Finite Group Databasebeta

← #21446837

Subgroups — #21446837

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
1C2×#14519805C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic, complemented
3C2×#14519774C211yesmaximal, characteristic, complemented
4C2×#14519705C211yesmaximal, characteristic, complemented
5#16839766C211yesmaximal, characteristic, complemented
6C2×#14519693C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244—22no—
10C22×D244C2211yescharacteristic
11C22×D244C2211yescharacteristic
12#14519805—22no—
13#14519805—22no—
14C2×#11758190—21no—
15C2×D488—21no—
16C2×#11758194C2211yescharacteristic
17#14519774—22no—
18#14519774—21no—
19#14519774—22no—
20#14519765—21no—
21#14519752—22no—
22#14519747—22no—
23#14519705—22no—
24#14519697—22no—
25#14519693—22no—
26C2×M16×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29C23×D61—21no—
30C23×D61D412yes—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—28no—
43C2×D244—21no—
44C2×D244—21no—
45C2×D244—21no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244—21no—
50C2×D244—24no—
51C2×D244—48no—
52C2×D244D412yescomplemented
53C2×D244D411yescharacteristic, complemented
54C2×C4×D61—21no—
55C2×Dic122D411yescharacteristic, complemented
56M16×C61—21no—
57M16×C61D412yescomplemented
58C2×C8×C61—21no—
59C4⋊C4×C61D412yescomplemented
60C22⋊C4×C61—21no—
61C42×C61—21no—
62C42×C61—21no—
63C42×C61D412yescomplemented
64#11758198—24no—
65#11758194—21no—
66#11758194—21no—
67C2×#92418—21no—
68D488—24no—
69#11758190—24no—
70C23×C61C2×D411yescharacteristic
71C22×D61—22no—
72C22×D61—21no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—44no—
77C22×D61—44no—
78C22×D61—41no—
79C22×D61—41no—
80C2×C4×C61—24no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61#4111yescharacteristic
89C22⋊D61—41no—
90C22⋊D61—41no—
91C2×Dic61—21no—
92D244—22no—
93D244—21no—
94D244—22no—
95D244—21no—
96D244—416no—
97D244—41no—
98D244—41no—
99D244—41no—
100D244—41no—
101D244—41no—
102D244—41no—
103D244—84no—
104C4×D61—41no—
105C4×D61—41no—
106Dic122—21no—
107Dic122—21no—
108C8×C61—22no—
109#92418—41no—
110C22×C61—22no—
111C22×C61#12011yescharacteristic
112C22×C61#12011yescharacteristic
113C22×C61#12111yescharacteristic
114C2×D61—44no—
115C2×D61—44no—
116C2×D61—41no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—44no—
121C2×D61—82no—
122C2×D61—82no—
123C2×D61—82no—
124C4×C61—24no—
125C4×C61—42no—
126C4×C61#12011yescharacteristic
127C4×C61#12111yescharacteristic
128C4×C61#12111yescharacteristic
129C4×C61#12711yescharacteristic
130Dic61—41no—
131#2002—611nomaximal, Sylow
132C2×C61—21no—
133C2×C61—21no—
134C2×C61#39211yescharacteristic
135C2×C61#45312yes—
136D61—81no—
137D61—82no—
138D61—82no—
139C2×AGL(1,ℤ/8)—611no—
140#535—611no—
141C2×#127—611no—
142C2×#104—611no—
143#418—611no—
144C2×#100—611no—
145#339D6111yescharacteristic, complemented
146C61#200211yescharacteristic, complemented, Sylow
147C2×#41—611no—
148C22×D4—611no—
149C22×D4—611no—
150C22×D4—1222no—
151AGL(1,ℤ/8)—1222no—
152AGL(1,ℤ/8)—1222no—
153C2×SD16—1221no—
154C2×D8—1221no—
155C2×M16—611no—
156C2×M16C2×D6111yescharacteristic
157#127—1222no—
158#127—1221no—
159#127—1222no—
160#124—1221no—
161#121—1222no—
162#120—1222no—
163#117C2×D6111yescharacteristic
164C2×C42C2×D6111yescharacteristic
165#104—1222no—
166#102—1222no—
167#100—1222no—
168C24—612no—
169C24—1221no—
170#41—1221no—
171#41—1221no—
172#41—1221no—
173#41—1221no—
174C2×Q8—611no—
175C2×D4—611no—
176C2×D4—612no—
177C2×D4—1224no—
178C2×D4—1228no—
179C2×D4—1221no—
180C2×D4—1221no—
181C2×D4—1221no—
182C2×D4—1221no—
183C2×D4—1221no—
184C2×D4—1221no—
185C2×D4—1221no—
186C2×D4—1221no—
187C2×D4—1221no—
188C2×D4—1221no—
189C2×D4—1221no—
190C2×D4—1221no—
191C2×D4—2448no—
192C22×C4—21no—
193C22×C4—1221no—
194C22×C4C22×D6111yescharacteristic
195SD16—1224no—
196D8—1224no—
197M16—21no—
198M16—1221no—
199M16—1221no—
200M16D24412yescomplemented
201C2×C8—21no—
202C2×C8—1221no—
203C4⋊C4D24412yescomplemented
204C22⋊C4—21no—
205C22⋊C4—1224no—
206C42—21no—
207C42—21no—
208C42D24412yescomplemented
209C23—1222no—
210C23—1222no—
211C23—1222no—
212C23—1222no—
213C23—1221no—
214C23—2444no—
215C23—2444no—
216C23—2441no—
217C23—2441no—
218C23D4×D6111yescharacteristic
219Q8—1221no—
220Q8—1221no—
221D4—1221no—
222D4—1222no—
223D4—1222no—
224D4—1221no—
225D4—4884no—
226D4—24416no—
227D4—2441no—
228D4—2441no—
229D4—2441no—
230D4—2441no—
231D4—2441no—
232D4—2441no—
233D4—2441no—
234D4—2441no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—1221no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4C2×D24411yescharacteristic
242C2×C4C2×D24411yescharacteristic
243C2×C4C2×D24411yescharacteristic
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4#1175822611yescharacteristic
247C8—22no—
248C8—2441no—
249C22—22no—
250C22—4882no—
251C22—4882no—
252C22—4882no—
253C22—2444no—
254C22—2444no—
255C22—2441no—
256C22—2442no—
257C22—2442no—
258C22—2442no—
259C22—2444no—
260C22#1451974711yescharacteristic
261C22#1451974711yescharacteristic
262C22#1451975211yescharacteristic
263C4—24no—
264C4—42no—
265C4—2441no—
266C4#1451974711yescharacteristic
267C4#1451975211yescharacteristic
268C4#1451975211yescharacteristic
269C4#1451977411yescharacteristic
270C2—21no—
271C2—21no—
272C2—4882no—
273C2—4882no—
274C2—4881no—
275C2#1683967211yescharacteristic
276C2#1683993112yes—
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#2002
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. #16840331C2semidirect
3. C2×#14519774C2semidirect
4. C2×#14519705C2semidirect
5. #16839766C2semidirect
6. C2×#14519693C2semidirect
7. C61×#339C2semidirect
52. C2×D244D4semidirect
53. C2×D244D4semidirect
55. C2×Dic122D4semidirect
57. M16×C61D4semidirect
59. C4⋊C4×C61D4semidirect
63. C42×C61D4semidirect
145. #339D61semidirect
146. C61#2002semidirect
200. M16D244semidirect
203. C4⋊C4D244semidirect
208. C42D244semidirect