Finite Group Databasebeta

← #24994598

Subgroups — #24994598

Order 11008.

626 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 91 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#19143634C211yesmaximal, characteristic, complemented
2#19139485C211yesmaximal, characteristic
3#19132931C211yesmaximal, characteristic, complemented
4#19132922C211yesmaximal, characteristic, complemented
5#19132502C211yesmaximal, characteristic, complemented
6#19132500C211yesmaximal, characteristic, complemented
7C43×#1462C211yesmaximal, characteristic, complemented
8C2×#13063308C411yescharacteristic
9C2×#13063294C411yescharacteristic
10C2×C4×C22⋊D43C2211yescharacteristic
11#14582975—22no—
12#14582974—22no—
13#14582949—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582861—21no—
17#14582822—21no—
18#14582815—21no—
19#14582787—21no—
20#14582775—21no—
21#14582762C411yescharacteristic
22#14582759C2211yescharacteristic
23#14582755C411yescharacteristic
24#14582624—21no—
25#14582623—22no—
26#14582622—21no—
27C22×C22⋊C4×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C43×#407C2211yescharacteristic
30C43×#323—22no—
31C22×C22⋊D43—21no—
32C22×C22⋊D43C2×C411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C2×#10621877—21no—
35C2×#10621877—21no—
36C2×#10621872—22no—
37#13063308—42no—
38#13063294—42no—
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43C2×C4⋊Dic43—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4D411yescharacteristic
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43C2×C411yescharacteristic
50C2×C22⋊Dic43C2×C411yescharacteristic
51C2×C22⋊Dic43C2×C411yescharacteristic
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55Dic43⋊C8—22no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)D412yescomplemented
60(C2×D43)⋊C8—22no—
61C8×Dic43—22no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C25×C43C2×C411yescharacteristic
66C23×C4×C43C2×C411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C2×M16×C43—21no—
69C2×M16×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43D412yescomplemented
80C24×C43—21no—
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—42no—
84C24×C43—41no—
85C24×C43—41no—
86C24×C43—81no—
87C24×C43C22×C411yescharacteristic
88C23×D43C22⋊C411yescharacteristic
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—81no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C2×C22⋊D43—22no—
102C2×C22⋊D43—21no—
103C2×C22⋊D43—21no—
104C2×C22⋊D43—41no—
105C2×C22⋊D43—42no—
106C2×C22⋊D43—42no—
107C2×C22⋊D43—81no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C2×C4×D43—21no—
114C2×C4×D43—21no—
115C2×C4×D43—81no—
116M16×C43—81no—
117M16×C43—81no—
118C2×C8×C43—22no—
119C2×C8×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C22⋊Dic43—21no—
125C22⋊Dic43—21no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128C22⋊Dic43—42no—
129C22⋊Dic43—42no—
130C22⋊Dic43—81no—
131(C2×D43)⋊C4—21no—
132(C2×D43)⋊C4—21no—
133(C2×D43)⋊C4—42no—
134C4⋊Dic43—81no—
135Dic43⋊C4—21no—
136Dic43⋊C4—21no—
137Dic43⋊C4—42no—
138C4×Dic43—21no—
139C4×Dic43—21no—
140#10621877—81no—
141#10621877—81no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—41no—
144#10621872—82no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—22no—
148C23×C43—22no—
149C23×C43—22no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43—41no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—81no—
161C23×C43—81no—
162C23×C43—81no—
163C23×C43—81no—
164C23×C43—84no—
165C23×C43—84no—
166C23×C43C2×C22⋊C411yescharacteristic
167C23×C43C4×D411yescharacteristic
168C23×C43C4×D411yescharacteristic
169C22×D43—21no—
170C22×D43—21no—
171C22×D43—21no—
172C22×D43—41no—
173C22×D43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—81no—
184C2×C4×C43—81no—
185C2×C4×C43#12011yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12311yescharacteristic
189C22⋊D43—42no—
190C22⋊D43—42no—
191C22⋊D43—84no—
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43#10012yes—
205C4×D43—42no—
206C4×D43—81no—
207C8×C43—42no—
208C8×C43—81no—
209C43⋊C8—42no—
210C43⋊C8—81no—
211#9516—431nomaximal, Sylow
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—42no—
221C22×C43—42no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—82no—
228C22×C43—82no—
229C22×C43—82no—
230C22×C43—82no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43#38611yescharacteristic
234C22×C43C2×#10011yescharacteristic
235C22×C43#41311yescharacteristic
236C2×D43—42no—
237C2×D43—41no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—81no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—81no—
246Dic43—22no—
247Dic43—41no—
248Dic43—41no—
249Dic43—81no—
250Dic43—81no—
251#2975—431no—
252#2534—431no—
253#1465—431no—
254#1462—431no—
255#1462D4311yescharacteristic, complemented
256#1305—431no—
257#1305—431no—
258C2×C43—21no—
259C2×C43—21no—
260C2×C43—41no—
261C2×C43—41no—
262C2×C43—82no—
263C2×C43#189111yescharacteristic
264C2×C43#190011yescharacteristic
265C2×C43#191311yescharacteristic
266D43—81no—
267C2×#123—431no—
268C2×#120—431no—
269C2×C4×D4—431no—
270C22×C22⋊C4C2×D4311yescharacteristic
271#436—862no—
272#436—862no—
273#431—861no—
274#407—431no—
275#407—431no—
276#407—861no—
277#407C2×D4311yescharacteristic
278#407C2×D4311yescharacteristic
279#396—861no—
280#394—861no—
281#388—861no—
282#386—861no—
283#381—431no—
284#380—431no—
285#379—431no—
286#324—861no—
287#323—22no—
288#323—861no—
289#323—862no—
290C43#951611yescharacteristic, complemented, Sylow
291C25C4×D4311yescharacteristic
292C22×D4—431no—
293C22×D4—861no—
294C23×C4—431no—
295C23×C4C4×D4311yescharacteristic
296C23×C4C22×D4311yescharacteristic
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—862no—
300C2×M16—861no—
301C2×M16—861no—
302#123—1722no—
303#120—1722no—
304C4×D4—861no—
305C4×D4—861no—
306C4×D4—861no—
307C4×D4—861no—
308C2×C4⋊C4—431no—
309C2×C4⋊C4—861no—
310C2×C4⋊C4—861no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—431no—
318C2×C22⋊C4—431no—
319C2×C22⋊C4—431no—
320C2×C22⋊C4—431no—
321C2×C22⋊C4—861no—
322C2×C22⋊C4—861no—
323C2×C22⋊C4—861no—
324C2×C22⋊C4—861no—
325C2×C42—431no—
326C4⋊C8—862no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—432no—
331C22⋊C8—862no—
332C22⋊C8—861no—
333C22⋊C8—861no—
334C22⋊C8—861no—
335C22⋊C8C22⋊D4312yescomplemented
336C4×C8—862no—
337#95—861no—
338#95—861no—
339#95—861no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—42no—
344C24—41no—
345C24—41no—
346C24—81no—
347C24—431no—
348C24C2×C4×D4311yescharacteristic
349C2×D4—862no—
350C2×D4—861no—
351C2×D4—861no—
352C2×D4—3441no—
353C2×D4—1721no—
354C2×D4—1722no—
355C2×D4—1722no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—81no—
362C22×C4—431no—
363C22×C4—431no—
364C22×C4—431no—
365C22×C4—861no—
366C22×C4—861no—
367C22×C4—861no—
368C22×C4—861no—
369C22×C4—3441no—
370C22×C4#1062189811yescharacteristic
371C22×C4D4×D4311yescharacteristic
372C22×C4D4×D4311yescharacteristic
373C22×C4D4×D4311yescharacteristic
374C22×C4#1062190011yescharacteristic
375C22×C4C2×C22⋊D4311yescharacteristic
376M16—81no—
377M16—81no—
378M16—3442no—
379M16—3441no—
380M16—3441no—
381C2×C8—22no—
382C2×C8—41no—
383C2×C8—862no—
384C2×C8—1721no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—3441no—
388C4⋊C4—1722no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—861no—
394C22⋊C4—861no—
395C22⋊C4—861no—
396C22⋊C4—861no—
397C22⋊C4—3441no—
398C22⋊C4—1722no—
399C22⋊C4—1722no—
400C22⋊C4—1722no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C42—861no—
404C42—861no—
405C23—21no—
406C23—21no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—81no—
421C23—81no—
422C23—81no—
423C23—81no—
424C23—84no—
425C23—84no—
426C23—861no—
427C23—861no—
428C23—861no—
429C23—1721no—
430C23—1721no—
431C23C22⋊C4×D4311yescharacteristic
432C23(C22⋊D43)⋊C411yescharacteristic
433C23C4×C22⋊D4311yescharacteristic
434D4—3444no—
435D4—1722no—
436D4—1722no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—432no—
449C2×C4—861no—
450C2×C4—861no—
451C2×C4—861no—
452C2×C4—861no—
453C2×C4—3441no—
454C2×C4—1722no—
455C2×C4—1721no—
456C2×C4—1721no—
457C2×C4—1721no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4—1721no—
463C2×C4#1306329311yescharacteristic
464C2×C4#1306329611yescharacteristic
465C2×C4#1306329811yescharacteristic
466C2×C4#1306330711yescharacteristic
467C8—42no—
468C8—81no—
469C8—3441no—
470C8—1722no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—81no—
485C22—81no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—81no—
491C22—81no—
492C22—3441no—
493C22—1722no—
494C22—1721no—
495C22—1721no—
496C22—1721no—
497C22#1458277511yescharacteristic
498C22#100×D4311yescharacteristic
499C22#1458288011yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—862no—
506C4—3441no—
507C4—3441no—
508C4—1721no—
509C4—1721no—
510C2—21no—
511C2—21no—
512C2—41no—
513C2—41no—
514C2—82no—
515C2—3441no—
516C2#1913501011yescharacteristic
517C2#1913505511yescharacteristic
518C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1462C2
socleC22×C43#386
prime radicalC2×#13063294C4
cosocleC23×C4×C43C23
hypercenter#1462D43
hypocenterC43#9516
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
1. #19143634C2semidirect
3. #19132931C2semidirect
4. #19132922C2semidirect
5. #19132502C2semidirect
6. #19132500C2semidirect
7. C43×#1462C2semidirect
59. C22⋊(C43⋊C8)D4semidirect
79. C22⋊C8×C43D4semidirect
255. #1462D43semidirect
290. C43#9516semidirect
335. C22⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191436342
#191394852
#191329312
#191329222
#191325022
#191325002
C43×#14622
#951643