Finite Group Databasebeta

← #24989244

Subgroups — #24989244

Order 11008.

1102 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 127 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×#13063305C211yesmaximal, characteristic
2#19134673C212yesmaximal, complemented
3#19132925C211yesmaximal, characteristic, complemented
4#19132921C212yesmaximal
5C43×#1463C211yesmaximal, characteristic, complemented
6C23×Dic86C411yescharacteristic
7C23×C4×D43C411yescharacteristic
8C2×#13063305—24no—
9C2×#13063305—24no—
10C2×#13063305—22no—
11C2×#13063305—22no—
12C22×C4⋊Dic43C411yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×(C2×D43)⋊C4C411yescharacteristic
15C22×(C2×D43)⋊C4C2211yescharacteristic
16#14582863C2212yes—
17#14582667—24no—
18#14582625—22no—
19#14582622—24no—
20C22×C4⋊C4×C43C2211yescharacteristic
21C43×#407C2212yes—
22C43×#324—22no—
23C24×D43C2×C411yescharacteristic
24C22×Dic86—22no—
25C22×Dic86—22no—
26C22×Dic86—22no—
27C22×Dic86—44no—
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43C2×C411yescharacteristic
30C23×Dic43C2×C411yescharacteristic
31C22×C4×D43—22no—
32C22×C4×D43—22no—
33C22×C4×D43—22no—
34C22×C4×D43—44no—
35C2×#10621877—22no—
36#13063305—216no—
37#13063305—216no—
38C2×C4⋊Dic43—22no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—22no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—22no—
43C2×C4⋊Dic43—22no—
44C2×C4⋊Dic43D414yes—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—22no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—22no—
51C2×(C2×D43)⋊C4D414yes—
52C22⋊(C43⋊C8)—22no—
53C22⋊(C43⋊C8)—22no—
54C23×C4×C43C2×C411yescharacteristic
55C23×C4×C43C2×C411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C2×M16×C43—22no—
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43—22no—
60C2×C4⋊C4×C43D412yes—
61C2×C4⋊C4×C43D412yes—
62C22⋊C8×C43—22no—
63C22⋊C8×C43—22no—
64C24×C43C22×C411yescharacteristic
65C23×D43—21no—
66C23×D43—21no—
67C23×D43—24no—
68C23×D43—42no—
69C23×D43—42no—
70C23×D43C22⋊C412yes—
71C22×C4×C43—24no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—42no—
77C22×C4×C43—42no—
78C22×C4×C43C22⋊C412yes—
79C22×C4×C43C22⋊C412yes—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D412yes—
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—42no—
91C22×Dic43—42no—
92C22×Dic43—42no—
93C22×Dic43C22⋊C412yes—
94C22×Dic43C22⋊C412yes—
95C22×Dic43C22⋊C412yes—
96C2×C4×D43—28no—
97C2×C4×D43—48no—
98C2×C4×D43—44no—
99C2×C4×D43—48no—
100C2×C4×D43—44no—
101C2×Dic86—28no—
102C2×Dic86—48no—
103C2×Dic86—48no—
104C2×Dic86—44no—
105C2×Dic86—44no—
106M16×C43—44no—
107C2×C8×C43—42no—
108C4⋊C4×C43—24no—
109C4⋊C4×C43—24no—
110(C2×D43)⋊C4—28no—
111(C2×D43)⋊C4—24no—
112(C2×D43)⋊C4—24no—
113C4⋊Dic43—28no—
114C4⋊Dic43—24no—
115C4⋊Dic43—24no—
116#10621877—44no—
117C2×C43⋊C8—42no—
118C23×C43—22no—
119C23×C43—22no—
120C23×C43—22no—
121C23×C43C2×C22⋊C411yescharacteristic
122C23×C43C2×C22⋊C411yescharacteristic
123C23×C43C2×C22⋊C411yescharacteristic
124C22×D43—24no—
125C22×D43—24no—
126C22×D43—22no—
127C22×D43—22no—
128C22×D43—42no—
129C22×D43—416no—
130C22×D43—42no—
131C22×D43—42no—
132C22×D43—42no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43#10114yes—
136C2×C4×C43—24no—
137C2×C4×C43—24no—
138C2×C4×C43—22no—
139C2×C4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43#10014yes—
149C2×C4×C43#12012yes—
150C2×C4×C43#12012yes—
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C4×D43—416no—
164Dic86—416no—
165C8×C43—82no—
166C43⋊C8—82no—
167#8555—431nomaximal, Sylow
168C22×C43—28no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43#37911yescharacteristic
176C22×C43#41012yes—
177C22×C43C2×#10012yes—
178C22×C43C2×#10112yes—
179C2×D43—24no—
180C2×D43—48no—
181C2×D43—48no—
182C2×D43—44no—
183C2×D43—42no—
184C2×D43—42no—
185C2×D43—44no—
186C4×C43—22no—
187C4×C43—22no—
188C4×C43—24no—
189C4×C43—42no—
190Dic43—42no—
191Dic43—42no—
192Dic43—42no—
193C22×C22⋊Q8—431no—
194#1821—432no—
195#1463—431no—
196#1463D4311yescharacteristic, complemented
197#1462—432no—
198C2×C43—22no—
199C2×C43—22no—
200C2×C43—22no—
201C2×C43#178211yescharacteristic
202C2×C43#178311yescharacteristic
203C2×C43#178411yescharacteristic
204D43—44no—
205C23×Q8—431no—
206C24×C4—431no—
207C2×C22⋊Q8—864no—
208C2×C22⋊Q8—864no—
209C2×C22⋊Q8—862no—
210C2×C22⋊Q8—862no—
211C22×C4⋊C4—431no—
212C22×C4⋊C4—431no—
213C22×C4⋊C4C2×D4311yescharacteristic
214C22×C22⋊C4—431no—
215C22×C22⋊C4—431no—
216#407—432no—
217#407C2×D4312yes—
218#343—864no—
219#324—22no—
220#324—862no—
221#323—864no—
222C43#855511yescharacteristic, complemented, Sylow
223C25—431no—
224C22×Q8—862no—
225C22×Q8—862no—
226C22×Q8—862no—
227C22×Q8—1724no—
228C23×C4—431no—
229C23×C4—431no—
230C23×C4—431no—
231C23×C4—862no—
232C23×C4—862no—
233C23×C4—862no—
234C23×C4—1724no—
235C23×C4C4×D4311yescharacteristic
236C23×C4C4×D4311yescharacteristic
237C23×C4C22×D4311yescharacteristic
238C2×M16—22no—
239C2×M16—862no—
240C22⋊Q8—8616no—
241C22⋊Q8—8616no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—434no—
245C2×C4⋊C4—862no—
246C2×C4⋊C4—862no—
247C2×C4⋊C4—862no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—862no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4D17212yes—
252C2×C4⋊C4C22⋊D4312yes—
253C2×C22⋊C4—434no—
254C2×C22⋊C4—862no—
255C2×C22⋊C4—862no—
256C2×C22⋊C4—862no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—862no—
259C2×C22⋊C4—861no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262C22⋊C8—862no—
263C22⋊C8—862no—
264C24—432no—
265C24—864no—
266C24—861no—
267C24—861no—
268C24—1722no—
269C24—1722no—
270C24C2×C4×D4311yescharacteristic
271C2×Q8—868no—
272C2×Q8—1728no—
273C2×Q8—1728no—
274C2×Q8—1724no—
275C2×Q8—1724no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—24no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—432no—
284C22×C4—432no—
285C22×C4—432no—
286C22×C4—868no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—1728no—
294C22×C4—1728no—
295C22×C4—1724no—
296C22×C4—1724no—
297C22×C4—1722no—
298C22×C4—1722no—
299C22×C4—1722no—
300C22×C4(C2×D43)⋊C412yes—
301C22×C4(C2×D43)⋊C412yes—
302C22×C4C2×D17211yescharacteristic
303C22×C4D4×D4312yes—
304C22×C4D4×D4312yes—
305C22×C4C2×C22⋊D4311yescharacteristic
306M16—44no—
307M16—1724no—
308C2×C8—42no—
309C2×C8—1722no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—868no—
313C4⋊C4—864no—
314C4⋊C4—864no—
315C22⋊C4—868no—
316C22⋊C4—864no—
317C22⋊C4—864no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—434no—
322C23—864no—
323C23—864no—
324C23—862no—
325C23—862no—
326C23—1722no—
327C23—1722no—
328C23—1722no—
329C23—17216no—
330C23—1722no—
331C23—1722no—
332C23—1722no—
333C23C22⋊C4×D4311yescharacteristic
334C23C22⋊C4×D4311yescharacteristic
335C23C2×(C2×D43)⋊C411yescharacteristic
336Q8—17216no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—17216no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4#1306324114yes—
363C2×C4#1306329312yes—
364C2×C4#1306329512yes—
365C8—82no—
366C8—3442no—
367C22—28no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—864no—
375C22—1724no—
376C22—1728no—
377C22—1728no—
378C22—1724no—
379C22—1722no—
380C22—1722no—
381C22#1458275411yescharacteristic
382C22#1458287112yes—
383C22C2×#1306324112yes—
384C22#101×D4312yes—
385C4—22no—
386C4—22no—
387C4—24no—
388C4—42no—
389C4—1722no—
390C4—1722no—
391C4—1722no—
392C2—22no—
393C2—22no—
394C2—22no—
395C2—1724no—
396C2#1913451111yescharacteristic
397C2#1913451511yescharacteristic
398C2#1913451711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1463C2
socleC22×C43#379
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1463D43
hypocenterC43#8555
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #19134673C2semidirect
3. #19132925C2semidirect
5. C43×#1463C2semidirect
196. #1463D43semidirect
222. C43#8555semidirect

Maximal subgroups

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

subgroupindex
C22×#130633052
#191346732
#191329252
#191329212
C43×#14632
#855543