Finite Group Databasebeta

← #21447030

Subgroups — #21447030

Order 7808.

326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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#16839804C211yesmaximal, characteristic, complemented
3C2×#14519703C211yesmaximal, characteristic, complemented
4#16839764C211yesmaximal, characteristic, complemented
5#16839665C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C2×#100×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519773—21no—
10#14519764—21no—
11#14519748—21no—
12#14519748—21no—
13#14519746—22no—
14#14519736C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C22⋊Dic61—22no—
17C2×C4×Dic61C2211yescharacteristic
18#14519711—21no—
19#14519709—21no—
20#14519703—22no—
21#14519702—21no—
22#14519699—21no—
23C22×D4×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25C2×M16×C61C2211yescharacteristic
26#100×C61—22no—
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×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C2×C22⋊D61—22no—
37C2×C22⋊D61—22no—
38C22×Dic61—21no—
39C22×Dic61—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122D411yescharacteristic
47M16×C61—21no—
48M16×C61—21no—
49M16×C61—21no—
50M16×C61D412yescomplemented
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C22⋊Dic61—22no—
54C22⋊Dic61—22no—
55C22⋊Dic61—21no—
56C22⋊Dic61—44no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61D411yescharacteristic
60C4⋊Dic61D411yescharacteristic
61C4×Dic61—21no—
62C4×Dic61—21no—
63C4×Dic61—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×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C22⋊D61—41no—
82C22⋊D61—41no—
83C22⋊D61—82no—
84C22⋊D61—82no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—42no—
92C2×Dic61—41no—
93D244—21no—
94D244—21no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—21no—
98Dic122—21no—
99C8×C61—22no—
100C8×C61—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#12111yescharacteristic
115C4×C61#12111yescharacteristic
116C4×C61#12311yescharacteristic
117C4×C61#12411yescharacteristic
118Dic61—42no—
119Dic61—41no—
120Dic61—41no—
121Dic61—41no—
122Dic61—81no—
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×#100D6111yescharacteristic, complemented
136#390—611no—
137#339—611no—
138C61#203711yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C22×D4C2×D6111yescharacteristic
141C2×M16C2×D6111yescharacteristic
142C2×M16C2×D6111yescharacteristic
143#127—1221no—
144#124—1221no—
145#121—1221no—
146#121—1221no—
147#120—1222no—
148#117—611no—
149C2×C4⋊C4—611no—
150C2×C22⋊C4—1222no—
151C2×C42—611no—
152#107—1221no—
153#106—1221no—
154#104—1222no—
155#103—1221no—
156#102—1221no—
157#100—22no—
158C24D24412yes—
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—1221no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178M16—21no—
179M16—21no—
180M16—21no—
181M16C22⋊D6112yescomplemented
182C2×C8—21no—
183C2×C8—21no—
184C4⋊C4—611no—
185C4⋊C4—611no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1221no—
191C22⋊C4—2444no—
192C42—1221no—
193C42—1221no—
194C42—1221no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—42no—
199C23—42no—
200C23—1221no—
201C23C2×D24411yescharacteristic
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—1222no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—2442no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4#1175822211yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4#1175822411yescharacteristic
228C2×C4#1175822411yescharacteristic
229C2×C4C2×C22⋊D6111yescharacteristic
230C8—22no—
231C8—41no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—82no—
239C22—2441no—
240C22—2441no—
241C22—2441no—
242C22#1451974711yescharacteristic
243C22#1451975111yescharacteristic
244C22#1451976111yescharacteristic
245C4—4881no—
246C4—2442no—
247C4—2441no—
248C4—2441no—
249C4—2441no—
250C4#1451974811yescharacteristic
251C4#1451974911yescharacteristic
252C4#1451975911yescharacteristic
253C4#1451976311yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—4881no—
258C2#1683967811yescharacteristic
259C2#1683993211yescharacteristic
260C2#1683994211yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#100×C61C2
socleC22×C61#120
hypercenterC2×#100D61
hypocenterC61#2037
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #16839804C2semidirect
3. C2×#14519703C2semidirect
4. #16839764C2semidirect
5. #16839665C2semidirect
6. #16839523C2semidirect
7. C2×#100×C61C2semidirect
50. M16×C61D4semidirect
135. C2×#100D61semidirect
138. C61#2037semidirect
181. M16C22⋊D61semidirect