Finite Group Databasebeta

← #21455371

Subgroups — #21455371

Order 7808.

472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519810C211yesmaximal, characteristic, complemented
2C2×#14519799C211yesmaximal, characteristic
3#16840338C211yesmaximal, characteristic, complemented
4#16840242C211yesmaximal, characteristic, complemented
5#16839985C212yesmaximal, complemented
6#16839978C212yesmaximal, complemented
7#16839973C212yesmaximal, complemented
8#16839968C212yesmaximal, complemented
9#16839764C211yesmaximal, characteristic, complemented
10C2×#14519702C211yesmaximal, characteristic, complemented
11C61×#424C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C22×Dic122C2211yescharacteristic
15#14519810—24no—
16#14519799—24no—
17C2×Dic244C2211yescharacteristic
18C2×Dic244C2212yes—
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2212yes—
21C2×#11758190C2211yescharacteristic
22C2×D488C2211yescharacteristic
23#14519777C2212yes—
24#14519765C2212yes—
25#14519761—22no—
26#14519757—21no—
27#14519757—21no—
28C4×Dic122C2212yes—
29C4×D244C2212yes—
30#14519737—22no—
31#14519735—21no—
32C2×C4⋊Dic61C2211yescharacteristic
33C4⋊C4×D61—21no—
34#14519702C2212yes—
35#14519702C2212yes—
36#14519702C2212yes—
37#14519699C2212yes—
38C2×M16×C61C2211yescharacteristic
39C22×C8×C61C2211yescharacteristic
40#117×C61C2211yescharacteristic
41C4⋊C8×C61C2212yes—
42C4⋊C8×C61C2212yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—21no—
45C2×C22⋊D61—21no—
46C22×Dic61—21no—
47C22×Dic61—21no—
48#11758222—22no—
49#11758222—22no—
50#11758222—22no—
51#11758222D414yes—
52C2×D244C2311yescharacteristic
53C2×D244C2311yescharacteristic
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—22no—
57C2×Dic122—22no—
58C2×Dic122—22no—
59C2×Dic122—21no—
60C2×Dic122C2312yes—
61C2×Dic122C2311yescharacteristic
62C2×Dic122C2311yescharacteristic
63M16×C61—22no—
64C2×C8×C61—22no—
65C2×C8×C61C2311yescharacteristic
66C2×C8×C61C2311yescharacteristic
67C2×C8×C61C2312yes—
68C4⋊C4×C61D411yescharacteristic
69C4⋊C4×C61D411yescharacteristic
70C22⋊C4×C61D412yes—
71C42×C61C2312yes—
72#11758198—22no—
73#11758198—22no—
74#11758198—22no—
75C4⋊Dic61—21no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61C2312yes—
79#11758196—22no—
80C4×Dic61—22no—
81Dic244—24no—
82Dic244—22no—
83D488—22no—
84#11758190—24no—
85#11758190—22no—
86#11758190—22no—
87C23×C61C2×D411yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90C2×C4×C61C2×D412yes—
91C2×C4×C61C2×D412yes—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D412yes—
94C2×C4×C61#4112yes—
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—24no—
97C22⋊D61—42no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—42no—
103C2×Dic61—81no—
104D244—21no—
105D244—21no—
106D244—21no—
107D244C2×D412yes—
108C4×D61—24no—
109C4×D61—42no—
110C4×D61—82no—
111Dic122—21no—
112Dic122—22no—
113Dic122—21no—
114Dic122—22no—
115Dic122—21no—
116Dic122—42no—
117Dic122C2×D412yes—
118C8×C61—21no—
119C8×C61—22no—
120C8×C61—21no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#12112yes—
124C22×C61C22×D411yescharacteristic
125C2×D61—22no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—41no—
131C4×C61—22no—
132C4×C61—22no—
133C4×C61#12112yes—
134C4×C61C22×D411yescharacteristic
135C4×C61C2×#4111yescharacteristic
136Dic61—22no—
137Dic61—42no—
138Dic61—41no—
139Dic61—42no—
140#3046—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61C2×#12111yescharacteristic
143C2×C61#57711yescharacteristic
144C2×C61#57811yescharacteristic
145D61—42no—
146D61—81no—
147C2×#137—611no—
148C2×#135—611no—
149#536—611no—
150#520—611no—
151#464—612no—
152#463—612no—
153#462—612no—
154#461—612no—
155#424D6111yescharacteristic, complemented
156#417—611no—
157C2×#103—611no—
158C61#304611yescharacteristic, complemented, Sylow
159C2×#41—611no—
160C2×#41—611no—
161C22×Q8—611no—
162#137—1224no—
163#135—1224no—
164C2×Q16—611no—
165C2×Q16—612no—
166C2×SD16—611no—
167C2×SD16—611no—
168C2×SD16—612no—
169C2×D8—611no—
170C2×M16C2×D6111yescharacteristic
171C22×C8C2×D6111yescharacteristic
172C4⋊Q8—612no—
173#124—612no—
174#123—1222no—
175C22⋊Q8—1221no—
176C22⋊Q8—1221no—
177C4×Q8—612no—
178C4×D4—612no—
179C4×D4—1222no—
180#117—1221no—
181#117C2×D6111yescharacteristic
182C2×C4⋊C4—611no—
183C2×C4⋊C4—1221no—
184C4⋊C8C2×D6112yes—
185C4⋊C8C2×D6112yes—
186#103—612no—
187#103—612no—
188#103—612no—
189#102—612no—
190#41—614no—
191#41—1222no—
192#41—1222no—
193#41—1222no—
194C2×Q8—611no—
195C2×Q8—612no—
196C2×Q8—611no—
197C2×Q8—1221no—
198C2×Q8—1222no—
199C2×Q8—1222no—
200C2×D4—611no—
201C2×D4—611no—
202C2×D4—1221no—
203C2×D4—1221no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4—1221no—
207C22×C4—1222no—
208C22×C4—1221no—
209C22×C4C22×D6111yescharacteristic
210Q16—1222no—
211Q16—1224no—
212SD16—1222no—
213SD16—1224no—
214SD16—1222no—
215D8—1222no—
216M16—22no—
217C2×C8—22no—
218C2×C8C22×D6112yes—
219C2×C8C22×D6111yescharacteristic
220C2×C8C22×D6111yescharacteristic
221C4⋊C4—612no—
222C4⋊C4—1221no—
223C4⋊C4—1222no—
224C4⋊C4—1222no—
225C4⋊C4—1222no—
226C4⋊C4D24411yescharacteristic
227C4⋊C4D24411yescharacteristic
228C22⋊C4—1222no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4D24412yes—
232C42—1222no—
233C42C22×D6112yes—
234C23—1221no—
235C23—1221no—
236C23C2×D24411yescharacteristic
237Q8—612no—
238Q8—1221no—
239Q8—1222no—
240Q8—1221no—
241Q8—1222no—
242Q8—1221no—
243Q8—2442no—
244D4—612no—
245D4—1224no—
246D4—1221no—
247D4—1221no—
248D4—1221no—
249D4—2442no—
250C2×C4—1221no—
251C2×C4—1224no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1221no—
255C2×C4—4882no—
256C2×C4—4881no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4C2×D24412yes—
260C2×C4C2×D24412yes—
261C2×C4C2×D24411yescharacteristic
262C2×C4D4×D6112yes—
263C2×C4#1175822612yes—
264C2×C4C23×D6111yescharacteristic
265C8—21no—
266C8—21no—
267C8—22no—
268C22—21no—
269C22—21no—
270C22—1222no—
271C22—2441no—
272C22—2441no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22#1451975212yes—
277C22C22×D24411yescharacteristic
278C4—22no—
279C4—22no—
280C4—1222no—
281C4—2441no—
282C4—2442no—
283C4—2442no—
284C4#1451975212yes—
285C4C2×D4×D6111yescharacteristic
286C4C2×#1175822611yescharacteristic
287C2—22no—
288C2—4881no—
289C2—2442no—
290C2C2×#1451975211yescharacteristic
291C2#1684057411yescharacteristic
292C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
3. #16840338C2semidirect
4. #16840242C2semidirect
5. #16839985C2semidirect
6. #16839978C2semidirect
7. #16839973C2semidirect
8. #16839968C2semidirect
9. #16839764C2semidirect
10. C2×#14519702C2semidirect
11. C61×#424C2semidirect
155. #424D61semidirect
158. C61#3046semidirect