Finite Group Databasebeta

← #21446850

Subgroups — #21446850

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×#14519810C211yesmaximal, characteristic, complemented
2#16840329C211yesmaximal, characteristic
3C2×#14519764C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic, complemented
5#16839772C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C2×#100×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519810—22no—
11#14519810—22no—
12C2×Dic244—21no—
13C2×#11758190—21no—
14#14519773—21no—
15#14519764—21no—
16#14519764—22no—
17#14519764—22no—
18#14519748—22no—
19#14519746—22no—
20#14519736C2211yescharacteristic
21C2×C22⋊Dic61—22no—
22C2×C4×Dic61C2211yescharacteristic
23#14519703—22no—
24#14519702—22no—
25C22×D4×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27C2×M16×C61C2211yescharacteristic
28#100×C61—22no—
29C24×C61D412yes—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38C2×C22⋊D61—24no—
39C22×Dic61—21no—
40C22×Dic61—21no—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45C2×D244D411yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×Dic122D411yescharacteristic
53C2×Dic122D412yescomplemented
54M16×C61—21no—
55M16×C61—21no—
56M16×C61—21no—
57M16×C61D412yescomplemented
58C2×C8×C61—21no—
59C2×C8×C61—21no—
60C22⋊Dic61—28no—
61C22⋊Dic61—24no—
62C22⋊Dic61—21no—
63C4⋊Dic61D412yes—
64C4×Dic61—21no—
65C4×Dic61—21no—
66C4×Dic61D412yescomplemented
67Dic244—24no—
68#11758190—24no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61—44no—
73C23×C61C2×D411yescharacteristic
74C22×D61—21no—
75D4×C61—41no—
76D4×C61—41no—
77D4×C61—41no—
78D4×C61—41no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C22⋊D61—41no—
86C22⋊D61—41no—
87C22⋊D61—84no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—21no—
92C2×Dic61—42no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95D244—21no—
96D244—21no—
97C4×D61—41no—
98C4×D61—41no—
99Dic122—22no—
100Dic122—21no—
101Dic122—22no—
102Dic122—21no—
103Dic122—41no—
104Dic122—41no—
105C8×C61—22no—
106C8×C61—41no—
107C22×C61—22no—
108C22×C61—44no—
109C22×C61—42no—
110C22×C61—44no—
111C22×C61—82no—
112C22×C61#12011yescharacteristic
113C22×C61#12011yescharacteristic
114C22×C61#12111yescharacteristic
115C2×D61—41no—
116C2×D61—42no—
117C4×C61#12011yescharacteristic
118C4×C61#12111yescharacteristic
119C4×C61#12111yescharacteristic
120C4×C61#12711yescharacteristic
121Dic61—42no—
122Dic61—42no—
123Dic61—41no—
124Dic61—42no—
125#2004—611nomaximal, Sylow
126C2×C61—21no—
127C2×C61—21no—
128C2×C61—82no—
129C2×C61#39211yescharacteristic
130C2×C61#45512yes—
131D61—81no—
132C2×#137—611no—
133#535—611no—
134C2×#124—611no—
135C2×#104—611no—
136#419—611no—
137C2×#100D6111yescharacteristic, complemented
138#339—611no—
139C61#200411yescharacteristic, complemented, Sylow
140C2×#41—611no—
141C22×Q8—611no—
142C22×D4C2×D6111yescharacteristic
143#137—1222no—
144#137—1222no—
145C2×Q16—1221no—
146C2×SD16—1221no—
147C2×M16C2×D6111yescharacteristic
148C2×M16C2×D6111yescharacteristic
149#127—1221no—
150#124—1222no—
151#124—1222no—
152#124—1221no—
153#121—1222no—
154#120—1222no—
155#117—611no—
156C2×C22⋊C4—1222no—
157C2×C42—611no—
158#104—1222no—
159#103—1222no—
160#100—22no—
161C24D24412yes—
162#41—1221no—
163#41—1221no—
164#41—1221no—
165#41—1221no—
166C2×Q8—611no—
167C2×Q8—612no—
168C2×Q8—1221no—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8—1221no—
172C2×Q8—1221no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—611no—
180C2×D4—1224no—
181C2×D4—1221no—
182C22×C4—1221no—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4C22×D6111yescharacteristic
186Q16—1224no—
187SD16—1224no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D6112yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—612no—
195C22⋊C4—1228no—
196C22⋊C4—1224no—
197C22⋊C4—1221no—
198C42—612no—
199C42—1221no—
200C42—1221no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—1221no—
206C23C2×D24411yescharacteristic
207Q8—1222no—
208Q8—1221no—
209Q8—1222no—
210Q8—1221no—
211Q8—2441no—
212Q8—2441no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—1221no—
218D4—1221no—
219D4—4884no—
220D4—2441no—
221D4—2441no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—2442no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4#1175822211yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4D4×D6111yescharacteristic
235C2×C4D4×D6111yescharacteristic
236C2×C4C2×C22⋊D6111yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—82no—
244C22—2442no—
245C22—2441no—
246C22#1451974711yescharacteristic
247C22#1451974711yescharacteristic
248C22#1451975111yescharacteristic
249C4—2442no—
250C4—2442no—
251C4—2441no—
252C4—2442no—
253C4#1451974511yescharacteristic
254C4#1451975011yescharacteristic
255C4#1451975011yescharacteristic
256C4#1451977311yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—4881no—
261C2#1683967111yescharacteristic
262C2#1683994212yes—
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#100×C61C2
socleC22×C61#120
hypercenterC2×#100D61
hypocenterC61#2004
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
3. C2×#14519764C2semidirect
4. C2×#14519703C2semidirect
5. #16839772C2semidirect
6. #16839523C2semidirect
7. C2×#100×C61C2semidirect
53. C2×Dic122D4semidirect
57. M16×C61D4semidirect
66. C4×Dic61D4semidirect
137. C2×#100D61semidirect
139. C61#2004semidirect
191. M16C22⋊D61semidirect