Finite Group Databasebeta

← #21457203

Subgroups — #21457203

Order 7808.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840317C211yesmaximal, characteristic, complemented
2#16840309C211yesmaximal, characteristic
3#16840055C212yesmaximal, complemented
4#16840043C211yesmaximal, characteristic, complemented
5#16840042C211yesmaximal, characteristic, complemented
6#16840011C212yesmaximal, complemented
7#16840005C212yesmaximal, complemented
8#16839964C211yesmaximal, characteristic, complemented
9#16839960C212yesmaximal, complemented
10#16839784C211yesmaximal, characteristic, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13C2×#11758201C2212yes—
14C2×#11758189C2212yes—
15#14519777C2211yescharacteristic
16#14519776C2211yescharacteristic
17#14519773C2211yescharacteristic
18#14519768—21no—
19#14519763—21no—
20#14519757—21no—
21#14519753C2212yes—
22#14519752C2211yescharacteristic
23#14519750—21no—
24#14519748C2211yescharacteristic
25Q8×Dic61C2212yes—
26#14519742—21no—
27C4×D244C2211yescharacteristic
28C4×C22⋊D61—21no—
29#14519735—21no—
30C42×D61C2211yescharacteristic
31#14519711C2212yes—
32#14519710C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519701C2212yes—
36#14519699C2212yes—
37#14519698C2212yes—
38C2×SD16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61C2312yes—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49#11758222—44no—
50C2×D244—21no—
51C2×D244C2311yescharacteristic
52C2×C4×D61—21no—
53C2×C4×D61D411yescharacteristic
54C2×C4×D61D411yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×Dic122—21no—
57C2×Dic122—21no—
58SD16×C61—42no—
59C2×C8×C61C2312yes—
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C42×C61C2311yescharacteristic
65C22⋊Dic61—21no—
66#11758201—42no—
67#11758198—22no—
68#11758198—21no—
69#11758198—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—22no—
72C4⋊Dic61C2312yes—
73C4⋊Dic61C2311yescharacteristic
74#11758196—21no—
75#11758196—22no—
76C4×Dic61—22no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81#11758189—42no—
82C23×C61—21no—
83C22×D61—21no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—22no—
86Q8×C61—22no—
87D4×C61—21no—
88D4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—42no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—42no—
96C22⋊D61—42no—
97C22⋊D61—42no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103D244—21no—
104D244—21no—
105D244—42no—
106C4×D61—22no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—22no—
110C4×D61—42no—
111Dic122—42no—
112Dic122—42no—
113C8×C61—22no—
114#92418—22no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61C22×D411yescharacteristic
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—41no—
125C4×C61—21no—
126C4×C61—42no—
127C4×C61—41no—
128C4×C61AGL(1,ℤ/8)12yes—
129C4×C61H(5,𝔽2)11yescharacteristic
130C4×C612−1+411yescharacteristic
131Dic61—21no—
132Dic61—21no—
133Dic61—41no—
134Dic61—42no—
135Dic61#13712yes—
136#3254—611nomaximal, Sylow
137C2×C61—81no—
138C2×C61#53711yescharacteristic
139C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
140C2×C61C2×#13711yescharacteristic
141D61—41no—
142D61—81no—
143#533—611no—
144#532—611no—
145#477—612no—
146#474—611no—
147#474—611no—
148#468—612no—
149#468—612no—
150#461—611no—
151#461D6111yescharacteristic, complemented
152#460—612no—
153#423—611no—
154C61#325411yescharacteristic, complemented, Sylow
155C2×#41—1221no—
156C2×SD16—612no—
157C2×SD16C2×D6112yes—
158C2×M16—612no—
159C4⋊Q8—611no—
160C4⋊Q8—611no—
161C4⋊Q8C2×D6111yescharacteristic
162#127—611no—
163#125—1221no—
164#124—1221no—
165C22⋊Q8—612no—
166C22⋊Q8—1221no—
167#121—611no—
168#121—611no—
169#121—1221no—
170C4×Q8—612no—
171C4×Q8—1221no—
172C4×D4—611no—
173C4×D4—1221no—
174C4×D4C2×D6111yescharacteristic
175#117—1221no—
176C2×C42—611no—
177#107—612no—
178#107—612no—
179C4⋊C8—612no—
180C4⋊C8—611no—
181C4⋊C8C2×D6111yescharacteristic
182#103—612no—
183#103C2×D6112yes—
184#102—612no—
185#102—612no—
186#41—2444no—
187C2×Q8—1221no—
188C2×Q8—1221no—
189C2×Q8C22×D6112yes—
190C2×D4—611no—
191C2×D4—1221no—
192C2×D4—1221no—
193C2×D4—1221no—
194C2×D4—1221no—
195C2×D4C22×D6111yescharacteristic
196C22×C4—21no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1221no—
201SD16—42no—
202SD16—2442no—
203M16—2442no—
204C2×C8—612no—
205C2×C8C22×D6112yes—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—612no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—1222no—
212C4⋊C4—1222no—
213C4⋊C4—1221no—
214C4⋊C4C22×D6111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—1221no—
217C22⋊C4—1222no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42—1222no—
224C42C22×D6111yescharacteristic
225C23—21no—
226C23—611no—
227C23—1221no—
228Q8—22no—
229Q8—22no—
230Q8—2442no—
231Q8—2442no—
232D4—21no—
233D4—21no—
234D4—1221no—
235D4—1221no—
236D4—2442no—
237D4—2442no—
238D4—2442no—
239D4—2442no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1221no—
252C2×C4—2442no—
253C2×C4D4×D6111yescharacteristic
254C2×C4D4×D6111yescharacteristic
255C2×C4C23×D6111yescharacteristic
256C8—22no—
257C8—1222no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—1221no—
262C22—1221no—
263C22—1221no—
264C22—2441no—
265C22—2441no—
266C22—2441no—
267C22C2×D4×D6111yescharacteristic
268C4—21no—
269C4—41no—
270C4—42no—
271C4—612no—
272C4—1221no—
273C4—1221no—
274C4—2441no—
275C4—2442no—
276C4#1451980412yes—
277C4#1451982211yescharacteristic
278C4#1451982411yescharacteristic
279C2—81no—
280C2—4881no—
281C2—2441no—
282C2#1684034111yescharacteristic
283C2C2×#1451980411yescharacteristic
284C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3254
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. #16840317C2semidirect
3. #16840055C2semidirect
4. #16840043C2semidirect
5. #16840042C2semidirect
6. #16840011C2semidirect
7. #16840005C2semidirect
8. #16839964C2semidirect
9. #16839960C2semidirect
10. #16839784C2semidirect
11. C61×#461C2semidirect
151. #461D61semidirect
154. C61#3254semidirect