Finite Group Databasebeta

← #21446959

Subgroups — #21446959

Order 7808.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14519776C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic
3C2×#14519700C211yesmaximal, characteristic
4#16839667C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122—21no—
9C22×Dic122C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519776—22no—
12#14519776—22no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×C4×Dic61C2211yescharacteristic
16#14519702—22no—
17#14519700—22no—
18#14519684—21no—
19#14519684—21no—
20C22×C8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61D411yescharacteristic
29C22×Dic61D411yescharacteristic
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—24no—
35C2×Dic122—21no—
36C2×Dic122—42no—
37C2×Dic122—42no—
38C2×Dic122Q812yescomplemented
39C2×C8×C61—21no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61D412yes—
46C4⋊Dic61—21no—
47C4⋊Dic61D412yes—
48#11758196—24no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C2×#92418—21no—
54C23×C61C2×D411yescharacteristic
55C2×C4×C61—22no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×Q811yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61SD1612yes—
78C2×Dic61Q1612yes—
79Dic122—22no—
80Dic122—22no—
81Dic122—48no—
82Dic122—41no—
83Dic122—41no—
84C8×C61—41no—
85#92418—41no—
86C22×C61#12011yescharacteristic
87C22×C61C22⋊Q811yescharacteristic
88C22×C61#12411yescharacteristic
89C22×C61C2×SD1611yescharacteristic
90C22×C61C2×Q1611yescharacteristic
91C22×C61AGL(1,ℤ/8)11yescharacteristic
92C22×C61#13711yescharacteristic
93C4×C61—42no—
94C4×C61—81no—
95C4×C61C22⋊Q811yescharacteristic
96C4×C61C22⋊Q811yescharacteristic
97C4×C61#12411yescharacteristic
98C4×C61#12411yescharacteristic
99Dic61—22no—
100Dic61—22no—
101Dic61—42no—
102Dic61—42no—
103#2024—611nomaximal, Sylow
104C2×C61#39311yescharacteristic
105C2×C61#45011yescharacteristic
106C2×C61#45111yescharacteristic
107C2×C61#47511yescharacteristic
108C2×C61#47711yescharacteristic
109C2×C61#48711yescharacteristic
110C2×C61#48911yescharacteristic
111C2×C4⋊Q8—611no—
112C2×#103—611no—
113C2×#103—611no—
114#391—611no—
115#340—611no—
116#340D6111yescharacteristic
117#336—611no—
118C61#202411yescharacteristic, complemented, Sylow
119C22×Q8—611no—
120C22×Q8—1221no—
121C22×C8—611no—
122C22×C8C2×D6111yescharacteristic
123C4⋊Q8—1222no—
124C4⋊Q8—1222no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—1221no—
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C4⋊C4C2×D6111yescharacteristic
129C2×C42—611no—
130#103—1222no—
131#103—1222no—
132#95—1221no—
133#95—1221no—
134C2×Q8—612no—
135C2×Q8—1224no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8—2442no—
142C2×Q8—2442no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4C22×D6111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—1221no—
154C2×C8—1221no—
155C2×C8—1221no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—612no—
160C4⋊C4—1224no—
161C4⋊C4—1221no—
162C4⋊C4D24412yes—
163C42—1221no—
164C42—1221no—
165C23D4×D6111yescharacteristic
166Q8—1222no—
167Q8—1222no—
168Q8—2448no—
169Q8—2441no—
170Q8—2441no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—612no—
178C2×C4—612no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4C2×D24411yescharacteristic
190C2×C4#1175822211yescharacteristic
191C2×C4#1175822211yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4#1175822411yescharacteristic
194C2×C4Q8×D6111yescharacteristic
195C8—41no—
196C8—2441no—
197C22#1451974711yescharacteristic
198C22#1451975511yescharacteristic
199C22#1451976311yescharacteristic
200C22SD16×D6111yescharacteristic
201C22Q16×D6111yescharacteristic
202C22#1451980111yescharacteristic
203C22#1451980611yescharacteristic
204C4—42no—
205C4—81no—
206C4—1222no—
207C4—1222no—
208C4—2442no—
209C4—2442no—
210C4#1451975511yescharacteristic
211C4#1451975711yescharacteristic
212C4#1451976311yescharacteristic
213C4#1451976511yescharacteristic
214C2#1683967511yescharacteristic
215C2#1683991411yescharacteristic
216C2#1683991911yescharacteristic
217C2#1684004611yescharacteristic
218C2#1684005611yescharacteristic
219C2#1684011111yescharacteristic
220C2#1684012011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2024
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
38. C2×Dic122Q8semidirect
118. C61#2024semidirect