Finite Group Databasebeta

← #21446841

Subgroups — #21446841

Order 7808.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#14519803C211yesmaximal, characteristic
2#16840336C211yesmaximal, characteristic, complemented
3C2×#14519705C211yesmaximal, characteristic, complemented
4#16839767C211yesmaximal, characteristic, complemented
5C2×#14519696C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×#124×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519803—22no—
10#14519803—22no—
11C2×#11758200—21no—
12C2×#11758199—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519775—21no—
16#14519766—21no—
17#14519760—22no—
18#14519753—22no—
19#14519736C2211yescharacteristic
20#14519705—22no—
21#14519698—22no—
22#14519696—22no—
23C22×Q8×C61C2211yescharacteristic
24C22×D4×C61C2211yescharacteristic
25#124×C61—22no—
26#124×C61—22no—
27C2×C22⋊C4×C61—22no—
28C2×C42×C61C2211yescharacteristic
29C24×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61—21no—
41C2×D4×C61D412yes—
42C22×C4×C61—21no—
43C22×C4×C61D412yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—21no—
46#11758222—21no—
47#11758222—21no—
48#11758222—21no—
49#11758222—21no—
50C2×D244D411yescharacteristic
51C2×C4×D61—21no—
52C2×Dic122D411yescharacteristic
53C22⋊C4×C61—28no—
54C42×C61—21no—
55C42×C61D412yes—
56C22⋊Dic61—21no—
57#11758200—24no—
58#11758199—24no—
59#11758198—24no—
60C4⋊Dic61D412yes—
61#11758196—24no—
62C4×Dic61—21no—
63#11758194—21no—
64#11758194—21no—
65#11758194—21no—
66#11758194D412yes—
67C2×#92418—21no—
68C2×#92418—21no—
69C23×C61—22no—
70C23×C61—44no—
71C23×C61—41no—
72C23×C61—41no—
73C23×C61C2×D411yescharacteristic
74C22×D61—21no—
75Q8×C61—41no—
76Q8×C61—41no—
77Q8×C61—41no—
78Q8×C61—41no—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—41no—
82D4×C61—41no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—42no—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61#4111yescharacteristic
94C22⋊D61—41no—
95C22⋊D61—41no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98D244—21no—
99D244—21no—
100C4×D61—41no—
101C4×D61—41no—
102Dic122—21no—
103Dic122—21no—
104#92418—22no—
105#92418—41no—
106C22×C61—22no—
107C22×C61—44no—
108C22×C61—42no—
109C22×C61—82no—
110C22×C61—82no—
111C22×C61#12011yescharacteristic
112C22×C61#12011yescharacteristic
113C22×C61#12111yescharacteristic
114C2×D61—41no—
115C2×D61—42no—
116C4×C61—42no—
117C4×C61—42no—
118C4×C61#12011yescharacteristic
119C4×C61#12111yescharacteristic
120C4×C61#12111yescharacteristic
121C4×C61#12711yescharacteristic
122Dic61—41no—
123Dic61—42no—
124#2003—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—21no—
127C2×C61—82no—
128C2×C61#39211yescharacteristic
129C2×C61#45412yes—
130D61—81no—
131C2×AGL(1,ℤ/8)—611no—
132#536—611no—
133C2×#124D6111yescharacteristic, complemented
134C2×#104—611no—
135#418—611no—
136C2×#101—611no—
137#339—611no—
138C61#200311yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C22×Q8C2×D6111yescharacteristic
141C22×D4C2×D6111yescharacteristic
142AGL(1,ℤ/8)—1222no—
143AGL(1,ℤ/8)—1222no—
144C2×SD16—1221no—
145C2×D8—1221no—
146C2×M16—611no—
147C2×M16—611no—
148C4⋊Q8—1221no—
149#124—22no—
150#124—22no—
151#124—1221no—
152#123—1222no—
153C22⋊Q8—1222no—
154#117—611no—
155C2×C22⋊C4—22no—
156C2×C42C2×D6111yescharacteristic
157#104—1222no—
158#102—1222no—
159#101—1222no—
160C24—21no—
161#41—1221no—
162#41—1221no—
163#41—1221no—
164#41—1221no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—611no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—611no—
178C2×D4—1221no—
179C2×D4C22⋊D6112yes—
180C22×C4—21no—
181C22×C4—1221no—
182C22×C4C22⋊D6112yes—
183C22×C4C22×D6111yescharacteristic
184SD16—1224no—
185D8—1224no—
186M16—612no—
187M16—1221no—
188M16—1221no—
189M16—1221no—
190C2×C8—1221no—
191C2×C8—1221no—
192C4⋊C4—612no—
193C4⋊C4—1224no—
194C22⋊C4—28no—
195C22⋊C4—1224no—
196C22⋊C4—1221no—
197C42—21no—
198C42—1221no—
199C42C22⋊D6112yes—
200C23—22no—
201C23—44no—
202C23—41no—
203C23—41no—
204C23—1221no—
205C23C2×C22⋊D6111yescharacteristic
206Q8—41no—
207Q8—41no—
208Q8—41no—
209Q8—41no—
210Q8—1221no—
211Q8—1221no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—1221no—
217D4—1221no—
218D4—2441no—
219D4—2441no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—1222no—
226C2×C4—1221no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4#1175822411yescharacteristic
233C2×C4C2×C22⋊D6111yescharacteristic
234C2×C4C2×C22⋊D6111yescharacteristic
235C8—1222no—
236C8—2441no—
237C22—22no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—82no—
242C22—2441no—
243C22—2442no—
244C22#1451974511yescharacteristic
245C22#1451974611yescharacteristic
246C22#1451974911yescharacteristic
247C4—42no—
248C4—42no—
249C4—2441no—
250C4—2442no—
251C4#1451974511yescharacteristic
252C4#1451974811yescharacteristic
253C4#1451974911yescharacteristic
254C4#1451977311yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—4881no—
259C2#1683967011yescharacteristic
260C2#1683993412yes—
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#124×C61C2
socleC22×C61#120
hypercenterC2×#124D61
hypocenterC61#2003
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #16840336C2semidirect
3. C2×#14519705C2semidirect
4. #16839767C2semidirect
5. C2×#14519696C2semidirect
6. #16839522C2semidirect
7. C2×#124×C61C2semidirect
133. C2×#124D61semidirect
138. C61#2003semidirect