Finite Group Databasebeta

← #21456211

Subgroups — #21456211

Order 7808.

424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#16840311C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840124C211yesmaximal, characteristic, complemented
4#16840122C211yesmaximal, characteristic, complemented
5#16840121C211yesmaximal, characteristic, complemented
6#16840111C212yesmaximal, complemented
7#16840107C212yesmaximal, complemented
8#16839762C212yesmaximal, complemented
9#16839760C212yesmaximal, complemented
10#16839714C211yesmaximal, characteristic, complemented
11C61×#489C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×#11758224C2211yescharacteristic
14C2×Q8×D61—21no—
15C2×#11758189C2212yes—
16#14519777C2211yescharacteristic
17#14519776—21no—
18#14519776C2212yes—
19#14519775—21no—
20#14519775C2211yescharacteristic
21#14519773C2211yescharacteristic
22#14519765C2211yescharacteristic
23#14519750—21no—
24#14519750—21no—
25#14519737—21no—
26#14519737—21no—
27C4⋊C4×D61—21no—
28C4⋊C4×D61C2212yes—
29C42×D61C2211yescharacteristic
30#14519702C2212yes—
31#14519701C2212yes—
32#14519700C2212yes—
33#14519699C2212yes—
34#14519698C2212yes—
35#14519697C2212yes—
36#14519688C2211yescharacteristic
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#124×C61C2211yescharacteristic
40#103×C61C2212yes—
41#102×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49C22×Dic61—21no—
50#11758226—24no—
51Q8×D61—44no—
52#11758224—24no—
53C2×D244—21no—
54C2×D244C2311yescharacteristic
55C2×C4×D61—22no—
56C2×C4×D61—21no—
57C2×C4×D61D411yescharacteristic
58C2×C4×D61D411yescharacteristic
59C2×C4×D61C2311yescharacteristic
60C2×Dic122—21no—
61C2×Dic122—22no—
62C2×Dic122C2311yescharacteristic
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2312yes—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—21no—
68C42×C61C2311yescharacteristic
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2312yes—
73#11758196—22no—
74#11758196—22no—
75#11758196—21no—
76#11758196—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81#11758189—24no—
82C23×C61—21no—
83C22×D61—21no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—22no—
86Q8×C61—42no—
87D4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—42no—
94C22⋊D61—42no—
95C22⋊D61—42no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—42no—
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102D244—22no—
103D244—42no—
104C4×D61—22no—
105C4×D61—22no—
106C4×D61—44no—
107C4×D61—42no—
108C4×D61#4114yes—
109Dic122—22no—
110Dic122—42no—
111Dic122—44no—
112C8×C61—22no—
113#92418—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61C22×D411yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61#12412yes—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—42no—
128C4×C61C2×#4112yes—
129Dic61—41no—
130Dic61—42no—
131Dic61#12412yes—
132Dic61AGL(1,ℤ/8)12yes—
133Dic61#13712yes—
134#3141—611nomaximal, Sylow
135C2×C61—81no—
136C2×C61C2×#12411yescharacteristic
137C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C61C2×#13711yescharacteristic
139D61—22no—
140D61—81no—
141#532—611no—
142C2×C4⋊Q8—611no—
143#489—611no—
144#489—611no—
145#489—611no—
146#489D6111yescharacteristic, complemented
147#487—612no—
148#486—612no—
149#417—612no—
150#417—612no—
151C4×M16—611no—
152C61#314111yescharacteristic, complemented, Sylow
153C2×#41—611no—
154C2×#41—611no—
155C22×Q8—1221no—
156C2×M16—612no—
157C4⋊Q8—612no—
158C4⋊Q8—611no—
159C4⋊Q8—611no—
160C4⋊Q8—1221no—
161C4⋊Q8—1221no—
162C4⋊Q8C2×D6111yescharacteristic
163#127—611no—
164#124—611no—
165#124C2×D6111yescharacteristic
166#121—1221no—
167#121—1221no—
168C4×D4—1221no—
169C4×D4—1221no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—1221no—
172C2×C42—611no—
173#103—612no—
174#103—612no—
175#103—612no—
176#103C2×D6112yes—
177#102—612no—
178#102—612no—
179#102—612no—
180#102C2×D6112yes—
181#97—611no—
182#97C2×D6111yescharacteristic
183C4×C8—612no—
184#41—1224no—
185#41—1224no—
186C2×Q8—21no—
187C2×Q8—611no—
188C2×Q8—1222no—
189C2×Q8—1221no—
190C2×Q8—2444no—
191C2×Q8C22×D6111yescharacteristic
192C2×D4—611no—
193C2×D4—1221no—
194C2×D4—1221no—
195C2×D4—1221no—
196C2×D4—1221no—
197C2×D4C22×D6111yescharacteristic
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—1221no—
202C22×C4—1222no—
203C22×C4—1221no—
204M16—1224no—
205C2×C8—612no—
206C2×C8C22×D6112yes—
207C4⋊C4—21no—
208C4⋊C4—612no—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4C22×D6112yes—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42C22×D6111yescharacteristic
223C23—21no—
224C23—611no—
225C23—1221no—
226Q8—22no—
227Q8—42no—
228Q8—1222no—
229Q8—2442no—
230Q8—2444no—
231D4—22no—
232D4—1222no—
233D4—2442no—
234D4—2442no—
235D4—2442no—
236D4—2442no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—614no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—2442no—
248C2×C4—2444no—
249C2×C4—2442no—
250C2×C4D4×D6111yescharacteristic
251C2×C4D4×D6111yescharacteristic
252C2×C4C23×D6111yescharacteristic
253C8—22no—
254C8—1222no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—612no—
259C22—1221no—
260C22—1221no—
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22C2×D4×D6111yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—42no—
269C4—612no—
270C4—612no—
271C4—612no—
272C4—2441no—
273C4—2442no—
274C4#41×D6112yes—
275C2—81no—
276C2—1222no—
277C2—4881no—
278C2#124×D6111yescharacteristic
279C2AGL(1,ℤ/8)×D6111yescharacteristic
280C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61#3141
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D61C2semidirect
3. #16840124C2semidirect
4. #16840122C2semidirect
5. #16840121C2semidirect
6. #16840111C2semidirect
7. #16840107C2semidirect
8. #16839762C2semidirect
9. #16839760C2semidirect
10. #16839714C2semidirect
11. C61×#489C2semidirect
146. #489D61semidirect
152. C61#3141semidirect