Finite Group Databasebeta

← #25069013

Subgroups — #25069013

Order 11008.

1054 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 183 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#19144539C212yesmaximal, complemented
2#19138869C211yesmaximal, characteristic
3#19133620C214yesmaximal, complemented
4#19133586C214yesmaximal, complemented
5#19133128C212yesmaximal, complemented
6#19132922C211yesmaximal, characteristic
7C2×C43×#543C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583237—24no—
10#14583232C2214yescomplemented
11#14583227C2214yescomplemented
12#14582939—22no—
13#14582908—22no—
14#14582863C2212yes—
15#14582835C2212yes—
16#14582824C2212yes—
17#14582787—22no—
18#14582772—21no—
19#14582762C2211yescharacteristic
20#14582755—21no—
21#14582636C2218yescomplemented
22#14582623C2214yes—
23C43×#543—24no—
24C43×#543—22no—
25C43×#543C2214yes—
26C2×C22⋊Q8×C43—22no—
27C2×C22⋊Q8×C43—21no—
28C2×C22⋊Q8×C43—22no—
29C2×C22⋊Q8×C43C2212yes—
30C22×C22⋊C4×C43—21no—
31C22×C22⋊C4×C43C2211yescharacteristic
32C2×#10621877—22no—
33#13063284—22no—
34#13063284—22no—
35C2×C4⋊Dic43C2311yescharacteristic
36C2×C4⋊Dic43C2311yescharacteristic
37C2×Dic43⋊C4—22no—
38C2×C22⋊Dic43—22no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—22no—
42C2×C4×Dic43—21no—
43#13063258—24no—
44#13063256—24no—
45#13063249—24no—
46#13063249—24no—
47C22⋊(C43⋊C8)—22no—
48C22⋊(C43⋊C8)C2314yes—
49C43⋊#95—21no—
50C43⋊#95—22no—
51C43⋊#95C2312yes—
52C25×C43D411yescharacteristic
53C22×Q8×C43—21no—
54C22×Q8×C43D412yes—
55C23×C4×C43—21no—
56C23×C4×C43—21no—
57C23×C4×C43D411yescharacteristic
58C23×C4×C43C2311yescharacteristic
59C22⋊Q8×C43—28no—
60C22⋊Q8×C43—28no—
61C22⋊Q8×C43—24no—
62C22⋊Q8×C43—28no—
63C22⋊Q8×C43—24no—
64C22⋊Q8×C43—22no—
65C22⋊Q8×C43—22no—
66C22⋊Q8×C43—28no—
67C22⋊Q8×C43D414yes—
68C22⋊Q8×C43C2314yes—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43D412yes—
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—24no—
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43—24no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43D412yes—
80C2×C22⋊C4×C43C2312yes—
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—24no—
84C24×C43—42no—
85C24×C43—81no—
86C24×C43C2×D411yescharacteristic
87C24×C43C2×D412yes—
88C2×Q8×C43—24no—
89C2×Q8×C43—22no—
90C2×Q8×C43—44no—
91C2×Q8×C43—82no—
92C2×Q8×C43C2×D414yes—
93C22×C4×C43—24no—
94C22×C4×C43—24no—
95C22×C4×C43—22no—
96C22×C4×C43—21no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—42no—
100C22×C4×C43—81no—
101C22×C4×C43—82no—
102C22×C4×C43—82no—
103C22×C4×C43C2×D412yes—
104C22×C4×C43C2×D412yes—
105C22×C4×C43C2×D412yes—
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2411yescharacteristic
108C22×Dic43—22no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C4⋊C4×C43—24no—
112C4⋊C4×C43—28no—
113C4⋊C4×C43—24no—
114C4⋊C4×C43—22no—
115C4⋊C4×C43—24no—
116C4⋊C4×C43C2×D414yes—
117C22⋊C4×C43—28no—
118C22⋊C4×C43—24no—
119C22⋊C4×C43—24no—
120C22⋊C4×C43—24no—
121C22⋊C4×C43—24no—
122C22⋊Dic43—42no—
123C22⋊Dic43—41no—
124C22⋊Dic43—41no—
125C22⋊Dic43—44no—
126C22⋊Dic43—82no—
127C4⋊Dic43—22no—
128C4⋊Dic43—22no—
129Dic43⋊C4—82no—
130C4×Dic43—42no—
131#10621877—44no—
132C2×C43⋊C8—24no—
133C23×C43—24no—
134C23×C43—24no—
135C23×C43—22no—
136C23×C43—22no—
137C23×C43—22no—
138C23×C43—22no—
139C23×C43—41no—
140C23×C43—42no—
141C23×C43—42no—
142C23×C43—42no—
143C23×C43—42no—
144C23×C43—81no—
145C23×C43—81no—
146C23×C43—88no—
147C23×C43#12011yescharacteristic
148C23×C43#12011yescharacteristic
149C23×C43#13714yes—
150C23×C43C22×D411yescharacteristic
151Q8×C43—44no—
152Q8×C43—82no—
153Q8×C43—84no—
154C2×C4×C43—24no—
155C2×C4×C43—24no—
156C2×C4×C43—22no—
157C2×C4×C43—24no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—44no—
163C2×C4×C43—44no—
164C2×C4×C43—42no—
165C2×C4×C43—81no—
166C2×C4×C43—84no—
167C2×C4×C43—84no—
168C2×C4×C43#12012yes—
169C2×C4×C43C22×D412yes—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C43⋊C8—44no—
178#18138—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—24no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—44no—
188C22×C43—44no—
189C22×C43—48no—
190C22×C43—42no—
191C22×C43—42no—
192C22×C43—82no—
193C22×C43—84no—
194C22×C43#45812yes—
195C22×C43C2×#12011yescharacteristic
196C22×C43C2×#13712yes—
197C4×C43—22no—
198C4×C43—22no—
199C4×C43—42no—
200C4×C43—44no—
201C4×C43—44no—
202Dic43—82no—
203Dic43—81no—
204Dic43—81no—
205C2×#543D4311yescharacteristic
206#3095—432no—
207#2482—431no—
208#1614—434no—
209#1608—434no—
210#1511—432no—
211#1462—431no—
212C2×C43—22no—
213C2×C43—22no—
214C2×C43—41no—
215C2×C43—44no—
216C2×C43#300411yescharacteristic
217C2×C43#301911yescharacteristic
218C2×C43C2×#45811yescharacteristic
219#543—24no—
220#543—22no—
221#543C2×D4314yes—
222C2×C22⋊Q8—22no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—22no—
225C2×C22⋊Q8C2×D4312yes—
226C2×#117—431no—
227C22×C22⋊C4—21no—
228C22×C22⋊C4C2×D4311yescharacteristic
229#485—864no—
230#484—434no—
231#483—434no—
232#428—862no—
233#419—862no—
234#407—432no—
235#399—432no—
236#397—432no—
237#388—862no—
238#385—861no—
239#381—431no—
240#379—861no—
241#328—438no—
242#323—434no—
243C43#1813811yescharacteristic, complemented, Sylow
244C25C22⋊D4311yescharacteristic
245C22×Q8—21no—
246C22×Q8C22⋊D4312yes—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C22⋊D4311yescharacteristic
250C23×C4C22×D4311yescharacteristic
251C2×M16—862no—
252C22⋊Q8—28no—
253C22⋊Q8—28no—
254C22⋊Q8—24no—
255C22⋊Q8—28no—
256C22⋊Q8—24no—
257C22⋊Q8—22no—
258C22⋊Q8—22no—
259C22⋊Q8—28no—
260C22⋊Q8C22⋊D4314yes—
261C22⋊Q8C22×D4314yes—
262#117—862no—
263#117—862no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—862no—
270C2×C4⋊C4C22⋊D4312yes—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—24no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—862no—
281C2×C22⋊C4C22⋊D4312yes—
282C2×C22⋊C4C22×D4312yes—
283C2×C42—861no—
284#107—864no—
285#106—864no—
286#103—864no—
287#103—864no—
288C22⋊C8—434no—
289C22⋊C8—862no—
290#95—432no—
291#95—861no—
292#95—862no—
293C24—21no—
294C24—21no—
295C24—24no—
296C24—42no—
297C24—81no—
298C24C2×C22⋊D4311yescharacteristic
299C24C2×C22⋊D4312yes—
300C2×Q8—24no—
301C2×Q8—22no—
302C2×Q8—44no—
303C2×Q8—82no—
304C2×Q8C2×C22⋊D4314yes—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—21no—
311C22×C4—42no—
312C22×C4—81no—
313C22×C4—82no—
314C22×C4—82no—
315C22×C4—862no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4C2×C22⋊D4312yes—
319C22×C4C2×C22⋊D4312yes—
320C22×C4C2×C22⋊D4311yescharacteristic
321C22×C4C2×C22⋊D4312yes—
322C22×C4C23×D4311yescharacteristic
323M16—1724no—
324C2×C8—864no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—24no—
330C4⋊C4—862no—
331C4⋊C4—862no—
332C4⋊C4—3442no—
333C4⋊C4C2×C22⋊D4314yes—
334C22⋊C4—28no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—3442no—
340C22⋊C4—1722no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C22⋊C4—1724no—
344C42—1722no—
345C23—24no—
346C23—24no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—81no—
357C23—81no—
358C23—88no—
359C23#1306329411yescharacteristic
360C23#1306329411yescharacteristic
361C23#1306335614yes—
362C23C22×C22⋊D4311yescharacteristic
363Q8—44no—
364Q8—82no—
365Q8—84no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—84no—
379C2×C4—84no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1722no—
386C2×C4—1722no—
387C2×C4#1306329412yes—
388C2×C4C22×C22⋊D4312yes—
389C8—1724no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—24no—
398C22—44no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—84no—
405C22#1458308912yes—
406C22C2×#1306329411yescharacteristic
407C22C2×#1306335612yes—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—44no—
412C4—44no—
413C4—3442no—
414C4—3441no—
415C4—3441no—
416C2—22no—
417C2—22no—
418C2—41no—
419C2—44no—
420C2#1914382911yescharacteristic
421C2#1914395211yescharacteristic
422C2C2×#1458308911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#543C2
socleC22×C43C2×#120
prime radicalC25×C43D4
hypercenterC2×#543D43
hypocenterC43#18138
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #19144539C2semidirect
3. #19133620C2semidirect
4. #19133586C2semidirect
5. #19133128C2semidirect
10. #14583232C22semidirect
11. #14583227C22semidirect
21. #14582636C22semidirect
243. C43#18138semidirect

Maximal subgroups

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

subgroupindex
#191445392
#191388692
#191336202
#191335862
#191331282
#191329222
C2×C43×#5432
#1813843