Finite Group Databasebeta

← #27172799

Subgroups — #27172799

Order 12928.

286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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#20265744C211yesmaximal, characteristic
2C2×#15692170C211yesmaximal, characteristic, complemented
3#20264971C212yesmaximal, complemented
4#20264969C212yesmaximal, complemented
5C2×#99×C101C211yesmaximal, characteristic, complemented
6C2×#13108074C411yescharacteristic, complemented
7#15692251C411yescharacteristic, complemented
8#15692251C2211yescharacteristic
9#15692242C411yescharacteristic, complemented
10#15692242C2211yescharacteristic
11#15692226—21no—
12#15692226—21no—
13#15692224—21no—
14#15692224—21no—
15#15692214C411yescharacteristic, complemented
16C2×C22⋊Dic101—21no—
17#15692170—21no—
18#15692170C2212yes—
19C22×D4×C101C2211yescharacteristic
20C2×C22⋊C4×C101—21no—
21#99×C101—21no—
22#99×C101C2212yes—
23#13108074—41no—
24#13108074—41no—
25C2×Dic202C2×C411yescharacteristic, complemented
26C2×D404C2×C411yescharacteristic, complemented
27C2×C22⋊D101—21no—
28C2×C22⋊D101—21no—
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C22×Dic101—41no—
33C2×C4×D101—21no—
34C4⋊Dic101—21no—
35C22⋊Dic101—21no—
36C22⋊Dic101—21no—
37C22⋊Dic101—21no—
38C22⋊Dic101—21no—
39C22⋊Dic101—21no—
40C22⋊Dic101—22no—
41C22⋊Dic101—41no—
42C4×Dic101C2×C411yescharacteristic, complemented
43C4×Dic101C2×C411yescharacteristic, complemented
44C24×C101D411yescharacteristic
45C24×C101D411yescharacteristic
46C2×D4×C101—41no—
47C2×D4×C101—41no—
48C2×D4×C101C2×C411yescharacteristic
49C2×D4×C101D411yescharacteristic
50C2×D4×C101D411yescharacteristic
51C2×D4×C101C2311yescharacteristic
52C22×C4×C101—41no—
53C22×C4×C101C2×C411yescharacteristic
54C22⋊C4×C101—22no—
55C22⋊C4×C101—41no—
56C23×C101—21no—
57C23×C101—21no—
58C23×C101—21no—
59C23×C101—21no—
60C23×C101—81no—
61C23×C101—81no—
62C23×C101C22⋊C411yescharacteristic
63C23×C101C22⋊C411yescharacteristic
64C23×C101C22⋊C411yescharacteristic
65C23×C101C2×D411yescharacteristic
66C23×C101C2×D411yescharacteristic
67C22×D101—21no—
68D4×C101—41no—
69D4×C101—41no—
70D4×C101—41no—
71D4×C101—41no—
72C2×C4×C101—21no—
73C2×C4×C101—21no—
74C2×C4×C101—42no—
75C2×C4×C101—82no—
76C2×C4×C101C22⋊C411yescharacteristic
77C2×C4×C101C22×C411yescharacteristic
78C22⋊D101—41no—
79C22⋊D101—41no—
80C22⋊D101—81no—
81C22⋊D101—81no—
82C22⋊D101—81no—
83C22⋊D101—81no—
84C2×Dic101—21no—
85C2×Dic101—21no—
86C2×Dic101—21no—
87C2×Dic101—42no—
88C2×Dic101—82no—
89D404—41no—
90C4×D101—42no—
91Dic202—41no—
92C22×C101—21no—
93C22×C101—21no—
94C22×C101—21no—
95C22×C101—21no—
96C22×C101—41no—
97C22×C101—41no—
98C22×C101—41no—
99C22×C101—41no—
100C22×C101—41no—
101C22×C101—42no—
102C22×C101—42no—
103C22×C101—81no—
104C22×C101—81no—
105C22×C101#9911yescharacteristic
106C22×C101#9911yescharacteristic
107C22×C101C2×C22⋊C411yescharacteristic
108C2×D101—41no—
109C2×D101—41no—
110C2×D101—41no—
111C4×C101—21no—
112C4×C101—21no—
113C4×C101—82no—
114Dic101—41no—
115Dic101—41no—
116Dic101—41no—
117Dic101—82no—
118C2×C101—21no—
119C2×C101—21no—
120C2×C101—21no—
121C2×C101—41no—
122C2×C101—41no—
123C2×C101—41no—
124C2×C101—41no—
125C2×C101C2×#9911yescharacteristic
126D101—81no—
127#2127—1011nomaximal, Sylow
128C101#212711yescharacteristic, complemented, Sylow
129#535—1011no—
130C2×#99—1011no—
131C2×#99D10111yescharacteristic, complemented
132#354—1012no—
133#353—1012no—
134C2×#41—1011no—
135C22×D4C2×D10111yescharacteristic
136#127—1011no—
137#127—1011no—
138#124—1011no—
139#124—1011no—
140#121—2021no—
141#121—2021no—
142#120—2021no—
143#120—2021no—
144#117—1011no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—2021no—
147#99—21no—
148#99—1012no—
149#99—2021no—
150#99C2×D10112yes—
151C24D40411yescharacteristic
152C24C22⋊D10111yescharacteristic
153#41—4041no—
154#41—4041no—
155C2×Q8—1011no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—1011no—
159C2×D4—2021no—
160C2×D4—2021no—
161C2×D4—2021no—
162C2×D4—2021no—
163C2×D4—2021no—
164C2×D4C4×D10111yescharacteristic
165C2×D4D40411yescharacteristic
166C2×D4C22⋊D10111yescharacteristic
167C2×D4C22×D10111yescharacteristic
168C22×C4—41no—
169C22×C4—4041no—
170C22×C4—2021no—
171C22×C4C4×D10111yescharacteristic
172C4⋊C4—2021no—
173C22⋊C4—22no—
174C22⋊C4—41no—
175C22⋊C4—4041no—
176C22⋊C4—2022no—
177C22⋊C4—2021no—
178C22⋊C4—2021no—
179C22⋊C4—2021no—
180C22⋊C4—2021no—
181C22⋊C4—2021no—
182C42—1011no—
183C42—1011no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—81no—
189C23—81no—
190C23—2021no—
191C23#1310805111yescharacteristic
192C23#1310805111yescharacteristic
193C23#1310805111yescharacteristic
194C23C2×C22⋊D10111yescharacteristic
195C23C2×D40411yescharacteristic
196Q8—4041no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—8081no—
202D4—8081no—
203D4—8081no—
204D4—8081no—
205D4—4041no—
206D4—4041no—
207D4—4041no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—8082no—
213C2×C4—4042no—
214C2×C4—4042no—
215C2×C4—2021no—
216C2×C4—2021no—
217C2×C4—2021no—
218C2×C4#1310805111yescharacteristic
219C2×C4C2×C4×D10111yescharacteristic
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—4041no—
234C22—4041no—
235C22—4041no—
236C22#1569216911yescharacteristic
237C22#1569216911yescharacteristic
238C22C2×#1310805111yescharacteristic
239C4—21no—
240C4—21no—
241C4—82no—
242C4—8082no—
243C4—4041no—
244C4—4041no—
245C4—4041no—
246C2—21no—
247C2—21no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—41no—
252C2—41no—
253C2—8081no—
254C2C2×#1569216911yescharacteristic
subgroupG/H
centerC2C2×#15692169
commutatorC2×C4×C101C22×C4
FrattiniC2×D4C22×D101
FittingC2×#99×C101C2
socleC2×C101C2×#99
prime radical#20265744C2
cosocleC2×D4×C101C23
hypercenterC2×#99D101
hypocenterC101#2127
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#15692170C2semidirect
3. #20264971C2semidirect
4. #20264969C2semidirect
5. C2×#99×C101C2semidirect
6. C2×#13108074C4semidirect
7. #15692251C4semidirect
9. #15692242C4semidirect
15. #15692214C4semidirect
25. C2×Dic202C2×C4semidirect
26. C2×D404C2×C4semidirect
42. C4×Dic101C2×C4semidirect
43. C4×Dic101C2×C4semidirect
128. C101#2127semidirect
131. C2×#99D101semidirect

Maximal subgroups

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

subgroupindex
#202657442
C2×#156921702
#202649712
#202649692
C2×#99×C1012
#2127101