159. #557D61semidirect
174. C61#3377semidirect