Finite Group Databasebeta

← #21447023

Subgroups — #21447023

Order 7808.

316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519756C211yesmaximal, characteristic
2C2×#14519711C211yesmaximal, characteristic, complemented
3C2×#14519702C211yesmaximal, characteristic, complemented
4C2×#14519702C211yesmaximal, characteristic, complemented
5#16839622C211yesmaximal, characteristic
6#16839525C211yesmaximal, characteristic, complemented
7C2×C22⋊C8×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9#14519756—22no—
10#14519756—22no—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×C22⋊Dic61—21no—
16C2×C22⋊Dic61—21no—
17#14519711—22no—
18#14519702—22no—
19#14519702—22no—
20#14519684—21no—
21C23×C4×C61C2211yescharacteristic
22C22×C8×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C22⋊C8×C61—22no—
25C24×C61D411yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61D411yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61—21no—
36C22×Dic61—21no—
37C22×Dic61—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122D412yes—
44C2×C8×C61—21no—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C2×C8×C61—21no—
49C2×C8×C61D412yes—
50C22⋊Dic61—24no—
51C22⋊Dic61—42no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61D412yes—
58#11758196—24no—
59C23×C61—21no—
60C23×C61—21no—
61C23×C61—21no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61—21no—
65C23×C61Q1612yes—
66C23×C61C2×D411yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61#4111yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92Dic122—22no—
93Dic122—22no—
94Dic122—41no—
95Dic122—41no—
96C8×C61—22no—
97C8×C61—41no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61#12011yescharacteristic
106C22×C61#12111yescharacteristic
107C22×C61#12311yescharacteristic
108C22×C61C2×Q1611yescharacteristic
109C22×C61#13511yescharacteristic
110C22×C61AGL(1,ℤ/8)11yescharacteristic
111C22×C61#13711yescharacteristic
112C4×C61—41no—
113C4×C61#12111yescharacteristic
114C4×C61#12111yescharacteristic
115C4×C61#12311yescharacteristic
116C4×C61#12411yescharacteristic
117Dic61—42no—
118Dic61—42no—
119Dic61—81no—
120Dic61—81no—
121#2036—611nomaximal, Sylow
122C2×C61—42no—
123C2×C61#39411yescharacteristic
124C2×C61#44911yescharacteristic
125C2×C61#45111yescharacteristic
126C2×C61#46711yescharacteristic
127C2×C61#46811yescharacteristic
128C2×C61#48411yescharacteristic
129C2×C61#48511yescharacteristic
130C2×C22⋊Q8—611no—
131C2×#107—611no—
132C2×#103—611no—
133C2×#103—611no—
134C2×C22⋊C8D6111yescharacteristic
135#380—611no—
136#340—611no—
137C61#203611yescharacteristic, complemented, Sylow
138C22×Q8—611no—
139C23×C4C2×D6111yescharacteristic
140C22×C8C2×D6111yescharacteristic
141C22×C8C2×D6111yescharacteristic
142C22⋊Q8—1222no—
143C22⋊Q8—1222no—
144C2×C4⋊C4—611no—
145C2×C4⋊C4—611no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—1221no—
148C2×C22⋊C4—1221no—
149C2×C22⋊C4—1221no—
150#107—1222no—
151#103—1222no—
152#103—1222no—
153C22⋊C8—22no—
154#95—1221no—
155C24D24411yescharacteristic
156C2×Q8—612no—
157C2×Q8—1221no—
158C2×Q8—1221no—
159C2×Q8—1221no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—1221no—
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4—1221no—
172C22×C4D24411yescharacteristic
173C22×C4C22×D6111yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8C22⋊D6112yes—
180C4⋊C4—612no—
181C4⋊C4—1224no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C22⋊C4—1224no—
188C22⋊C4—2442no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23Dic24412yes—
196C23C2×D24411yescharacteristic
197Q8—1222no—
198Q8—1222no—
199Q8—2441no—
200Q8—2441no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4#1175822211yescharacteristic
221C2×C4D4×D6111yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4#1175822411yescharacteristic
224C2×C4#1175822411yescharacteristic
225C2×C4C2×C22⋊D6111yescharacteristic
226C8—22no—
227C8—41no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#1451974711yescharacteristic
236C22#1451975111yescharacteristic
237C22#1451976111yescharacteristic
238C22C2×Dic24411yescharacteristic
239C22#1451979911yescharacteristic
240C22#1451980511yescharacteristic
241C22#1451981011yescharacteristic
242C4—41no—
243C4—4881no—
244C4—4881no—
245C4—2442no—
246C4—2442no—
247C4#1451974811yescharacteristic
248C4#1451974911yescharacteristic
249C4#1451975911yescharacteristic
250C4#1451976311yescharacteristic
251C2—42no—
252C2#1683967811yescharacteristic
253C2#1683990911yescharacteristic
254C2#1683992011yescharacteristic
255C2#1684000311yescharacteristic
256C2#1684000811yescharacteristic
257C2#1684009811yescharacteristic
258C2#1684010411yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×C22⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#2036
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14519711C2semidirect
3. C2×#14519702C2semidirect
4. C2×#14519702C2semidirect
6. #16839525C2semidirect
137. C61#2036semidirect