Finite Group Databasebeta

← #21446627

Subgroups — #21446627

Order 7808.

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

normal subgroups only

This group has 336 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×C8×Dic61C211yesmaximal, characteristic, complemented
6#16839627C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519766—22no—
11#14519766C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758198—22no—
14C2×C4×Dic61C2211yescharacteristic
15#14519701—22no—
16#14519699—22no—
17#14519697—22no—
18C8×Dic61—22no—
19#14519684—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—
50C4×Dic61C2×C412yes—
51C4×Dic61D412yes—
52C2×#92418—21no—
53C2×#92418—21no—
54C2×#92418D412yes—
55C23×C61C2×D411yescharacteristic
56C22×D61—22no—
57C22×D61—41no—
58C22×D61—41no—
59C22×D61—42no—
60C22×D61—42no—
61Q8×C61—22no—
62Q8×C61—22no—
63Q8×C61—41no—
64Q8×C61—41no—
65C2×C4×C61—22no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—42no—
70C2×C4×C61C22×C411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—41no—
79C2×Dic61—42no—
80C2×Dic61C22⋊C414yes—
81D244—22no—
82D244—22no—
83D244—41no—
84D244—41no—
85C8×C61—22no—
86#92418—22no—
87C22×C61C2×C22⋊C411yescharacteristic
88C22×C61#12411yescharacteristic
89C22×C61#12711yescharacteristic
90C22×C61#13512yes—
91C22×C61#13512yes—
92C2×D61—42no—
93C2×D61—44no—
94C2×D61—82no—
95C2×D61—81no—
96C2×D61—81no—
97C4×C61—42no—
98C4×C61—81no—
99C4×C61C4×D411yescharacteristic
100C4×C61C4×D411yescharacteristic
101C4×C61#12111yescharacteristic
102C4×C61#12111yescharacteristic
103Dic61—24no—
104Dic61—81no—
105#1958—611nomaximal, Sylow
106C2×C61#39011yescharacteristic
107C2×C61#41612yes—
108C2×C61#48812yes—
109C2×C61#49511yescharacteristic
110C2×C61#49511yescharacteristic
111D61—82no—
112C2×#124—611no—
113C2×#103—611no—
114C2×#103D6111yescharacteristic, complemented
115C2×#102—611no—
116C2×#102—611no—
117C2×C4×C8—611no—
118#382—611no—
119C61#195811yescharacteristic, complemented, Sylow
120C22×Q8C2×D6111yescharacteristic
121C22×D4—611no—
122C22×C8—611no—
123C22×C8C2×D6111yescharacteristic
124#124—614no—
125#124—1222no—
126C2×C4⋊C4—611no—
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C22⋊C4—1222no—
129C2×C42—611no—
130#103—22no—
131#103—1222no—
132#102—1222no—
133#102—1222no—
134C4×C8—1222no—
135#95—1222no—
136C24—1221no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C4×D6112yes—
143C2×D4—612no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—612no—
152C22×C4—1221no—
153C22×C4C22×D6111yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—612no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8C22⋊D6112yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C22⋊C4—1228no—
165C42—612no—
166C42—612no—
167C23—1222no—
168C23—2441no—
169C23—2441no—
170C23—2442no—
171C23—2442no—
172C23D4×D6111yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—41no—
176Q8—41no—
177D4—1222no—
178D4—1222no—
179D4—2441no—
180D4—2441no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—614no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—2441no—
190C2×C4—2442no—
191C2×C4C2×C4×D6111yescharacteristic
192C2×C4#1175822211yescharacteristic
193C2×C4D4×D6111yescharacteristic
194C2×C4D4×D6111yescharacteristic
195C2×C4#1175822411yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C8—22no—
198C8—1222no—
199C22—4882no—
200C22—4881no—
201C22—4881no—
202C22—2444no—
203C22—2442no—
204C22C22⋊C4×D6111yescharacteristic
205C22#1451976311yescharacteristic
206C22#1451977311yescharacteristic
207C22#1451979812yes—
208C22#1451980012yes—
209C4—42no—
210C4—81no—
211C4—1224no—
212C4—4881no—
213C4#1451973711yescharacteristic
214C4C4×C22⋊D6111yescharacteristic
215C4#1451974911yescharacteristic
216C4#1451975011yescharacteristic
217C2—4882no—
218C2#1683966211yescharacteristic
219C2#1683975712yes—
220C2#1684011812yes—
221C2#1684014311yescharacteristic
222C2#1684014711yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1958
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×C8×Dic61C2semidirect
6. #16839627C2semidirect
7. C2×#103×C61C2semidirect
11. #14519766C4semidirect
114. C2×#103D61semidirect
119. C61#1958semidirect