Finite Group Databasebeta

← #27171671

Subgroups — #27171671

Order 12928.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#20265736C211yesmaximal, characteristic
2#20265650C211yesmaximal, characteristic, complemented
3C2×#15692170C211yesmaximal, characteristic, complemented
4C2×#15692169C211yesmaximal, characteristic, complemented
5#20264944C211yesmaximal, characteristic, complemented
6#20264943C211yesmaximal, characteristic, complemented
7C2×#99×C101C211yesmaximal, characteristic, complemented
8C22×C22⋊D101C2211yescharacteristic
9#15692238C412yescomplemented
10#15692236—21no—
11#15692227—22no—
12#15692224C412yescomplemented
13#15692223—21no—
14C4×C22⋊D101—22no—
15#15692215—22no—
16#15692211—21no—
17C2×C22⋊Dic101C2211yescharacteristic
18C2×C22⋊Dic101C2211yescharacteristic
19C2×C22⋊Dic101C2211yescharacteristic
20C22⋊C4×D101—21no—
21#15692170—22no—
22#15692169—22no—
23C22×D4×C101C2211yescharacteristic
24C2×C22⋊C4×C101C2211yescharacteristic
25C2×C22⋊C4×C101C2211yescharacteristic
26#99×C101—22no—
27C23×D101D411yescharacteristic
28C2×C22⋊D101—21no—
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C2×C22⋊D101—22no—
33C2×C22⋊D101C2×C412yes—
34C2×C22⋊D101D412yes—
35C22×Dic101—21no—
36C22×Dic101—21no—
37C22×Dic101—21no—
38C22×Dic101D411yescharacteristic
39C2×C4×D101—22no—
40#13108053—22no—
41#13108053—22no—
42C22⋊Dic101—21no—
43C22⋊Dic101—21no—
44C22⋊Dic101—22no—
45C22⋊Dic101—21no—
46C22⋊Dic101—21no—
47C22⋊Dic101C2×C412yescomplemented
48C22⋊Dic101D412yescomplemented
49#13108051—22no—
50#13108051—22no—
51C4×Dic101—22no—
52C24×C101C2×C411yescharacteristic, complemented
53C24×C101C2311yescharacteristic
54C2×D4×C101—21no—
55C2×D4×C101—21no—
56C2×D4×C101—21no—
57C2×D4×C101—21no—
58C2×D4×C101—21no—
59C2×D4×C101—21no—
60C22×C4×C101—21no—
61C22×C4×C101—21no—
62C22×C4×C101C2×C411yescharacteristic, complemented
63C22⋊C4×C101—21no—
64C22⋊C4×C101—21no—
65C22⋊C4×C101—21no—
66C22⋊C4×C101D412yescomplemented
67C23×C101—21no—
68C23×C101—21no—
69C23×C101—21no—
70C23×C101—81no—
71C23×C101—81no—
72C23×C101C22×C411yescharacteristic
73C23×C101C2×D411yescharacteristic
74C23×C101C2×D411yescharacteristic
75C23×C101C2×D411yescharacteristic
76C23×C101C2×D411yescharacteristic
77C23×C101#4111yescharacteristic
78C23×C101#4111yescharacteristic
79C22×D101—21no—
80C22×D101—21no—
81C22×D101—81no—
82C22×D101C22⋊C412yes—
83D4×C101—41no—
84D4×C101—41no—
85D4×C101—41no—
86D4×C101—41no—
87C2×C4×C101—21no—
88C2×C4×C101—21no—
89C2×C4×C101—21no—
90C2×C4×C101—22no—
91C2×C4×C101—41no—
92C2×C4×C101—81no—
93C2×C4×C101—81no—
94C22⋊D101—22no—
95C22⋊D101—22no—
96C22⋊D101—22no—
97C22⋊D101—22no—
98C22⋊D101—82no—
99C2×Dic101—21no—
100C2×Dic101—21no—
101C2×Dic101—22no—
102C2×Dic101—22no—
103C2×Dic101—41no—
104C2×Dic101—81no—
105C2×Dic101—81no—
106C2×Dic101—81no—
107C2×Dic101C22⋊C412yes—
108C4×D101—82no—
109C22×C101—41no—
110C22×C101—41no—
111C22×C101—41no—
112C22×C101—41no—
113C22×C101—41no—
114C22×C101—41no—
115C22×C101—41no—
116C22×C101—42no—
117C22×C101—41no—
118C22×C101—81no—
119C22×C101—81no—
120C22×C101C2×C22⋊C411yescharacteristic
121C22×C101C4×D411yescharacteristic
122C22×C101C4×D411yescharacteristic
123C22×C101#12011yescharacteristic
124C22×C101#12111yescharacteristic
125C22×C101#12111yescharacteristic
126C22×C101#12311yescharacteristic
127C2×D101—22no—
128C2×D101—42no—
129C2×D101—42no—
130C2×D101—81no—
131C4×C101—42no—
132C4×C101—41no—
133C4×C101—81no—
134Dic101—22no—
135Dic101—42no—
136Dic101—42no—
137Dic101—81no—
138C2×C101—21no—
139C2×C101—21no—
140C2×C101—21no—
141C2×C101—21no—
142C2×C101—21no—
143C2×C101—21no—
144C2×C101—21no—
145C2×C101—81no—
146C2×C101#38611yescharacteristic
147D101—42no—
148#1913—1011nomaximal, Sylow
149C101#191311yescharacteristic, complemented, Sylow
150#534—1011no—
151#518—1011no—
152C2×#99—1011no—
153C2×#99—1011no—
154C2×#99D10111yescharacteristic, complemented
155#342—1011no—
156#342—1011no—
157C22×D4—1011no—
158C22×D4C2×D10111yescharacteristic
159#123—1012no—
160#123—2021no—
161#121—2022no—
162#120—1012no—
163#120—2021no—
164C4×D4—2022no—
165C4×D4—2022no—
166#117—2021no—
167C2×C22⋊C4—1011no—
168C2×C22⋊C4—1011no—
169C2×C22⋊C4—1011no—
170C2×C22⋊C4—2021no—
171C2×C22⋊C4C2×D10111yescharacteristic
172C2×C22⋊C4C2×D10111yescharacteristic
173#99—22no—
174#99—2022no—
175#99—2022no—
176C24—1011no—
177C24C4×D10111yescharacteristic, complemented
178C24C22×D10111yescharacteristic
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—1012no—
186C2×D4—1012no—
187C2×D4—2022no—
188C2×D4—2021no—
189C2×D4—2021no—
190C2×D4—2021no—
191C2×D4—2021no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—1011no—
195C22×C4—2022no—
196C22×C4—2021no—
197C22×C4—2021no—
198C22×C4—2021no—
199C22×C4C4×D10111yescharacteristic, complemented
200C4⋊C4—2022no—
201C4⋊C4—2022no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—1012no—
206C22⋊C4—1012no—
207C22⋊C4—2022no—
208C22⋊C4—2022no—
209C22⋊C4—2022no—
210C22⋊C4—2021no—
211C22⋊C4—2021no—
212C22⋊C4—2021no—
213C22⋊C4—2021no—
214C22⋊C4C22⋊D10112yescomplemented
215C42—2022no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—81no—
220C23—81no—
221C23—8081no—
222C23—1012no—
223C23—2021no—
224C23—2021no—
225C23C2×C4×D10111yescharacteristic
226C23D4×D10111yescharacteristic
227C23D4×D10111yescharacteristic
228C23D4×D10111yescharacteristic
229C23C2×C22⋊D10111yescharacteristic
230C23#1310807311yescharacteristic
231C23#1310807411yescharacteristic
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—8082no—
237D4—2022no—
238D4—2022no—
239D4—2022no—
240D4—2022no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—8082no—
249C2×C4—8081no—
250C2×C4—8081no—
251C2×C4—8081no—
252C2×C4—1012no—
253C2×C4—4041no—
254C2×C4—2022no—
255C2×C4—2022no—
256C2×C4—2021no—
257C2×C4—2021no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22—8081no—
270C22—4042no—
271C22—4042no—
272C22—2022no—
273C22C22⋊C4×D10111yescharacteristic
274C22#1569221511yescharacteristic
275C22C4×C22⋊D10111yescharacteristic
276C22#1569222311yescharacteristic
277C22#1569222611yescharacteristic
278C22#1569222811yescharacteristic
279C22#1569223711yescharacteristic
280C4—42no—
281C4—41no—
282C4—81no—
283C4—8081no—
284C4—4042no—
285C4—4042no—
286C4—2022no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—81no—
295C2—4042no—
296C2#2026505311yescharacteristic
subgroupG/H
centerC2#20265053
commutatorC23×C101C22×C4
FrattiniC24C22×D101
FittingC2×#99×C101C2
socleC2×C101#386
prime radical#20265736C2
cosocleC24×C101C23
hypercenterC2×#99D101
hypocenterC101#1913
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #20265650C2semidirect
3. C2×#15692170C2semidirect
4. C2×#15692169C2semidirect
5. #20264944C2semidirect
6. #20264943C2semidirect
7. C2×#99×C101C2semidirect
9. #15692238C4semidirect
12. #15692224C4semidirect
47. C22⋊Dic101C2×C4semidirect
48. C22⋊Dic101D4semidirect
52. C24×C101C2×C4semidirect
62. C22×C4×C101C2×C4semidirect
66. C22⋊C4×C101D4semidirect
149. C101#1913semidirect
154. C2×#99D101semidirect
177. C24C4×D101semidirect
199. C22×C4C4×D101semidirect
214. C22⋊C4C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
#202657362
#202656502
C2×#156921702
C2×#156921692
#202649442
#202649432
C2×#99×C1012
#1913101