Finite Group Databasebeta

← #21447812

Subgroups — #21447812

Order 7808.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#16840442C211yesmaximal, characteristic, complemented
2#16839953C211yesmaximal, characteristic, complemented
3#16839950C211yesmaximal, characteristic
4#16839939C211yesmaximal, characteristic, complemented
5#16839551C211yesmaximal, characteristic, complemented
6#16839548C211yesmaximal, characteristic, complemented
7C61×#354C211yesmaximal, characteristic, complemented
8#14519822C2211yescharacteristic
9#14519808—21no—
10#14519770—21no—
11#14519761—21no—
12#14519759—21no—
13#14519758C2211yescharacteristic
14#14519753—21no—
15#14519747—21no—
16#14519745C2211yescharacteristic
17#14519737—21no—
18#14519734—21no—
19C22⋊C4×D61—21no—
20#14519705—21no—
21#14519694C2211yescharacteristic
22#14519691—21no—
23#14519691—21no—
24#124×C61C2211yescharacteristic
25#99×C61C2211yescharacteristic
26#99×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C2×Q8×C61D411yescharacteristic, complemented
29C2×D4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C22×Dic61D411yescharacteristic, complemented
34#11758224—41no—
35D4×D61—41no—
36#11758222—21no—
37C2×D244—41no—
38C2×C4×D61—21no—
39C2×C4×D61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—21no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C42×C61D411yescharacteristic, complemented
45C22⋊Dic61—21no—
46C22⋊Dic61D411yescharacteristic
47C22⋊Dic61D411yescharacteristic, complemented
48#11758202—41no—
49#11758201—41no—
50#11758198—21no—
51#11758198—21no—
52#11758198—21no—
53#11758198—41no—
54#11758198—41no—
55C4⋊Dic61—21no—
56C4⋊Dic61—41no—
57#11758196—21no—
58#11758196—21no—
59#11758196—21no—
60C4×Dic61—21no—
61#11758194—21no—
62C23×C61C2×D411yescharacteristic
63C23×C61C2×D411yescharacteristic
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—42no—
68C22×D61—41no—
69Q8×C61—41no—
70D4×C61—41no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61C2×D411yescharacteristic
76C22⋊D61—42no—
77C22⋊D61—41no—
78C22⋊D61—41no—
79C22⋊D61—41no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—41no—
86D244—21no—
87D244—82no—
88C4×D61—41no—
89C4×D61—42no—
90C4×D61—81no—
91Dic122—21no—
92#92418—41no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61#12011yescharacteristic
98C2×D61—22no—
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—42no—
102C2×D61—41no—
103C2×D61—81no—
104C2×D61—81no—
105C2×D61—81no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—41no—
109C4×C61—81no—
110C4×C61—81no—
111Dic61—41no—
112Dic61—41no—
113Dic61—41no—
114Dic61—41no—
115#2197—611nomaximal, Sylow
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—41no—
119C2×C61B(4,𝔽2)11yescharacteristic
120D61—42no—
121D61—81no—
122#551—611no—
123#458—611no—
124B(4,𝔽2)—611no—
125#455—611no—
126#354D6111yescharacteristic, complemented
127#352—611no—
128AΣL(1,𝔽16)—611no—
129C61#219711yescharacteristic, complemented, Sylow
130H(5,𝔽2)—611no—
131#137—1221no—
132#126—1221no—
133#124C2×D6111yescharacteristic
134#123—611no—
135#123—1221no—
136#123—1221no—
137C22⋊Q8—1221no—
138#120—611no—
139#120—1221no—
140C4×D4—1221no—
141#117—1221no—
142C2×C22⋊C4—1221no—
143#104—1221no—
144#100—611no—
145#99—1221no—
146#99—1221no—
147#99C2×D6111yescharacteristic
148#99C2×D6111yescharacteristic
149C24—611no—
150#41—1221no—
151#41—2441no—
152C2×Q8D24411yescharacteristic, complemented
153C2×D4—1221no—
154C2×D4—1221no—
155C2×D4—1221no—
156C2×D4—2441no—
157C2×D4—2441no—
158C2×D4C22×D6111yescharacteristic
159C22×C4—611no—
160C22×C4—1221no—
161C22×C4—1221no—
162Q16—2441no—
163SD16—2441no—
164M16—1221no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4—2441no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—611no—
175C22⋊C4—611no—
176C22⋊C4—1221no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4—2441no—
181C22⋊C4—2441no—
182C42—1221no—
183C42D24411yescharacteristic, complemented
184C23—1221no—
185C23—1221no—
186C23—1221no—
187C23—2441no—
188C23—2442no—
189C23D4×D6111yescharacteristic
190C23D4×D6111yescharacteristic
191Q8—41no—
192Q8—1221no—
193D4—41no—
194D4—1221no—
195D4—4882no—
196D4—2441no—
197D4—2441no—
198D4—2442no—
199D4—2441no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—4881no—
210C2×C4—2441no—
211C2×C4—2442no—
212C2×C4—2441no—
213C2×C4C2×D24411yescharacteristic
214C8—2441no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—1222no—
220C22—4881no—
221C22—4881no—
222C22—4881no—
223C22—2441no—
224C22—2442no—
225C22—2441no—
226C22—2441no—
227C22#1451974711yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—81no—
233C4—2441no—
234C4—2441no—
235C4—2441no—
236C4—2441no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—4881no—
241C2—2442no—
242C2#1683995011yescharacteristic
subgroupG/H
centerC2#16839950
commutatorC2×D4×C61C23
FrattiniC2×D4C22×D61
FittingC61×#354C2
socleC2×C61B(4,𝔽2)
hypercenter#354D61
hypocenterC61#2197
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
1. #16840442C2semidirect
2. #16839953C2semidirect
4. #16839939C2semidirect
5. #16839551C2semidirect
6. #16839548C2semidirect
7. C61×#354C2semidirect
28. C2×Q8×C61D4semidirect
33. C22×Dic61D4semidirect
44. C42×C61D4semidirect
47. C22⋊Dic61D4semidirect
126. #354D61semidirect
129. C61#2197semidirect
152. C2×Q8D244semidirect
183. C42D244semidirect