Finite Group Databasebeta

← #27170110

Subgroups — #27170110

Order 12928.

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

normal subgroups only

This group has 260 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#20265765C211yesmaximal, characteristic
2#20265333C211yesmaximal, characteristic, complemented
3#20265316C211yesmaximal, characteristic, complemented
4#20264913C211yesmaximal, characteristic, complemented
5#20264910C211yesmaximal, characteristic, complemented
6#20264901C211yesmaximal, characteristic, complemented
7#393×C101C211yesmaximal, characteristic, complemented
8C2×#13108064—21no—
9C2×#13108061—21no—
10#15692248—21no—
11#15692241—21no—
12#15692237—21no—
13#15692234C2211yescharacteristic
14#15692229C2211yescharacteristic
15#15692228—21no—
16#15692224—21no—
17C4×C22⋊D101—21no—
18#15692179—21no—
19#15692179—21no—
20C22⋊#11717579C2211yescharacteristic
21C22⋊#11717579C2211yescharacteristic
22C22×Q8×C101C2211yescharacteristic
23C2×C22⋊C4×C101—21no—
24C2×C22⋊C4×C101C2211yescharacteristic
25#95×C101—21no—
26#95×C101C2211yescharacteristic
27C2×Dic202D411yescharacteristic
28C2×D404D411yescharacteristic
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C2×C4×D101—21no—
33#13108064—42no—
34#13108061—42no—
35C2×#11717579—21no—
36C2×#11717579—21no—
37C4⋊Dic101D411yescharacteristic
38C4⋊Dic101D411yescharacteristic
39#13108053—21no—
40#13108053—21no—
41C22⋊Dic101—21no—
42C22⋊Dic101—21no—
43C22⋊Dic101—21no—
44#13108051—21no—
45#13108051—21no—
46C4×Dic101—21no—
47C24×C101D411yescharacteristic
48C2×Q8×C101—21no—
49C2×Q8×C101—21no—
50C2×Q8×C101—42no—
51C22×C4×C101—21no—
52C22×C4×C101—21no—
53C22×C4×C101D411yescharacteristic
54C22×C4×C101C2311yescharacteristic
55C22⋊C4×C101—21no—
56C22⋊C4×C101—21no—
57C22⋊C4×C101—42no—
58C23×C101—21no—
59C23×C101—21no—
60C23×C101—21no—
61C23×C101—41no—
62C23×C101—41no—
63C23×C101C2×D411yescharacteristic
64C22×D101—21no—
65Q8×C101—22no—
66Q8×C101—22no—
67Q8×C101—41no—
68Q8×C101—41no—
69C2×C4×C101—22no—
70C2×C4×C101—21no—
71C2×C4×C101—41no—
72C2×C4×C101—41no—
73C2×C4×C101—41no—
74C2×C4×C101—41no—
75C2×C4×C101—41no—
76C2×C4×C101—41no—
77C2×C4×C101—41no—
78C2×C4×C101C2×D411yescharacteristic
79C2×C4×C101C2×D411yescharacteristic
80C22⋊D101—41no—
81C22⋊D101—41no—
82C22⋊D101—81no—
83C22⋊D101—81no—
84C2×Dic101—21no—
85C2×Dic101—21no—
86C2×Dic101—21no—
87D404—41no—
88C4×D101—81no—
89Dic202—41no—
90#11717579—41no—
91#11717579—41no—
92C22×C101—21no—
93C22×C101—21no—
94C22×C101—42no—
95C22×C101—41no—
96C22×C101—41no—
97C22×C101—41no—
98C22×C101—81no—
99C22×C101#12011yescharacteristic
100C22×C101#13511yescharacteristic
101C22×C101#13711yescharacteristic
102C2×D101—41no—
103C2×D101—41no—
104C2×D101—41no—
105C4×C101—21no—
106C4×C101—21no—
107C4×C101—41no—
108C4×C101—42no—
109C4×C101—81no—
110Dic101—41no—
111Dic101—41no—
112Dic101—41no—
113C2×C101—21no—
114C2×C101—21no—
115C2×C101—81no—
116C2×C101#45211yescharacteristic
117C2×C101#45511yescharacteristic
118C2×C101B(4,𝔽2)11yescharacteristic
119D101—81no—
120#1606—1011nomaximal, Sylow
121C101#160611yescharacteristic, complemented, Sylow
122#538—1011no—
123#451—1011no—
124#448—1011no—
125#393D10111yescharacteristic, complemented
126#328—1011no—
127#327—1011no—
128#323—1011no—
129C22×Q8C2×D10111yescharacteristic
130C2×Q16—2021no—
131C2×SD16—2021no—
132#126—2021no—
133#124—2021no—
134#123—2021no—
135C22⋊Q8—1011no—
136#121—1011no—
137#121—2021no—
138#120—2021no—
139C4×D4—2021no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4C2×D10111yescharacteristic
142#103—2021no—
143#103—2021no—
144C22⋊C8—1011no—
145C22⋊C8—1011no—
146#95—21no—
147#95C2×D10111yescharacteristic
148C24C22⋊D10111yescharacteristic
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—1011no—
153C2×D4—1011no—
154C2×D4—2021no—
155C2×D4—2021no—
156C2×D4—2021no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—2021no—
160C22×C4C22⋊D10111yescharacteristic
161C22×C4C22×D10111yescharacteristic
162Q16—4042no—
163SD16—4042no—
164C2×C8—2021no—
165C2×C8—2021no—
166C4⋊C4—1011no—
167C4⋊C4—1011no—
168C4⋊C4—2021no—
169C4⋊C4—2021no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—42no—
173C22⋊C4—2021no—
174C22⋊C4—2021no—
175C22⋊C4—2021no—
176C22⋊C4—2021no—
177C22⋊C4—2021no—
178C42—2021no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—2021no—
185C23C2×C22⋊D10111yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—4041no—
191D4—8081no—
192D4—8081no—
193D4—4041no—
194D4—4041no—
195D4—4041no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—8081no—
206C2×C4—2021no—
207C2×C4—2021no—
208C2×C4—2021no—
209C2×C4D4×D10111yescharacteristic
210C2×C4D4×D10111yescharacteristic
211C8—4041no—
212C8—4041no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—4041no—
221C22—4041no—
222C22—4041no—
223C22#1569222311yescharacteristic
224C22#1569227511yescharacteristic
225C22#1569228611yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—81no—
231C4—4041no—
232C4—4041no—
233C4—4041no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—8081no—
238C2#2026533711yescharacteristic
239C2#2026535411yescharacteristic
240C2#2026536311yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#393×C101C2
socleC22×C101#120
prime radical#20265765C2
hypercenter#393D101
hypocenterC101#1606
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #20265333C2semidirect
3. #20265316C2semidirect
4. #20264913C2semidirect
5. #20264910C2semidirect
6. #20264901C2semidirect
7. #393×C101C2semidirect
121. C101#1606semidirect
125. #393D101semidirect

Maximal subgroups

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

subgroupindex
#202657652
#202653332
#202653162
#202649132
#202649102
#202649012
#393×C1012
#1606101