Finite Group Databasebeta

← #21457211

Subgroups — #21457211

Order 7808.

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

normal subgroups only

This group has 342 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
2#16840316C211yesmaximal, characteristic
3#16840048C211yesmaximal, characteristic, complemented
4#16840047C211yesmaximal, characteristic, complemented
5#16840045C212yesmaximal, complemented
6#16840019C212yesmaximal
7#16840017C212yesmaximal
8#16839970C212yesmaximal, complemented
9#16839969C211yesmaximal, characteristic, complemented
10#16839784C211yesmaximal, characteristic
11C61×#462C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×#11758189C2212yes—
14#14519777C2211yescharacteristic
15#14519776C2211yescharacteristic
16#14519775C2211yescharacteristic
17#14519768—21no—
18#14519767—21no—
19#14519757—21no—
20#14519757C2211yescharacteristic
21#14519755—21no—
22#14519753C2211yescharacteristic
23#14519753C2212yes—
24Q8×Dic61C2212yes—
25C4×Dic122—21no—
26C4×Dic122C2211yescharacteristic
27#14519742—21no—
28#14519735—21no—
29#14519734—21no—
30C42×D61C2211yescharacteristic
31#14519709C2212yes—
32#14519708C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519702C2212yes—
36#14519701C2212yes—
37#14519701C2212yes—
38C2×Q16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4×Q8×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61C2312yes—
44C2×Q8×C61C2311yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61D411yescharacteristic
47C2×C4×D61C2311yescharacteristic
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122C2311yescharacteristic
51Q16×C61—42no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2311yescharacteristic
57C42×C61—21no—
58C42×C61C2311yescharacteristic
59#11758202—42no—
60#11758198—21no—
61#11758198—21no—
62#11758198—22no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61C2311yescharacteristic
67C4⋊Dic61C2312yes—
68#11758196—21no—
69#11758196—21no—
70#11758196—21no—
71#11758196—22no—
72#11758196—21no—
73#11758196—21no—
74C4×Dic61—21no—
75C4×Dic61—22no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80#11758189—42no—
81C22×D61C2×D411yescharacteristic
82Q8×C61—22no—
83Q8×C61—21no—
84Q8×C61—22no—
85Q8×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C4×D61—22no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—22no—
102Dic122—21no—
103Dic122—21no—
104Dic122—42no—
105Dic122—42no—
106C8×C61—22no—
107#92418—22no—
108C22×C61C22×D411yescharacteristic
109C2×D61—21no—
110C2×D61—21no—
111C2×D61—21no—
112C4×C61—21no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—41no—
116C4×C61#13712yes—
117C4×C61H(5,𝔽2)11yescharacteristic
118C4×C612−1+411yescharacteristic
119Dic61—21no—
120Dic61—21no—
121Dic61—41no—
122Dic61—41no—
123Dic61—42no—
124Dic61#13712yes—
125#3255—611nomaximal, Sylow
126C2×C61#53711yescharacteristic
127C2×C61C2×#13711yescharacteristic
128C2×C61C2×#13711yescharacteristic
129D61—41no—
130#533—611no—
131#533—611no—
132#475—611no—
133#475—611no—
134#475—612no—
135#470—612no—
136#470—612no—
137#462—612no—
138#462—611no—
139#462D6111yescharacteristic, complemented
140#423—611no—
141C61#325511yescharacteristic, complemented, Sylow
142C2×Q16—612no—
143C2×Q16C2×D6112yes—
144C2×M16—612no—
145C4⋊Q8—611no—
146C4⋊Q8—611no—
147C4⋊Q8—611no—
148C4⋊Q8C2×D6111yescharacteristic
149#125—1221no—
150#125—1221no—
151C22⋊Q8—611no—
152C22⋊Q8—612no—
153C22⋊Q8—611no—
154C22⋊Q8—1221no—
155C22⋊Q8—1221no—
156C4×Q8—612no—
157C4×Q8—611no—
158C4×Q8—1221no—
159C4×Q8—1221no—
160C4×Q8C2×D6111yescharacteristic
161#117—1221no—
162#117—1221no—
163C2×C42—611no—
164#106—612no—
165#106—612no—
166C4⋊C8—612no—
167C4⋊C8—611no—
168C4⋊C8C2×D6111yescharacteristic
169#103—612no—
170#103—612no—
171#103—612no—
172#103C2×D6112yes—
173C2×Q8—611no—
174C2×Q8—1221no—
175C2×Q8—1221no—
176C2×Q8C22×D6111yescharacteristic
177C2×Q8C22×D6112yes—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181Q16—42no—
182Q16—2442no—
183M16—2442no—
184C2×C8—612no—
185C2×C8C22×D6112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—611no—
190C4⋊C4—612no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1222no—
195C4⋊C4—1221no—
196C4⋊C4—1222no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C4⋊C4—1221no—
200C4⋊C4C22×D6111yescharacteristic
201C22⋊C4—1221no—
202C22⋊C4—1221no—
203C22⋊C4—1222no—
204C42—21no—
205C42—611no—
206C42—611no—
207C42—611no—
208C42—1222no—
209C42—1221no—
210C42C22×D6111yescharacteristic
211C23—611no—
212Q8—21no—
213Q8—22no—
214Q8—21no—
215Q8—22no—
216Q8—1221no—
217Q8—1221no—
218Q8—2442no—
219Q8—2442no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1222no—
232C2×C4—1221no—
233C2×C4D4×D6111yescharacteristic
234C2×C4D4×D6111yescharacteristic
235C2×C4C23×D6111yescharacteristic
236C8—22no—
237C8—1222no—
238C22—1221no—
239C22—1221no—
240C22—1221no—
241C22C2×D4×D6111yescharacteristic
242C4—21no—
243C4—41no—
244C4—41no—
245C4—42no—
246C4—612no—
247C4—1221no—
248C4—1221no—
249C4—2441no—
250C4—2442no—
251C4—2441no—
252C4#1451980912yes—
253C4#1451982211yescharacteristic
254C4#1451982411yescharacteristic
255C2—2441no—
256C2#1684034111yescharacteristic
257C2#137×D6111yescharacteristic
258C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3255
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #16840048C2semidirect
4. #16840047C2semidirect
5. #16840045C2semidirect
8. #16839970C2semidirect
9. #16839969C2semidirect
11. C61×#462C2semidirect
139. #462D61semidirect
141. C61#3255semidirect