Finite Group Databasebeta

← #21446835

Subgroups — #21446835

Order 7808.

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

normal subgroups only

This group has 478 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×#14519803C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic, complemented
3C2×#14519773C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#418C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C22×C22⋊D61—22no—
11#14519803—22no—
12#14519803—22no—
13C2×#11758200—21no—
14C2×#11758199—21no—
15C2×#11758194C2211yescharacteristic
16#14519774—21no—
17#14519773—22no—
18#14519773—22no—
19#14519765—21no—
20#14519752—22no—
21#14519747—22no—
22C2×C4×Dic61C2211yescharacteristic
23#14519703—22no—
24#14519693—22no—
25C22×D4×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28#102×C61—22no—
29C24×C61—21no—
30C23×D61D412yes—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61D412yescomplemented
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—28no—
39C2×C22⋊D61—21no—
40C2×C22⋊D61—48no—
41C22×Dic61—21no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45#11758222—21no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244—21no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244—24no—
53C2×D244D411yescharacteristic, complemented
54C2×C4×D61—21no—
55C2×Dic122D411yescharacteristic, complemented
56M16×C61—21no—
57M16×C61—21no—
58C2×C8×C61—21no—
59C4⋊C4×C61D412yescomplemented
60C22⋊C4×C61—21no—
61C42×C61—21no—
62#11758200—24no—
63#11758199—24no—
64#11758198—24no—
65C4×Dic61—21no—
66C4×Dic61D412yescomplemented
67#11758194—21no—
68#11758194D412yescomplemented
69C2×#92418—21no—
70C23×C61—22no—
71C23×C61—44no—
72C23×C61—41no—
73C23×C61—41no—
74C23×C61C2×D411yescharacteristic
75C22×D61—22no—
76C22×D61—21no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—44no—
80D4×C61—22no—
81D4×C61—22no—
82D4×C61—41no—
83D4×C61—41no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61#4111yescharacteristic
91C22⋊D61—416no—
92C22⋊D61—41no—
93C22⋊D61—41no—
94C2×Dic61—24no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97D244—21no—
98D244—21no—
99D244—41no—
100D244—41no—
101D244—41no—
102D244—41no—
103D244—84no—
104C4×D61—41no—
105C4×D61—41no—
106Dic122—21no—
107Dic122—21no—
108C8×C61—41no—
109#92418—22no—
110C22×C61—22no—
111C22×C61—44no—
112C22×C61—42no—
113C22×C61—82no—
114C22×C61—82no—
115C22×C61#12011yescharacteristic
116C22×C61#12011yescharacteristic
117C22×C61#12111yescharacteristic
118C2×D61—44no—
119C2×D61—41no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—44no—
123C2×D61—82no—
124C4×C61—42no—
125C4×C61#12011yescharacteristic
126C4×C61#12111yescharacteristic
127C4×C61#12111yescharacteristic
128C4×C61#12711yescharacteristic
129Dic61—24no—
130Dic61—41no—
131#2002—611nomaximal, Sylow
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—82no—
135C2×C61#39211yescharacteristic
136C2×C61#45312yes—
137D61—81no—
138D61—82no—
139C2×AGL(1,ℤ/8)—611no—
140#535—611no—
141C2×#127—611no—
142C2×#104—611no—
143#418D6111yescharacteristic, complemented
144C2×#100—611no—
145#339—611no—
146C61#200211yescharacteristic, complemented, Sylow
147C2×#41—611no—
148C22×D4—611no—
149C22×D4—1222no—
150C22×D4C2×D6111yescharacteristic
151AGL(1,ℤ/8)—1222no—
152AGL(1,ℤ/8)—1222no—
153C2×SD16—1221no—
154C2×D8—1221no—
155C2×M16—611no—
156C2×M16C2×D6111yescharacteristic
157#127—1221no—
158#127—1222no—
159#127—1222no—
160#124—1221no—
161#121—1222no—
162#120—1222no—
163#117C2×D6111yescharacteristic
164C2×C42—611no—
165#104—1222no—
166#102—22no—
167#100—1222no—
168C24—21no—
169C24—612no—
170#41—1221no—
171#41—1221no—
172#41—1221no—
173#41—1221no—
174C2×Q8—611no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—611no—
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—1221no—
190C2×D4—2448no—
191C2×D4D24412yescomplemented
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4C22×D6111yescharacteristic
195SD16—1224no—
196D8—1224no—
197M16—21no—
198M16—21no—
199M16—612no—
200M16—1221no—
201C2×C8—21no—
202C2×C8—1221no—
203C4⋊C4C22⋊D6112yescomplemented
204C22⋊C4—21no—
205C22⋊C4—1224no—
206C42—21no—
207C42—612no—
208C42—1221no—
209C23—22no—
210C23—44no—
211C23—41no—
212C23—41no—
213C23—1222no—
214C23—1222no—
215C23—1221no—
216C23—1222no—
217C23—2444no—
218C23D4×D6111yescharacteristic
219Q8—1221no—
220Q8—1221no—
221D4—22no—
222D4—22no—
223D4—41no—
224D4—41no—
225D4—1221no—
226D4—1221no—
227D4—4884no—
228D4—24416no—
229D4—2441no—
230D4—2441no—
231D4—2441no—
232D4—2441no—
233D4—2441no—
234D4—2441no—
235C2×C4—22no—
236C2×C4—1224no—
237C2×C4—1222no—
238C2×C4—1221no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4C2×D24411yescharacteristic
242C2×C4#1175822211yescharacteristic
243C2×C4D4×D6111yescharacteristic
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4C2×C22⋊D6111yescharacteristic
247C8—41no—
248C8—1222no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—82no—
253C22—82no—
254C22—4882no—
255C22—2444no—
256C22—2441no—
257C22—2442no—
258C22—2442no—
259C22—2444no—
260C22#1451974511yescharacteristic
261C22#1451974711yescharacteristic
262C22#1451975011yescharacteristic
263C4—42no—
264C4—1224no—
265C4—2441no—
266C4#1451974711yescharacteristic
267C4#1451975011yescharacteristic
268C4#1451975111yescharacteristic
269C4#1451977311yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—4882no—
274C2—4881no—
275C2#1683967111yescharacteristic
276C2#1683992812yes—
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#418C2
socleC22×C61#120
hypercenter#418D61
hypocenterC61#2002
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. #16840331C2semidirect
3. C2×#14519773C2semidirect
4. C2×#14519703C2semidirect
5. C2×#14519693C2semidirect
6. #16839521C2semidirect
7. C61×#418C2semidirect
36. C2×D4×C61D4semidirect
53. C2×D244D4semidirect
55. C2×Dic122D4semidirect
59. C4⋊C4×C61D4semidirect
66. C4×Dic61D4semidirect
68. #11758194D4semidirect
143. #418D61semidirect
146. C61#2002semidirect
191. C2×D4D244semidirect
203. C4⋊C4C22⋊D61semidirect