Finite Group Databasebeta

← #21446843

Subgroups — #21446843

Order 7808.

382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14519805C211yesmaximal, characteristic
2#16840336C211yesmaximal, characteristic, complemented
3C2×#14519766C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic, complemented
5#16839768C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C2×#101×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519805—22no—
11#14519805—22no—
12C2×#11758190—21no—
13C2×D488—21no—
14#14519775—21no—
15#14519766—22no—
16#14519766—21no—
17#14519766—22no—
18#14519760—22no—
19#14519753—22no—
20#14519736C2211yescharacteristic
21C2×#11758198—22no—
22C2×C4×Dic61C2211yescharacteristic
23#14519703—22no—
24#14519699—22no—
25C22×Q8×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27C2×M16×C61C2211yescharacteristic
28#101×C61—22no—
29C23×D61—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—
36C22×C4×C61D412yes—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—21no—
39C22×Dic61—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44C2×D244—21no—
45C2×D244—21no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244D412yes—
50C2×D244D411yescharacteristic
51C2×C4×D61—21no—
52C2×Dic122D411yescharacteristic
53M16×C61—21no—
54M16×C61—21no—
55M16×C61—21no—
56M16×C61D412yes—
57C2×C8×C61—21no—
58C2×C8×C61—21no—
59C22⋊Dic61—21no—
60#11758198—28no—
61#11758198—24no—
62C4⋊Dic61D412yes—
63#11758196—24no—
64C4×Dic61—21no—
65C4×Dic61—21no—
66C4×Dic61D412yes—
67D488—24no—
68#11758190—24no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71C22×D61—22no—
72C22×D61—44no—
73C22×D61—41no—
74C22×D61—41no—
75Q8×C61—41no—
76Q8×C61—41no—
77Q8×C61—41no—
78Q8×C61—41no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61#4111yescharacteristic
88C22⋊D61—41no—
89C22⋊D61—41no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—42no—
94D244—22no—
95D244—21no—
96D244—22no—
97D244—21no—
98D244—41no—
99D244—41no—
100C4×D61—41no—
101C4×D61—41no—
102Dic122—21no—
103Dic122—21no—
104C8×C61—22no—
105C8×C61—41no—
106C22×C61—22no—
107C22×C61#12011yescharacteristic
108C22×C61#12011yescharacteristic
109C22×C61#12111yescharacteristic
110C2×D61—44no—
111C2×D61—41no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—82no—
115C2×D61—82no—
116C4×C61—42no—
117C4×C61#12011yescharacteristic
118C4×C61#12111yescharacteristic
119C4×C61#12111yescharacteristic
120C4×C61#12711yescharacteristic
121Dic61—42no—
122Dic61—41no—
123Dic61—42no—
124#2003—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—21no—
127C2×C61#39211yescharacteristic
128C2×C61#45412yes—
129D61—81no—
130D61—82no—
131C2×AGL(1,ℤ/8)—611no—
132#536—611no—
133C2×#124—611no—
134C2×#104—611no—
135#418—611no—
136C2×#101D6111yescharacteristic, complemented
137#339—611no—
138C61#200311yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C22×Q8C2×D6111yescharacteristic
141C22×D4—611no—
142AGL(1,ℤ/8)—1222no—
143AGL(1,ℤ/8)—1222no—
144C2×SD16—1221no—
145C2×D8—1221no—
146C2×M16C2×D6111yescharacteristic
147C2×M16C2×D6111yescharacteristic
148C4⋊Q8—1221no—
149#124—1222no—
150#124—1222no—
151#124—1221no—
152#123—1222no—
153C22⋊Q8—1222no—
154#117—611no—
155C2×C22⋊C4—1222no—
156C2×C42—611no—
157#104—1222no—
158#102—1222no—
159#101—22no—
160C24—1221no—
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—611no—
173C2×D4—612no—
174C2×D4—1221no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4—1221no—
180C22×C4—1221no—
181C22×C4—1221no—
182C22×C4D24412yes—
183C22×C4C22×D6111yescharacteristic
184SD16—1224no—
185D8—1224no—
186M16—21no—
187M16—21no—
188M16—21no—
189M16C22⋊D6112yes—
190C2×C8—21no—
191C2×C8—21no—
192C4⋊C4—612no—
193C4⋊C4—1224no—
194C22⋊C4—1228no—
195C22⋊C4—1224no—
196C22⋊C4—1221no—
197C42—612no—
198C42—1221no—
199C42—1221no—
200C23—1222no—
201C23—1221no—
202C23—2444no—
203C23—2441no—
204C23—2441no—
205C23C2×D24411yescharacteristic
206Q8—41no—
207Q8—41no—
208Q8—41no—
209Q8—41no—
210Q8—1221no—
211Q8—1221no—
212D4—1221no—
213D4—1222no—
214D4—1222no—
215D4—1221no—
216D4—2441no—
217D4—2441no—
218D4—2441no—
219D4—2441no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—2442no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4#1175822211yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4C2×C22⋊D6111yescharacteristic
235C8—22no—
236C8—41no—
237C22—22no—
238C22—4882no—
239C22—4882no—
240C22—2444no—
241C22—2442no—
242C22—2441no—
243C22—2442no—
244C22#1451974711yescharacteristic
245C22#1451974711yescharacteristic
246C22#1451975111yescharacteristic
247C4—42no—
248C4—2442no—
249C4—2442no—
250C4—2441no—
251C4#1451974511yescharacteristic
252C4#1451975011yescharacteristic
253C4#1451975011yescharacteristic
254C4#1451977311yescharacteristic
255C2—21no—
256C2—21no—
257C2—4882no—
258C2—4881no—
259C2#1683967111yescharacteristic
260C2#1683993712yes—
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#120
hypercenterC2×#101D61
hypocenterC61#2003
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #16840336C2semidirect
3. C2×#14519766C2semidirect
4. C2×#14519703C2semidirect
5. #16839768C2semidirect
6. #16839523C2semidirect
7. C2×#101×C61C2semidirect
136. C2×#101D61semidirect
138. C61#2003semidirect