Finite Group Databasebeta

← #21446196

Subgroups — #21446196

Order 7808.

370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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#16840242C211yesmaximal, characteristic, complemented
3C2×#14519705C211yesmaximal, characteristic, complemented
4#16839766C211yesmaximal, characteristic, complemented
5#16839664C211yesmaximal, characteristic, complemented
6#16839530C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519805—22no—
11#14519805C414yescomplemented
12C2×#11758190—21no—
13C2×D488—21no—
14C2×#11758194C2211yescharacteristic
15C4×Dic122—21no—
16C4×D244—21no—
17#14519737—22no—
18#14519735—21no—
19C2×C4⋊Dic61C2211yescharacteristic
20C4⋊C4×D61—21no—
21C2×#11758198—22no—
22#14519705—22no—
23#14519697—21no—
24#14519697—21no—
25C2×M16×C61C2211yescharacteristic
26#117×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28C23×D61—21no—
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C22×Dic61D412yes—
33#11758222—21no—
34#11758222—21no—
35#11758222C2×C412yes—
36#11758222D412yes—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2×C412yescomplemented
43C2×D244D411yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—22no—
46C2×Dic122D411yescharacteristic
47M16×C61—21no—
48M16×C61C2×C412yescomplemented
49C2×C8×C61—21no—
50C4⋊C4×C61D411yescharacteristic
51C4⋊C4×C61D411yescharacteristic
52C22⋊C4×C61—21no—
53C42×C61—21no—
54C42×C61—21no—
55C42×C61—21no—
56#11758198—22no—
57#11758198—44no—
58C4⋊Dic61—21no—
59C4⋊Dic61—21no—
60#11758196—22no—
61C4×Dic61—22no—
62#11758194—21no—
63#11758194—21no—
64C2×#92418—21no—
65D488—24no—
66#11758190—24no—
67C23×C61C2×D411yescharacteristic
68C22×D61—21no—
69C22×D61—22no—
70C22×D61—42no—
71C22×D61—42no—
72C22×D61—41no—
73C22×D61—41no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C22×C411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C22⋊D61—22no—
86C22⋊D61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—42no—
90D244—22no—
91D244—22no—
92D244—21no—
93D244—41no—
94D244—41no—
95D244C22⋊C412yescomplemented
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—82no—
99Dic122—21no—
100Dic122C22⋊C412yescomplemented
101C8×C61—22no—
102#92418—41no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61C4×D411yescharacteristic
106C22×C61#12011yescharacteristic
107C22×C61#12111yescharacteristic
108C2×D61—22no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—44no—
112C2×D61—42no—
113C2×D61—82no—
114C2×D61—81no—
115C2×D61—81no—
116C4×C61—42no—
117C4×C61—41no—
118C4×C61—41no—
119C4×C61C2×C22⋊C411yescharacteristic
120C4×C61C4×D411yescharacteristic
121C4×C61#12111yescharacteristic
122C4×C61#12311yescharacteristic
123Dic61—22no—
124Dic61—42no—
125#1883—611nomaximal, Sylow
126C2×C61—21no—
127C2×C61—21no—
128C2×C61#38611yescharacteristic
129C2×C61#45311yescharacteristic
130C2×C61#45411yescharacteristic
131D61—42no—
132D61—82no—
133C2×AGL(1,ℤ/8)—611no—
134#520—611no—
135C2×#104—611no—
136#418—611no—
137#390—611no—
138#343—611no—
139#339D6111yescharacteristic, complemented
140C61#188311yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C22×D4—611no—
143AGL(1,ℤ/8)—614no—
144AGL(1,ℤ/8)—1222no—
145C2×SD16—1221no—
146C2×D8—1221no—
147C2×M16—611no—
148C2×M16C2×D6111yescharacteristic
149C4×Q8—1221no—
150C4×D4—1221no—
151C4×D4—1222no—
152#117—1221no—
153#117C2×D6111yescharacteristic
154C2×C4⋊C4—611no—
155C2×C4⋊C4—1221no—
156C2×C22⋊C4—1222no—
157C2×C42C2×D6111yescharacteristic
158#104—1222no—
159#102—1221no—
160#102—1221no—
161C24—1221no—
162#41—612no—
163#41—612no—
164#41—1221no—
165#41—1221no—
166C2×Q8—611no—
167C2×D4—612no—
168C2×D4—611no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—1221no—
174C2×D4—1221no—
175C22×C4—21no—
176C22×C4—612no—
177C22×C4—1222no—
178C22×C4—1221no—
179C22×C4C22×D6111yescharacteristic
180SD16—1224no—
181D8—1224no—
182M16—21no—
183M16—1221no—
184M16—1221no—
185M16C4×D6112yescomplemented
186C2×C8—21no—
187C2×C8—1221no—
188C4⋊C4—1222no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4D24411yescharacteristic
192C4⋊C4D24411yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—1222no—
195C22⋊C4—2444no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—1222no—
200C23—1221no—
201C23—1222no—
202C23—2442no—
203C23—2442no—
204C23—2441no—
205C23—2441no—
206C23D4×D6111yescharacteristic
207Q8—612no—
208Q8—1221no—
209D4—612no—
210D4—1222no—
211D4—1222no—
212D4—1222no—
213D4—1222no—
214D4—1221no—
215D4—2441no—
216D4—2441no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—4882no—
227C2×C4—2442no—
228C2×C4C2×C4×D6111yescharacteristic
229C2×C4C2×D24411yescharacteristic
230C2×C4#1175822211yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4#1175822611yescharacteristic
234C8—22no—
235C8—2441no—
236C22—21no—
237C22—21no—
238C22—1222no—
239C22—4882no—
240C22—4881no—
241C22—4881no—
242C22—2444no—
243C22—2442no—
244C22—2441no—
245C22—2441no—
246C22#1451973911yescharacteristic
247C22#1451974711yescharacteristic
248C22#1451975011yescharacteristic
249C4—42no—
250C4—41no—
251C4—41no—
252C4—1222no—
253C4—2442no—
254C4C22⋊C4×D6111yescharacteristic
255C4C4×D24411yescharacteristic
256C4#1451975211yescharacteristic
257C4#1451976211yescharacteristic
258C2—21no—
259C2—21no—
260C2—4882no—
261C2—2442no—
262C2#1683964011yescharacteristic
263C2#1683993111yescharacteristic
264C2#1683993611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#1883
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16840242C2semidirect
3. C2×#14519705C2semidirect
4. #16839766C2semidirect
5. #16839664C2semidirect
6. #16839530C2semidirect
7. C61×#339C2semidirect
11. #14519805C4semidirect
42. C2×D244C2×C4semidirect
48. M16×C61C2×C4semidirect
95. D244C22⋊C4semidirect
100. Dic122C22⋊C4semidirect
139. #339D61semidirect
140. C61#1883semidirect
185. M16C4×D61semidirect