Finite Group Databasebeta

← #27172197

Subgroups — #27172197

Order 12928.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#20265975C211yesmaximal, characteristic, complemented
2#20265688C211yesmaximal, characteristic, complemented
3#20265195C211yesmaximal, characteristic, complemented
4#20265194C211yesmaximal, characteristic, complemented
5#20265141C211yesmaximal, characteristic, complemented
6#20264933C211yesmaximal, characteristic, complemented
7#525×C101C211yesmaximal, characteristic, complemented
8C2×#13108074C2211yescharacteristic
9#15692286—21no—
10#15692285—21no—
11#15692281—21no—
12#15692280—21no—
13#15692275—22no—
14C2×#13108058C2211yescharacteristic
15C2×#13108058C2211yescharacteristic
16#15692238—21no—
17#15692234—21no—
18#15692229—21no—
19#15692224—21no—
20C4×C22⋊D101—22no—
21#15692214C2211yescharacteristic
22#15692183—22no—
23#15692182—22no—
24C22⋊#11717579—22no—
25C2×#41×C101C2211yescharacteristic
26C23×C4×C101C2211yescharacteristic
27#123×C101—21no—
28C22⋊Q8×C101—21no—
29#121×C101—21no—
30#120×C101—21no—
31C4×D4×C101—22no—
32#117×C101C2211yescharacteristic
33#13108074—21no—
34#13108074—21no—
35#13108074—21no—
36#13108074—21no—
37C2×Dic202D411yescharacteristic, complemented
38C2×D404D411yescharacteristic, complemented
39C2×C22⋊D101—22no—
40C2×C22⋊D101—21no—
41C2×C4×D101—21no—
42#13108064—22no—
43#13108062—22no—
44#13108061—22no—
45#13108059—22no—
46#13108058—21no—
47#13108058—21no—
48#13108058—21no—
49#13108058—21no—
50C2×#11717579—21no—
51C2×#11717579D412yescomplemented
52C4⋊Dic101—21no—
53#13108053—22no—
54C22⋊Dic101—22no—
55C22⋊Dic101—21no—
56#13108051—22no—
57C4×Dic101D412yescomplemented
58C24×C101D411yescharacteristic
59#41×C101—21no—
60#41×C101—21no—
61#41×C101—21no—
62#41×C101—21no—
63C2×Q8×C101D411yescharacteristic, complemented
64C2×D4×C101—22no—
65C2×D4×C101—21no—
66C2×D4×C101D411yescharacteristic, complemented
67C22×C4×C101—21no—
68C22×C4×C101—21no—
69C22×C4×C101—21no—
70C22×C4×C101—21no—
71C22×C4×C101—21no—
72C22×C4×C101—21no—
73C22×C4×C101—21no—
74C22×C4×C101D411yescharacteristic
75C22×C4×C101C2311yescharacteristic
76C4⋊C4×C101—22no—
77C4⋊C4×C101—21no—
78C22⋊C4×C101—22no—
79C22⋊C4×C101—22no—
80C22⋊C4×C101—21no—
81C42×C101D412yescomplemented
82C23×C101—21no—
83C23×C101—21no—
84C23×C101—21no—
85C23×C101—21no—
86C23×C101—42no—
87C23×C101C2×D411yescharacteristic
88C22×D101—21no—
89Q8×C101—21no—
90Q8×C101—21no—
91D4×C101—21no—
92D4×C101—21no—
93D4×C101—44no—
94D4×C101—41no—
95D4×C101—41no—
96C2×C4×C101—22no—
97C2×C4×C101—21no—
98C2×C4×C101—21no—
99C2×C4×C101—21no—
100C2×C4×C101—21no—
101C2×C4×C101—41no—
102C2×C4×C101—41no—
103C2×C4×C101—41no—
104C2×C4×C101—41no—
105C2×C4×C101—41no—
106C2×C4×C101—41no—
107C2×C4×C101C2×D411yescharacteristic
108C2×C4×C101C2×D411yescharacteristic
109C2×C4×C101C2×D411yescharacteristic
110C2×C4×C101C2×D411yescharacteristic
111C2×C4×C101C2×D411yescharacteristic
112C2×C4×C101#4111yescharacteristic
113C22⋊D101—44no—
114C22⋊D101—41no—
115C22⋊D101—41no—
116C2×Dic101—22no—
117C2×Dic101—21no—
118D404—21no—
119D404—21no—
120C4×D101—41no—
121C4×D101—41no—
122Dic202—21no—
123Dic202—21no—
124#11717579—22no—
125#11717579—41no—
126C22×C101—22no—
127C22×C101—22no—
128C22×C101—22no—
129C22×C101—41no—
130C22×C101—41no—
131C22×C101—41no—
132C22×C101—41no—
133C22×C101—42no—
134C22×C101—41no—
135C22×C101—41no—
136C22×C101#12011yescharacteristic
137C22×C101#12011yescharacteristic
138C22×C101#12111yescharacteristic
139C2×D101—42no—
140C2×D101—41no—
141C4×C101—42no—
142C4×C101—41no—
143C4×C101—41no—
144C4×C101#12011yescharacteristic
145C4×C101#12111yescharacteristic
146C4×C101#12111yescharacteristic
147C4×C101#12711yescharacteristic
148Dic101—42no—
149Dic101—41no—
150C2×C101—21no—
151C2×C101—21no—
152C2×C101—21no—
153C2×C101—42no—
154C2×C101—81no—
155C2×C101#39211yescharacteristic
156D101—81no—
157#2010—1011nomaximal, Sylow
158C101#201011yescharacteristic, complemented, Sylow
159#575—1011no—
160#525—1011no—
161#525D10111yescharacteristic, complemented
162#421—1011no—
163#421—1011no—
164#407—1011no—
165H(3,ℤ/4)—1011no—
166C2×#41—1011no—
167C2×#41C2×D10111yescharacteristic
168C23×C4C2×D10111yescharacteristic
169#137—2021no—
170#137—2021no—
171AGL(1,ℤ/8)—2021no—
172AGL(1,ℤ/8)—2021no—
173#135—2022no—
174C2×M16—1011no—
175C2×M16—1011no—
176#123—21no—
177#123—2021no—
178C22⋊Q8—21no—
179C22⋊Q8—2021no—
180#121—21no—
181#121—2021no—
182#120—21no—
183#120—2021no—
184C4×D4—22no—
185C4×D4—2022no—
186#117—1011no—
187#117C2×D10111yescharacteristic
188#104—2022no—
189#104—2022no—
190C22⋊C8—2022no—
191C24C22⋊D10111yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—2021no—
197#41—2021no—
198#41—2021no—
199#41—2021no—
200C2×Q8—1011no—
201C2×Q8C22⋊D10111yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—1011no—
205C2×D4—2022no—
206C2×D4—2021no—
207C2×D4C22⋊D10111yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—2021no—
216C22×C4C22⋊D10111yescharacteristic
217C22×C4C22×D10111yescharacteristic
218Q16—2022no—
219SD16—2022no—
220SD16—2022no—
221D8—2022no—
222M16—2021no—
223M16—2021no—
224M16—2021no—
225M16—2021no—
226C2×C8—1012no—
227C2×C8—2021no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—2022no—
231C4⋊C4—2021no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—2022no—
236C22⋊C4—2022no—
237C22⋊C4—2021no—
238C42—1012no—
239C42C22⋊D10112yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—2021no—
246C23C2×C22⋊D10111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—2021no—
250Q8—2021no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—4044no—
257D4—4041no—
258D4—4041no—
259D4—2021no—
260D4—2021no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—4041no—
273C2×C4—4041no—
274C2×C4—2022no—
275C2×C4—2021no—
276C2×C4D4×D10111yescharacteristic
277C2×C4D4×D10111yescharacteristic
278C2×C4D4×D10111yescharacteristic
279C2×C4C2×C22⋊D10111yescharacteristic
280C2×C4C2×C22⋊D10111yescharacteristic
281C2×C4#1310807311yescharacteristic
282C8—4041no—
283C8—2022no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—4042no—
295C22—4041no—
296C22#1569222311yescharacteristic
297C22#1569222411yescharacteristic
298C22#1569222711yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—4042no—
303C4—4041no—
304C4#1569222311yescharacteristic
305C4#1569222611yescharacteristic
306C4#1569222711yescharacteristic
307C4#1569225111yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—8081no—
314C2#2026508511yescharacteristic
subgroupG/H
centerC4#15692251
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#525×C101C2
socleC2×C101#392
hypercenter#525D101
hypocenterC101#2010
LCSG ▷ C22×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #20265975C2semidirect
2. #20265688C2semidirect
3. #20265195C2semidirect
4. #20265194C2semidirect
5. #20265141C2semidirect
6. #20264933C2semidirect
7. #525×C101C2semidirect
37. C2×Dic202D4semidirect
38. C2×D404D4semidirect
51. C2×#11717579D4semidirect
57. C4×Dic101D4semidirect
63. C2×Q8×C101D4semidirect
66. C2×D4×C101D4semidirect
81. C42×C101D4semidirect
158. C101#2010semidirect
161. #525D101semidirect
201. C2×Q8C22⋊D101semidirect
207. C2×D4C22⋊D101semidirect
239. C42C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
#202659752
#202656882
#202651952
#202651942
#202651412
#202649332
#525×C1012
#2010101