Finite Group Databasebeta

← #21462074

Subgroups — #21462074

Order 7808.

280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×#14519837C211yesmaximal, characteristic, complemented
2C2×#14519835C211yesmaximal, characteristic, complemented
3#16840664C212yesmaximal, complemented
4#16840662C212yesmaximal, complemented
5#16840321C211yesmaximal, characteristic
6C2×#11758217—21no—
7C2×C22⋊#6923—21no—
8#14519837—21no—
9#14519837C2212yes—
10#14519835—21no—
11#14519835C2212yes—
12C22×C22⋊D61C2211yescharacteristic
13#14519760C411yescharacteristic, complemented
14#14519760C2211yescharacteristic
15#14519758—21no—
16#14519749—21no—
17#14519749—21no—
18#14519746C411yescharacteristic, complemented
19#14519746C2211yescharacteristic
20#14519745—21no—
21C2×C22⋊Dic61C411yescharacteristic, complemented
22C22×D4×C61C411yescharacteristic, complemented
23C24×C61C2×C411yescharacteristic
24C24×C61C2×C411yescharacteristic, complemented
25C23×D61D411yescharacteristic
26C22×#6923—41no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—41no—
30C2×D4×C61—41no—
31C22×C4×C61C2×C411yescharacteristic, complemented
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—41no—
35C2×C22⋊D61—41no—
36C2×C22⋊D61C2×C411yescharacteristic
37C2×C22⋊D61D411yescharacteristic
38C2×C22⋊D61D411yescharacteristic
39C2×C22⋊D61C2311yescharacteristic
40C22×Dic61—21no—
41C22×Dic61D411yescharacteristic
42C22⋊#6923—22no—
43C22⋊#6923—41no—
44#11758217—22no—
45#11758217—41no—
46C2×#92420—41no—
47C22⋊Dic61—21no—
48C22⋊Dic61—21no—
49C22⋊Dic61—21no—
50C22⋊Dic61C2×C411yescharacteristic, complemented
51C22⋊Dic61C2×C411yescharacteristic, complemented
52#11758198—21no—
53#11758198—21no—
54#11758196—21no—
55#11758196—21no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61—21no—
59C23×C61—41no—
60C23×C61—81no—
61C23×C61—81no—
62C23×C61C22⋊C411yescharacteristic
63C23×C61C22⋊C411yescharacteristic
64C23×C61C22×C411yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—81no—
68C22×D61C22⋊C411yescharacteristic
69C22×D61C2×D411yescharacteristic
70C2×#6923—42no—
71C2×#6923—82no—
72D4×C61—42no—
73D4×C61—41no—
74D4×C61—41no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C22⋊D61—41no—
78C22⋊D61—41no—
79C22⋊D61—41no—
80C22⋊D61—41no—
81C22⋊D61—81no—
82C22⋊D61—81no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—81no—
88C2×Dic61C22⋊C411yescharacteristic
89C2×Dic61C2×D411yescharacteristic
90#92420—42no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—41no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—81no—
100C22×C61—81no—
101C22×C61—82no—
102C22×C61#9911yescharacteristic
103C22×C61#9911yescharacteristic
104C22×C61C2×C22⋊C411yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—42no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—81no—
111#6923—82no—
112C4×C61—41no—
113Dic61—21no—
114Dic61—21no—
115Dic61—41no—
116Dic61—41no—
117#2121—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—21no—
120C2×C61—21no—
121C2×C61—41no—
122C2×C61—41no—
123C2×C61—81no—
124C2×C61C2×#9911yescharacteristic
125D61—41no—
126D61—41no—
127#534—611no—
128C2×#100—611no—
129C2×#99—611no—
130#352—612no—
131AΣL(1,𝔽16)—612no—
132C61#212111yescharacteristic, complemented, Sylow
133C22×D4—611no—
134C22×D4#692311yescharacteristic, complemented
135C2×M16—1221no—
136#123—611no—
137#123—611no—
138#123—1221no—
139#121—1221no—
140#121—1221no—
141#120—611no—
142#120—611no—
143#120—1221no—
144C2×C22⋊C4—611no—
145C2×C22⋊C4—1221no—
146#100—612no—
147#100—1221no—
148#99—612no—
149#99—1221no—
150C24—611no—
151C24C2×#692311yescharacteristic
152C24C2×#692311yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—611no—
158C2×D4—611no—
159C2×D4—611no—
160C2×D4—611no—
161C2×D4—1221no—
162C2×D4—1221no—
163C2×D4—2441no—
164C2×D4—2441no—
165C22×C4—611no—
166C22×C4—1221no—
167C22×C4—2441no—
168C22×C4C2×#692311yescharacteristic, complemented
169M16—1222no—
170M16—2441no—
171C2×C8—2441no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C22⋊C4—611no—
175C22⋊C4—611no—
176C22⋊C4—1221no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1222no—
182C22⋊C4—2441no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—41no—
187C23—81no—
188C23—81no—
189C23—611no—
190C23—611no—
191C23—1221no—
192C23—1221no—
193C23—4881no—
194C23C22⋊#692311yescharacteristic
195C23C22⋊#692311yescharacteristic
196C23C22×#692311yescharacteristic
197D4—42no—
198D4—41no—
199D4—41no—
200D4—4881no—
201D4—4881no—
202D4—2441no—
203D4—2441no—
204D4—2441no—
205D4—2441no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—611no—
209C2×C4—611no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—4882no—
215C2×C4—4881no—
216C2×C4—2442no—
217C8—2442no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—81no—
227C22—81no—
228C22—82no—
229C22—1221no—
230C22—1221no—
231C22—4881no—
232C22—2441no—
233C22—2441no—
234C22—2442no—
235C22#1451983511yescharacteristic
236C22#1451983511yescharacteristic
237C22C2×C22⋊#692311yescharacteristic
238C4—41no—
239C4—1221no—
240C4—1221no—
241C4—4882no—
242C4—2441no—
243C4—2441no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—81no—
250C2—2441no—
251C2—2441no—
252C2C2×#1451983511yescharacteristic
subgroupG/H
centerC2C2×#14519835
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC22×D4×C61C4
socleC2×C61C2×#99
hypercenterC22×D4#6923
hypocenterC61#2121
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519837C2semidirect
2. C2×#14519835C2semidirect
3. #16840664C2semidirect
4. #16840662C2semidirect
13. #14519760C4semidirect
18. #14519746C4semidirect
21. C2×C22⋊Dic61C4semidirect
22. C22×D4×C61C4semidirect
24. C24×C61C2×C4semidirect
31. C22×C4×C61C2×C4semidirect
50. C22⋊Dic61C2×C4semidirect
51. C22⋊Dic61C2×C4semidirect
132. C61#2121semidirect
134. C22×D4#6923semidirect
152. C24C2×#6923semidirect
168. C22×C4C2×#6923semidirect