Finite Group Databasebeta

← #21446632

Subgroups — #21446632

Order 7808.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14519766C211yesmaximal, characteristic
2C2×#14519701C211yesmaximal, characteristic, complemented
3C2×#14519699C211yesmaximal, characteristic
4C2×#14519697C211yesmaximal, characteristic
5C2×#14519687C211yesmaximal, characteristic, complemented
6#16839631C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519766—22no—
11#14519766C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196—22no—
14C2×#11758198—22no—
15C2×C4×Dic61C2211yescharacteristic
16#14519701—22no—
17#14519699—22no—
18#14519697—22no—
19#14519687—22no—
20C22×Q8×C61C2211yescharacteristic
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23#103×C61—22no—
24C23×D61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61C2×C412yes—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61D412yes—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244C2×C412yes—
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C2×C8×C61D412yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47#11758198—28no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50#11758196—44no—
51C4×Dic61C2×C412yes—
52C4×Dic61D412yes—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418D412yes—
56C23×C61C2×D411yescharacteristic
57C22×D61—22no—
58C22×D61—41no—
59C22×D61—41no—
60C22×D61—42no—
61C22×D61—42no—
62Q8×C61—22no—
63Q8×C61—22no—
64Q8×C61—41no—
65Q8×C61—41no—
66C2×C4×C61—22no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—42no—
71C2×C4×C61C22×C411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—41no—
80C2×Dic61—42no—
81C2×Dic61C22⋊C414yes—
82D244—22no—
83D244—22no—
84D244—41no—
85D244—41no—
86C8×C61—22no—
87#92418—22no—
88C22×C61C2×C22⋊C411yescharacteristic
89C22×C61#12411yescharacteristic
90C22×C61#12711yescharacteristic
91C22×C61AGL(1,ℤ/8)12yes—
92C22×C61#13712yes—
93C2×D61—42no—
94C2×D61—44no—
95C2×D61—82no—
96C2×D61—81no—
97C2×D61—81no—
98C4×C61—42no—
99C4×C61—81no—
100C4×C61C4×D411yescharacteristic
101C4×C61C4×D411yescharacteristic
102C4×C61#12111yescharacteristic
103C4×C61#12111yescharacteristic
104Dic61—24no—
105Dic61—81no—
106#1959—611nomaximal, Sylow
107C2×C61#39011yescharacteristic
108C2×C61#41712yes—
109C2×C61#48912yes—
110C2×C61#49611yescharacteristic
111C2×C61#49711yescharacteristic
112D61—82no—
113C2×#124—611no—
114C2×#103—611no—
115C2×#103D6111yescharacteristic, complemented
116C2×#102—611no—
117C2×#102—611no—
118C2×#97—611no—
119#384—611no—
120C61#195911yescharacteristic, complemented, Sylow
121C22×Q8C2×D6111yescharacteristic
122C22×D4—611no—
123C22×C8—611no—
124C22×C8C2×D6111yescharacteristic
125#124—614no—
126#124—1222no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—1222no—
129C2×C4⋊C4C2×D6111yescharacteristic
130C2×C22⋊C4—1222no—
131C2×C42—611no—
132#103—22no—
133#103—1222no—
134#102—1222no—
135#102—1222no—
136#97—1222no—
137C24—1221no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8C4×D6112yes—
144C2×D4—612no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—612no—
153C22×C4—1221no—
154C22×C4C22×D6111yescharacteristic
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—612no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8C22⋊D6112yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—2444no—
166C22⋊C4—1228no—
167C42—612no—
168C42—612no—
169C23—1222no—
170C23—2442no—
171C23—2441no—
172C23—2441no—
173C23—2442no—
174C23D4×D6111yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179D4—1222no—
180D4—1222no—
181D4—2441no—
182D4—2441no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—614no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—2441no—
192C2×C4—2442no—
193C2×C4C2×C4×D6111yescharacteristic
194C2×C4#1175822211yescharacteristic
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4#1175822411yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C8—22no—
200C8—1222no—
201C22—4882no—
202C22—4881no—
203C22—4881no—
204C22—2444no—
205C22—2442no—
206C22C22⋊C4×D6111yescharacteristic
207C22#1451976311yescharacteristic
208C22#1451977311yescharacteristic
209C22#1451980412yes—
210C22#1451980912yes—
211C4—42no—
212C4—81no—
213C4—1224no—
214C4—4881no—
215C4#1451973711yescharacteristic
216C4C4×C22⋊D6111yescharacteristic
217C4#1451974911yescharacteristic
218C4#1451975011yescharacteristic
219C2—4882no—
220C2#1683966211yescharacteristic
221C2#1683976212yes—
222C2#1684012312yes—
223C2#1684014811yescharacteristic
224C2#1684015511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1959
LCSG ▷ C2×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
2. C2×#14519701C2semidirect
5. C2×#14519687C2semidirect
6. #16839631C2semidirect
7. C2×#103×C61C2semidirect
11. #14519766C4semidirect
115. C2×#103D61semidirect
120. C61#1959semidirect