Finite Group Databasebeta

← #21449475

Subgroups — #21449475

Order 7808.

852 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic122C211yesmaximal, characteristic, complemented
2C2×#14519763C212yesmaximal, complemented
3C2×#14519749C211yesmaximal, characteristic
4#16839675C212yesmaximal, complemented
5#16839674C212yesmaximal, complemented
6#16839666C212yesmaximal, complemented
7#16839642C211yesmaximal, characteristic, complemented
8#16839641C211yesmaximal, characteristic, complemented
9#16839639C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
11C61×#386C211yesmaximal, characteristic, complemented
12C22×Dic122—24no—
13C22×Dic122—28no—
14C22×Dic122C2212yes—
15C22×Dic122C2212yes—
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20#14519763—28no—
21#14519749—24no—
22C2×#11758196C2211yescharacteristic
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2212yes—
25C2×C22⋊Dic61C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34C22×D4×C61C2211yescharacteristic
35C23×C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2212yes—
37C2×C22⋊C4×C61C2211yescharacteristic
38#95×C61C2212yes—
39C24×C61C2311yescharacteristic
40C24×C61C2311yescharacteristic
41C23×D61C2311yescharacteristic
42C2×D4×C61—22no—
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—24no—
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2312yes—
49C22×C4×C61C2312yes—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—24no—
55C22×Dic61—22no—
56C22×Dic61—24no—
57C22×Dic61—24no—
58C22×Dic61D414yes—
59C22×Dic61C2311yescharacteristic
60C22×Dic61C2312yes—
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2312yes—
63C22×Dic61C2311yescharacteristic
64C2×Dic122—232no—
65C2×Dic122—24no—
66C2×Dic122—24no—
67C2×Dic122—24no—
68C2×Dic122—24no—
69C2×Dic122—24no—
70C2×Dic122D418yescomplemented
71C22⋊C4×C61—22no—
72C22⋊C4×C61—24no—
73C22⋊Dic61—22no—
74C22⋊Dic61—22no—
75C22⋊Dic61—24no—
76#11758198—24no—
77#11758198—22no—
78#11758198—24no—
79#11758196—22no—
80C4×Dic61—24no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—22no—
88C23×C61C2×D412yes—
89C23×C61#4112yes—
90C23×C61#4112yes—
91C23×C61C2411yescharacteristic
92C22×D61—22no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—22no—
97D4×C61—44no—
98C2×C4×C61—28no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61C2×D414yes—
108C22⋊D61—44no—
109C22⋊D61—44no—
110C2×Dic61—28no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—28no—
115C2×Dic61—22no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—22no—
121C2×Dic61C2×D412yes—
122C2×Dic61C2×D414yes—
123C2×Dic61C2×D414yes—
124C2×Dic61C2×D412yes—
125Dic122—216no—
126Dic122—216no—
127C22×C61—22no—
128C22×C61—22no—
129C22×C61—24no—
130C22×C61—24no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—42no—
135C22×C61—42no—
136C22×C61#12414yescomplemented
137C22×C61C22×D411yescharacteristic
138C22×C61C22×D412yes—
139C22×C61C2×#4111yescharacteristic
140C22×C61C2×#4111yescharacteristic
141C22×C612−1+412yes—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61—42no—
146C2×D61—42no—
147C4×C61—24no—
148C4×C61—41no—
149C4×C61—42no—
150Dic61—22no—
151Dic61—24no—
152Dic61—41no—
153Dic61—42no—
154Dic61#12014yes—
155#2436—611nomaximal, Sylow
156C2×C61—24no—
157C2×C61—81no—
158C2×C61C2×#12011yescharacteristic
159C2×C61C2×#12411yescharacteristic
160C2×C61#53611yescharacteristic
161C2×C61#54812yes—
162C2×C61#54812yes—
163D61—81no—
164C23×Q8—611no—
165C2×#124—612no—
166C2×#121—611no—
167#393—612no—
168#393—612no—
169#391—612no—
170#386—611no—
171#386—611no—
172#386—611no—
173#386D6111yescharacteristic, complemented
174C4×C22⋊C4—611no—
175C61#243611yescharacteristic, complemented, Sylow
176C22×Q8—612no—
177C22×Q8—612no—
178C22×Q8—1224no—
179C22×Q8—1228no—
180C22×D4—611no—
181C22×D4—611no—
182C22×D4C2×D6111yescharacteristic
183C23×C4—611no—
184C23×C4—611no—
185C23×C4C2×D6111yescharacteristic
186#124—1228no—
187#121—1224no—
188C2×C4⋊C4—611no—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—612no—
191C2×C22⋊C4—611no—
192C2×C22⋊C4—611no—
193C2×C22⋊C4—612no—
194C2×C22⋊C4—612no—
195C2×C22⋊C4C2×D6112yes—
196C2×C22⋊C4C2×D6111yescharacteristic
197C2×C42—612no—
198#95—612no—
199#95—612no—
200#95—612no—
201#95—612no—
202#95C2×D6112yes—
203C24—611no—
204C24C22×D6111yescharacteristic
205C24C22×D6111yescharacteristic
206C2×Q8—618no—
207C2×Q8—1224no—
208C2×Q8—1224no—
209C2×Q8—1224no—
210C2×Q8—1224no—
211C2×Q8—12232no—
212C2×Q8—1224no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—1222no—
217C2×D4—1224no—
218C2×D4—1222no—
219C2×D4—1222no—
220C2×D4—1222no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—611no—
224C22×C4—614no—
225C22×C4—611no—
226C22×C4—612no—
227C22×C4—611no—
228C22×C4—612no—
229C22×C4—1224no—
230C22×C4—1224no—
231C22×C4—1222no—
232C22×C4C22×D6111yescharacteristic
233C22×C4C22×D6112yes—
234C22×C4C22×D6112yes—
235C4⋊C4—1222no—
236C22⋊C4—22no—
237C22⋊C4—24no—
238C22⋊C4—1222no—
239C22⋊C4—1224no—
240C22⋊C4—1222no—
241C22⋊C4—1224no—
242C22⋊C4—1222no—
243C22⋊C4—1224no—
244C42—1224no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—22no—
252C23—1222no—
253C23—1221no—
254C23—1221no—
255C23—1221no—
256C23—1222no—
257C23#1175822212yes—
258C23D4×D6112yes—
259C23#1175822412yes—
260C23C23×D6111yescharacteristic
261Q8—12216no—
262Q8—12216no—
263D4—44no—
264D4—2444no—
265D4—2444no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—614no—
276C2×C4—612no—
277C2×C4—612no—
278C2×C4—614no—
279C2×C4—1228no—
280C2×C4—1228no—
281C2×C4—1222no—
282C2×C4—1222no—
283C2×C4—1222no—
284C2×C4—1222no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1222no—
288C2×C4—1221no—
289C2×C4—1222no—
290C2×C4D4×D6114yes—
291C22—22no—
292C22—22no—
293C22—24no—
294C22—24no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—2441no—
301C22—2441no—
302C22—2441no—
303C22—2442no—
304C22—2442no—
305C22#1451976314yescomplemented
306C22C2×D4×D6111yescharacteristic
307C22C2×D4×D6112yes—
308C22C2×#1175822411yescharacteristic
309C22C2×#1175822211yescharacteristic
310C22#1451982412yes—
311C4—24no—
312C4—41no—
313C4—42no—
314C4—614no—
315C4—1222no—
316C4—1224no—
317C4—2441no—
318C4—2442no—
319C2—24no—
320C2—81no—
321C2—4881no—
322C2#120×D6111yescharacteristic
323C2C2×#1451976311yescharacteristic
324C2#1684033411yescharacteristic
325C2#1684041812yes—
326C2#1684042112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2436
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C23×Dic122C2semidirect
2. C2×#14519763C2semidirect
4. #16839675C2semidirect
5. #16839674C2semidirect
6. #16839666C2semidirect
7. #16839642C2semidirect
8. #16839641C2semidirect
9. #16839639C2semidirect
10. C22⋊C4×Dic61C2semidirect
11. C61×#386C2semidirect
70. C2×Dic122D4semidirect
136. C22×C61#124semidirect
173. #386D61semidirect
175. C61#2436semidirect
305. C22#14519763semidirect