Finite Group Databasebeta

← #21446849

Subgroups — #21446849

Order 7808.

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

normal subgroups only

This group has 394 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×#14519808C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic
3C2×#14519766C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#419C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519808—22no—
11#14519808—22no—
12C2×#11758202—21no—
13C2×#11758201—21no—
14C2×#11758194C2211yescharacteristic
15#14519774—21no—
16#14519766—22no—
17#14519766—22no—
18#14519765—21no—
19#14519752—22no—
20#14519747—22no—
21C2×#11758198—22no—
22C2×C4×Dic61C2211yescharacteristic
23#14519703—22no—
24#14519693—22no—
25C22×Q8×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28#103×C61—22no—
29C23×D61D412yes—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61D412yescomplemented
36C22×C4×C61—21no—
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×D244—21no—
50C2×D244—24no—
51C2×D244D411yescharacteristic
52C2×C4×D61—21no—
53C2×Dic122D411yescharacteristic
54M16×C61—21no—
55M16×C61—21no—
56C2×C8×C61—21no—
57C4⋊C4×C61D412yes—
58C22⋊C4×C61—21no—
59C42×C61—21no—
60#11758202—24no—
61#11758201—24no—
62#11758198—28no—
63#11758198—24no—
64C4×Dic61—21no—
65C4×Dic61D412yescomplemented
66#11758194—21no—
67#11758194D412yescomplemented
68C2×#92418—21no—
69C23×C61C2×D411yescharacteristic
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—21no—
73C22×D61—22no—
74C22×D61—44no—
75Q8×C61—22no—
76Q8×C61—22no—
77Q8×C61—41no—
78Q8×C61—41no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
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—22no—
92C2×Dic61—21no—
93C2×Dic61—42no—
94D244—21no—
95D244—21no—
96D244—41no—
97D244—41no—
98D244—41no—
99D244—41no—
100D244—84no—
101C4×D61—41no—
102C4×D61—41no—
103Dic122—21no—
104Dic122—21no—
105C8×C61—41no—
106#92418—22no—
107C22×C61—22no—
108C22×C61#12011yescharacteristic
109C22×C61#12011yescharacteristic
110C22×C61#12111yescharacteristic
111C2×D61—44no—
112C2×D61—41no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—44no—
116C2×D61—82no—
117C4×C61—42no—
118C4×C61—42no—
119C4×C61#12011yescharacteristic
120C4×C61#12111yescharacteristic
121C4×C61#12111yescharacteristic
122C4×C61#12711yescharacteristic
123Dic61—42no—
124Dic61—41no—
125#2004—611nomaximal, Sylow
126C2×C61—21no—
127C2×C61—21no—
128C2×C61#39211yescharacteristic
129C2×C61#45512yes—
130D61—81no—
131D61—82no—
132C2×#137—611no—
133#535—611no—
134C2×#124—611no—
135C2×#104—611no—
136#419D6111yescharacteristic, complemented
137C2×#100—611no—
138#339—611no—
139C61#200411yescharacteristic, complemented, Sylow
140C2×#41—611no—
141C22×Q8C2×D6111yescharacteristic
142C22×D4—611no—
143#137—1222no—
144#137—1222no—
145C2×Q16—1221no—
146C2×SD16—1221no—
147C2×M16—611no—
148C2×M16C2×D6111yescharacteristic
149#127—1221no—
150#124—1221no—
151#124—1222no—
152#124—1222no—
153#121—1222no—
154#120—1222no—
155#117C2×D6111yescharacteristic
156C2×C22⋊C4—1222no—
157C2×C42—611no—
158#104—1222no—
159#103—22no—
160#100—1222no—
161C24—612no—
162#41—1221no—
163#41—1221no—
164#41—1221no—
165#41—1221no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—611no—
172C2×Q8D24412yescomplemented
173C2×D4—611no—
174C2×D4—1224no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4—1221no—
180C2×D4—1221no—
181C2×D4—1221no—
182C22×C4—21no—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4C22×D6111yescharacteristic
186Q16—1224no—
187SD16—1224no—
188M16—21no—
189M16—21no—
190M16—612no—
191M16—1221no—
192C2×C8—21no—
193C2×C8—1221no—
194C4⋊C4C22⋊D6112yes—
195C22⋊C4—21no—
196C22⋊C4—1228no—
197C22⋊C4—1224no—
198C42—21no—
199C42—612no—
200C42—1221no—
201C23—1222no—
202C23—1222no—
203C23—1221no—
204C23—1222no—
205C23—2444no—
206C23D4×D6111yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—1221no—
212Q8—1221no—
213D4—1221no—
214D4—1221no—
215D4—4884no—
216D4—2441no—
217D4—2441no—
218D4—2441no—
219D4—2441no—
220D4—2441no—
221D4—2441no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—2442no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4C2×D24411yescharacteristic
232C2×C4#1175822211yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4D4×D6111yescharacteristic
235C2×C4D4×D6111yescharacteristic
236C2×C4C2×C22⋊D6111yescharacteristic
237C8—41no—
238C8—1222no—
239C22—22no—
240C22—4882no—
241C22—2444no—
242C22—2442no—
243C22—2444no—
244C22—2441no—
245C22—2442no—
246C22#1451974511yescharacteristic
247C22#1451974711yescharacteristic
248C22#1451975011yescharacteristic
249C4—42no—
250C4—42no—
251C4—2442no—
252C4—2441no—
253C4#1451974711yescharacteristic
254C4#1451975011yescharacteristic
255C4#1451975111yescharacteristic
256C4#1451977311yescharacteristic
257C2—21no—
258C2—21no—
259C2—4882no—
260C2—4881no—
261C2#1683967111yescharacteristic
262C2#1683993812yes—
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#419C2
socleC22×C61#120
hypercenter#419D61
hypocenterC61#2004
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
3. C2×#14519766C2semidirect
4. C2×#14519703C2semidirect
5. C2×#14519693C2semidirect
6. #16839521C2semidirect
7. C61×#419C2semidirect
35. C2×Q8×C61D4semidirect
65. C4×Dic61D4semidirect
67. #11758194D4semidirect
136. #419D61semidirect
139. C61#2004semidirect
172. C2×Q8D244semidirect