Finite Group Databasebeta

← #21457193

Subgroups — #21457193

Order 7808.

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

normal subgroups only

This group has 348 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#16840319C211yesmaximal, characteristic, complemented
2#16840296C211yesmaximal, characteristic
3#16840070C212yesmaximal, complemented
4#16840058C211yesmaximal, characteristic, complemented
5#16840053C211yesmaximal, characteristic, complemented
6#16840020C212yesmaximal, complemented
7#16840008C212yesmaximal
8#16839985C212yesmaximal, complemented
9#16839973C211yesmaximal, characteristic, complemented
10#16839968C211yesmaximal, characteristic, complemented
11C61×#423C211yesmaximal, characteristic, complemented
12C2×Dic244C2212yes—
13C2×#11758190C2212yes—
14#14519777C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519771—21no—
17#14519769—21no—
18#14519769C2211yescharacteristic
19#14519765C2211yescharacteristic
20#14519760—21no—
21#14519756—21no—
22#14519756C2212yes—
23#14519756C2211yescharacteristic
24#14519751C2211yescharacteristic
25C4×Dic122—21no—
26C4×Dic122C2211yescharacteristic
27C4×Dic122C2212yes—
28C4×D244C2211yescharacteristic
29C4×C22⋊D61—21no—
30#14519736—21no—
31#14519734—21no—
32#14519711C2212yes—
33#14519709C2212yes—
34#14519702C2212yes—
35#14519702C2212yes—
36#14519702C2212yes—
37#14519699C2212yes—
38C2×M16×C61C2212yes—
39C2×C42×C61C2211yescharacteristic
40C4⋊C8×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42C4⋊C8×C61C2212yes—
43C22×C4×C61D411yescharacteristic
44C22×C4×C61D411yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—21no—
49C2×Dic122—21no—
50C2×Dic122C2311yescharacteristic
51C2×Dic122C2312yes—
52M16×C61—42no—
53C2×C8×C61C2312yes—
54C2×C8×C61C2312yes—
55C42×C61D411yescharacteristic
56C42×C61D411yescharacteristic
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60C22⋊Dic61—21no—
61#11758198—21no—
62#11758198—21no—
63#11758198—21no—
64#11758198—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61C2312yes—
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74#11758196—22no—
75#11758196—22no—
76#11758196—21no—
77C4×Dic61—21no—
78C4×Dic61—22no—
79Dic244—42no—
80#11758190—42no—
81C23×C61C2×D411yescharacteristic
82C22×D61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—42no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99D244—21no—
100D244—21no—
101C4×D61—42no—
102Dic122—22no—
103Dic122—21no—
104Dic122—21no—
105Dic122—22no—
106Dic122—42no—
107C8×C61—22no—
108C8×C61—22no—
109C22×C61—21no—
110C22×C61—21no—
111C22×C61—21no—
112C22×C61C22×D411yescharacteristic
113C2×D61—41no—
114C2×D61—41no—
115C2×D61—41no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61#13712yes—
121C4×C61H(5,𝔽2)11yescharacteristic
122C4×C612−1+411yescharacteristic
123Dic61—42no—
124Dic61—41no—
125Dic61—41no—
126Dic61—42no—
127Dic61—41no—
128#3252—611nomaximal, Sylow
129C2×C61—41no—
130C2×C61#53711yescharacteristic
131C2×C61C2×#13711yescharacteristic
132C2×C61#57511yescharacteristic
133D61—81no—
134#533—611no—
135#529—611no—
136#479—612no—
137#477—611no—
138#476—611no—
139#470—612no—
140#468—612no—
141#464—612no—
142#462—611no—
143#461—611no—
144#423D6111yescharacteristic, complemented
145C61#325211yescharacteristic, complemented, Sylow
146C2×Q16—612no—
147C2×SD16—612no—
148C2×M16C2×D6112yes—
149C4⋊Q8—611no—
150C4⋊Q8—611no—
151#126—1221no—
152#125—611no—
153#125—1221no—
154#124—611no—
155#123—1221no—
156C22⋊Q8—611no—
157C22⋊Q8—612no—
158C22⋊Q8—1221no—
159#121—611no—
160C4×Q8—611no—
161C4×Q8—612no—
162C4×Q8—1221no—
163C4×D4—611no—
164C4×D4—1221no—
165#117—1221no—
166#117—1221no—
167C2×C42C2×D6111yescharacteristic
168#107—612no—
169#106—612no—
170C4⋊C8C2×D6111yescharacteristic
171C4⋊C8C2×D6111yescharacteristic
172C4⋊C8C2×D6112yes—
173#103—612no—
174#103—612no—
175#103—612no—
176#102—612no—
177C2×Q8—611no—
178C2×Q8—612no—
179C2×Q8—1221no—
180C2×D4—611no—
181C2×D4—1221no—
182C22×C4—1221no—
183C22×C4D24411yescharacteristic
184C22×C4D24411yescharacteristic
185C22×C4C22×D6111yescharacteristic
186Q16—2442no—
187SD16—2442no—
188M16—42no—
189C2×C8C22×D6112yes—
190C2×C8C22×D6112yes—
191C4⋊C4—612no—
192C4⋊C4—611no—
193C4⋊C4—611no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1222no—
198C4⋊C4—1221no—
199C4⋊C4—1222no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4—1221no—
203C22⋊C4—1222no—
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C22⋊C4—1221no—
207C22⋊C4—1221no—
208C22⋊C4—1221no—
209C42—1221no—
210C42—1222no—
211C42D24411yescharacteristic
212C42D24411yescharacteristic
213C42C22×D6111yescharacteristic
214C42C22×D6111yescharacteristic
215C23—1221no—
216C23C2×D24411yescharacteristic
217Q8—1222no—
218Q8—1221no—
219Q8—1221no—
220Q8—1222no—
221Q8—2442no—
222D4—1221no—
223D4—1221no—
224D4—2442no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—2442no—
235C2×C4C2×D24411yescharacteristic
236C2×C4C2×D24411yescharacteristic
237C2×C4C2×D24411yescharacteristic
238C2×C4C2×D24411yescharacteristic
239C2×C4C2×D24411yescharacteristic
240C2×C4C23×D6111yescharacteristic
241C8—22no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—2441no—
247C22—2441no—
248C22—2441no—
249C22C22×D24411yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—2441no—
255C4—2441no—
256C4—2442no—
257C4—2441no—
258C4—2442no—
259C4#1451981012yes—
260C4#1451982211yescharacteristic
261C4#1451982511yescharacteristic
262C2—41no—
263C2—4881no—
264C2#1684034311yescharacteristic
265C2C2×#1451981011yescharacteristic
266C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#423C2
socleC22×C61C22×D4
hypercenter#423D61
hypocenterC61#3252
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
3. #16840070C2semidirect
4. #16840058C2semidirect
5. #16840053C2semidirect
6. #16840020C2semidirect
8. #16839985C2semidirect
9. #16839973C2semidirect
10. #16839968C2semidirect
11. C61×#423C2semidirect
144. #423D61semidirect
145. C61#3252semidirect