Finite Group Databasebeta

← #21446964

Subgroups — #21446964

Order 7808.

294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519768C211yesmaximal, characteristic, complemented
2C2×#14519699C211yesmaximal, characteristic
3C2×#14519697C211yesmaximal, characteristic
4#16839663C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519768—22no—
11#14519768—22no—
12C2×C4⋊Dic61—21no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×#11758198—21no—
16C2×#11758198—21no—
17C2×C4×Dic61C2211yescharacteristic
18#14519699—22no—
19#14519697—22no—
20C22×C8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
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×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61D412yes—
43#11758198—42no—
44#11758198—42no—
45C4⋊Dic61—24no—
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
55C22×D61—22no—
56C22×D61—41no—
57C22×D61—41no—
58C22×D61—41no—
59C22×D61—41no—
60C22×D61—41no—
61C22×D61—41no—
62C2×C4×C61—22no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×Q811yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83D244—22no—
84D244—22no—
85D244—41no—
86D244—41no—
87C8×C61—41no—
88#92418—41no—
89C22×C61#12011yescharacteristic
90C22×C61C22⋊Q811yescharacteristic
91C22×C61#12411yescharacteristic
92C22×C61#13511yescharacteristic
93C22×C61#13511yescharacteristic
94C22×C61AGL(1,ℤ/8)11yescharacteristic
95C22×C61AGL(1,ℤ/8)11yescharacteristic
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—81no—
100C2×D61—81no—
101C2×D61—81no—
102C2×D61—81no—
103C4×C61—42no—
104C4×C61—81no—
105C4×C61C22⋊Q811yescharacteristic
106C4×C61C22⋊Q811yescharacteristic
107C4×C61#12411yescharacteristic
108C4×C61#12411yescharacteristic
109Dic61—41no—
110Dic61—41no—
111Dic61—42no—
112#2025—611nomaximal, Sylow
113C2×C61#39311yescharacteristic
114C2×C61#44911yescharacteristic
115C2×C61#44911yescharacteristic
116C2×C61#47811yescharacteristic
117C2×C61#47811yescharacteristic
118C2×C61#48811yescharacteristic
119C2×C61#49011yescharacteristic
120D61—82no—
121C2×#125—611no—
122C2×#102—611no—
123C2×#102—611no—
124#390—611no—
125#340—611no—
126#340D6111yescharacteristic, complemented
127#336—611no—
128C61#202511yescharacteristic, complemented, Sylow
129C22×D4—611no—
130C22×C8—611no—
131C22×C8C2×D6111yescharacteristic
132#125—1222no—
133#125—1222no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—1221no—
136C2×C4⋊C4—1221no—
137C2×C4⋊C4C2×D6111yescharacteristic
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C22⋊C4—1221no—
140C2×C22⋊C4—1221no—
141C2×C42—611no—
142#102—1222no—
143#102—1222no—
144C24—1221no—
145C2×D4—612no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1221no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—1221no—
156C22×C4C22×D6111yescharacteristic
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—1221no—
161C2×C8—1221no—
162C2×C8—1221no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—612no—
167C4⋊C4—1224no—
168C4⋊C4—1224no—
169C4⋊C4—1221no—
170C4⋊C4D24412yes—
171C22⋊C4—2442no—
172C22⋊C4—2442no—
173C42—1221no—
174C42—1221no—
175C23—1222no—
176C23—2441no—
177C23—2441no—
178C23—2441no—
179C23—2441no—
180C23—2441no—
181C23—2441no—
182C23D4×D6111yescharacteristic
183D4—1222no—
184D4—1222no—
185D4—2441no—
186D4—2441no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—2441no—
201C2×C4—2441no—
202C2×C4C2×D24411yescharacteristic
203C2×C4#1175822211yescharacteristic
204C2×C4#1175822211yescharacteristic
205C2×C4D4×D6111yescharacteristic
206C2×C4#1175822411yescharacteristic
207C2×C4Q8×D6111yescharacteristic
208C8—41no—
209C8—2441no—
210C22—4881no—
211C22—4881no—
212C22—4881no—
213C22—4881no—
214C22—2442no—
215C22—2442no—
216C22—2442no—
217C22#1451974711yescharacteristic
218C22#1451975511yescharacteristic
219C22#1451976311yescharacteristic
220C22#1451979811yescharacteristic
221C22#1451980011yescharacteristic
222C22#1451980111yescharacteristic
223C22#1451980411yescharacteristic
224C4—42no—
225C4—81no—
226C4—2441no—
227C4—2441no—
228C4—2442no—
229C4#1451975511yescharacteristic
230C4#1451975711yescharacteristic
231C4#1451976311yescharacteristic
232C4#1451976511yescharacteristic
233C2—4882no—
234C2#1683967511yescharacteristic
235C2#1683990811yescharacteristic
236C2#1683991011yescharacteristic
237C2#1684006111yescharacteristic
238C2#1684006511yescharacteristic
239C2#1684011811yescharacteristic
240C2#1684012511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2025
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
1. C2×#14519768C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
7. C61×#340C2semidirect
126. #340D61semidirect
128. C61#2025semidirect