Finite Group Databasebeta

← #21444746

Subgroups — #21444746

Order 7808.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#16840359C211yesmaximal, characteristic, complemented
2#16839913C211yesmaximal, characteristic, complemented
3#16839896C211yesmaximal, characteristic
4#16839498C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839488C211yesmaximal, characteristic, complemented
7C61×#394C211yesmaximal, characteristic, complemented
8C2×#11758200—21no—
9C2×#11758199—21no—
10#14519772—21no—
11#14519767—21no—
12#14519762—21no—
13#14519760—21no—
14#14519756C2211yescharacteristic
15#14519755—21no—
16#14519751C2211yescharacteristic
17C4×C22⋊D61—21no—
18#14519698—21no—
19#14519698—21no—
20C22⋊#92418C2211yescharacteristic
21C22⋊#92418C2211yescharacteristic
22C22×D4×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C22⋊C4×C61—21no—
25C2×C22⋊C4×C61—21no—
26#95×C61C2211yescharacteristic
27C24×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—42no—
31C22×C4×C61—21no—
32C22×C4×C61D411yescharacteristic
33C22×C4×C61D411yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C2×D244D411yescharacteristic
37C2×C4×D61—21no—
38C2×Dic122D411yescharacteristic
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C22⋊C4×C61—42no—
42C22⋊C4×C61—42no—
43C22⋊Dic61—21no—
44#11758200—42no—
45#11758199—42no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50C4⋊Dic61D411yescharacteristic
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53#11758196—21no—
54#11758196—21no—
55#11758196—21no—
56C4×Dic61—21no—
57C2×#92418—21no—
58C2×#92418—21no—
59C23×C61—22no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61—41no—
63C23×C61—41no—
64C23×C61—41no—
65C23×C61—41no—
66C23×C61C2×D411yescharacteristic
67C22×D61—21no—
68D4×C61—22no—
69D4×C61—22no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C22⋊D61—41no—
84C22⋊D61—41no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88D244—41no—
89C4×D61—81no—
90Dic122—41no—
91#92418—41no—
92#92418—41no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61—42no—
98C22×C61—81no—
99C22×C61—81no—
100C22×C61—81no—
101C22×C61—81no—
102C22×C61#12011yescharacteristic
103C22×C61#13511yescharacteristic
104C22×C61AGL(1,ℤ/8)11yescharacteristic
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—41no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—41no—
112C4×C61—81no—
113Dic61—41no—
114Dic61—41no—
115Dic61—41no—
116#1597—611nomaximal, Sylow
117C2×C61—21no—
118C2×C61—21no—
119C2×C61—82no—
120C2×C61#44911yescharacteristic
121C2×C61#45411yescharacteristic
122C2×C61B(4,𝔽2)11yescharacteristic
123D61—81no—
124#539—611no—
125#450—611no—
126#447—611no—
127#394D6111yescharacteristic, complemented
128#328—611no—
129#327—611no—
130#324—611no—
131C61#159711yescharacteristic, complemented, Sylow
132C22×D4C2×D6111yescharacteristic
133C2×SD16—1221no—
134C2×D8—1221no—
135#126—1221no—
136#125—1221no—
137#123—1221no—
138#123—1221no—
139C22⋊Q8—611no—
140C22⋊Q8—1221no—
141#121—611no—
142C4×D4—1221no—
143C2×C4⋊C4C2×D6111yescharacteristic
144C2×C22⋊C4—21no—
145C2×C22⋊C4—21no—
146#102—1221no—
147#102—1221no—
148C22⋊C8—611no—
149C22⋊C8—611no—
150#95C2×D6111yescharacteristic
151C24—21no—
152C2×Q8—611no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—42no—
156C2×D4—611no—
157C2×D4—1221no—
158C22×C4—21no—
159C22×C4—1221no—
160C22×C4C22⋊D6111yescharacteristic
161C22×C4C22⋊D6111yescharacteristic
162C22×C4C22×D6111yescharacteristic
163SD16—2442no—
164D8—2442no—
165C2×C8—1221no—
166C2×C8—1221no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—611no—
170C4⋊C4—611no—
171C4⋊C4—1221no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C22⋊C4—42no—
176C22⋊C4—42no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C42—1221no—
183C23—22no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—1221no—
191C23C2×C22⋊D6111yescharacteristic
192Q8—2441no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—2441no—
198D4—2441no—
199D4—2441no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—4881no—
213C2×C4D4×D6111yescharacteristic
214C2×C4D4×D6111yescharacteristic
215C8—2441no—
216C8—2441no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—81no—
223C22—81no—
224C22—81no—
225C22—81no—
226C22—2441no—
227C22—2441no—
228C22—2441no—
229C22#1451974511yescharacteristic
230C22#1451979711yescharacteristic
231C22#1451980311yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—81no—
237C4—2441no—
238C4—2441no—
239C4—2441no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—4881no—
244C2#1683990511yescharacteristic
245C2#1683993411yescharacteristic
246C2#1683994811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#394C2
socleC22×C61#120
hypercenter#394D61
hypocenterC61#1597
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #16840359C2semidirect
2. #16839913C2semidirect
4. #16839498C2semidirect
5. #16839495C2semidirect
6. #16839488C2semidirect
7. C61×#394C2semidirect
127. #394D61semidirect
131. C61#1597semidirect