Finite Group Databasebeta

← #21446897

Subgroups — #21446897

Order 7808.

426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C22×#11758201C211yesmaximal, characteristic, complemented
2C22×D488C211yesmaximal, characteristic
3C2×#14519766C211yesmaximal, characteristic, complemented
4C2×#14519697C211yesmaximal, characteristic, complemented
5#16839663C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758201—22no—
11C2×#11758201—22no—
12C2×#11758201—22no—
13C2×D488—22no—
14C2×D488—22no—
15C2×D488—22no—
16C22×#92418C2211yescharacteristic
17#14519766—22no—
18#14519766—22no—
19C2×#11758198—22no—
20C2×#11758198—22no—
21C2×C4×Dic61C2211yescharacteristic
22#14519697—22no—
23C22×Q8×C61C2211yescharacteristic
24C22×C8×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26#103×C61—22no—
27C23×D61—21no—
28C23×D61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61D412yes—
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61C2311yescharacteristic
38C22×Dic61D412yes—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244—21no—
45C2×D244—21no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244D412yes—
50C2×D244D412yes—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C2×C8×C61D412yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56#11758201—28no—
57#11758198—28no—
58#11758198—44no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C2×#92418—21no—
62C2×#92418—21no—
63C2×#92418D412yes—
64D488—28no—
65C23×C61C2×D411yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—41no—
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—41no—
72C22×D61—42no—
73C22×D61—42no—
74C22×D61—42no—
75C22×D61—42no—
76Q8×C61—22no—
77Q8×C61—22no—
78Q8×C61—41no—
79Q8×C61—41no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61#4111yescharacteristic
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94D244—22no—
95D244—22no—
96D244—22no—
97D244—22no—
98D244—41no—
99D244—41no—
100D244—41no—
101D244—41no—
102C8×C61—22no—
103#92418—22no—
104C22×C61#12011yescharacteristic
105C22×C61#12111yescharacteristic
106C22×C61#12711yescharacteristic
107C22×C61#13512yes—
108C22×C61AGL(1,ℤ/8)12yes—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—44no—
112C2×D61—44no—
113C2×D61—82no—
114C2×D61—82no—
115C2×D61—81no—
116C2×D61—81no—
117C2×D61—81no—
118C2×D61—81no—
119C4×C61—42no—
120C4×C61—81no—
121C4×C61#12011yescharacteristic
122C4×C61#12011yescharacteristic
123C4×C61#12111yescharacteristic
124C4×C61#12111yescharacteristic
125Dic61—42no—
126#2012—611nomaximal, Sylow
127C2×C61#39211yescharacteristic
128C2×C61#44912yes—
129C2×C61#46312yes—
130C2×C61#49511yescharacteristic
131C2×C61#49611yescharacteristic
132D61—82no—
133D61—82no—
134C22×SD16—611no—
135C22×D8—611no—
136C2×#124—611no—
137C2×#103D6111yescharacteristic, complemented
138C2×#102—611no—
139#390—611no—
140#336—611no—
141C61#201211yescharacteristic, complemented, Sylow
142C22×Q8C2×D6111yescharacteristic
143C22×D4—611no—
144C22×D4—611no—
145C2×SD16—1222no—
146C2×SD16—1222no—
147C2×SD16—1222no—
148C2×D8—1222no—
149C2×D8—1222no—
150C2×D8—1222no—
151C22×C8—611no—
152C22×C8C2×D6111yescharacteristic
153#124—1222no—
154#124—1222no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C22⋊C4—1222no—
157C2×C22⋊C4—1222no—
158C2×C42—611no—
159#103—22no—
160#102—1222no—
161C24—1221no—
162C24—1221no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8D24412yes—
169C2×D4—612no—
170C2×D4—612no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—1221no—
174C2×D4—1221no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4—1221no—
180C2×D4—1221no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—612no—
184C22×C4C22×D6111yescharacteristic
185SD16—1228no—
186D8—1228no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—612no—
190C2×C8—1221no—
191C2×C8—1221no—
192C2×C8C22⋊D6112yes—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C22⋊C4—1228no—
196C22⋊C4—2444no—
197C42—1221no—
198C42—1221no—
199C23—1222no—
200C23—1222no—
201C23—2441no—
202C23—2441no—
203C23—2441no—
204C23—2441no—
205C23—2442no—
206C23—2442no—
207C23—2442no—
208C23—2442no—
209C23D4×D6111yescharacteristic
210Q8—22no—
211Q8—22no—
212Q8—41no—
213Q8—41no—
214D4—1222no—
215D4—1222no—
216D4—1222no—
217D4—1222no—
218D4—2441no—
219D4—2441no—
220D4—2441no—
221D4—2441no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4C2×D24411yescharacteristic
231C2×C4#1175822211yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4D4×D6111yescharacteristic
235C2×C4C2×C22⋊D6111yescharacteristic
236C8—22no—
237C8—1222no—
238C22—4882no—
239C22—4881no—
240C22—4881no—
241C22—4881no—
242C22—4881no—
243C22—4882no—
244C22—2444no—
245C22—2444no—
246C22—2442no—
247C22—2442no—
248C22#1451974711yescharacteristic
249C22#1451975011yescharacteristic
250C22#1451977311yescharacteristic
251C22#1451980012yes—
252C22#1451980412yes—
253C4—42no—
254C4—81no—
255C4—2442no—
256C4#1451974511yescharacteristic
257C4#1451974711yescharacteristic
258C4#1451975011yescharacteristic
259C4#1451975111yescharacteristic
260C2—4882no—
261C2—4882no—
262C2#1683967111yescharacteristic
263C2#1683991012yes—
264C2#1683998012yes—
265C2#1684014711yescharacteristic
266C2#1684014811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#2012
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#11758201C2semidirect
3. C2×#14519766C2semidirect
4. C2×#14519697C2semidirect
5. #16839663C2semidirect
6. #16839516C2semidirect
7. C2×#103×C61C2semidirect
137. C2×#103D61semidirect
141. C61#2012semidirect