Finite Group Databasebeta

← #25100489

Subgroups — #25100489

Order 11008.

1790 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582937C211yesmaximal, characteristic, complemented
2C2×#14582904C212yesmaximal, complemented
3C2×#14582854C211yesmaximal, characteristic, complemented
4#19137177C212yesmaximal, complemented
5#19135472C214yesmaximal, complemented
6#19135462C214yesmaximal, complemented
7C23×D8×C43C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C2×#13063284C2212yes—
10C2×#13063284C2211yescharacteristic
11#14582937—24no—
12C2×#13063259C2212yescomplemented
13C2×#13063257C2212yescomplemented
14#14582904—28no—
15C2×#13063246C2218yescomplemented
16#14582854—24no—
17C2×#13063235C2212yescomplemented
18C2×C8×Dic43C2212yescomplemented
19#14582802—24no—
20#14582802C2218yescomplemented
21#14582755—24no—
22C23×D4×C43C2212yes—
23C22×D8×C43—24no—
24C22×D8×C43—24no—
25C22×D8×C43C418yescomplemented
26C22×D8×C43C2212yes—
27C22×D8×C43C2212yes—
28C23×C8×C43C2211yescharacteristic
29C2×#10621877—22no—
30C2×#10621877—22no—
31C2×#10621877D414yes—
32C22×C43⋊C8C2312yes—
33#13063284—22no—
34#13063284—22no—
35#13063284—24no—
36#13063284—24no—
37C2×C4⋊Dic43D412yes—
38C2×C4⋊Dic43C2314yes—
39C2×C22⋊Dic43—22no—
40C2×C22⋊Dic43—216no—
41C2×C22⋊Dic43D412yes—
42C2×C4×Dic43—22no—
43C2×C4×Dic43C2312yes—
44#13063259—24no—
45#13063257—24no—
46#13063246—216no—
47#13063235—24no—
48C8×Dic43—24no—
49C25×C43—22no—
50C22×D4×C43—24no—
51C22×D4×C43—24no—
52C22×D4×C43—24no—
53C22×D4×C43—22no—
54C22×D4×C43—24no—
55C22×D4×C43—24no—
56C22×D4×C43C2×C418yes—
57C22×D4×C43C2314yes—
58C23×C4×C43C2311yescharacteristic
59C2×D8×C43—232no—
60C2×D8×C43—24no—
61C2×D8×C43—24no—
62C2×D8×C43—24no—
63C2×D8×C43—24no—
64C2×D8×C43C2×C418yes—
65C2×D8×C43C2×C418yes—
66C22×C8×C43C2×C414yes—
67C22×C8×C43D414yes—
68C22×C8×C43D414yes—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C24×C43—24no—
72C24×C43—28no—
73C24×C43—44no—
74C24×C43—44no—
75C24×C43—88no—
76C24×C43C2×D411yescharacteristic
77C2×D4×C43—28no—
78C2×D4×C43—24no—
79C2×D4×C43—216no—
80C2×D4×C43—216no—
81C2×D4×C43—24no—
82C2×D4×C43—24no—
83C2×D4×C43—24no—
84C2×D4×C43—24no—
85C2×D4×C43—44no—
86C2×D4×C43—48no—
87C2×D4×C43—48no—
88C2×D4×C43—44no—
89C2×D4×C43C22×C418yes—
90C22×C4×C43C22×C412yes—
91C22×C4×C43C2×D412yes—
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4112yes—
96C22×C4×C43#4112yes—
97C22×C4×C43C2411yescharacteristic
98C22×Dic43—24no—
99C22×Dic43C2×D414yes—
100D8×C43—216no—
101D8×C43—216no—
102C2×C8×C43C22⋊C4116yescomplemented
103C2×C8×C43C22×C412yes—
104C2×C8×C43C22×C412yes—
105C2×C8×C43C2×D412yes—
106C2×C8×C43C2×D412yes—
107C2×C8×C43C2×D412yes—
108C2×C8×C43C2×D412yes—
109C22⋊Dic43—24no—
110C22⋊Dic43—44no—
111C22⋊Dic43—816no—
112C4⋊Dic43—24no—
113C4⋊Dic43—24no—
114C4⋊Dic43—24no—
115C4×Dic43—22no—
116C4×Dic43—22no—
117C4×Dic43—44no—
118#10621877—28no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8C2×D414yes—
122C23×C43—24no—
123C23×C43—28no—
124C23×C43—44no—
125C23×C43—44no—
126C23×C43—416no—
127C23×C43—416no—
128C23×C43—816no—
129C23×C43—816no—
130C23×C43—816no—
131C23×C43C4×D412yes—
132C23×C43#12112yes—
133C23×C43#12712yes—
134C23×C43C22×D411yescharacteristic
135D4×C43—28no—
136D4×C43—28no—
137D4×C43—44no—
138D4×C43—44no—
139D4×C43—416no—
140C2×C4×C43C2×C22⋊C414yes—
141C2×C4×C43C4×D414yes—
142C2×C4×C43C4×D412yes—
143C2×C4×C43#12114yes—
144C2×C4×C43#12112yes—
145C2×C4×C43#12414yes—
146C2×C4×C43#12712yes—
147C2×C4×C43C23×C411yescharacteristic
148C2×C4×C43C22×D411yescharacteristic
149C2×C4×C43C22×D411yescharacteristic
150C2×C4×C43C22×D411yescharacteristic
151C2×C4×C43C2×#4111yescharacteristic
152C2×C4×C43C2×#4111yescharacteristic
153C2×Dic43—24no—
154C2×Dic43—28no—
155C2×Dic43—44no—
156C2×Dic43—48no—
157C8×C43C2×C22⋊C414yes—
158C8×C43C2×C22⋊C414yes—
159C43⋊C8—24no—
160#21233—431nomaximal, Sylow
161C22×C43—24no—
162C22×C43—24no—
163C22×C43—24no—
164C22×C43—416no—
165C22×C43—48no—
166C22×C43—832no—
167C22×C43—88no—
168C22×C43—88no—
169C22×C43#39014yes—
170C22×C43C2×C4×D411yescharacteristic
171C22×C43C2×#12111yescharacteristic
172C22×C43C2×#12711yescharacteristic
173C22×C43#57614yes—
174C4×C43#39014yes—
175C4×C43C22×C22⋊C411yescharacteristic
176C4×C43C2×C4×D411yescharacteristic
177C4×C43C2×#12111yescharacteristic
178C4×C43C2×#12411yescharacteristic
179Dic43—44no—
180Dic43—84no—
181C23×D8D4311yescharacteristic
182C2×#427—431no—
183C2×#418—432no—
184C2×#405—431no—
185#2309—432no—
186#1972—434no—
187#1970—434no—
188C2×C43—24no—
189C2×C43—88no—
190C2×C43C2×#39011yescharacteristic
191C2×C43#294812yes—
192C2×C43#305812yes—
193C2×C43#315512yes—
194C23×D4C2×D4312yes—
195C22×D8—24no—
196C22×D8—24no—
197C22×D8Dic4318yescomplemented
198C22×D8C2×D4312yes—
199C22×D8C2×D4312yes—
200C22×M16—431no—
201C23×C8C2×D4311yescharacteristic
202C2×#117—431no—
203C2×#117—432no—
204#427—864no—
205C2×#107—432no—
206C2×#106—432no—
207#418—868no—
208C2×#102—438no—
209#405—864no—
210C2×#97—432no—
211C2×C4×C8—432no—
212#390—438no—
213#390—864no—
214#379—864no—
215C43#2123311yescharacteristic, complemented, Sylow
216C25—22no—
217C22×D4—24no—
218C22×D4—22no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4C2×Dic4318yes—
224C22×D4C22×D4314yes—
225C23×C4C22×D4311yescharacteristic
226C2×D8—232no—
227C2×D8—24no—
228C2×D8—24no—
229C2×D8—24no—
230C2×D8—24no—
231C2×D8C2×Dic4318yes—
232C2×D8C2×Dic4318yes—
233C2×M16—434no—
234C2×M16—862no—
235C2×M16—862no—
236C22×C8—432no—
237C22×C8C2×Dic4314yes—
238C22×C8C22⋊D4314yes—
239C22×C8C22⋊D4314yes—
240C22×C8C22×D4311yescharacteristic
241C22×C8C22×D4311yescharacteristic
242#117—862no—
243#117—862no—
244#117—864no—
245#117—864no—
246C2×C4⋊C4—432no—
247C2×C4⋊C4—434no—
248C2×C22⋊C4—432no—
249C2×C22⋊C4—8616no—
250C2×C22⋊C4—862no—
251C2×C42—432no—
252C2×C42—862no—
253#107—864no—
254#106—864no—
255#102—8616no—
256#97—864no—
257C4×C8—864no—
258C24—24no—
259C24—28no—
260C24—44no—
261C24—44no—
262C24—88no—
263C24D4×D4311yescharacteristic
264C2×D4—216no—
265C2×D4—216no—
266C2×D4—28no—
267C2×D4—24no—
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—44no—
273C2×D4—48no—
274C2×D4—48no—
275C2×D4—44no—
276C2×D4C22×Dic4318yes—
277C22×C4—434no—
278C22×C4—864no—
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4312yes—
281C22×C4#1062190012yes—
282C22×C4#1062190012yes—
283C22×C4C22×Dic4312yes—
284C22×C4C2×C22⋊D4312yes—
285C22×C4C2×C22⋊D4312yes—
286C22×C4C23×D4311yescharacteristic
287D8—216no—
288D8—216no—
289M16—868no—
290C2×C8—434no—
291C2×C8—862no—
292C2×C8—862no—
293C2×C8C22⋊Dic43116yescomplemented
294C2×C8C22×Dic4312yes—
295C2×C8C22×Dic4312yes—
296C2×C8C2×C22⋊D4312yes—
297C2×C8C2×C22⋊D4312yes—
298C2×C8C2×C22⋊D4312yes—
299C2×C8C2×C22⋊D4312yes—
300C4⋊C4—864no—
301C4⋊C4—864no—
302C4⋊C4—864no—
303C22⋊C4—864no—
304C22⋊C4—34416no—
305C22⋊C4—1724no—
306C42—862no—
307C42—862no—
308C42—1724no—
309C23—24no—
310C23—28no—
311C23—416no—
312C23—44no—
313C23—44no—
314C23—416no—
315C23—816no—
316C23—816no—
317C23—816no—
318C23D4×Dic4312yes—
319C23#1306329612yes—
320C23#1306332112yes—
321C23C2×D4×D4311yescharacteristic
322D4—28no—
323D4—28no—
324D4—416no—
325D4—44no—
326D4—44no—
327C2×C4—864no—
328C2×C4—868no—
329C2×C4—1724no—
330C2×C4—1728no—
331C2×C4C2×C22⋊Dic4314yes—
332C2×C4D4×Dic4312yes—
333C2×C4D4×Dic4314yes—
334C2×C4#1306329612yes—
335C2×C4#1306329614yes—
336C2×C4#1306331214yes—
337C2×C4#1306332112yes—
338C2×C4C23×Dic4311yescharacteristic
339C2×C4C2×D4×D4311yescharacteristic
340C2×C4C22×C22⋊D4311yescharacteristic
341C2×C4C22×C22⋊D4311yescharacteristic
342C2×C4C2×#1062190011yescharacteristic
343C2×C4C2×#1062190011yescharacteristic
344C8—864no—
345C8C2×C22⋊Dic4314yes—
346C8C2×C22⋊Dic4314yes—
347C22—24no—
348C22—24no—
349C22—24no—
350C22—416no—
351C22—48no—
352C22—832no—
353C22—88no—
354C22—88no—
355C22#1458280214yes—
356C22C2×D4×Dic4311yescharacteristic
357C22C2×#1306329611yescharacteristic
358C22C2×#1306332111yescharacteristic
359C22#1458370014yes—
360C4—3444no—
361C4—1724no—
362C4#1458280214yes—
363C4C22×C22⋊Dic4311yescharacteristic
364C4C2×D4×Dic4311yescharacteristic
365C4C2×#1306329611yescharacteristic
366C4C2×#1306331211yescharacteristic
367C2—24no—
368C2—88no—
369C2C2×#1458280211yescharacteristic
370C2#1914344712yes—
371C2#1914423912yes—
372C2#1914507612yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC23×D8×C43C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC23×D8D43
hypocenterC43#21233
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14582937C2semidirect
2. C2×#14582904C2semidirect
3. C2×#14582854C2semidirect
4. #19137177C2semidirect
5. #19135472C2semidirect
6. #19135462C2semidirect
12. C2×#13063259C22semidirect
13. C2×#13063257C22semidirect
15. C2×#13063246C22semidirect
17. C2×#13063235C22semidirect
18. C2×C8×Dic43C22semidirect
20. #14582802C22semidirect
25. C22×D8×C43C4semidirect
102. C2×C8×C43C22⋊C4semidirect
197. C22×D8Dic43semidirect
215. C43#21233semidirect
293. C2×C8C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829372
C2×#145829042
C2×#145828542
#191371772
#191354722
#191354622
C23×D8×C432
#2123343