Finite Group Databasebeta

← #21447032

Subgroups — #21447032

Order 7808.

326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840331C211yesmaximal, characteristic
2#16839805C211yesmaximal, characteristic, complemented
3C2×#14519705C211yesmaximal, characteristic, complemented
4#16839764C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839664C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519774—21no—
12#14519765—21no—
13#14519752—21no—
14#14519752—21no—
15#14519747—22no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758198—22no—
18#14519710—21no—
19#14519708—21no—
20#14519705—22no—
21#14519702—21no—
22#14519699—21no—
23#14519693—22no—
24C2×M16×C61C2211yescharacteristic
25#117×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27C23×D61D412yes—
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32#11758222—21no—
33#11758222—21no—
34#11758222—21no—
35#11758222—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—22no—
43C2×D244—22no—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122D411yescharacteristic
47M16×C61—21no—
48M16×C61—21no—
49C2×C8×C61—21no—
50C4⋊C4×C61D411yescharacteristic
51C4⋊C4×C61D411yescharacteristic
52C22⋊C4×C61—21no—
53C42×C61—21no—
54C42×C61—21no—
55C42×C61—21no—
56#11758198—22no—
57#11758198—22no—
58#11758198—44no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61#11758194—21no—
62#11758194D412yescomplemented
63C2×#92418—21no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66C22×D61—21no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—42no—
70C22×D61—42no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C22⋊D61—41no—
83C22⋊D61—41no—
84C2×Dic61—21no—
85C2×Dic61—42no—
86C2×Dic61—41no—
87D244—21no—
88D244—21no—
89D244—41no—
90D244—41no—
91D244—41no—
92D244—41no—
93D244—82no—
94D244—82no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—21no—
98Dic122—21no—
99C8×C61—41no—
100#92418—22no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61#12011yescharacteristic
104C22×C61#12111yescharacteristic
105C22×C61#12311yescharacteristic
106C2×D61—44no—
107C2×D61—41no—
108C2×D61—42no—
109C2×D61—41no—
110C2×D61—42no—
111C2×D61—41no—
112C2×D61—42no—
113C2×D61—82no—
114C4×C61—42no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C61#12111yescharacteristic
118C4×C61#12111yescharacteristic
119C4×C61#12311yescharacteristic
120C4×C61#12411yescharacteristic
121Dic61—41no—
122Dic61—81no—
123#2037—611nomaximal, Sylow
124C2×C61—21no—
125C2×C61—21no—
126C2×C61#39411yescharacteristic
127C2×C61#45311yescharacteristic
128C2×C61#45511yescharacteristic
129D61—81no—
130D61—82no—
131#535—611no—
132#428—611no—
133C2×#104—611no—
134#417—611no—
135C2×#100—611no—
136#390—611no—
137#339D6111yescharacteristic, complemented
138C61#203711yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C22×D4—611no—
141C2×M16—611no—
142C2×M16C2×D6111yescharacteristic
143#127—1221no—
144#124—1221no—
145#121—1221no—
146#121—1221no—
147#120—1222no—
148#117C2×D6111yescharacteristic
149C2×C4⋊C4—611no—
150C2×C22⋊C4—1222no—
151C2×C42C2×D6111yescharacteristic
152#107—1221no—
153#106—1221no—
154#104—1222no—
155#103—1221no—
156#102—1221no—
157#100—1222no—
158C24—612no—
159#41—1221no—
160#41—1221no—
161#41—1221no—
162#41—1221no—
163C2×Q8—611no—
164C2×D4—611no—
165C2×D4—1222no—
166C2×D4—1222no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—1221no—
174C22×C4—21no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178M16—21no—
179M16—21no—
180M16—612no—
181M16—1221no—
182C2×C8—21no—
183C2×C8—1221no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4D24411yescharacteristic
187C4⋊C4D24411yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—2444no—
192C42—21no—
193C42—21no—
194C42—21no—
195C23—1222no—
196C23—1222no—
197C23—1221no—
198C23—1222no—
199C23—2442no—
200C23—2442no—
201C23D4×D6111yescharacteristic
202Q8—1221no—
203Q8—1221no—
204D4—1221no—
205D4—1221no—
206D4—4882no—
207D4—4882no—
208D4—2441no—
209D4—2441no—
210D4—2441no—
211D4—2441no—
212D4—2441no—
213D4—2441no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—1221no—
220C2×C4—2442no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4C2×D24411yescharacteristic
225C2×C4#1175822211yescharacteristic
226C2×C4#1175822211yescharacteristic
227C2×C4D4×D6111yescharacteristic
228C2×C4D4×D6111yescharacteristic
229C2×C4#1175822611yescharacteristic
230C8—41no—
231C8—1222no—
232C22—21no—
233C22—21no—
234C22—4882no—
235C22—2444no—
236C22—2441no—
237C22—2442no—
238C22—2441no—
239C22—2442no—
240C22—2441no—
241C22—2442no—
242C22#1451974711yescharacteristic
243C22#1451975011yescharacteristic
244C22#1451976211yescharacteristic
245C4—42no—
246C4—41no—
247C4—41no—
248C4—4881no—
249C4—2441no—
250C4#1451975011yescharacteristic
251C4#1451975211yescharacteristic
252C4#1451976211yescharacteristic
253C4#1451976511yescharacteristic
254C2—21no—
255C2—21no—
256C2—4882no—
257C2—4881no—
258C2#1683968011yescharacteristic
259C2#1683993111yescharacteristic
260C2#1683994111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#2037
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16839805C2semidirect
3. C2×#14519705C2semidirect
4. #16839764C2semidirect
5. C2×#14519693C2semidirect
6. #16839664C2semidirect
7. C61×#339C2semidirect
62. #11758194D4semidirect
137. #339D61semidirect
138. C61#2037semidirect