Finite Group Databasebeta

← #21457152

Subgroups — #21457152

Order 7808.

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

normal subgroups only

This group has 354 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#16840294C211yesmaximal, characteristic
3#16840067C212yesmaximal, complemented
4#16840048C211yesmaximal, characteristic, complemented
5#16840042C211yesmaximal, characteristic, complemented
6#16840002C212yesmaximal, complemented
7#16839988C212yesmaximal
8#16839982C212yesmaximal, complemented
9#16839969C211yesmaximal, characteristic, complemented
10C4⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×C8×D61C2212yes—
14#14519777C2211yescharacteristic
15#14519770—21no—
16#14519768—21no—
17#14519768C2211yescharacteristic
18#14519764C2211yescharacteristic
19#14519759—21no—
20#14519757—21no—
21#14519757C2211yescharacteristic
22#14519753C2212yes—
23#14519748C2211yescharacteristic
24Q8×Dic61C2212yes—
25C4×Dic122C2211yescharacteristic
26#14519742—21no—
27C4×C22⋊D61—21no—
28#14519736—21no—
29#14519735—21no—
30C42×D61C2211yescharacteristic
31#14519710C2212yes—
32#14519709C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519702C2212yes—
36#14519701C2212yes—
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×C4×D61D411yescharacteristic
48C2×C4×D61D411yescharacteristic
49C2×C4×D61C2311yescharacteristic
50C2×Dic122—21no—
51C2×Dic122C2311yescharacteristic
52SD16×C61—42no—
53C2×C8×C61C2312yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2311yescharacteristic
57C22⋊C4×C61—21no—
58C42×C61C2311yescharacteristic
59C22⋊Dic61—21no—
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62#11758202—42no—
63#11758198—22no—
64#11758198—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—22no—
69C4⋊Dic61C2312yes—
70C4⋊Dic61C2311yescharacteristic
71#11758196—21no—
72#11758196—21no—
73#11758196—22no—
74C4×Dic61—21no—
75C4×Dic61—22no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80C8×D61—42no—
81C23×C61—21no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—22no—
84Q8×C61—22no—
85D4×C61—21no—
86D4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—42no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100C4×D61—22no—
101C4×D61—22no—
102C4×D61—21no—
103C4×D61—21no—
104Dic122—21no—
105Dic122—21no—
106Dic122—42no—
107C8×C61—22no—
108#92418—22no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61C22×D411yescharacteristic
113C2×D61—21no—
114C2×D61—21no—
115C2×D61#13712yes—
116C4×C61—21no—
117C4×C61—42no—
118C4×C61—41no—
119C4×C61#13512yes—
120C4×C61H(5,𝔽2)11yescharacteristic
121C4×C612−1+411yescharacteristic
122Dic61—21no—
123Dic61—21no—
124Dic61—21no—
125Dic61—41no—
126Dic61—42no—
127Dic61—41no—
128#3248—611nomaximal, Sylow
129C2×C61—81no—
130C2×C61#53711yescharacteristic
131C2×C61C2×#13511yescharacteristic
132C2×C61C2×#13711yescharacteristic
133D61—22no—
134#533—611no—
135#529—611no—
136#479—612no—
137#475—611no—
138#474—611no—
139#467—612no—
140#465—612no—
141#464—612no—
142#462—611no—
143#461D6111yescharacteristic, complemented
144C2×C4⋊C8—611no—
145C61#324811yescharacteristic, complemented, Sylow
146C2×Q16—612no—
147C2×SD16C2×D6112yes—
148C22×C8—612no—
149C4⋊Q8—611no—
150C4⋊Q8C2×D6111yescharacteristic
151#126—1221no—
152#125—611no—
153#125—1221no—
154#124—611no—
155#123—1221no—
156C22⋊Q8—612no—
157C22⋊Q8—611no—
158C22⋊Q8—1221no—
159#121—611no—
160C4×Q8—612no—
161C4×Q8—611no—
162C4×Q8—1221no—
163C4×D4—1221no—
164C4×D4C2×D6111yescharacteristic
165#117—1221no—
166#117—1221no—
167C2×C42—611no—
168#107—612no—
169#106—612no—
170C4⋊C8—612no—
171C4⋊C8—611no—
172C4⋊C8C2×D6111yescharacteristic
173#103—612no—
174#103—612no—
175#103C2×D6112yes—
176#102—612no—
177C2×Q8—611no—
178C2×Q8—1221no—
179C2×Q8C22×D6112yes—
180C2×D4—1221no—
181C2×D4C22×D6111yescharacteristic
182C22×C4—21no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186Q16—2442no—
187SD16—42no—
188C2×C8—612no—
189C2×C8—2442no—
190C2×C8C22×D6112yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—612no—
194C4⋊C4—611no—
195C4⋊C4—1221no—
196C4⋊C4—1222no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C4⋊C4—1222no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4C22×D6111yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—1222no—
205C22⋊C4—1221no—
206C22⋊C4—1221no—
207C22⋊C4—1221no—
208C22⋊C4—1221no—
209C42—611no—
210C42—611no—
211C42—611no—
212C42—1222no—
213C42—1221no—
214C42C22×D6111yescharacteristic
215C23—21no—
216C23—611no—
217Q8—22no—
218Q8—22no—
219Q8—1221no—
220Q8—1221no—
221Q8—2442no—
222D4—21no—
223D4—21no—
224D4—2442no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—1222no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1222no—
238C2×C4D4×D6111yescharacteristic
239C2×C4D4×D6111yescharacteristic
240C2×C4C23×D6111yescharacteristic
241C8—22no—
242C8—1222no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—612no—
247C22—1221no—
248C22—1221no—
249C22C2×D4×D6111yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—1221no—
254C4—1221no—
255C4—1221no—
256C4—2442no—
257C4—2441no—
258C4—2441no—
259C4#1451979812yes—
260C4#1451982211yescharacteristic
261C4#1451982411yescharacteristic
262C2—81no—
263C2—1222no—
264C2#1684034111yescharacteristic
265C2C2×#1451979811yescharacteristic
266C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3248
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. #16840067C2semidirect
4. #16840048C2semidirect
5. #16840042C2semidirect
6. #16840002C2semidirect
8. #16839982C2semidirect
9. #16839969C2semidirect
10. C4⋊C8×D61C2semidirect
11. C61×#461C2semidirect
143. #461D61semidirect
145. C61#3248semidirect