Finite Group Databasebeta

← #21455622

Subgroups — #21455622

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840318C211yesmaximal, characteristic
2C4×Q8×D61C211yesmaximal, characteristic
3#16840070C211yesmaximal, characteristic, complemented
4#16840069C211yesmaximal, characteristic, complemented
5#16840066C211yesmaximal, characteristic, complemented
6#16840056C211yesmaximal, characteristic, complemented
7#16840055C211yesmaximal, characteristic, complemented
8#16840046C211yesmaximal, characteristic, complemented
9#16840045C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic
11#16839801C211yesmaximal, characteristic
12#16839784C211yesmaximal, characteristic
13#16839769C211yesmaximal, characteristic
14#16839769C211yesmaximal, characteristic
15C61×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×#11758189C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19#14519776C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519769C2211yescharacteristic
22#14519755—21no—
23#14519755—21no—
24Q8×Dic61C2211yescharacteristic
25C4×Dic122—21no—
26C4×Dic122C2211yescharacteristic
27#14519742—21no—
28#14519742—21no—
29#14519742—21no—
30#14519742C2211yescharacteristic
31#14519735C2211yescharacteristic
32#14519735C2211yescharacteristic
33C4⋊C4×D61—21no—
34C4⋊C4×D61C2211yescharacteristic
35C42×D61—21no—
36C42×D61C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519700C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60Q8×D61—22no—
61Q8×D61Q814yescomplemented
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61D411yescharacteristic
65C2×C4×D61D411yescharacteristic
66C2×C4×D61C2311yescharacteristic
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C42×C61—21no—
80C42×C61C2311yescharacteristic
81#11758198—21no—
82#11758198—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61C2311yescharacteristic
85C4⋊Dic61C2311yescharacteristic
86C4⋊Dic61C2311yescharacteristic
87#11758196—21no—
88#11758196—21no—
89#11758196—21no—
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61D411yescharacteristic
100C4×Dic61D411yescharacteristic
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104#11758189—22no—
105#11758189—22no—
106C22×D61C2×D411yescharacteristic
107Q8×C61—21no—
108Q8×C61C2×Q812yes—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2411yescharacteristic
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122C2×Dic61C2×D411yescharacteristic
123C4×D61—24no—
124C4×D61—22no—
125C4×D61—41no—
126C4×D61—42no—
127C4×D61C2×Q812yes—
128C4×D61#4112yes—
129Dic122—21no—
130Dic122—24no—
131Dic122—42no—
132Dic122—42no—
133Dic122C2×Q812yes—
134C8×C61—21no—
135C8×C61—21no—
136#92418—21no—
137#92418—21no—
138C22×C61C22×D411yescharacteristic
139C2×D61—21no—
140C2×D61—21no—
141C2×D61C22⋊Q812yes—
142C4×C61—22no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61C22×Q811yescharacteristic
149C4×C61C2×#4111yescharacteristic
150Dic61—22no—
151Dic61—21no—
152Dic61—41no—
153Dic61—41no—
154Dic61—41no—
155Dic61C22⋊Q812yes—
156Dic61#13712yes—
157#3078—611nomaximal, Sylow
158C2×C61C2×C22⋊Q811yescharacteristic
159C2×C61C2×#13711yescharacteristic
160C2×C61#57511yescharacteristic
161D61—22no—
162#533—611no—
163C2×C4×Q8—611no—
164#479—611no—
165#479—611no—
166#479—611no—
167#479D6111yescharacteristic, complemented
168#477—611no—
169#477—611no—
170#475—611no—
171#475—611no—
172#428—611no—
173#428—611no—
174#423—611no—
175#419—611no—
176#419—611no—
177C61#307811yescharacteristic, complemented, Sylow
178C22×Q8—611no—
179C2×M16—611no—
180C2×M16—611no—
181C4⋊Q8—611no—
182C4⋊Q8—611no—
183#125—611no—
184#125C2×D6111yescharacteristic
185C22⋊Q8—1221no—
186C22⋊Q8—1221no—
187C4×Q8—611no—
188C4×Q8—611no—
189C4×Q8—611no—
190C4×Q8—1221no—
191C4×Q8—1221no—
192C4×Q8—1221no—
193C4×Q8—1221no—
194C4×Q8C2×D6111yescharacteristic
195#117—611no—
196#117—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—1221no—
199C2×C42—611no—
200C2×C42—1221no—
201#107—611no—
202#107—611no—
203#107—611no—
204#107C2×D6111yescharacteristic
205#106—611no—
206#106—611no—
207#106—611no—
208#106C2×D6111yescharacteristic
209C4⋊C8—611no—
210C4⋊C8—611no—
211C4⋊C8—611no—
212C4⋊C8C2×D6111yescharacteristic
213#103—611no—
214#103—611no—
215#103—611no—
216#103—611no—
217#103—611no—
218#103—611no—
219#103C2×D6111yescharacteristic
220#103C2×D6111yescharacteristic
221C2×Q8—614no—
222C2×Q8—611no—
223C2×Q8—1221no—
224C2×Q8—1221no—
225C2×Q8—1221no—
226C2×Q8—1222no—
227C2×Q8C22×D6111yescharacteristic
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1221no—
232C22×C4—1221no—
233M16—1222no—
234M16—1222no—
235C2×C8—611no—
236C2×C8—611no—
237C2×C8C22×D6111yescharacteristic
238C2×C8C22×D6111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
254C4⋊C4C22×D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C22⋊C4—1221no—
257C22⋊C4—1221no—
258C42—21no—
259C42—611no—
260C42—611no—
261C42—611no—
262C42—1221no—
263C42—1221no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C42C22×D6111yescharacteristic
268C23—611no—
269Q8—21no—
270Q8—612no—
271Q8—1224no—
272Q8—1221no—
273Q8—2442no—
274Q8—2442no—
275Q8Q8×D6112yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—612no—
283C2×C4—612no—
284C2×C4—611no—
285C2×C4—1222no—
286C2×C4—1224no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—2441no—
292C2×C4—2442no—
293C2×C4D4×D6111yescharacteristic
294C2×C4D4×D6111yescharacteristic
295C2×C4C23×D6111yescharacteristic
296C8—21no—
297C8—21no—
298C8—1221no—
299C8—1221no—
300C22—612no—
301C22—1221no—
302C22—1221no—
303C22C2×D4×D6111yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—612no—
311C4—612no—
312C4—1222no—
313C4—1221no—
314C4—2441no—
315C4—2441no—
316C4—2441no—
317C4C2×Q8×D6111yescharacteristic
318C4#41×D6111yescharacteristic
319C2—1222no—
320C2C22⋊Q8×D6111yescharacteristic
321C2#137×D6111yescharacteristic
322C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3078
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
3. #16840070C2semidirect
4. #16840069C2semidirect
5. #16840066C2semidirect
6. #16840056C2semidirect
7. #16840055C2semidirect
8. #16840046C2semidirect
9. #16840045C2semidirect
15. C61×#479C2semidirect
61. Q8×D61Q8semidirect
167. #479D61semidirect
177. C61#3078semidirect