Finite Group Databasebeta

← #25027779

Subgroups — #25027779

Order 11008.

2430 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic43C211yesmaximal, characteristic
2C2×#14582762C211yesmaximal, characteristic
3C2×#14582757C212yesmaximal
4Dic43⋊#95C214yesmaximal, complemented
5#19132821C214yesmaximal, complemented
6#19132817C212yesmaximal
7C2×C43×#381C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9C24×Dic43C2211yescharacteristic
10C22×Dic43⋊C4C2214yes—
11C22×C22⋊Dic43C2212yes—
12C22×C4×Dic43—28no—
13C22×C4×Dic43C418yescomplemented
14C22×C4×Dic43C2212yes—
15C22×C4×Dic43C2212yes—
16#14582762—24no—
17#14582757—28no—
18C2×C43⋊#95C2218yes—
19C2×C43⋊#95C2214yes—
20C2×C43⋊#95C2214yes—
21C24×C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43C2212yes—
23C43×#381—24no—
24C2×#95×C43C2214yes—
25C23×Dic43—24no—
26C23×Dic43—28no—
27C23×Dic43—28no—
28C23×Dic43C2×C414yes—
29C23×Dic43C2×C414yes—
30C23×Dic43D418yes—
31C23×Dic43C2314yes—
32C23×Dic43C2311yescharacteristic
33C23×Dic43C2312yes—
34C23×Dic43C2311yescharacteristic
35C2×Dic43⋊C4—28no—
36C2×Dic43⋊C4—216no—
37C2×C22⋊Dic43—24no—
38C2×C22⋊Dic43—24no—
39C2×C22⋊Dic43—24no—
40C2×C4×Dic43—232no—
41C2×C4×Dic43—28no—
42C2×C4×Dic43—28no—
43C2×C4×Dic43C2×C418yes—
44C2×C4×Dic43C2×C418yes—
45C43⋊#95—28no—
46C43⋊#95—28no—
47C43⋊#95—216no—
48C25×C43C2311yescharacteristic
49C23×C4×C43—24no—
50C23×C4×C43—24no—
51C23×C4×C43C2×C414yes—
52C23×C4×C43D414yes—
53C23×C4×C43Q814yes—
54C23×C4×C43C2314yes—
55C23×C4×C43C2312yes—
56C2×C22⋊C4×C43—24no—
57C2×C22⋊C4×C43—24no—
58C2×C22⋊C4×C43—24no—
59#95×C43—28no—
60C24×C43—24no—
61C24×C43—24no—
62C24×C43C22×C412yes—
63C24×C43C2×D414yes—
64C24×C43C2×D412yes—
65C24×C43C2×Q812yes—
66C24×C43#4114yes—
67C24×C43C2411yescharacteristic
68C22×C4×C43—28no—
69C22×C4×C43—28no—
70C22×C4×C43—216no—
71C22×C4×C43—216no—
72C22×C4×C43—24no—
73C22×C4×C43—24no—
74C22×C4×C43—24no—
75C22×C4×C43—24no—
76C22×C4×C43—24no—
77C22×C4×C43—28no—
78C22×C4×C43—28no—
79C22×C4×C43C4⋊C4116yescomplemented
80C22×C4×C43C22×C414yes—
81C22×C4×C43C2×D414yes—
82C22×C4×C43C2×Q814yes—
83C22×Dic43—232no—
84C22×Dic43—216no—
85C22×Dic43—216no—
86C22×Dic43—232no—
87C22×Dic43—28no—
88C22×Dic43—24no—
89C22×Dic43—24no—
90C22×Dic43—24no—
91C22×Dic43—24no—
92C22×Dic43—24no—
93C22×Dic43—28no—
94C22×Dic43—24no—
95C22×Dic43—28no—
96C22×Dic43C22⋊C4116yes—
97C22×Dic43C22×C412yes—
98C22×Dic43C22×C414yes—
99C22×Dic43C22×C412yes—
100C22×Dic43C2×D414yes—
101C22×Dic43C2×D414yes—
102C22×Dic43#4118yes—
103C22×Dic43#4118yes—
104C22⋊C4×C43—48no—
105C22⋊Dic43—48no—
106Dic43⋊C4—416no—
107C4×Dic43—216no—
108C4×Dic43—216no—
109C23×C43—24no—
110C23×C43—24no—
111C23×C43—28no—
112C23×C43—28no—
113C23×C43—216no—
114C23×C43—28no—
115C23×C43—28no—
116C23×C43C2×C22⋊C414yes—
117C23×C43C2×C4⋊C414yes—
118C23×C43#11714yes—
119C23×C43#12118yes—
120C23×C43C22⋊Q818yes—
121C23×C43C23×C411yescharacteristic
122C23×C43C22×D412yes—
123C23×C43C22×D411yescharacteristic
124C23×C43C22×Q811yescharacteristic
125C23×C43C2×#4114yes—
126C23×C43C2×#4114yes—
127C23×C43C2×#4112yes—
128C2×C4×C43—24no—
129C2×C4×C43—24no—
130C2×C4×C43—28no—
131C2×C4×C43—28no—
132C2×C4×C43—232no—
133C2×C4×C43—44no—
134C2×C4×C43—44no—
135C2×C4×C43—44no—
136C2×C4×C43—48no—
137C2×C4×C43—48no—
138C2×C4×C43C2×C4⋊C418yes—
139C2×Dic43—232no—
140C2×Dic43—24no—
141C2×Dic43—24no—
142C2×Dic43—24no—
143C2×Dic43—28no—
144C2×Dic43—216no—
145C2×Dic43—232no—
146C2×Dic43—44no—
147C2×Dic43—44no—
148C2×Dic43—44no—
149C2×Dic43—48no—
150C2×Dic43—48no—
151C2×Dic43C2×C22⋊C414yes—
152C2×Dic43C2×C22⋊C414yes—
153C2×Dic43#11718yes—
154C2×Dic43#11718yes—
155C2×Dic43#123116yes—
156#14685—431nomaximal, Sylow
157C22×C43—216no—
158C22×C43—216no—
159C22×C43—24no—
160C22×C43—24no—
161C22×C43—28no—
162C22×C43—28no—
163C22×C43#38018yes—
164C22×C43C22×C22⋊C411yescharacteristic
165C22×C43C22×C4⋊C411yescharacteristic
166C22×C43C2×#11712yes—
167C22×C43C2×#11712yes—
168C22×C43C2×#11711yescharacteristic
169C22×C43C2×#12112yes—
170C22×C43C2×C22⋊Q812yes—
171C22×C43C2×#12314yes—
172C22×C43#52514yes—
173C22×C43#52918yes—
174C22×C43#53214yes—
175C22×C43#53314yes—
176C4×C43—28no—
177C4×C43—84no—
178Dic43—24no—
179Dic43—28no—
180Dic43—84no—
181Dic43#38118yescomplemented
182C23×C42—431no—
183C2×#381—431no—
184C2×#381D4311yescharacteristic
185C2×#380—432no—
186C4⋊#95—434no—
187#1434—434no—
188C22⋊#95—432no—
189C2×C43—28no—
190C2×C43C2×#38011yescharacteristic
191C2×C43C2×#38111yescharacteristic
192C2×C43#228011yescharacteristic
193C2×C43#228312yes—
194C2×C43#228512yes—
195C2×C43#285414yes—
196C2×C43#285514yes—
197C24×C4—431no—
198C24×C4—431no—
199C24×C4C2×D4311yescharacteristic
200C22×C4⋊C4—434no—
201C22×C22⋊C4—432no—
202C22×C22⋊C4C2×D4312yes—
203C22×C42—432no—
204C22×C42—432no—
205C22×C42—438no—
206C22×C42—868no—
207#381—24no—
208#381—864no—
209#380—868no—
210C2×#95—438no—
211C2×#95—434no—
212C2×#95—434no—
213C2×#95C2×D4314yes—
214C43#1468511yescharacteristic, complemented, Sylow
215C25C22×D4311yescharacteristic
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—431no—
219C23×C4—434no—
220C23×C4—438no—
221C23×C4—431no—
222C23×C4—432no—
223C23×C4—434no—
224C23×C4—434no—
225C23×C4—868no—
226C23×C4—868no—
227C23×C4—864no—
228C23×C4Dic8614yes—
229C23×C4C4×D4314yes—
230C23×C4C22⋊D4314yes—
231C23×C4C22×D4314yes—
232C23×C4C22×D4312yes—
233C2×C4⋊C4—8616no—
234C2×C4⋊C4—868no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—864no—
239C2×C22⋊C4—864no—
240C2×C22⋊C4—864no—
241C2×C42—438no—
242C2×C42—438no—
243C2×C42—8632no—
244C2×C42—868no—
245C2×C42—868no—
246#95—28no—
247#95—8616no—
248#95—868no—
249#95—868no—
250C24—24no—
251C24—24no—
252C24C2×Dic8612yes—
253C24C2×C4×D4312yes—
254C24D4×D4314yes—
255C24#1062190014yes—
256C24C2×C22⋊D4312yes—
257C24C23×D4311yescharacteristic
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—216no—
261C22×C4—216no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—28no—
267C22×C4—28no—
268C22×C4—24no—
269C22×C4—432no—
270C22×C4—434no—
271C22×C4—438no—
272C22×C4—4316no—
273C22×C4—432no—
274C22×C4—434no—
275C22×C4—434no—
276C22×C4—438no—
277C22×C4—8616no—
278C22×C4—8632no—
279C22×C4—8616no—
280C22×C4—8632no—
281C22×C4—868no—
282C22×C4—864no—
283C22×C4—864no—
284C22×C4—864no—
285C22×C4—864no—
286C22×C4—864no—
287C22×C4—868no—
288C22×C4—868no—
289C22×C4—864no—
290C22×C4Dic43⋊C4116yescomplemented
291C22×C4C2×Dic8614yes—
292C22×C4C2×C4×D4314yes—
293C22×C4C2×C22⋊D4314yes—
294C4⋊C4—17216no—
295C22⋊C4—48no—
296C22⋊C4—1728no—
297C42—8616no—
298C42—8616no—
299C23—24no—
300C23—24no—
301C23—28no—
302C23—28no—
303C23—216no—
304C23—28no—
305C23—28no—
306C23C22⋊C4×D4314yes—
307C23C2×Dic43⋊C414yes—
308C23#1306328114yes—
309C23#1306329718yes—
310C23#1306330218yes—
311C23C22×C4×D4311yescharacteristic
312C23C2×D4×D4312yes—
313C23C22×C22⋊D4311yescharacteristic
314C23C22×Dic8611yescharacteristic
315C23#41×D4314yes—
316C23#41×D4314yes—
317C23C2×#1062190012yes—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—28no—
321C2×C4—28no—
322C2×C4—232no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—48no—
328C2×C4—434no—
329C2×C4—438no—
330C2×C4—4316no—
331C2×C4—434no—
332C2×C4—438no—
333C2×C4—8632no—
334C2×C4—8632no—
335C2×C4—864no—
336C2×C4—864no—
337C2×C4—864no—
338C2×C4—868no—
339C2×C4—8616no—
340C2×C4—1724no—
341C2×C4—1724no—
342C2×C4—1724no—
343C2×C4—1728no—
344C2×C4—1728no—
345C2×C4C2×Dic43⋊C418yes—
346C22—216no—
347C22—216no—
348C22—24no—
349C22—24no—
350C22—28no—
351C22—28no—
352C22#1458275718yes—
353C22C2×C22⋊C4×D4311yescharacteristic
354C22C22×Dic43⋊C411yescharacteristic
355C22#117×D4312yes—
356C22#117×D4312yes—
357C22C2×#1306328111yescharacteristic
358C22C2×#1306329712yes—
359C22C2×#1306330212yes—
360C22#123×D4314yes—
361C22#1458340714yes—
362C22#1458342618yes—
363C22#1458344514yes—
364C22#1458345214yes—
365C4—28no—
366C4—84no—
367C4—438no—
368C4—864no—
369C4—868no—
370C4—3444no—
371C2—28no—
372C2C2×#1458275711yescharacteristic
373C2#381×D4311yescharacteristic
374C2#1913697511yescharacteristic
375C2#1913698612yes—
376C2#1913699812yes—
377C2#1914292414yes—
378C2#1914293214yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#381C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#381D43
hypocenterC43#14685
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. Dic43⋊#95C2semidirect
5. #19132821C2semidirect
13. C22×C4×Dic43C4semidirect
79. C22×C4×C43C4⋊C4semidirect
181. Dic43#381semidirect
214. C43#14685semidirect
290. C22×C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic432
C2×#145827622
C2×#145827572
Dic43⋊#952
#191328212
#191328172
C2×C43×#3812
#1468543