Finite Group Databasebeta

← #21455284

Subgroups — #21455284

Order 7808.

548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#14519804C212yesmaximal, complemented
2#16840313C211yesmaximal, characteristic, complemented
3C4×D4×D61C211yesmaximal, characteristic, complemented
4#16839980C212yesmaximal, complemented
5#16839979C212yesmaximal, complemented
6#16839964C211yesmaximal, characteristic, complemented
7#16839958C211yesmaximal, characteristic, complemented
8#16839957C211yesmaximal, characteristic, complemented
9#16839784C211yesmaximal, characteristic, complemented
10#16839762C212yesmaximal, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×D4×D61C2211yescharacteristic
14C22×C4×D61—21no—
15#14519804—28no—
16C2×#11758201C2212yes—
17C2×D488C2212yes—
18C2×#11758199C2212yes—
19C2×#11758189C2212yes—
20#14519774C2211yescharacteristic, complemented
21#14519766C2212yescomplemented
22#14519752—21no—
23#14519752—21no—
24C4×D244C2211yescharacteristic
25D4×Dic61C2211yescharacteristic
26#14519739—21no—
27#14519739—21no—
28#14519739C2211yescharacteristic
29C4×C22⋊D61—21no—
30#14519737—21no—
31C4⋊C4×D61C2211yescharacteristic
32C22⋊C4×D61—21no—
33C42×D61C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic, complemented
35#14519706C2212yescomplemented
36#14519701C2212yescomplemented
37#14519699C2212yescomplemented
38#14519697C2212yescomplemented
39C2×SD16×C61C2212yes—
40C4⋊Q8×C61C2211yescharacteristic, complemented
41C4×D4×C61C2211yescharacteristic
42C4⋊C8×C61C2211yescharacteristic, complemented
43#103×C61C2212yescomplemented
44C23×D61—21no—
45C2×Q8×C61C2312yes—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C2×C22⋊D61—21no—
49C22×Dic61—21no—
50#11758226—24no—
51#11758226—24no—
52D4×D61—22no—
53D4×D61D414yescomplemented
54C2×D244—22no—
55C2×D244—21no—
56C2×D244—21no—
57C2×D244C2312yes—
58C2×D244C2311yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—22no—
63C2×C4×D61—44no—
64C2×C4×D61D411yescharacteristic
65C2×C4×D61D411yescharacteristic
66C2×C4×D61C2311yescharacteristic
67SD16×C61—24no—
68C2×C8×C61C2312yes—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61C2311yescharacteristic
72C22⋊C4×C61—21no—
73C42×C61C2311yescharacteristic
74C22⋊Dic61—21no—
75#11758201—24no—
76#11758199—24no—
77#11758198—21no—
78#11758198—21no—
79#11758198—22no—
80#11758198—22no—
81C4⋊Dic61C2311yescharacteristic
82#11758196—21no—
83C4×Dic61D411yescharacteristic
84C4×Dic61D411yescharacteristic
85C4×Dic61C2311yescharacteristic
86C2×#92418C2312yes—
87D488—24no—
88#11758189—24no—
89C23×C61—21no—
90C22×D61—21no—
91C22×D61—24no—
92C22×D61—22no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61C2×D411yescharacteristic
96Q8×C61—22no—
97Q8×C61—22no—
98D4×C61—21no—
99D4×C61C2×D412yes—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—42no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2411yescharacteristic
106C22⋊D61—24no—
107C2×Dic61—21no—
108C2×Dic61—42no—
109C2×Dic61C2×D411yescharacteristic
110C2×Dic61C2×D411yescharacteristic
111C2×Dic61C2×D411yescharacteristic
112D244—22no—
113D244—21no—
114D244—22no—
115D244—42no—
116D244—44no—
117D244—42no—
118D244C2×D412yes—
119C4×D61—22no—
120C4×D61—41no—
121C4×D61—42no—
122C4×D61—42no—
123C4×D61—42no—
124C4×D61—44no—
125C4×D61C2×D412yes—
126C4×D61#4112yes—
127C8×C61—22no—
128#92418—22no—
129C22×C61—22no—
130C22×C61—41no—
131C22×C61—41no—
132C22×C61C22×D411yescharacteristic
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—22no—
136C2×D61—48no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—42no—
142C2×D61#12112yes—
143C4×C61—21no—
144C4×C61—42no—
145C4×C61—41no—
146C4×C61AGL(1,ℤ/8)12yescomplemented
147C4×C61C22×D411yescharacteristic
148C4×C61C2×#4111yescharacteristic
149Dic61—21no—
150Dic61—21no—
151Dic61—41no—
152Dic61#12112yes—
153#3036—611nomaximal, Sylow
154C2×C61—42no—
155C2×C61C2×#12111yescharacteristic
156C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
157C2×C61#57511yescharacteristic
158D61—22no—
159D61—42no—
160D61—82no—
161C2×AGL(1,ℤ/8)—612no—
162#532—611no—
163C2×C4×D4—611no—
164#463—612no—
165#463—612no—
166#461—611no—
167#461D6111yescharacteristic, complemented
168#459—611no—
169#459—611no—
170#423—611no—
171#417—612no—
172C61#303611yescharacteristic, complemented, Sylow
173C2×#41—612no—
174C22×D4—611no—
175C23×C4—1221no—
176AGL(1,ℤ/8)—1228no—
177C2×SD16—612no—
178C2×SD16C2×D6112yes—
179C2×D8—612no—
180C2×D8—612no—
181C2×M16—612no—
182C4⋊Q8C2×D6111yescharacteristic, complemented
183#127—611no—
184#124—612no—
185#121—1221no—
186#121—1221no—
187C4×D4—611no—
188C4×D4—611no—
189C4×D4—611no—
190C4×D4—1221no—
191C4×D4—1221no—
192C4×D4—1221no—
193C4×D4—1221no—
194C4×D4C2×D6111yescharacteristic
195C2×C4⋊C4—611no—
196C2×C22⋊C4—1221no—
197C2×C42—611no—
198C4⋊C8—612no—
199C4⋊C8—611no—
200C4⋊C8C2×D6111yescharacteristic, complemented
201#103—612no—
202#103C2×D6112yescomplemented
203#102—612no—
204#102—612no—
205C24—1221no—
206#41—1224no—
207#41—1224no—
208C2×Q8C22×D6112yes—
209C2×D4—614no—
210C2×D4—611no—
211C2×D4—612no—
212C2×D4—1222no—
213C2×D4—1222no—
214C2×D4—1221no—
215C2×D4—1221no—
216C2×D4—1221no—
217C2×D4C22×D6111yescharacteristic
218C22×C4—21no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—1221no—
223C22×C4—1222no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—2444no—
228SD16—24no—
229SD16—1224no—
230D8—1224no—
231D8—1224no—
232M16—1224no—
233C2×C8—612no—
234C2×C8C22×D6112yes—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—611no—
238C4⋊C4—1221no—
239C4⋊C4C22×D6111yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—1221no—
242C22⋊C4—1222no—
243C22⋊C4—1222no—
244C22⋊C4—1221no—
245C22⋊C4—1221no—
246C42—611no—
247C42—611no—
248C42—611no—
249C42C22×D6111yescharacteristic
250C23—21no—
251C23—611no—
252C23—1224no—
253C23—1221no—
254C23—1222no—
255C23—2442no—
256C23—2442no—
257Q8—22no—
258Q8—22no—
259D4—21no—
260D4—612no—
261D4—1224no—
262D4—1222no—
263D4—1221no—
264D4—1222no—
265D4—2442no—
266D4—2444no—
267D4—2442no—
268D4D4×D6112yes—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—611no—
273C2×C4—612no—
274C2×C4—612no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—1222no—
278C2×C4—1221no—
279C2×C4—2441no—
280C2×C4—2444no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4D4×D6111yescharacteristic
286C2×C4D4×D6111yescharacteristic
287C2×C4C23×D6111yescharacteristic
288C8—22no—
289C8—1222no—
290C22—22no—
291C22—41no—
292C22—41no—
293C22—612no—
294C22—1221no—
295C22—1221no—
296C22—1222no—
297C22—2448no—
298C22—2442no—
299C22—2442no—
300C22—2442no—
301C22—2441no—
302C22—2441no—
303C22C2×D4×D6111yescharacteristic
304C4—21no—
305C4—42no—
306C4—41no—
307C4—612no—
308C4—1221no—
309C4—1221no—
310C4—2441no—
311C4#1451980412yescomplemented
312C4C2×D4×D6111yescharacteristic
313C4#41×D6111yescharacteristic
314C2—42no—
315C2—1222no—
316C2—4882no—
317C2—2442no—
318C2#121×D6111yescharacteristic
319C2C2×#1451980411yescharacteristic
320C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3036
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. #16840313C2semidirect
3. C4×D4×D61C2semidirect
4. #16839980C2semidirect
5. #16839979C2semidirect
6. #16839964C2semidirect
7. #16839958C2semidirect
8. #16839957C2semidirect
9. #16839784C2semidirect
10. #16839762C2semidirect
11. C61×#461C2semidirect
20. #14519774C22semidirect
21. #14519766C22semidirect
34. C4⋊#92418C22semidirect
35. #14519706C22semidirect
36. #14519701C22semidirect
37. #14519699C22semidirect
38. #14519697C22semidirect
40. C4⋊Q8×C61C22semidirect
42. C4⋊C8×C61C22semidirect
43. #103×C61C22semidirect
53. D4×D61D4semidirect
146. C4×C61AGL(1,ℤ/8)semidirect
167. #461D61semidirect
172. C61#3036semidirect
182. C4⋊Q8C2×D61semidirect
200. C4⋊C8C2×D61semidirect
202. #103C2×D61semidirect
311. C4#14519804semidirect