Finite Group Databasebeta

← #24989172

Subgroups — #24989172

Order 11008.

1062 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 139 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#19135049C214yesmaximal, complemented
2#19134669C211yesmaximal, characteristic, complemented
3#19132844C211yesmaximal, characteristic, complemented
4C43×#3490C211yesmaximal, characteristic
5C22×C22⋊Dic43C2212yes—
6C2×#13063240—24no—
7#14582755C2212yes—
8C2×C43⋊#95—22no—
9#14582666—24no—
10#14582666—22no—
11C43×#551—24no—
12C43×#546—24no—
13C43×#543C411yescharacteristic, complemented
14C43×#538—22no—
15C43×#534C411yescharacteristic, complemented
16C43×#525—22no—
17C2×#120×C43C2212yes—
18C43×#518C412yescomplemented
19C22×C22⋊C4×C43C2211yescharacteristic
20C23×Dic43—22no—
21C2×C22⋊Dic43—24no—
22C2×C22⋊Dic43—24no—
23C2×C22⋊Dic43—22no—
24C2×C22⋊Dic43—44no—
25#13063240—48no—
26C43⋊#95—44no—
27C25×C43C2311yescharacteristic
28C2×#41×C43—22no—
29C22×D4×C43C2×C412yes—
30C22×D4×C43D414yes—
31C23×C4×C43D412yes—
32#126×C43—24no—
33#124×C43—24no—
34#123×C43—24no—
35#123×C43—24no—
36#123×C43—22no—
37C22⋊Q8×C43—22no—
38C22⋊Q8×C43—22no—
39C22⋊Q8×C43—24no—
40#121×C43—22no—
41#121×C43—24no—
42#121×C43—22no—
43#120×C43—22no—
44#120×C43—22no—
45#120×C43—22no—
46#120×C43—24no—
47C4×D4×C43—24no—
48C4×D4×C43—24no—
49C4×D4×C43—24no—
50#117×C43—22no—
51#117×C43—22no—
52C2×C22⋊C4×C43—22no—
53C2×C22⋊C4×C43—24no—
54C2×C22⋊C4×C43C2×C411yescharacteristic
55C2×C22⋊C4×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43C2×C412yes—
57C2×C22⋊C4×C43D412yes—
58C2×C22⋊C4×C43D414yes—
59C24×C43—42no—
60C24×C43—42no—
61C24×C43—42no—
62C24×C43C22⋊C412yes—
63C24×C43C22×C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C24×C43C2×D414yes—
66C24×C43C2×D411yescharacteristic
67#41×C43—82no—
68#41×C43—82no—
69C2×Q8×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—24no—
74C2×D4×C43—24no—
75C2×D4×C43—44no—
76C2×D4×C43—44no—
77C2×D4×C43—44no—
78C22×C4×C43—24no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43C22⋊C412yes—
84C22×C4×C43C22⋊C414yes—
85C22×C4×C43C22⋊C412yes—
86C22×C4×C43C22⋊C412yes—
87C22×Dic43—24no—
88C22×Dic43—42no—
89C22×Dic43—42no—
90C22×Dic43—42no—
91C22×Dic43—42no—
92C22×Dic43—42no—
93C22×Dic43—42no—
94C22×Dic43—42no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—24no—
99C22⋊C4×C43—24no—
100C22⋊C4×C43—24no—
101C22⋊C4×C43—22no—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—22no—
104C22⋊C4×C43—22no—
105C22⋊C4×C43—24no—
106C22⋊C4×C43—24no—
107C22⋊C4×C43—24no—
108C42×C43—24no—
109C22⋊Dic43—28no—
110C22⋊Dic43—44no—
111C22⋊Dic43—44no—
112C22⋊Dic43—44no—
113C22⋊Dic43—44no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—22no—
117C23×C43—22no—
118C23×C43—22no—
119C23×C43—24no—
120C23×C43—24no—
121C23×C43—22no—
122C23×C43—42no—
123C23×C43—44no—
124C23×C43—42no—
125C23×C43—44no—
126C23×C43—42no—
127C23×C43—44no—
128C23×C43—82no—
129C23×C43—82no—
130C23×C43—82no—
131C23×C43—82no—
132C23×C43C2×C22⋊C412yes—
133C23×C43C2×C22⋊C411yescharacteristic
134C23×C43#12012yes—
135C23×C43#12012yes—
136Q8×C43—82no—
137D4×C43—44no—
138D4×C43—44no—
139D4×C43—44no—
140D4×C43—44no—
141D4×C43—84no—
142D4×C43—82no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—24no—
146C2×C4×C43—22no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—44no—
153C2×C4×C43—82no—
154C2×C4×C43—84no—
155C2×Dic43—44no—
156C2×Dic43—44no—
157C2×Dic43—44no—
158C2×Dic43—82no—
159C2×Dic43—82no—
160C2×Dic43—82no—
161C2×Dic43—82no—
162C2×Dic43—82no—
163C2×Dic43—84no—
164#8535—431nomaximal, Sylow
165C22×C43—22no—
166C22×C43—22no—
167C22×C43—22no—
168C22×C43—22no—
169C22×C43—22no—
170C22×C43—22no—
171C22×C43—22no—
172C22×C43—22no—
173C22×C43—22no—
174C22×C43—24no—
175C22×C43—24no—
176C22×C43—42no—
177C22×C43—44no—
178C22×C43—84no—
179C22×C43—82no—
180C22×C43—82no—
181C22×C43—84no—
182C22×C43—162no—
183C22×C43#37911yescharacteristic
184C22×C43#41012yes—
185C22×C43B(4,𝔽2)12yes—
186C22×C43#45812yes—
187C4×C43—42no—
188C4×C43—42no—
189C4×C43—42no—
190C4×C43—44no—
191Dic43—84no—
192Dic43—162no—
193#3490D4311yescharacteristic
194#1898—434no—
195#1819—431no—
196#1440—431no—
197C2×C43—22no—
198C2×C43—22no—
199C2×C43—22no—
200C2×C43—42no—
201C2×C43—42no—
202C2×C43—82no—
203C2×C43#178211yescharacteristic
204C2×C43#179012yes—
205#551—24no—
206#546—24no—
207#543Dic4311yescharacteristic, complemented
208#538—22no—
209#534Dic4311yescharacteristic, complemented
210#525—22no—
211C2×#120C2×D4312yes—
212#518Dic4312yescomplemented
213C22×C22⋊C4—432no—
214C22×C22⋊C4C2×D4311yescharacteristic
215C2×#99—864no—
216#379—432no—
217C2×#95—862no—
218#342—862no—
219#342—864no—
220C43#853511yescharacteristic, complemented, Sylow
221C25C22×D4311yescharacteristic
222C2×#41—22no—
223C22×D4C2×Dic4312yes—
224C22×D4C22⋊D4314yes—
225C23×C4—862no—
226C23×C4C22⋊D4312yes—
227#126—24no—
228#124—24no—
229#123—24no—
230#123—24no—
231#123—22no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234C22⋊Q8—24no—
235#121—22no—
236#121—24no—
237#121—22no—
238#120—22no—
239#120—22no—
240#120—22no—
241#120—24no—
242C4×D4—24no—
243C4×D4—24no—
244C4×D4—24no—
245#117—22no—
246#117—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—24no—
249C2×C22⋊C4—864no—
250C2×C22⋊C4—862no—
251C2×C22⋊C4—864no—
252C2×C22⋊C4—1724no—
253C2×C22⋊C4C2×Dic4311yescharacteristic
254C2×C22⋊C4C2×Dic4311yescharacteristic
255C2×C22⋊C4C2×Dic4312yes—
256C2×C22⋊C4C22⋊D4312yes—
257C2×C22⋊C4C22⋊D4314yes—
258#99—1728no—
259#95—1724no—
260C24—42no—
261C24—42no—
262C24—42no—
263C24C22⋊Dic4312yes—
264C24C22×Dic4311yescharacteristic
265C24C2×C22⋊D4311yescharacteristic
266C24C2×C22⋊D4314yes—
267C24C2×C22⋊D4311yescharacteristic
268#41—82no—
269#41—82no—
270C2×Q8—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—24no—
274C2×D4—22no—
275C2×D4—24no—
276C2×D4—44no—
277C2×D4—44no—
278C2×D4—44no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—864no—
285C22×C4—1722no—
286C22×C4—1722no—
287C22×C4—1722no—
288C22×C4—1722no—
289C22×C4—1722no—
290C22×C4—1722no—
291C22×C4—1722no—
292C22×C4C22⋊Dic4312yes—
293C22×C4C22⋊Dic4314yes—
294C22×C4C22⋊Dic4312yes—
295C22×C4C22⋊Dic4312yes—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—24no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—24no—
307C22⋊C4—24no—
308C22⋊C4—24no—
309C22⋊C4—868no—
310C22⋊C4—1724no—
311C22⋊C4—1724no—
312C22⋊C4—1724no—
313C22⋊C4—1724no—
314C42—24no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—24no—
319C23—24no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—42no—
324C23—44no—
325C23—42no—
326C23—44no—
327C23—42no—
328C23—44no—
329C23—82no—
330C23—82no—
331C23—82no—
332C23—82no—
333C23C2×C22⋊Dic4312yes—
334C23C2×C22⋊Dic4311yescharacteristic
335C23#1306329412yes—
336C23#1306329412yes—
337Q8—82no—
338D4—44no—
339D4—44no—
340D4—44no—
341D4—44no—
342D4—84no—
343D4—82no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—82no—
355C2×C4—84no—
356C2×C4—3442no—
357C2×C4—3442no—
358C2×C4—3442no—
359C2×C4—3442no—
360C2×C4—3442no—
361C2×C4—3444no—
362C2×C4—1724no—
363C2×C4—1724no—
364C2×C4—1724no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—24no—
375C22—24no—
376C22—42no—
377C22—44no—
378C22—84no—
379C22—84no—
380C22—82no—
381C22—82no—
382C22—162no—
383C22#1458275511yescharacteristic
384C22#1458287312yes—
385C22#1458308612yes—
386C22#1458308912yes—
387C4—42no—
388C4—42no—
389C4—42no—
390C4—44no—
391C4—3444no—
392C4—6882no—
393C2—22no—
394C2—22no—
395C2—22no—
396C2—42no—
397C2—42no—
398C2—82no—
399C2#1913451311yescharacteristic
400C2#1913454312yes—
subgroupG/H
centerC22#14582755
commutatorC24×C43C22×C4
FrattiniC25C22×D43
Fitting, prime radicalC43×#3490C2
socleC22×C43#379
cosocleC25×C43C23
hypercenter#3490D43
hypocenterC43#8535
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #3490

Complements

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

NH ≅ G/Ntype
1. #19135049C2semidirect
2. #19134669C2semidirect
3. #19132844C2semidirect
13. C43×#543C4semidirect
15. C43×#534C4semidirect
18. C43×#518C4semidirect
207. #543Dic43semidirect
209. #534Dic43semidirect
212. #518Dic43semidirect
220. C43#8535semidirect

Maximal subgroups

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

subgroupindex
#191350492
#191346692
#191328442
C43×#34902
#853543