Finite Group Databasebeta

← #21447057

Subgroups — #21447057

Order 7808.

318 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14519766C211yesmaximal, characteristic
2C2×#14519701C211yesmaximal, characteristic, complemented
3C2×#14519699C211yesmaximal, characteristic
4C2×#14519697C211yesmaximal, characteristic
5#16839661C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519766—22no—
11#14519766—22no—
12C2×C4⋊Dic61—21no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758198—21no—
15C2×#11758198—21no—
16C2×C4×Dic61C2211yescharacteristic
17#14519701—22no—
18#14519699—22no—
19#14519697—22no—
20#14519684—21no—
21C22×Q8×C61C2211yescharacteristic
22C22×C8×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24#103×C61—22no—
25C23×D61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61D412yes—
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61—21no—
36C22×Dic61D411yescharacteristic
37C22×Dic61D411yescharacteristic
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244D412yes—
44C2×C8×C61—21no—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61D412yes—
49#11758198—24no—
50#11758198—24no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C4⋊Dic61—42no—
54C4×Dic61—21no—
55C4×Dic61—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C2×#92418—21no—
59C23×C61C2×D411yescharacteristic
60C22×D61—22no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61—41no—
64C22×D61—41no—
65C22×D61—41no—
66C22×D61—41no—
67Q8×C61—22no—
68Q8×C61—22no—
69Q8×C61—41no—
70Q8×C61—41no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92D244—22no—
93D244—22no—
94D244—41no—
95D244—41no—
96C8×C61—41no—
97#92418—41no—
98C22×C61#12011yescharacteristic
99C22×C61#12111yescharacteristic
100C22×C61#12411yescharacteristic
101C22×C61#13511yescharacteristic
102C22×C61#13511yescharacteristic
103C22×C61AGL(1,ℤ/8)11yescharacteristic
104C22×C61#13711yescharacteristic
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—81no—
109C2×D61—81no—
110C2×D61—81no—
111C2×D61—81no—
112C4×C61—42no—
113C4×C61—42no—
114C4×C61#12111yescharacteristic
115C4×C61#12111yescharacteristic
116C4×C61#12311yescharacteristic
117C4×C61#12311yescharacteristic
118Dic61—41no—
119Dic61—41no—
120Dic61—81no—
121#2042—611nomaximal, Sylow
122C2×C61#39411yescharacteristic
123C2×C61#44911yescharacteristic
124C2×C61#45211yescharacteristic
125C2×C61#46311yescharacteristic
126C2×C61#46411yescharacteristic
127C2×C61#48811yescharacteristic
128C2×C61#48911yescharacteristic
129D61—82no—
130C2×#124—611no—
131C2×#103—611no—
132C2×#103D6111yescharacteristic, complemented
133C2×#102—611no—
134C2×#102—611no—
135#389—611no—
136#336—611no—
137C61#204211yescharacteristic, complemented, Sylow
138C22×Q8C2×D6111yescharacteristic
139C22×D4—611no—
140C22×C8—611no—
141C22×C8C2×D6111yescharacteristic
142#124—1222no—
143#124—1222no—
144C2×C4⋊C4—611no—
145C2×C4⋊C4—1221no—
146C2×C4⋊C4C2×D6111yescharacteristic
147C2×C22⋊C4—1221no—
148C2×C22⋊C4—1221no—
149C2×C42—611no—
150#103—22no—
151#103—1222no—
152#102—1222no—
153#102—1222no—
154#95—1221no—
155C24—1221no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8D24412yes—
162C2×D4—612no—
163C2×D4—1221no—
164C2×D4—1221no—
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4—1221no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—1221no—
173C22×C4C22×D6111yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C4⋊C4—21no—
181C4⋊C4—1221no—
182C4⋊C4—1221no—
183C4⋊C4—2442no—
184C4⋊C4C22⋊D6112yes—
185C22⋊C4—1224no—
186C22⋊C4—1224no—
187C42—1221no—
188C42—1221no—
189C23—1222no—
190C23—2441no—
191C23—2441no—
192C23—2441no—
193C23—2441no—
194C23—2441no—
195C23—2441no—
196C23D4×D6111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—1222no—
202D4—1222no—
203D4—2441no—
204D4—2441no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4C2×D24411yescharacteristic
221C2×C4#1175822211yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4#1175822411yescharacteristic
224C2×C4#1175822411yescharacteristic
225C2×C4C2×C22⋊D6111yescharacteristic
226C8—41no—
227C8—2441no—
228C22—4881no—
229C22—4881no—
230C22—4881no—
231C22—4881no—
232C22—2442no—
233C22—2442no—
234C22—2442no—
235C22#1451974711yescharacteristic
236C22#1451974911yescharacteristic
237C22#1451976311yescharacteristic
238C22#1451979811yescharacteristic
239C22#1451980011yescharacteristic
240C22#1451980411yescharacteristic
241C22#1451980911yescharacteristic
242C4—42no—
243C4—42no—
244C4—4881no—
245C4—2441no—
246C4—2441no—
247C4#1451974811yescharacteristic
248C4#1451975111yescharacteristic
249C4#1451975911yescharacteristic
250C4#1451976111yescharacteristic
251C2—4882no—
252C2#1683967811yescharacteristic
253C2#1683991011yescharacteristic
254C2#1683992711yescharacteristic
255C2#1683997911yescharacteristic
256C2#1683998611yescharacteristic
257C2#1684011811yescharacteristic
258C2#1684012311yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#2042
LCSG ▷ C22×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
2. C2×#14519701C2semidirect
5. #16839661C2semidirect
6. #16839516C2semidirect
7. C2×#103×C61C2semidirect
132. C2×#103D61semidirect
137. C61#2042semidirect