Finite Group Databasebeta

← #21457464

Subgroups — #21457464

Order 7808.

472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519809C212yesmaximal, complemented
2#16840427C211yesmaximal, characteristic, complemented
3#16840415C211yesmaximal, characteristic
4#16840017C212yesmaximal, complemented
5#16839969C211yesmaximal, characteristic, complemented
6#16839964C211yesmaximal, characteristic, complemented
7#16839923C212yesmaximal, complemented
8#16839916C212yesmaximal, complemented
9C4×#11758190C211yesmaximal, characteristic, complemented
10#16839841C211yesmaximal, characteristic, complemented
11C61×#494C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×Q8×D61C2212yes—
14#14519809—28no—
15C2×#11758202C2212yes—
16C2×#11758190C2211yescharacteristic
17C2×#11758201C2212yes—
18C2×#11758189C2212yes—
19#14519776—21no—
20#14519762—22no—
21#14519755—22no—
22#14519753C2212yes—
23#14519753C2212yes—
24#14519752—21no—
25C4×Dic122C2211yescharacteristic
26C4×D244C2211yescharacteristic
27C4×D244C2211yescharacteristic
28#14519739—21no—
29C4⋊C4×D61—21no—
30#14519709C2211yescharacteristic
31C4⋊#92418C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519701C2212yes—
34#14519701C2212yes—
35#14519699C2211yescharacteristic
36#14519689C2212yes—
37C2×Q16×C61C2212yes—
38C2×Q16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4⋊Q8×C61C2211yescharacteristic
41C4×C8×C61C2211yescharacteristic
42C2×Q8×C61C2312yes—
43C2×Q8×C61C2312yes—
44#11758226—24no—
45#11758226—42no—
46Q8×D61—24no—
47Q8×D61—42no—
48C2×D244—22no—
49C2×D244D411yescharacteristic
50C2×D244C2311yescharacteristic
51C2×C4×D61—22no—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×C4×D61C2312yes—
55C2×Dic122—22no—
56C2×Dic122C2311yescharacteristic
57Q16×C61—24no—
58Q16×C61—42no—
59C2×C8×C61C2311yescharacteristic
60C2×C8×C61C2311yescharacteristic
61C4⋊C4×C61—21no—
62C4⋊C4×C61—21no—
63C4⋊C4×C61—21no—
64C4⋊C4×C61—21no—
65C42×C61C2311yescharacteristic
66#11758202—24no—
67#11758201—24no—
68#11758198—22no—
69#11758198—22no—
70#11758198—21no—
71#11758198D412yes—
72C4⋊Dic61D411yescharacteristic
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—22no—
77#11758196—22no—
78C4×Dic61—21no—
79C2×#92418C2312yes—
80#11758190D414yescomplemented
81#11758189—24no—
82C22×D61—21no—
83C22×D61C2×D412yes—
84Q8×C61—22no—
85Q8×C61—22no—
86Q8×C61—22no—
87Q8×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61C2×D412yes—
97D244—22no—
98D244—21no—
99D244—44no—
100D244C2×D412yes—
101C4×D61—22no—
102C4×D61—22no—
103C4×D61—44no—
104C4×D61—44no—
105C4×D61—42no—
106Dic122—21no—
107Dic122—44no—
108Dic122C2×D412yes—
109C8×C61—21no—
110C8×C61C2×D412yes—
111#92418—22no—
112C22×C61C22×D411yescharacteristic
113C2×D61—22no—
114C2×D61—22no—
115C2×D61—22no—
116C2×D61—22no—
117C2×D61—41no—
118C2×D61—41no—
119C4×C61—21no—
120C4×C61—42no—
121C4×C61—42no—
122C4×C61#13712yescomplemented
123C4×C61C22×D411yescharacteristic
124C4×C61H(5,𝔽2)11yescharacteristic
125Dic61—22no—
126Dic61—22no—
127Dic61—41no—
128Dic61—41no—
129#3276—611nomaximal, Sylow
130C2×C61D4211yescharacteristic
131C2×C61C2×#13711yescharacteristic
132C2×C61#57811yescharacteristic
133D61—42no—
134D61—42no—
135C2×#137—612no—
136D4×Q8—611no—
137#547—611no—
138#494D6111yescharacteristic, complemented
139#470—612no—
140#462—611no—
141#461—611no—
142#452—612no—
143#451—612no—
144C4×SD16—611no—
145#436—611no—
146C61#327611yescharacteristic, complemented, Sylow
147C2×#41—612no—
148C22×Q8—612no—
149#137—1228no—
150C2×Q16—612no—
151C2×Q16C2×D6112yes—
152C2×Q16C2×D6112yes—
153C2×SD16—612no—
154C2×SD16—611no—
155C2×M16—612no—
156C4⋊Q8—1221no—
157C4⋊Q8C2×D6111yescharacteristic
158C4⋊Q8C2×D6111yescharacteristic
159#123—1222no—
160C22⋊Q8—612no—
161C22⋊Q8—612no—
162C22⋊Q8—1222no—
163#121—1221no—
164C4×Q8—611no—
165C4×D4—611no—
166C4×D4—611no—
167C4×D4—1221no—
168C2×C4⋊C4—1221no—
169#106—611no—
170C4⋊C8—611no—
171#103—612no—
172#103—612no—
173#103—611no—
174#102—611no—
175C22⋊C8—612no—
176C4×C8C2×D6111yescharacteristic
177#41—1224no—
178#41—2442no—
179C2×Q8—611no—
180C2×Q8—1222no—
181C2×Q8—1224no—
182C2×Q8—2442no—
183C2×Q8C22×D6112yes—
184C2×Q8C22×D6112yes—
185C2×D4—611no—
186C2×D4—611no—
187C2×D4—1222no—
188C22×C4—612no—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4—1221no—
192Q16—24no—
193Q16—42no—
194Q16—1224no—
195SD16—614no—
196SD16—1224no—
197M16—1224no—
198C2×C8—612no—
199C2×C8C22×D6111yescharacteristic
200C2×C8C22×D6111yescharacteristic
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—611no—
206C4⋊C4—611no—
207C4⋊C4—611no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C4⋊C4—1221no—
211C22⋊C4—612no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C22⋊C4—1221no—
215C42—1221no—
216C42C22×D6111yescharacteristic
217C23—612no—
218C23—1221no—
219Q8—22no—
220Q8—22no—
221Q8—22no—
222Q8—22no—
223Q8—612no—
224Q8—1221no—
225Q8—2444no—
226D4—612no—
227D4—1222no—
228D4—1221no—
229D4—2444no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—612no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—2444no—
239C2×C4—2444no—
240C2×C4—2442no—
241C2×C4D4×D6111yescharacteristic
242C2×C4D4×D6111yescharacteristic
243C2×C4C23×D6111yescharacteristic
244C8—21no—
245C8—1222no—
246C8D4×D6112yes—
247C22—1222no—
248C22—1222no—
249C22—1222no—
250C22—1222no—
251C22—2441no—
252C22—2441no—
253C22C2×D4×D6111yescharacteristic
254C4—21no—
255C4—42no—
256C4—42no—
257C4—1222no—
258C4—1222no—
259C4—2441no—
260C4—2441no—
261C4#1451980912yescomplemented
262C4C2×D4×D6111yescharacteristic
263C4#1451982211yescharacteristic
264C2—2442no—
265C2—2442no—
266C2#1684039711yescharacteristic
267C2C2×#1451980911yescharacteristic
268C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#494C2
socleC22×C61C22×D4
hypercenter#494D61
hypocenterC61#3276
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. #16840427C2semidirect
4. #16840017C2semidirect
5. #16839969C2semidirect
6. #16839964C2semidirect
7. #16839923C2semidirect
8. #16839916C2semidirect
9. C4×#11758190C2semidirect
10. #16839841C2semidirect
11. C61×#494C2semidirect
80. #11758190D4semidirect
122. C4×C61#137semidirect
138. #494D61semidirect
146. C61#3276semidirect
261. C4#14519809semidirect