Finite Group Databasebeta

← #25027619

Subgroups — #25027619

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063309C211yesmaximal, characteristic
2C2×#14582757C212yesmaximal, complemented
3#19132847C214yesmaximal, complemented
4#19132844C211yesmaximal, characteristic, complemented
5#19132839C214yesmaximal, complemented
6#19132834C212yesmaximal
7C43×#1440C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9C24×Dic43C2211yescharacteristic
10C2×#13063309—28no—
11C2×#13063309C418yescomplemented
12C22×C4⋊Dic43C2212yes—
13C22×Dic43⋊C4C2214yes—
14C22×C22⋊Dic43C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2214yes—
17#14582757—28no—
18C2×C43⋊#95C2214yes—
19C2×C43⋊#95C2214yes—
20C2×C43⋊#95C2214yes—
21C22×C22⋊C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43C2212yes—
23C2×#95×C43C2214yes—
24C24×D43C2311yescharacteristic
25C22×C22⋊D43—24no—
26C22×C22⋊D43—44no—
27C22×C22⋊D43C2×C414yes—
28C23×Dic43—44no—
29C23×Dic43C2×C414yes—
30C23×Dic43D418yes—
31C23×Dic43C2314yes—
32C23×Dic43C2311yescharacteristic
33C23×Dic43C2312yes—
34#13063309—232no—
35C2×C4⋊Dic43—24no—
36C2×C4⋊Dic43—24no—
37C2×C4⋊Dic43C2×C418yes—
38C2×Dic43⋊C4—28no—
39C2×Dic43⋊C4—44no—
40C2×Dic43⋊C4—44no—
41C2×C22⋊Dic43—24no—
42C2×C22⋊Dic43—44no—
43C2×(C2×D43)⋊C4—24no—
44C2×(C2×D43)⋊C4—24no—
45C2×(C2×D43)⋊C4—44no—
46C2×(C2×D43)⋊C4—44no—
47C2×(C2×D43)⋊C4—44no—
48C2×(C2×D43)⋊C4C2×C418yes—
49C43⋊#95—28no—
50C43⋊#95—44no—
51C43⋊#95—44no—
52C25×C43C2311yescharacteristic
53C23×C4×C43C2314yes—
54C23×C4×C43C2312yes—
55C2×C22⋊C4×C43—24no—
56C2×C22⋊C4×C43—24no—
57C2×C22⋊C4×C43—44no—
58C2×C22⋊C4×C43C2×C414yes—
59#95×C43—44no—
60C24×C43—24no—
61C24×C43—24no—
62C24×C43—24no—
63C24×C43C22×C412yes—
64C24×C43C2×D414yes—
65C24×C43C2411yescharacteristic
66C23×D43—22no—
67C23×D43—24no—
68C23×D43—24no—
69C23×D43—24no—
70C23×D43C22×C412yes—
71C22×C4×C43—22no—
72C22×C4×C43—22no—
73C22×C4×C43—24no—
74C22×C4×C43—24no—
75C22×C4×C43—24no—
76C22×C4×C43—24no—
77C22×C4×C43—24no—
78C22×C4×C43—24no—
79C22×C4×C43—24no—
80C22×C4×C43—24no—
81C22×C4×C43—24no—
82C22×C4×C43C22×C414yes—
83C2×C22⋊D43—28no—
84C2×C22⋊D43—48no—
85C2×C22⋊D43—416no—
86C22×Dic43—22no—
87C22×Dic43—24no—
88C22×Dic43—24no—
89C22×Dic43—24no—
90C22×Dic43—24no—
91C22×Dic43—24no—
92C22×Dic43—24no—
93C22×Dic43—24no—
94C22×Dic43—24no—
95C22×Dic43—24no—
96C22×Dic43—24no—
97C22×Dic43—48no—
98C22×Dic43—416no—
99C22×Dic43C22⋊C4116yescomplemented
100C22×Dic43C22×C412yes—
101C22×Dic43C22×C414yes—
102C22×Dic43C2×D414yes—
103C22×Dic43C2×D414yes—
104C22⋊C4×C43—28no—
105C22⋊C4×C43—48no—
106C22⋊Dic43—48no—
107(C2×D43)⋊C4—216no—
108(C2×D43)⋊C4—416no—
109C4⋊Dic43—216no—
110Dic43⋊C4—416no—
111C23×C43—24no—
112C23×C43—28no—
113C23×C43—28no—
114C23×C43—24no—
115C23×C43—24no—
116C23×C43—28no—
117C23×C43—44no—
118C23×C43—44no—
119C23×C43—44no—
120C23×C43—44no—
121C23×C43C2×C22⋊C414yes—
122C23×C43C23×C411yescharacteristic
123C23×C43C22×D412yes—
124C23×C43H(5,𝔽2)14yes—
125C23×C43H(5,𝔽2)14yes—
126C23×C432−1+414yes—
127C22×D43—22no—
128C22×D43—24no—
129C22×D43—28no—
130C22×D43—44no—
131C22×D43—42no—
132C22×D43—42no—
133C22×D43—44no—
134C22×D43—44no—
135C22×D43—44no—
136C22×D43—44no—
137C22×D43—44no—
138C2×C4×C43—24no—
139C2×C4×C43—28no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—44no—
143C2×C4×C43—44no—
144C2×C4×C43—44no—
145C2×C4×C43—44no—
146C2×C4×C43—44no—
147C2×C4×C43—44no—
148C2×C4×C43—44no—
149C2×C4×C43—44no—
150C22⋊D43—416no—
151C2×Dic43—24no—
152C2×Dic43—24no—
153C2×Dic43—28no—
154C2×Dic43—28no—
155C2×Dic43—22no—
156C2×Dic43—24no—
157C2×Dic43—416no—
158C2×Dic43—44no—
159C2×Dic43—44no—
160C2×Dic43—44no—
161C2×Dic43—44no—
162C2×Dic43—44no—
163C2×Dic43—44no—
164C2×Dic43—44no—
165C2×Dic43—44no—
166C2×Dic43C2×C22⋊C418yes—
167#14658—431nomaximal, Sylow
168C22×C43—24no—
169C22×C43—28no—
170C22×C43—48no—
171C22×C43—48no—
172C22×C43—48no—
173C22×C43C22×C22⋊C411yescharacteristic
174C22×C43#51812yes—
175C22×C43#52014yes—
176C22×C43#53414yes—
177C22×C43#53512yes—
178C22×C43#53612yes—
179C22×C43#53714yes—
180C22×C43#56014yes—
181C22×C43#56214yes—
182C22×C43#56214yes—
183C22×C43#56314yes—
184C2×D43—42no—
185C2×D43—44no—
186C2×D43—48no—
187C2×D43—84no—
188C2×D43—84no—
189C4×C43—44no—
190C4×C43—84no—
191Dic43—28no—
192Dic43—42no—
193Dic43—84no—
194C22×#123—431no—
195C2×#380—432no—
196#1441—434no—
197#1440—431no—
198#1440D4311yescharacteristic, complemented
199#1439—434no—
200#1438—432no—
201C2×C43—44no—
202C2×C43#230811yescharacteristic
203C2×C43#231112yes—
204C2×C43#237614yes—
205C2×C43#281314yes—
206C2×C43#281414yes—
207D43—82no—
208C23×D4—431no—
209C24×C4—431no—
210C2×#123—438no—
211C2×#123—868no—
212C22×C4⋊C4—432no—
213C22×C4⋊C4—434no—
214C22×C22⋊C4—432no—
215C22×C22⋊C4—432no—
216C22×C22⋊C4—434no—
217C22×C22⋊C4C2×D4311yescharacteristic
218C22×C22⋊C4C2×D4312yes—
219#380—868no—
220C2×#95—434no—
221C2×#95—434no—
222C2×#95—434no—
223C2×#95C2×D4314yes—
224C43#1465811yescharacteristic, complemented, Sylow
225C25—431no—
226C25C22×D4311yescharacteristic
227C22×D4—434no—
228C22×D4—864no—
229C22×D4—1724no—
230C23×C4—432no—
231C23×C4—434no—
232C23×C4—438no—
233C23×C4—431no—
234C23×C4—434no—
235C23×C4—1724no—
236C23×C4C22×D4314yes—
237C23×C4C22×D4312yes—
238#123—8632no—
239C2×C4⋊C4—438no—
240C2×C4⋊C4—864no—
241C2×C4⋊C4—864no—
242C2×C4⋊C4—868no—
243C2×C4⋊C4—1724no—
244C2×C4⋊C4—1724no—
245C2×C22⋊C4—24no—
246C2×C22⋊C4—24no—
247C2×C22⋊C4—44no—
248C2×C22⋊C4—438no—
249C2×C22⋊C4—864no—
250C2×C22⋊C4—864no—
251C2×C22⋊C4—864no—
252C2×C22⋊C4—1724no—
253C2×C22⋊C4—1724no—
254C2×C22⋊C4—1724no—
255C2×C22⋊C4—1724no—
256C2×C22⋊C4C4×D4314yes—
257#95—44no—
258#95—868no—
259#95—1724no—
260#95—1724no—
261C24—24no—
262C24—24no—
263C24—24no—
264C24—432no—
265C24—862no—
266C24—864no—
267C24—864no—
268C24—864no—
269C24C2×C4×D4312yes—
270C24D4×D4314yes—
271C24C23×D4311yescharacteristic
272C2×D4—868no—
273C2×D4—1728no—
274C2×D4—17216no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—434no—
287C22×C4—434no—
288C22×C4—434no—
289C22×C4—4316no—
290C22×C4—432no—
291C22×C4—864no—
292C22×C4—864no—
293C22×C4—862no—
294C22×C4—864no—
295C22×C4—864no—
296C22×C4—864no—
297C22×C4—864no—
298C22×C4—864no—
299C22×C4—864no—
300C22×C4—864no—
301C22×C4—864no—
302C22×C4—1728no—
303C22×C4—17216no—
304C22×C4C2×C4×D4314yes—
305C4⋊C4—8616no—
306C4⋊C4—17216no—
307C22⋊C4—28no—
308C22⋊C4—48no—
309C22⋊C4—8616no—
310C22⋊C4—17216no—
311C22⋊C4—1728no—
312C23—24no—
313C23—28no—
314C23—28no—
315C23—24no—
316C23—24no—
317C23—28no—
318C23—44no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—862no—
323C23—864no—
324C23—868no—
325C23—1724no—
326C23—1724no—
327C23—1724no—
328C23—1724no—
329C23—1724no—
330C23—1722no—
331C23—1722no—
332C23—1724no—
333C23C22⋊C4×D4314yes—
334C23C22×C4×D4311yescharacteristic
335C23C2×D4×D4312yes—
336C23#1306337014yes—
337C23#1306337114yes—
338C23#1306337214yes—
339D4—17216no—
340C2×C4—24no—
341C2×C4—28no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—438no—
353C2×C4—864no—
354C2×C4—864no—
355C2×C4—868no—
356C2×C4—868no—
357C2×C4—862no—
358C2×C4—864no—
359C2×C4—17216no—
360C2×C4—1724no—
361C2×C4—1724no—
362C2×C4—1724no—
363C2×C4—1724no—
364C2×C4—1724no—
365C2×C4—1724no—
366C2×C4—1724no—
367C2×C4—1724no—
368C22—24no—
369C22—28no—
370C22—48no—
371C22—48no—
372C22—48no—
373C22—3444no—
374C22—3444no—
375C22—1722no—
376C22—1724no—
377C22—1728no—
378C22C2×C22⋊C4×D4311yescharacteristic
379C22#1458337312yes—
380C22#1458337814yes—
381C22#1458346014yes—
382C22#1458346412yes—
383C22#1458347112yes—
384C22#1458347614yes—
385C22#1458363714yes—
386C22#1458364314yes—
387C22#1458364614yes—
388C22#1458365114yes—
389C4—44no—
390C4—84no—
391C4—868no—
392C4—3444no—
393C4—1722no—
394C2—44no—
395C2—3442no—
396C2#1913717211yescharacteristic
397C2#1913718212yes—
398C2#1913774114yes—
399C2#1914260314yes—
400C2#1914261414yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1440C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1440D43
hypocenterC43#14658
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#14582757C2semidirect
3. #19132847C2semidirect
4. #19132844C2semidirect
5. #19132839C2semidirect
7. C43×#1440C2semidirect
11. C2×#13063309C4semidirect
99. C22×Dic43C22⋊C4semidirect
198. #1440D43semidirect
224. C43#14658semidirect

Maximal subgroups

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

subgroupindex
C22×#130633092
C2×#145827572
#191328472
#191328442
#191328392
#191328342
C43×#14402
#1465843