Finite Group Databasebeta

← #27170058

Subgroups — #27170058

Order 12928.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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#20265772C211yesmaximal, characteristic, complemented
2#20265328C211yesmaximal, characteristic, complemented
3#20265091C211yesmaximal, characteristic, complemented
4#20264915C211yesmaximal, characteristic, complemented
5#20264911C211yesmaximal, characteristic, complemented
6#20264902C211yesmaximal, characteristic, complemented
7#447×C101C211yesmaximal, characteristic
8C2×#13108062—21no—
9#15692248—21no—
10#15692245—21no—
11#15692236—21no—
12#15692236—21no—
13#15692234C2211yescharacteristic
14#15692232—21no—
15D4×Dic101—21no—
16C2×#13108053C2211yescharacteristic
17C2×C22⋊Dic101—21no—
18C2×C22⋊Dic101—21no—
19#15692176—21no—
20C22⋊#11717579C2211yescharacteristic
21#15692162C2211yescharacteristic
22C22×D4×C101C2211yescharacteristic
23C2×D8×C101—21no—
24#121×C101C2211yescharacteristic
25#102×C101—21no—
26C22⋊C8×C101C2211yescharacteristic
27C2×Dic202D411yescharacteristic
28C22×Dic101—21no—
29C22×Dic101—21no—
30C22×Dic101D411yescharacteristic
31C22×Dic101D411yescharacteristic
32#13108062—42no—
33C2×#11717579—21no—
34C4⋊Dic101—21no—
35C4⋊Dic101D411yescharacteristic
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41C22⋊Dic101—21no—
42C22⋊Dic101—21no—
43C22⋊Dic101—21no—
44C22⋊Dic101—21no—
45C22⋊Dic101—42no—
46C22⋊Dic101—42no—
47C4×Dic101—21no—
48C24×C101—21no—
49C2×D4×C101—21no—
50C2×D4×C101—21no—
51C2×D4×C101—21no—
52C2×D4×C101—42no—
53C2×D4×C101D411yescharacteristic
54C22×C4×C101C2311yescharacteristic
55D8×C101—42no—
56C2×C8×C101—21no—
57C4⋊C4×C101D411yescharacteristic
58C22⋊C4×C101—21no—
59C23×C101—22no—
60C23×C101—21no—
61C23×C101—41no—
62C23×C101—41no—
63C23×C101—41no—
64C23×C101—41no—
65C23×C101—41no—
66C23×C101—41no—
67C23×C101C2×D411yescharacteristic
68D4×C101—22no—
69D4×C101—22no—
70D4×C101—41no—
71D4×C101—41no—
72D4×C101—41no—
73D4×C101—41no—
74D4×C101—41no—
75C2×C4×C101—21no—
76C2×C4×C101—41no—
77C2×C4×C101C2×D411yescharacteristic
78C2×C4×C101C2×D411yescharacteristic
79C2×Dic101—21no—
80C2×Dic101—21no—
81C2×Dic101—21no—
82C2×Dic101—21no—
83C2×Dic101—21no—
84C2×Dic101—21no—
85C2×Dic101—41no—
86C2×Dic101—41no—
87C2×Dic101—41no—
88C2×Dic101—41no—
89C2×Dic101—81no—
90Dic202—41no—
91C8×C101—41no—
92#11717579—41no—
93C22×C101—21no—
94C22×C101—21no—
95C22×C101—42no—
96C22×C101—42no—
97C22×C101—41no—
98C22×C101—41no—
99C22×C101—41no—
100C22×C101—42no—
101C22×C101—81no—
102C22×C101—81no—
103C22×C101—81no—
104C22×C101—81no—
105C22×C101#12011yescharacteristic
106C22×C101#13511yescharacteristic
107C22×C101AGL(1,ℤ/8)11yescharacteristic
108C4×C101—21no—
109C4×C101—21no—
110C4×C101—41no—
111Dic101—41no—
112Dic101—41no—
113Dic101—41no—
114Dic101—41no—
115Dic101—81no—
116C2×C101—21no—
117C2×C101—21no—
118C2×C101—81no—
119C2×C101—82no—
120C2×C101#44911yescharacteristic
121C2×C101#45411yescharacteristic
122C2×C101B(4,𝔽2)11yescharacteristic
123#1597—1011nomaximal, Sylow
124C101#159711yescharacteristic, complemented, Sylow
125#539—1011no—
126#450—1011no—
127#447D10111yescharacteristic
128#394—1011no—
129#328—1011no—
130#327—1011no—
131#324—1011no—
132C22×D4C2×D10111yescharacteristic
133C2×SD16—2021no—
134C2×D8—21no—
135#126—2021no—
136#125—2021no—
137#123—2021no—
138#123—2021no—
139C22⋊Q8—1011no—
140C22⋊Q8—2021no—
141#121C2×D10111yescharacteristic
142C4×D4—2021no—
143C2×C4⋊C4—1011no—
144C2×C22⋊C4—2021no—
145C2×C22⋊C4—2021no—
146#102—21no—
147#102—2021no—
148C22⋊C8—1011no—
149C22⋊C8C2×D10111yescharacteristic
150#95—1011no—
151C24—21no—
152C2×Q8—1011no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—42no—
157C2×D4C22⋊D10111yescharacteristic
158C22×C4—1011no—
159C22×C4—1011no—
160C22×C4—2021no—
161C22×C4—2021no—
162C22×C4C22×D10111yescharacteristic
163SD16—4042no—
164D8—42no—
165C2×C8—21no—
166C2×C8—2021no—
167C4⋊C4—1011no—
168C4⋊C4—2021no—
169C4⋊C4—2021no—
170C4⋊C4—2021no—
171C4⋊C4—2021no—
172C4⋊C4—2021no—
173C4⋊C4—2021no—
174C4⋊C4C22⋊D10111yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—4042no—
177C22⋊C4—4042no—
178C22⋊C4—2021no—
179C22⋊C4—2021no—
180C22⋊C4—2021no—
181C22⋊C4—2021no—
182C42—2021no—
183C23—22no—
184C23—21no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—41no—
191C23D4×D10111yescharacteristic
192Q8—4041no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—41no—
199D4—41no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—8081no—
203C2×C4—4041no—
204C2×C4—4041no—
205C2×C4—4041no—
206C2×C4—4041no—
207C2×C4—2021no—
208C2×C4—2021no—
209C2×C4—2021no—
210C2×C4—2021no—
211C2×C4—2021no—
212C2×C4—2021no—
213C2×C4D4×D10111yescharacteristic
214C2×C4C2×C22⋊D10111yescharacteristic
215C8—41no—
216C8—4041no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—81no—
226C22—81no—
227C22—81no—
228C22—81no—
229C22#1569222311yescharacteristic
230C22#1569227411yescharacteristic
231C22#1569227911yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—8081no—
236C4—4041no—
237C4—4041no—
238C4—4041no—
239C4—4041no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—81no—
244C2#2026531911yescharacteristic
245C2#2026534811yescharacteristic
246C2#2026536311yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting, prime radical#447×C101C2
socleC22×C101#120
hypercenter#447D101
hypocenterC101#1597
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20265772C2semidirect
2. #20265328C2semidirect
3. #20265091C2semidirect
4. #20264915C2semidirect
5. #20264911C2semidirect
6. #20264902C2semidirect
124. C101#1597semidirect

Maximal subgroups

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

subgroupindex
#202657722
#202653282
#202650912
#202649152
#202649112
#202649022
#447×C1012
#1597101