Finite Group Databasebeta

← #25027634

Subgroups — #25027634

Order 11008.

2502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 331 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
1C22×#13063321C211yesmaximal, characteristic
2C2×#14582766C212yesmaximal, complemented
3#19132836C211yesmaximal, characteristic, complemented
4#19132835C212yesmaximal, complemented
5#19132834C218yesmaximal, complemented
6C43×#1438C211yesmaximal, characteristic, complemented
7C23×D172C2211yescharacteristic
8C23×C22⋊D43C2214yes—
9C2×#13063321—28no—
10C2×#13063321C418yescomplemented
11C22×C22⋊Dic43C2214yes—
12C22×(C2×D43)⋊C4C2218yes—
13C22×C4×Dic43C2211yescharacteristic
14#14582766—28no—
15C2×C43⋊#95C2214yes—
16C2×C43⋊#95C2214yes—
17C2×C43⋊#95C2212yes—
18C23×D4×C43C2211yescharacteristic
19C22×C22⋊C4×C43C2214yes—
20C2×#95×C43C2212yes—
21C24×D43C2312yes—
22C22×D172—24no—
23C22×D172—44no—
24C22×D172C2×C414yes—
25C22×C22⋊D43—28no—
26C22×C22⋊D43—28no—
27C22×C22⋊D43—48no—
28C22×C22⋊D43—48no—
29C22×C22⋊D43C2×C4116yes—
30C23×Dic43C2314yes—
31C23×Dic43C2312yes—
32#13063321—232no—
33C2×C22⋊Dic43—44no—
34C2×C22⋊Dic43—48no—
35C2×(C2×D43)⋊C4—48no—
36C2×(C2×D43)⋊C4—48no—
37C2×(C2×D43)⋊C4—48no—
38C2×C4×Dic43C2×C414yes—
39C2×C4×Dic43D418yes—
40C43⋊#95—24no—
41C43⋊#95—28no—
42C43⋊#95—28no—
43C25×C43C2312yes—
44C22×D4×C43—24no—
45C22×D4×C43—44no—
46C22×D4×C43C2×C414yes—
47C23×C4×C43C2314yes—
48C23×C4×C43C2311yescharacteristic
49C2×C22⋊C4×C43—48no—
50C2×C22⋊C4×C43—44no—
51#95×C43—24no—
52C24×C43—24no—
53C24×C43—24no—
54C24×C43—28no—
55C24×C43—24no—
56C24×C43—28no—
57C24×C43C22×C414yes—
58C24×C43C2411yescharacteristic
59C23×D43—24no—
60C23×D43—28no—
61C23×D43—28no—
62C23×D43—28no—
63C23×D43C22×C414yes—
64C2×D4×C43—28no—
65C2×D4×C43—48no—
66C2×D4×C43—416no—
67C22×C4×C43—24no—
68C22×C4×C43—24no—
69C22×C4×C43—24no—
70C22×C4×C43—28no—
71C22×C4×C43—28no—
72C22×C4×C43—24no—
73C22×C4×C43C22×C412yes—
74C22×C4×C43C2×D414yes—
75C2×C22⋊D43—232no—
76C2×C22⋊D43—432no—
77C2×C22⋊D43—416no—
78C2×C22⋊D43—432no—
79C2×C22⋊D43—416no—
80C22×Dic43—24no—
81C22×Dic43—24no—
82C22×Dic43—24no—
83C22×Dic43—24no—
84C22×Dic43—28no—
85C22×Dic43—28no—
86C22×Dic43—24no—
87C22×Dic43C22×C414yes—
88C22×Dic43C2×D414yes—
89C22×Dic43C2×D414yes—
90C2×D172—28no—
91C2×D172—48no—
92C2×D172—416no—
93C22⋊C4×C43—416no—
94C22⋊Dic43—416no—
95(C2×D43)⋊C4—432no—
96C4×Dic43C22⋊C4116yescomplemented
97C23×C43—24no—
98C23×C43—216no—
99C23×C43—24no—
100C23×C43—24no—
101C23×C43—44no—
102C23×C43—48no—
103C23×C43—44no—
104C23×C43—48no—
105C23×C43—44no—
106C23×C43—44no—
107C23×C43—48no—
108C23×C43—48no—
109C23×C43—44no—
110C23×C43—44no—
111C23×C43C23×C411yescharacteristic
112C23×C43C22×D412yes—
113C23×C43H(5,𝔽2)14yes—
114C23×C43H(5,𝔽2)14yes—
115C23×C43H(5,𝔽2)14yes—
116C22×D43—24no—
117C22×D43—28no—
118C22×D43—216no—
119C22×D43—48no—
120C22×D43—44no—
121C22×D43—48no—
122C22×D43—44no—
123C22×D43—48no—
124C22×D43—48no—
125C22×D43—48no—
126C22×D43—48no—
127D4×C43—416no—
128C2×C4×C43—24no—
129C2×C4×C43—28no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43—44no—
133C2×C4×C43—48no—
134C2×C4×C43—48no—
135C2×C4×C43C2×C22⋊C414yes—
136C22⋊D43—464no—
137C2×Dic43—28no—
138C2×Dic43—24no—
139C2×Dic43—28no—
140C2×Dic43—24no—
141C2×Dic43—44no—
142C2×Dic43—44no—
143C2×Dic43—44no—
144C2×Dic43—48no—
145C2×Dic43—48no—
146C2×Dic43C2×C22⋊C418yes—
147D172—416no—
148#14661—431nomaximal, Sylow
149C22×C43—48no—
150C22×C43—44no—
151C22×C43—48no—
152C22×C43—48no—
153C22×C43—88no—
154C22×C43—88no—
155C22×C43C22×C22⋊C411yescharacteristic
156C22×C43#51814yes—
157C22×C43#51812yes—
158C22×C43#53512yes—
159C22×C43#53514yes—
160C22×C43#53514yes—
161C22×C43#53512yes—
162C22×C43#56018yes—
163C22×C43#56014yes—
164C22×C43#56014yes—
165C2×D43—44no—
166C2×D43—48no—
167C2×D43—416no—
168C2×D43—88no—
169C2×D43—88no—
170C4×C43—24no—
171C4×C43—84no—
172Dic43—28no—
173Dic43—84no—
174C22×#127—431no—
175C2×#383—432no—
176#1438—432no—
177#1438—431no—
178#1438—438no—
179#1438D4311yescharacteristic, complemented
180C2×C43—84no—
181C2×C43#230912yes—
182C2×C43#230911yescharacteristic
183C2×C43#238014yes—
184C2×C43#281814yes—
185C2×C43#281814yes—
186D43—84no—
187C23×D4—434no—
188C23×D4—431no—
189C23×D4C2×D4311yescharacteristic
190C2×#127—438no—
191C2×#127—868no—
192C22×C22⋊C4—434no—
193C22×C22⋊C4—438no—
194C22×C22⋊C4C2×D4314yes—
195C22×C42—431no—
196#383—868no—
197C2×#95—434no—
198C2×#95—434no—
199C2×#95—432no—
200C2×#95C2×D4312yes—
201C43#1466111yescharacteristic, complemented, Sylow
202C25—432no—
203C25C22×D4312yes—
204C22×D4—24no—
205C22×D4—44no—
206C22×D4—4316no—
207C22×D4—434no—
208C22×D4—868no—
209C22×D4—868no—
210C22×D4—864no—
211C22×D4—1724no—
212C22×D4—1728no—
213C22×D4—1728no—
214C22×D4C4×D4314yes—
215C23×C4—432no—
216C23×C4—434no—
217C23×C4C22×D4314yes—
218C23×C4C22×D4311yescharacteristic
219#127—8632no—
220C2×C22⋊C4—48no—
221C2×C22⋊C4—44no—
222C2×C22⋊C4—1728no—
223C2×C22⋊C4—1728no—
224C2×C22⋊C4—1728no—
225C2×C22⋊C4—1724no—
226C2×C22⋊C4—1728no—
227C2×C42—434no—
228C2×C42—438no—
229#95—24no—
230#95—868no—
231#95—868no—
232#95—864no—
233C24—24no—
234C24—24no—
235C24—28no—
236C24—24no—
237C24—28no—
238C24—434no—
239C24—864no—
240C24—868no—
241C24—868no—
242C24—868no—
243C24C2×C4×D4314yes—
244C24C23×D4311yescharacteristic
245C2×D4—28no—
246C2×D4—48no—
247C2×D4—416no—
248C2×D4—8632no—
249C2×D4—868no—
250C2×D4—1728no—
251C2×D4—17216no—
252C2×D4—17232no—
253C2×D4—17216no—
254C2×D4—17232no—
255C2×D4—17216no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—24no—
262C22×C4—434no—
263C22×C4—434no—
264C22×C4—434no—
265C22×C4—864no—
266C22×C4—864no—
267C22×C4—864no—
268C22×C4—864no—
269C22×C4—868no—
270C22×C4—868no—
271C22×C4—864no—
272C22×C4C2×C4×D4312yes—
273C22×C4D4×D4314yes—
274C22⋊C4—416no—
275C22⋊C4—17232no—
276C22⋊C4—17216no—
277C42—4316no—
278C23—24no—
279C23—216no—
280C23—24no—
281C23—24no—
282C23—48no—
283C23—48no—
284C23—44no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23—44no—
289C23—48no—
290C23—48no—
291C23—44no—
292C23—864no—
293C23—8616no—
294C23—868no—
295C23—1728no—
296C23—1728no—
297C23—1728no—
298C23—1728no—
299C23—1724no—
300C23—1728no—
301C23—1728no—
302C23—1724no—
303C23C22×C4×D4311yescharacteristic
304C23C2×D4×D4312yes—
305C23#1306337014yes—
306C23#1306337014yes—
307C23#1306337114yes—
308D4—416no—
309D4—17216no—
310D4—17264no—
311C2×C4—24no—
312C2×C4—28no—
313C2×C4—48no—
314C2×C4—48no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—438no—
319C2×C4—868no—
320C2×C4—864no—
321C2×C4—868no—
322C2×C4—864no—
323C2×C4—1728no—
324C2×C4—1728no—
325C2×C4—1724no—
326C2×C4—1724no—
327C2×C4—1724no—
328C2×C4C22⋊C4×D4314yes—
329C22—48no—
330C22—44no—
331C22—48no—
332C22—48no—
333C22—88no—
334C22—88no—
335C22—3448no—
336C22—3448no—
337C22—1728no—
338C22—1724no—
339C22—17216no—
340C22C2×C22⋊C4×D4311yescharacteristic
341C22#1458337114yes—
342C22#1458337212yes—
343C22#1458346212yes—
344C22#1458346414yes—
345C22#1458346514yes—
346C22#1458346712yes—
347C22#1458363718yes—
348C22#1458363814yes—
349C22#1458363914yes—
350C4—24no—
351C4—84no—
352C4—868no—
353C4—3444no—
354C2—84no—
355C2—3444no—
356C2#1913717412yes—
357C2#1913717611yescharacteristic
358C2#1913777014yes—
359C2#1914263414yes—
360C2#1914263714yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1438C2
socle, cosocleC24×C43C24
prime radicalC22×#13063321C2
hypercenter#1438D43
hypocenterC43#14661
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#14582766C2semidirect
3. #19132836C2semidirect
4. #19132835C2semidirect
5. #19132834C2semidirect
6. C43×#1438C2semidirect
10. C2×#13063321C4semidirect
96. C4×Dic43C22⋊C4semidirect
179. #1438D43semidirect
201. C43#14661semidirect

Maximal subgroups

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

subgroupindex
C22×#130633212
C2×#145827662
#191328362
#191328352
#191328342
C43×#14382
#1466143