Finite Group Databasebeta

← #21447188

Subgroups — #21447188

Order 7808.

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

normal subgroups only

This group has 284 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×#14519706C211yesmaximal, characteristic, complemented
2C2×#14519699C211yesmaximal, characteristic
3C2×#14519697C211yesmaximal, characteristic
4#16839663C211yesmaximal, characteristic
5#16839661C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C2×#106×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61—21no—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198—21no—
13C2×#11758198—21no—
14C2×C4×Dic61C2211yescharacteristic
15#14519706—22no—
16#14519699—22no—
17#14519697—22no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22#106×C61—22no—
23C23×D61—21no—
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61—21no—
28C22×Dic61D411yescharacteristic
29C22×Dic61D411yescharacteristic
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244Q812yes—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61D412yes—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61D412yes—
43#11758198—42no—
44#11758198—42no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61—42no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50C2×#92418—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C23×C61C2×D411yescharacteristic
54C22×D61—22no—
55C22×D61—41no—
56C22×D61—41no—
57C22×D61—41no—
58C22×D61—41no—
59C22×D61—41no—
60C22×D61—41no—
61C2×C4×C61—22no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×Q811yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61SD1612yes—
82D244—22no—
83D244—22no—
84D244—41no—
85D244—41no—
86C8×C61—22no—
87#92418—41no—
88C22×C61#12111yescharacteristic
89C22×C61#12111yescharacteristic
90C22×C61C22⋊Q811yescharacteristic
91C22×C61C2×SD1611yescharacteristic
92C22×C61#13511yescharacteristic
93C22×C61AGL(1,ℤ/8)11yescharacteristic
94C22×C61AGL(1,ℤ/8)11yescharacteristic
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—81no—
99C2×D61—81no—
100C2×D61—81no—
101C2×D61—81no—
102C4×C61—42no—
103C4×C61—81no—
104C4×C61#12111yescharacteristic
105C4×C61C22⋊Q811yescharacteristic
106C4×C61C22⋊Q811yescharacteristic
107C4×C61#12611yescharacteristic
108Dic61—22no—
109Dic61—41no—
110Dic61—81no—
111#2065—611nomaximal, Sylow
112C2×C61#39611yescharacteristic
113C2×C61#46011yescharacteristic
114C2×C61#46311yescharacteristic
115C2×C61#46511yescharacteristic
116C2×C61#46911yescharacteristic
117C2×C61#47611yescharacteristic
118C2×C61#47811yescharacteristic
119D61—82no—
120C2×#106D6111yescharacteristic, complemented
121C2×C4⋊C8—611no—
122C2×#102—611no—
123C2×#102—611no—
124#390—611no—
125#389—611no—
126#340—611no—
127C61#206511yescharacteristic, complemented, Sylow
128C22×D4—611no—
129C22×C8—611no—
130C22×C8C2×D6111yescharacteristic
131C2×C4⋊C4—611no—
132C2×C4⋊C4—1221no—
133C2×C4⋊C4C2×D6111yescharacteristic
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C22⋊C4—1221no—
136C2×C22⋊C4—1221no—
137C2×C42—611no—
138#106—22no—
139C4⋊C8—1222no—
140#102—1222no—
141#102—1222no—
142#95—1221no—
143C24—1221no—
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—611no—
153C22×C4—611no—
154C22×C4—1221no—
155C22×C4C22×D6111yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8—1221no—
161C2×C8D24412yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—2442no—
168C4⋊C4C22⋊D6112yes—
169C22⋊C4—2442no—
170C22⋊C4—2442no—
171C42—1221no—
172C42—1221no—
173C23—1222no—
174C23—2441no—
175C23—2441no—
176C23—2441no—
177C23—2441no—
178C23—2441no—
179C23—2441no—
180C23D4×D6111yescharacteristic
181D4—1222no—
182D4—1222no—
183D4—2441no—
184D4—2441no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—612no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4C2×D24411yescharacteristic
201C2×C4#1175822211yescharacteristic
202C2×C4#1175822411yescharacteristic
203C2×C4Q8×D6111yescharacteristic
204C2×C4#1175822611yescharacteristic
205C2×C4C2×C22⋊D6111yescharacteristic
206C8—22no—
207C8—2441no—
208C22—4881no—
209C22—4881no—
210C22—4881no—
211C22—4881no—
212C22—2442no—
213C22—2442no—
214C22—2442no—
215C22#1451974911yescharacteristic
216C22#1451975211yescharacteristic
217C22#1451975511yescharacteristic
218C22SD16×D6111yescharacteristic
219C22#1451979811yescharacteristic
220C22#1451980411yescharacteristic
221C22#1451980411yescharacteristic
222C4—42no—
223C4—81no—
224C4—1222no—
225C4—4881no—
226C4—2441no—
227C4#1451975111yescharacteristic
228C4#1451975311yescharacteristic
229C4#1451975711yescharacteristic
230C4#1451977211yescharacteristic
231C2—4882no—
232C2#1683968411yescharacteristic
233C2#1683996011yescharacteristic
234C2#1683997911yescharacteristic
235C2#1683999211yescharacteristic
236C2#1684001611yescharacteristic
237C2#1684005111yescharacteristic
238C2#1684006111yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#106×C61C2
socleC23×C61C2×D4
hypercenterC2×#106D61
hypocenterC61#2065
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×#14519706C2semidirect
5. #16839661C2semidirect
6. #16839524C2semidirect
7. C2×#106×C61C2semidirect
120. C2×#106D61semidirect
127. C61#2065semidirect