Finite Group Databasebeta

← #24989187

Subgroups — #24989187

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135064C211yesmaximal, characteristic, complemented
2#19135059C211yesmaximal, characteristic, complemented
3#19134893C211yesmaximal, characteristic, complemented
4#19132959C211yesmaximal, characteristic, complemented
5#19132955C211yesmaximal, characteristic, complemented
6#19132933C211yesmaximal, characteristic, complemented
7C43×#3505C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C2×#13063244—21no—
10C2×#13063242—21no—
11#14582863C2211yescharacteristic
12#14582863C2211yescharacteristic
13C2×C22⋊(C43⋊C8)—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15#14582668—21no—
16#14582668—21no—
17#14582654—21no—
18#14582625—21no—
19#14582625—22no—
20#14582623—21no—
21#14582623—22no—
22C43×#553—22no—
23C43×#553—21no—
24C43×#552—21no—
25C43×#551—22no—
26C43×#548—21no—
27C43×#546—21no—
28C43×#539—21no—
29C43×#538—21no—
30C43×#534C412yes—
31C43×#529—21no—
32C43×#525—21no—
33C2×C22⋊Q8×C43C2211yescharacteristic
34C2×#121×C43C2211yescharacteristic
35C43×#518C412yes—
36C2×C4×D4×C43C2211yescharacteristic
37C2×#10621877—21no—
38C2×#10621877—21no—
39C2×#10621877—21no—
40C2×#10621877—21no—
41C2×#10621877—42no—
42C22×C43⋊C8—21no—
43C22×C43⋊C8—21no—
44#13063244—42no—
45#13063242—42no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—42no—
53C2×#41×C43—21no—
54C22×Q8×C43D411yescharacteristic
55C22×D4×C43C2×C411yescharacteristic
56C22×D4×C43C2×C412yes—
57C22×D4×C43D411yescharacteristic
58C23×C4×C43D411yescharacteristic
59C23×C4×C43C2311yescharacteristic
60#126×C43—22no—
61#126×C43—22no—
62#126×C43—22no—
63#125×C43—21no—
64#125×C43—22no—
65#124×C43—21no—
66#124×C43—22no—
67#123×C43—22no—
68#123×C43—22no—
69#123×C43—22no—
70#123×C43—22no—
71#123×C43—22no—
72C22⋊Q8×C43—21no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—21no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—21no—
77C22⋊Q8×C43—21no—
78#121×C43—21no—
79#121×C43—22no—
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—21no—
83#121×C43—21no—
84#121×C43—21no—
85#121×C43—21no—
86#120×C43—22no—
87#120×C43—22no—
88C4×Q8×C43—21no—
89C4×D4×C43—22no—
90C4×D4×C43—21no—
91C4×D4×C43—22no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99#117×C43—21no—
100#117×C43—22no—
101#117×C43—22no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D412yes—
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43C2×C411yescharacteristic
108C2×C22⋊C4×C43C2×C412yes—
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C22⋊C4×C43D412yes—
111C2×C42×C43D411yescharacteristic
112C24×C43C22⋊C411yescharacteristic
113C24×C43C22⋊C412yes—
114C24×C43C22×C411yescharacteristic
115#41×C43—81no—
116#41×C43—81no—
117C2×Q8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43—41no—
120C2×Q8×C43—41no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—41no—
130C2×D4×C43—41no—
131C2×D4×C43—42no—
132C2×D4×C43—42no—
133C2×D4×C43—41no—
134C2×D4×C43—41no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43—41no—
142C22×C4×C43—41no—
143C22×C4×C43C22⋊C411yescharacteristic
144C22×C4×C43C22⋊C411yescharacteristic
145C22×C4×C43C22⋊C412yes—
146C22×C4×C43C22⋊C411yescharacteristic
147C22×C4×C43C22⋊C412yes—
148C22×C4×C43C22⋊C412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—21no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—22no—
181C42×C43—22no—
182C42×C43—22no—
183C42×C43—21no—
184C42×C43—21no—
185#10621877—22no—
186#10621877—22no—
187#10621877—41no—
188#10621877—41no—
189#10621877—41no—
190#10621877—41no—
191#10621877—41no—
192#10621877—41no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C2×C43⋊C8—41no—
198C2×C43⋊C8—41no—
199C2×C43⋊C8—41no—
200C2×C43⋊C8—41no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—22no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43C2×C22⋊C411yescharacteristic
215C23×C43C2×C22⋊C411yescharacteristic
216C23×C43C2×C22⋊C411yescharacteristic
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220D4×C43—42no—
221D4×C43—42no—
222D4×C43—44no—
223D4×C43—42no—
224D4×C43—42no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—81no—
228D4×C43—82no—
229D4×C43—82no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—81no—
255C2×C4×C43—82no—
256C2×C4×C43—82no—
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43#12011yescharacteristic
260C2×C4×C43#12011yescharacteristic
261C43⋊C8—42no—
262C43⋊C8—81no—
263C43⋊C8—81no—
264C43⋊C8—81no—
265#8538—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—42no—
275C22×C43—41no—
276C22×C43—42no—
277C22×C43—41no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—41no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—162no—
285C22×C43#37911yescharacteristic
286C22×C43#41311yescharacteristic
287C22×C43#41311yescharacteristic
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43B(4,𝔽2)11yescharacteristic
298C4×C43#45811yescharacteristic
299#3505D4311yescharacteristic
300#1901—431no—
301#1900—431no—
302#1870—431no—
303#1472—431no—
304#1471—431no—
305#1465—431no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—41no—
309C2×C43—41no—
310C2×C43—81no—
311C2×C43—82no—
312C2×C43#178511yescharacteristic
313C2×C43#179011yescharacteristic
314C2×C43#179111yescharacteristic
315C22×M16—431no—
316#553—22no—
317#553—21no—
318#552—21no—
319#551—22no—
320#548—21no—
321#546—21no—
322#539—21no—
323#538—21no—
324#534Dic4312yes—
325#529—21no—
326#525—21no—
327C2×C22⋊Q8C2×D4311yescharacteristic
328C2×#121C2×D4311yescharacteristic
329#518Dic4312yes—
330C2×C4×D4C2×D4311yescharacteristic
331C2×#101—861no—
332C2×#100—861no—
333#407—431no—
334#407—431no—
335C2×C22⋊C8—431no—
336C2×C22⋊C8—861no—
337#343—861no—
338#343—861no—
339#336—861no—
340#324—861no—
341#324—862no—
342#323—861no—
343#323—862no—
344C43#853811yescharacteristic, complemented, Sylow
345C2×#41—21no—
346C22×Q8C22⋊D4311yescharacteristic
347C22×D4C2×Dic4311yescharacteristic
348C22×D4C2×Dic4312yes—
349C22×D4C22⋊D4311yescharacteristic
350C23×C4C22⋊D4311yescharacteristic
351C23×C4C22×D4311yescharacteristic
352C2×M16—861no—
353C2×M16—861no—
354C2×M16—861no—
355C2×M16—861no—
356C2×M16—1722no—
357C22×C8—861no—
358C22×C8—861no—
359#126—22no—
360#126—22no—
361#126—22no—
362#125—21no—
363#125—22no—
364#124—21no—
365#124—22no—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—22no—
370#123—22no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377#121—21no—
378#121—22no—
379#121—22no—
380#121—22no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—21no—
385#120—22no—
386#120—22no—
387C4×Q8—21no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398#117—21no—
399#117—22no—
400#117—22no—
401C2×C4⋊C4C22⋊D4311yescharacteristic
402C2×C4⋊C4C22⋊D4311yescharacteristic
403C2×C4⋊C4C22⋊D4312yes—
404C2×C4⋊C4C22⋊D4311yescharacteristic
405C2×C22⋊C4—22no—
406C2×C22⋊C4C2×Dic4311yescharacteristic
407C2×C22⋊C4C2×Dic4312yes—
408C2×C22⋊C4C22⋊D4311yescharacteristic
409C2×C22⋊C4C22⋊D4312yes—
410C2×C42C22⋊D4311yescharacteristic
411#101—1722no—
412#100—1722no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—1722no—
420C24C22⋊Dic4311yescharacteristic
421C24C22⋊Dic4312yes—
422C24C22×Dic4311yescharacteristic
423#41—81no—
424#41—81no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C22⋊Dic4311yescharacteristic
452C22×C4C22⋊Dic4311yescharacteristic
453C22×C4C22⋊Dic4312yes—
454C22×C4C22⋊Dic4311yescharacteristic
455C22×C4C22⋊Dic4312yes—
456C22×C4C22⋊Dic4312yes—
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463M16—862no—
464M16—862no—
465M16—1721no—
466M16—1721no—
467M16—1721no—
468M16—1721no—
469M16—1721no—
470M16—1721no—
471C2×C8—862no—
472C2×C8—1721no—
473C2×C8—1721no—
474C2×C8—1721no—
475C2×C8—1721no—
476C2×C8—1721no—
477C2×C8—1721no—
478C2×C8—1721no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C42—22no—
506C42—22no—
507C42—21no—
508C42—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—22no—
514C23—21no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23C2×C22⋊Dic4311yescharacteristic
523C23C2×C22⋊Dic4311yescharacteristic
524C23C2×C22⋊Dic4311yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—81no—
528D4—42no—
529D4—42no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—41no—
534D4—41no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—81no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4#1306329411yescharacteristic
566C2×C4#1306329411yescharacteristic
567C2×C4#1306329411yescharacteristic
568C2×C4#1306329411yescharacteristic
569C8—3441no—
570C8—3441no—
571C8—3441no—
572C8—1722no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—41no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—42no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—162no—
592C22#1458275511yescharacteristic
593C22#1458288311yescharacteristic
594C22#1458288311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—42no—
604C4#1458308611yescharacteristic
605C4#1458308911yescharacteristic
606C2—21no—
607C2—21no—
608C2—41no—
609C2—41no—
610C2—81no—
611C2—82no—
612C2#1913452311yescharacteristic
613C2#1913454311yescharacteristic
614C2#1913454611yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3505C2
socleC22×C43#379
cosocleC23×C4×C43C23
hypercenter#3505D43
hypocenterC43#8538
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #19135064C2semidirect
2. #19135059C2semidirect
3. #19134893C2semidirect
4. #19132959C2semidirect
5. #19132955C2semidirect
6. #19132933C2semidirect
344. C43#8538semidirect

Maximal subgroups

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

subgroupindex
#191350642
#191350592
#191348932
#191329592
#191329552
#191329332
C43×#35052
#853843