Finite Group Databasebeta

← #21446619

Subgroups — #21446619

Order 7808.

332 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14519775C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic
3C2×#14519701C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5C2×C8×Dic61C211yesmaximal, characteristic
6#16839631C211yesmaximal, characteristic
7C2×#103×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519775—22no—
11#14519775C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196—22no—
14C2×#11758196—22no—
15C2×C4×Dic61C2211yescharacteristic
16#14519702—22no—
17#14519701—22no—
18#14519700—22no—
19C8×Dic61—22no—
20C22×Q8×C61C2211yescharacteristic
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23#103×C61—22no—
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61C2×C412yes—
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61D412yes—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122C2×C412yes—
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C2×C8×C61D412yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49#11758196—28no—
50#11758196—44no—
51C4×Dic61C2×C412yes—
52C4×Dic61D412yes—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418D412yes—
56C23×C61C2×D411yescharacteristic
57Q8×C61—22no—
58Q8×C61—22no—
59Q8×C61—41no—
60Q8×C61—41no—
61C2×C4×C61—22no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—42no—
66C2×C4×C61C22×C411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×Dic61—22no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—42no—
77C2×Dic61C22⋊C414yes—
78C2×Dic61SD1614yes—
79C2×Dic61Q1614yes—
80Dic122—22no—
81Dic122—22no—
82Dic122—41no—
83Dic122—41no—
84C8×C61—22no—
85#92418—22no—
86C22×C61C2×C22⋊C411yescharacteristic
87C22×C61#12411yescharacteristic
88C22×C61#12711yescharacteristic
89C22×C61C2×SD1612yes—
90C22×C61C2×Q1612yes—
91C4×C61—42no—
92C4×C61—81no—
93C4×C61C4×D411yescharacteristic
94C4×C61C4×D411yescharacteristic
95C4×C61#12111yescharacteristic
96C4×C61#12111yescharacteristic
97Dic61—42no—
98Dic61—81no—
99Dic61#10318yescomplemented
100#1956—611nomaximal, Sylow
101C2×C61#39011yescharacteristic
102C2×C61C2×#10312yes—
103C2×C61#48712yes—
104C2×C61#49211yescharacteristic
105C2×C61#49411yescharacteristic
106C2×C4⋊Q8—611no—
107C2×#103—611no—
108C2×#103—611no—
109C2×#103—611no—
110C2×#103D6111yescharacteristic
111C2×C4×C8—611no—
112#384—611no—
113C61#195611yescharacteristic, complemented, Sylow
114C22×Q8—611no—
115C22×Q8C2×D6111yescharacteristic
116C22×C8—611no—
117C22×C8C2×D6111yescharacteristic
118C4⋊Q8—614no—
119C4⋊Q8—1222no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—1222no—
122C2×C4⋊C4—1222no—
123C2×C4⋊C4C2×D6111yescharacteristic
124C2×C42—611no—
125#103—22no—
126#103—1222no—
127#103—1222no—
128#103—1222no—
129C4×C8—1222no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—612no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8C4×D6112yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—612no—
145C22×C4—1221no—
146C22×C4—1221no—
147C22×C4C22×D6111yescharacteristic
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—612no—
151C2×C8—1221no—
152C2×C8—1221no—
153C2×C8C22⋊D6112yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1228no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C4⋊C4—2444no—
160C42—612no—
161C42—612no—
162C23D4×D6111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—1222no—
168Q8—1222no—
169Q8—2441no—
170Q8—2441no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—614no—
177C2×C4—614no—
178C2×C4—614no—
179C2×C4—1222no—
180C2×C4—2441no—
181C2×C4—2442no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4C2×C4×D6111yescharacteristic
185C2×C4#1175822211yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4#1175822411yescharacteristic
189C2×C4C2×C22⋊D6111yescharacteristic
190C8—22no—
191C8—1222no—
192C22C22⋊C4×D6111yescharacteristic
193C22#1451976311yescharacteristic
194C22#1451977311yescharacteristic
195C22SD16×D6112yes—
196C22Q16×D6112yes—
197C4—42no—
198C4—81no—
199C4—618no—
200C4—4881no—
201C4—2442no—
202C4#1451973711yescharacteristic
203C4C4×C22⋊D6111yescharacteristic
204C4#1451974911yescharacteristic
205C4#1451975011yescharacteristic
206C2#1683966211yescharacteristic
207C2#103×D6112yes—
208C2#1684011112yes—
209C2#1684013311yescharacteristic
210C2#1684014011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1956
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
11. #14519775C4semidirect
99. Dic61#103semidirect
113. C61#1956semidirect