Finite Group Databasebeta

← #27173139

Subgroups — #27173139

Order 12928.

260 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 45 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#20265366C211yesmaximal, characteristic, complemented
2#20265363C211yesmaximal, characteristic, complemented
3#20265344C211yesmaximal, characteristic, complemented
4#20264970C211yesmaximal, characteristic, complemented
5#20264967C211yesmaximal, characteristic, complemented
6#20264964C211yesmaximal, characteristic, complemented
7#560×C101C211yesmaximal, characteristic, complemented
8#15692300C2211yescharacteristic
9#15692281—21no—
10#15692238—21no—
11#15692224—21no—
12#15692183—21no—
13#15692172C2211yescharacteristic
14#15692170C2211yescharacteristic
15#15692170C2211yescharacteristic
16#15692169—21no—
17#15692169—21no—
18#127×C101C2211yescharacteristic
19#126×C101—21no—
20#123×C101—21no—
21#123×C101C2211yescharacteristic
22#121×C101—21no—
23#121×C101—21no—
24#121×C101—21no—
25#120×C101—21no—
26#120×C101C2211yescharacteristic
27#13108074—21no—
28#13108073—41no—
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—41no—
32D4×D101—41no—
33#13108062—41no—
34#13108059—41no—
35#13108058—21no—
36#13108053—41no—
37C22⋊Dic101—21no—
38C22⋊Dic101—21no—
39C22⋊Dic101—41no—
40#13108051—41no—
41C24×C101D411yescharacteristic
42C2×D4×C101—21no—
43C2×D4×C101—21no—
44C2×D4×C101—21no—
45C2×D4×C101—21no—
46C2×D4×C101—21no—
47C2×D4×C101D411yescharacteristic, complemented
48C2×D4×C101C2311yescharacteristic
49C22×C4×C101—21no—
50C22×C4×C101D411yescharacteristic, complemented
51C4⋊C4×C101—21no—
52C4⋊C4×C101—21no—
53C4⋊C4×C101—21no—
54C22⋊C4×C101—21no—
55C22⋊C4×C101—21no—
56C22⋊C4×C101—21no—
57C22⋊C4×C101—21no—
58C22⋊C4×C101—21no—
59C22⋊C4×C101D411yescharacteristic
60C22⋊C4×C101D411yescharacteristic, complemented
61C42×C101D411yescharacteristic, complemented
62C23×C101—21no—
63C23×C101—21no—
64C23×C101—41no—
65C23×C101—81no—
66C23×C101C2×D411yescharacteristic
67C23×C101C2×D411yescharacteristic
68C22×D101—21no—
69C22×D101—21no—
70D4×C101—41no—
71D4×C101—41no—
72D4×C101—81no—
73D4×C101—81no—
74D4×C101—81no—
75D4×C101—81no—
76D4×C101—81no—
77C2×C4×C101—21no—
78C2×C4×C101—21no—
79C2×C4×C101—21no—
80C2×C4×C101—21no—
81C2×C4×C101—41no—
82C2×C4×C101—81no—
83C2×C4×C101C2×D411yescharacteristic
84C22⋊D101—41no—
85C22⋊D101—41no—
86C22⋊D101—41no—
87C22⋊D101—82no—
88C2×Dic101—21no—
89C2×Dic101—21no—
90C2×Dic101—41no—
91C2×Dic101—41no—
92D404—21no—
93C4×D101—41no—
94Dic202—21no—
95#11717579—41no—
96C22×C101—21no—
97C22×C101—21no—
98C22×C101—41no—
99C22×C101—41no—
100C22×C101—41no—
101C22×C101—41no—
102C22×C101—41no—
103C22×C101—41no—
104C22×C101—42no—
105C22×C101—41no—
106C22×C101—41no—
107C22×C101—81no—
108C22×C101#12011yescharacteristic
109C2×D101—41no—
110C2×D101—81no—
111C2×D101—81no—
112C4×C101—21no—
113C4×C101—41no—
114C4×C101—41no—
115C4×C101—41no—
116C4×C101—41no—
117Dic101—41no—
118Dic101—81no—
119Dic101—81no—
120C2×C101—21no—
121C2×C101—41no—
122C2×C101—41no—
123C2×C101—81no—
124C2×C101—81no—
125C2×C101B(4,𝔽2)11yescharacteristic
126D101—81no—
127#2200—1011nomaximal, Sylow
128C101#220011yescharacteristic, complemented, Sylow
129#560D10111yescharacteristic, complemented
130#458—1011no—
131B(4,𝔽2)—1011no—
132#453—1011no—
133#353—1011no—
134#352—1011no—
135AΣL(1,𝔽16)—1011no—
136H(5,𝔽2)—1011no—
137AGL(1,ℤ/8)—2021no—
138#127C2×D10111yescharacteristic
139#126—21no—
140#123—21no—
141#123—2021no—
142#123C2×D10111yescharacteristic
143#121—21no—
144#121—21no—
145#121—21no—
146#120—21no—
147#120—2021no—
148#120C2×D10111yescharacteristic
149#104—2021no—
150#100—1011no—
151#99—1011no—
152#99—1011no—
153#99—2021no—
154#99—2021no—
155C24C22⋊D10111yescharacteristic
156#41—4041no—
157#41—2021no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—4041no—
164C2×D4—4041no—
165C2×D4—2021no—
166C2×D4—2021no—
167C2×D4C22⋊D10111yescharacteristic, complemented
168C2×D4C22×D10111yescharacteristic
169C22×C4—21no—
170C22×C4C22⋊D10111yescharacteristic, complemented
171SD16—4041no—
172D8—4041no—
173M16—2021no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—4041no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—4041no—
184C22⋊C4—4041no—
185C22⋊C4—2021no—
186C22⋊C4—2021no—
187C22⋊C4C22⋊D10111yescharacteristic
188C22⋊C4C22⋊D10111yescharacteristic, complemented
189C42C22⋊D10111yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—41no—
193C23—81no—
194C23—2021no—
195C23—2021no—
196C23C2×C22⋊D10111yescharacteristic
197C23C2×C22⋊D10111yescharacteristic
198Q8—2021no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—81no—
204D4—81no—
205D4—81no—
206D4—8082no—
207D4—4041no—
208D4—4041no—
209D4—4041no—
210D4—2021no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—4041no—
218C2×C4—4041no—
219C2×C4—4041no—
220C2×C4—2021no—
221C2×C4—2021no—
222C2×C4C2×C22⋊D10111yescharacteristic
223C8—4041no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22—81no—
236C22—8081no—
237C22—8081no—
238C22—4041no—
239C22#1569222411yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—8081no—
246C4—8081no—
247C4—4041no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—8081no—
254C2#2026536411yescharacteristic
subgroupG/H
centerC2#20265364
commutator, cosocleC2×D4×C101C23
FrattiniC2×D4C22×D101
Fitting#560×C101C2
socleC2×C101B(4,𝔽2)
hypercenter#560D101
hypocenterC101#2200
LCSG ▷ C2×D4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #560

Complements

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

NH ≅ G/Ntype
1. #20265366C2semidirect
2. #20265363C2semidirect
3. #20265344C2semidirect
4. #20264970C2semidirect
5. #20264967C2semidirect
6. #20264964C2semidirect
7. #560×C101C2semidirect
47. C2×D4×C101D4semidirect
50. C22×C4×C101D4semidirect
60. C22⋊C4×C101D4semidirect
61. C42×C101D4semidirect
128. C101#2200semidirect
129. #560D101semidirect
167. C2×D4C22⋊D101semidirect
170. C22×C4C22⋊D101semidirect
188. C22⋊C4C22⋊D101semidirect
189. C42C22⋊D101semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202653662
#202653632
#202653442
#202649702
#202649672
#202649642
#560×C1012
#2200101