Finite Group Databasebeta

← #21447029

Subgroups — #21447029

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#16840329C211yesmaximal, characteristic
2#16839802C211yesmaximal, characteristic, complemented
3C2×#14519705C211yesmaximal, characteristic, complemented
4#16839761C211yesmaximal, characteristic, complemented
5C2×#14519694C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C61×#390C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519773—21no—
12#14519764—21no—
13#14519748—21no—
14#14519748—21no—
15#14519746—22no—
16#14519736C2211yescharacteristic
17#14519710—21no—
18#14519708—21no—
19#14519705—22no—
20#14519700—21no—
21#14519697—21no—
22#14519694—22no—
23C22×D4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C22⋊C4×C61—22no—
26C2×C42×C61C2211yescharacteristic
27C24×C61D412yes—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38C2×C22⋊D61—22no—
39C2×C22⋊D61—22no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122D411yescharacteristic
47C4⋊C4×C61—21no—
48C4⋊C4×C61—21no—
49C22⋊C4×C61—44no—
50C42×C61—21no—
51C42×C61—21no—
52C22⋊Dic61—22no—
53C22⋊Dic61—22no—
54C22⋊Dic61—21no—
55C4⋊Dic61D411yescharacteristic
56C4⋊Dic61D411yescharacteristic
57C4×Dic61—21no—
58#11758194—21no—
59#11758194—21no—
60#11758194—21no—
61#11758194D412yescomplemented
62C2×#92418—21no—
63C2×#92418—21no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—42no—
68C23×C61—42no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71D4×C61—41no—
72D4×C61—41no—
73D4×C61—41no—
74D4×C61—41no—
75C2×C4×C61—22no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—42no—
79C2×C4×C61—41no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C2×C4×C61#4111yescharacteristic
86C22⋊D61—41no—
87C22⋊D61—41no—
88C22⋊D61—82no—
89C22⋊D61—82no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93D244—21no—
94D244—21no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—21no—
98Dic122—21no—
99#92418—22no—
100#92418—41no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—44no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—82no—
108C22×C61#12011yescharacteristic
109C22×C61#12111yescharacteristic
110C22×C61#12311yescharacteristic
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C4×C61—42no—
115C4×C61—81no—
116C4×C61#12111yescharacteristic
117C4×C61#12111yescharacteristic
118C4×C61#12311yescharacteristic
119C4×C61#12411yescharacteristic
120Dic61—41no—
121Dic61—41no—
122Dic61—41no—
123#2037—611nomaximal, Sylow
124C2×C61—21no—
125C2×C61—21no—
126C2×C61—82no—
127C2×C61#39411yescharacteristic
128C2×C61#45311yescharacteristic
129C2×C61#45511yescharacteristic
130D61—81no—
131#535—611no—
132#428—611no—
133C2×#104—611no—
134#417—611no—
135C2×#100—611no—
136#390D6111yescharacteristic, complemented
137#339—611no—
138C61#203711yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C22×D4C2×D6111yescharacteristic
141C2×M16—611no—
142C2×M16—611no—
143#127—1221no—
144#124—1221no—
145#121—1221no—
146#121—1221no—
147#120—1222no—
148#117—611no—
149C2×C4⋊C4C2×D6111yescharacteristic
150C2×C22⋊C4—22no—
151C2×C42C2×D6111yescharacteristic
152#107—1221no—
153#106—1221no—
154#104—1222no—
155#103—1221no—
156#102—1221no—
157#100—1222no—
158C24C22⋊D6112yes—
159#41—1221no—
160#41—1221no—
161#41—1221no—
162#41—1221no—
163C2×Q8—611no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—611no—
171C2×D4—1222no—
172C2×D4—1222no—
173C2×D4—1221no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178M16—612no—
179M16—1221no—
180M16—1221no—
181M16—1221no—
182C2×C8—1221no—
183C2×C8—1221no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—611no—
187C4⋊C4—611no—
188C22⋊C4—44no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1221no—
192C42—21no—
193C42—21no—
194C42—1221no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—42no—
199C23—42no—
200C23—1221no—
201C23C2×C22⋊D6111yescharacteristic
202Q8—1221no—
203Q8—1221no—
204D4—41no—
205D4—41no—
206D4—41no—
207D4—41no—
208D4—1221no—
209D4—1221no—
210D4—4882no—
211D4—4882no—
212D4—2441no—
213D4—2441no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4#1175822211yescharacteristic
225C2×C4#1175822211yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4D4×D6111yescharacteristic
228C2×C4D4×D6111yescharacteristic
229C2×C4#1175822411yescharacteristic
230C8—1222no—
231C8—2441no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—82no—
239C22—2441no—
240C22—2441no—
241C22—2441no—
242C22#1451974511yescharacteristic
243C22#1451974911yescharacteristic
244C22#1451976011yescharacteristic
245C4—42no—
246C4—81no—
247C4—2441no—
248C4—2441no—
249C4—2441no—
250C4#1451975011yescharacteristic
251C4#1451975011yescharacteristic
252C4#1451975911yescharacteristic
253C4#1451976311yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—4881no—
258C2#1683967711yescharacteristic
259C2#1683992911yescharacteristic
260C2#1683993911yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#390C2
socleC22×C61#120
hypercenter#390D61
hypocenterC61#2037
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #16839802C2semidirect
3. C2×#14519705C2semidirect
4. #16839761C2semidirect
5. C2×#14519694C2semidirect
6. #16839522C2semidirect
7. C61×#390C2semidirect
61. #11758194D4semidirect
136. #390D61semidirect
138. C61#2037semidirect