Finite Group Databasebeta

← #27170095

Subgroups — #27170095

Order 12928.

244 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 53 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#20265332C211yesmaximal, characteristic, complemented
2#20265315C211yesmaximal, characteristic
3#20265097C211yesmaximal, characteristic, complemented
4#20264914C211yesmaximal, characteristic, complemented
5#20264911C211yesmaximal, characteristic
6#20264903C211yesmaximal, characteristic, complemented
7#539×C101C211yesmaximal, characteristic
8C22×Dic202C2211yescharacteristic
9C2×#13108064—21no—
10C2×#13108062—21no—
11C2×#13108053—21no—
12#15692178—21no—
13#15692178—21no—
14C22⋊#11717579C2211yescharacteristic
15C22⋊#11717579C2211yescharacteristic
16#15692162—21no—
17#15692162C2211yescharacteristic
18#126×C101—21no—
19#125×C101—21no—
20#123×C101—21no—
21#123×C101—21no—
22C22⋊Q8×C101—21no—
23C22⋊Q8×C101C2211yescharacteristic
24#121×C101C2211yescharacteristic
25C4×D4×C101—21no—
26C2×C4⋊C4×C101C2211yescharacteristic
27C2×Dic202—21no—
28C2×Dic202—21no—
29C2×Dic202—42no—
30C22×Dic101—21no—
31C22×Dic101—21no—
32#13108064—42no—
33#13108062—42no—
34C2×#11717579—21no—
35C2×#11717579—21no—
36#13108053—42no—
37C2×Q8×C101D411yescharacteristic
38C2×D4×C101—21no—
39C2×D4×C101D411yescharacteristic
40C22×C4×C101—21no—
41C22×C4×C101D411yescharacteristic
42C22×C4×C101D411yescharacteristic
43C22×C4×C101C2311yescharacteristic
44C4⋊C4×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101—21no—
47C4⋊C4×C101—21no—
48C4⋊C4×C101—21no—
49C4⋊C4×C101—21no—
50C4⋊C4×C101D411yescharacteristic
51C4⋊C4×C101D411yescharacteristic
52C22⋊C4×C101—21no—
53C22⋊C4×C101—21no—
54C22⋊C4×C101—21no—
55C22⋊C4×C101—21no—
56C22⋊C4×C101—21no—
57C42×C101—21no—
58C23×C101—21no—
59C23×C101C2×D411yescharacteristic
60Q8×C101—41no—
61D4×C101—41no—
62D4×C101—41no—
63D4×C101—41no—
64C2×C4×C101—21no—
65C2×C4×C101—21no—
66C2×C4×C101—21no—
67C2×C4×C101—21no—
68C2×C4×C101—21no—
69C2×C4×C101—21no—
70C2×C4×C101—21no—
71C2×C4×C101—41no—
72C2×C4×C101—41no—
73C2×C4×C101—81no—
74C2×C4×C101C2×D411yescharacteristic
75C2×C4×C101C2×D411yescharacteristic
76C2×Dic101—22no—
77C2×Dic101—22no—
78C2×Dic101—41no—
79C2×Dic101—41no—
80C2×Dic101—41no—
81C2×Dic101—41no—
82Dic202—22no—
83Dic202—22no—
84Dic202—41no—
85Dic202—41no—
86#11717579—41no—
87#11717579—41no—
88C22×C101—21no—
89C22×C101—21no—
90C22×C101—41no—
91C22×C101—41no—
92C22×C101—41no—
93C22×C101#12011yescharacteristic
94C22×C101#13511yescharacteristic
95C22×C101#13711yescharacteristic
96C4×C101—21no—
97C4×C101—21no—
98C4×C101—41no—
99C4×C101—41no—
100C4×C101—41no—
101C4×C101—41no—
102C4×C101—41no—
103Dic101—42no—
104Dic101—42no—
105C2×C101—21no—
106C2×C101—21no—
107C2×C101—81no—
108C2×C101#45211yescharacteristic
109C2×C101#45611yescharacteristic
110C2×C101B(4,𝔽2)11yescharacteristic
111#1603—1011nomaximal, Sylow
112C101#160311yescharacteristic, complemented, Sylow
113#539D10111yescharacteristic
114#451—1011no—
115#448—1011no—
116#395—1011no—
117#328—1011no—
118#327—1011no—
119#324—1011no—
120C22×Q8—1011no—
121C2×Q16—2021no—
122C2×SD16—2021no—
123#126—21no—
124#125—21no—
125#123—21no—
126#123—21no—
127C22⋊Q8—21no—
128C22⋊Q8C2×D10111yescharacteristic
129#121C2×D10111yescharacteristic
130C4×D4—21no—
131C2×C4⋊C4—2021no—
132C2×C4⋊C4C2×D10111yescharacteristic
133#103—2021no—
134#103—2021no—
135C22⋊C8—1011no—
136C22⋊C8—1011no—
137#95—1011no—
138#95—2021no—
139C2×Q8—4042no—
140C2×Q8—2021no—
141C2×Q8—2021no—
142C2×Q8C22⋊D10111yescharacteristic
143C2×D4—21no—
144C2×D4C22⋊D10111yescharacteristic
145C22×C4—21no—
146C22×C4—2021no—
147C22×C4—2021no—
148C22×C4C22⋊D10111yescharacteristic
149C22×C4C22⋊D10111yescharacteristic
150C22×C4C22×D10111yescharacteristic
151Q16—4042no—
152SD16—4042no—
153C2×C8—2021no—
154C2×C8—2021no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—4042no—
162C4⋊C4C22⋊D10111yescharacteristic
163C4⋊C4C22⋊D10111yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C42—21no—
170C23—21no—
171C23C2×C22⋊D10111yescharacteristic
172Q8—41no—
173Q8—4041no—
174Q8—4041no—
175Q8—2022no—
176Q8—2022no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—4041no—
191C2×C4—4041no—
192C2×C4—4041no—
193C2×C4—4041no—
194C2×C4—2022no—
195C2×C4—2022no—
196C2×C4C2×C22⋊D10111yescharacteristic
197C2×C4C2×C22⋊D10111yescharacteristic
198C8—4041no—
199C8—4041no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1569222411yescharacteristic
206C22#1569227511yescharacteristic
207C22#1569228511yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—4042no—
216C4—4042no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#2026533911yescharacteristic
221C2#2026536011yescharacteristic
222C2#2026536411yescharacteristic
subgroupG/H
centerC22#15692224
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#539×C101C2
socleC22×C101#120
prime radical#121×C101C22
hypercenter#539D101
hypocenterC101#1603
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #20265332C2semidirect
3. #20265097C2semidirect
4. #20264914C2semidirect
6. #20264903C2semidirect
112. C101#1603semidirect

Maximal subgroups

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

subgroupindex
#202653322
#202653152
#202650972
#202649142
#202649112
#202649032
#539×C1012
#1603101