Finite Group Databasebeta

← #21446831

Subgroups — #21446831

Order 7808.

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

normal subgroups only

This group has 478 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
1#16840326C211yesmaximal, characteristic, complemented
2C2×#14519773C211yesmaximal, characteristic, complemented
3C2×#14519704C211yesmaximal, characteristic, complemented
4#16839767C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×C22⋊D61—22no—
10C2×#11758194C2211yescharacteristic
11#14519773—22no—
12#14519773—21no—
13#14519773—22no—
14#14519766—21no—
15#14519751—22no—
16#14519745—22no—
17#14519736C2211yescharacteristic
18C2×C4×Dic61C2211yescharacteristic
19#14519704—22no—
20#14519698—22no—
21#14519693—22no—
22C2×#41×C61C2211yescharacteristic
23C22×D4×C61C2211yescharacteristic
24AGL(1,ℤ/8)×C61—22no—
25AGL(1,ℤ/8)×C61—22no—
26C2×SD16×C61—21no—
27C2×D8×C61—21no—
28C2×M16×C61C2211yescharacteristic
29C24×C61—21no—
30C23×D61D412yes—
31#41×C61—21no—
32#41×C61—21no—
33#41×C61—21no—
34#41×C61—21no—
35C2×Q8×C61D411yescharacteristic, complemented
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61—21no—
41C2×D4×C61—21no—
42C2×D4×C61D411yescharacteristic, complemented
43C2×D4×C61D412yescomplemented
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—28no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—48no—
49C22×Dic61—21no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244—21no—
53C2×D244—21no—
54C2×D244—21no—
55C2×D244—21no—
56SD16×C61—24no—
57D8×C61—24no—
58M16×C61—21no—
59M16×C61D412yescomplemented
60C2×C8×C61—21no—
61C22⋊Dic61—21no—
62#11758198—24no—
63C4⋊Dic61D412yescomplemented
64C4×Dic61—21no—
65C4×Dic61—21no—
66C4×Dic61D412yescomplemented
67#11758194—21no—
68#11758194—21no—
69C2×#92418—21no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—44no—
73C23×C61—41no—
74C23×C61—41no—
75C23×C61C2×D411yescharacteristic
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—44no—
80Q8×C61—21no—
81Q8×C61—21no—
82D4×C61—21no—
83D4×C61—22no—
84D4×C61—22no—
85D4×C61—21no—
86D4×C61—41no—
87D4×C61—41no—
88D4×C61—41no—
89D4×C61—41no—
90C2×C4×C61—21no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61#4111yescharacteristic
99C22⋊D61—416no—
100C22⋊D61—84no—
101C2×Dic61—24no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104D244—41no—
105D244—41no—
106D244—41no—
107D244—41no—
108C8×C61—22no—
109#92418—41no—
110C22×C61—22no—
111C22×C61—44no—
112C22×C61—41no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—82no—
116C22×C61—82no—
117C22×C61#12011yescharacteristic
118C22×C61#12011yescharacteristic
119C22×C61#12111yescharacteristic
120C2×D61—44no—
121C2×D61—42no—
122C2×D61—44no—
123C2×D61—82no—
124C4×C61—41no—
125C4×C61#12011yescharacteristic
126C4×C61#12111yescharacteristic
127C4×C61#12111yescharacteristic
128C4×C61#12711yescharacteristic
129Dic61—24no—
130Dic61—42no—
131#2002—611nomaximal, Sylow
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—81no—
135C2×C61—82no—
136C2×C61#39211yescharacteristic
137C2×C61#45312yes—
138D61—82no—
139C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
140#535—611no—
141C2×#127—611no—
142C2×#104—611no—
143#418—611no—
144C2×#100—611no—
145#339—611no—
146C61#200211yescharacteristic, complemented, Sylow
147C2×#41C2×D6111yescharacteristic
148C22×D4—611no—
149C22×D4—1222no—
150C22×D4C2×D6111yescharacteristic
151AGL(1,ℤ/8)—22no—
152AGL(1,ℤ/8)—22no—
153C2×SD16—21no—
154C2×D8—21no—
155C2×M16—611no—
156C2×M16C2×D6111yescharacteristic
157#127—1222no—
158#127—1222no—
159#127—1221no—
160#124—1221no—
161#121—1222no—
162#120—1222no—
163#117—611no—
164C2×C42—611no—
165#104—1222no—
166#102—1222no—
167#100—1222no—
168C24—21no—
169C24—612no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8C22⋊D6111yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—1224no—
182C2×D4—1228no—
183C2×D4—1221no—
184C2×D4—1221no—
185C2×D4—1221no—
186C2×D4—1221no—
187C2×D4—1221no—
188C2×D4—1221no—
189C2×D4—2448no—
190C2×D4C22⋊D6111yescharacteristic, complemented
191C2×D4C22⋊D6112yescomplemented
192C22×C4—21no—
193C22×C4—1221no—
194C22×C4C22×D6111yescharacteristic
195SD16—24no—
196D8—24no—
197M16—21no—
198M16—1221no—
199M16—1221no—
200M16C22⋊D6112yescomplemented
201C2×C8—21no—
202C2×C8—1221no—
203C4⋊C4—612no—
204C22⋊C4—1224no—
205C22⋊C4—1221no—
206C42—612no—
207C42—1221no—
208C42—1221no—
209C23—22no—
210C23—21no—
211C23—44no—
212C23—41no—
213C23—41no—
214C23—1222no—
215C23—1222no—
216C23—1222no—
217C23—2444no—
218C23D4×D6111yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—22no—
223D4—22no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—4884no—
230D4—24416no—
231D4—2441no—
232D4—2441no—
233D4—2441no—
234D4—2441no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—1224no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4D4×D6111yescharacteristic
242C2×C4D4×D6111yescharacteristic
243C2×C4#1175822411yescharacteristic
244C2×C4C2×C22⋊D6111yescharacteristic
245C2×C4C2×C22⋊D6111yescharacteristic
246C2×C4C2×C22⋊D6111yescharacteristic
247C8—22no—
248C8—2441no—
249C22—22no—
250C22—44no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—82no—
255C22—82no—
256C22—4882no—
257C22—2444no—
258C22—2442no—
259C22—2444no—
260C22#1451974511yescharacteristic
261C22#1451974511yescharacteristic
262C22#1451974811yescharacteristic
263C4—41no—
264C4—1224no—
265C4—2442no—
266C4#1451974611yescharacteristic
267C4#1451974911yescharacteristic
268C4#1451974911yescharacteristic
269C4#1451977311yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—81no—
274C2—4882no—
275C2#1683967011yescharacteristic
276C2#1683992812yes—
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC22×C61#120
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#2002
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #16840326C2semidirect
2. C2×#14519773C2semidirect
3. C2×#14519704C2semidirect
4. #16839767C2semidirect
5. C2×#14519693C2semidirect
6. #16839523C2semidirect
7. C2×AGL(1,ℤ/8)×C61C2semidirect
35. C2×Q8×C61D4semidirect
42. C2×D4×C61D4semidirect
43. C2×D4×C61D4semidirect
59. M16×C61D4semidirect
63. C4⋊Dic61D4semidirect
66. C4×Dic61D4semidirect
139. C2×AGL(1,ℤ/8)D61semidirect
146. C61#2002semidirect
174. C2×Q8C22⋊D61semidirect
190. C2×D4C22⋊D61semidirect
191. C2×D4C22⋊D61semidirect
200. M16C22⋊D61semidirect