Finite Group Databasebeta

← #25200633

Subgroups — #25200633

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142963C211yesmaximal, characteristic, complemented
2#19137142C211yesmaximal, characteristic, complemented
3#19136081C211yesmaximal, characteristic, complemented
4#19136012C211yesmaximal, characteristic, complemented
5#19135834C211yesmaximal, characteristic, complemented
6#19135674C211yesmaximal, characteristic
7#19135460C211yesmaximal, characteristic
8#19135449C211yesmaximal, characteristic, complemented
9#19135270C211yesmaximal, characteristic, complemented
10#19134951C211yesmaximal, characteristic, complemented
11#19134941C211yesmaximal, characteristic
12#19134858C211yesmaximal, characteristic, complemented
13#19134850C211yesmaximal, characteristic, complemented
14#19134340C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063320—21no—
19C2×#13063312C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582791—21no—
38#14582789—21no—
39#14582788—21no—
40#14582787—21no—
41#14582787—21no—
42#14582764C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44C22⋊C4×Dic43—21no—
45C42×Dic43C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×C4×C8×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C23×Dic43—21no—
62C2×#10621873—22no—
63C2×#10621873—22no—
64C2×#10621873—41no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063320—44no—
71#13063312—22no—
72#13063312—22no—
73#13063290—41no—
74#13063290—41no—
75D4×Dic43—41no—
76D4×Dic43—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43D411yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063258—41no—
99#13063257—41no—
100#13063250—41no—
101#13063248—22no—
102#13063248—22no—
103#13063247—41no—
104#13063246—41no—
105#13063245—41no—
106C4×C43⋊C8—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43—22no—
125C4×C8×C43—22no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86#4112yes—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43#4112yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—42no—
178C42×C43—21no—
179C42×C43—21no—
180C22⋊Dic43—24no—
181C22⋊Dic43—24no—
182C22⋊Dic43—42no—
183#10621882—44no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—22no—
204C4×Dic43—41no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8#4112yes—
212#10621873—44no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C22×D411yescharacteristic
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—41no—
231D4×C43—41no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43#13512yes—
246C2×C4×C43AGL(1,ℤ/8)12yes—
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—84no—
274C2×Dic43#13512yes—
275D172—41no—
276D172—41no—
277D172—41no—
278D172—41no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283C8×C43—22no—
284C8×C43—41no—
285C43⋊C8—22no—
286C43⋊C8—41no—
287#29497—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43#52511yescharacteristic
296C22×C43#53211yescharacteristic
297C22×C43#53511yescharacteristic
298C22×C43C2×#13511yescharacteristic
299C22×C43C2×#13511yescharacteristic
300C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C43#57511yescharacteristic
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C4×C43—22no—
310C4×C43—22no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43#55111yescharacteristic
315C4×C43#55111yescharacteristic
316C4×C43#55311yescharacteristic
317C4×C43#55311yescharacteristic
318Dic43—22no—
319Dic43—41no—
320Dic43—41no—
321Dic43—42no—
322Dic43—41no—
323Dic43—81no—
324Dic43—81no—
325#2860—431no—
326C4×#124—431no—
327#2085—431no—
328#2073—431no—
329#2042—431no—
330#2012—431no—
331#1970—431no—
332#1968—431no—
333#1934D4311yescharacteristic, complemented
334#1933—431no—
335#1880—431no—
336#1879—431no—
337#1864—431no—
338#1863—431no—
339#1744—431no—
340C2×C43—82no—
341C2×C43#260311yescharacteristic
342C2×C43#310211yescharacteristic
343C2×C43#310611yescharacteristic
344C2×C43#316811yescharacteristic
345C2×C43#318011yescharacteristic
346C2×C43#320711yescharacteristic
347C2×C43#321111yescharacteristic
348D43—161no—
349C22×SD16—431no—
350C22×D8—431no—
351C2×#126—861no—
352C2×#124—431no—
353C2×C4×Q8—431no—
354C2×C4×D4—431no—
355C2×#107—431no—
356C2×#106—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102C2×D4311yescharacteristic
364C2×#102C2×D4311yescharacteristic
365C2×C4×C8—431no—
366C2×C4×C8C2×D4311yescharacteristic
367#391—431no—
368#390—431no—
369#390—431no—
370#390—431no—
371#390C2×D4311yescharacteristic
372#389—431no—
373#389—431no—
374#389C2×D4311yescharacteristic
375#388—861no—
376#388—861no—
377#388—861no—
378#388—861no—
379#388—861no—
380#382—431no—
381C4×C22⋊C4—861no—
382C4×C22⋊C4—861no—
383C43—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388#336—431no—
389#336—431no—
390#336—431no—
391#336—431no—
392C43#2949711yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×D4—431no—
395C22×D4C22×D4311yescharacteristic
396C23×C4—861no—
397C2×SD16—862no—
398C2×SD16—862no—
399C2×SD16—1721no—
400C2×D8—862no—
401C2×D8—862no—
402C2×D8—1721no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407#126—1724no—
408#124—862no—
409#124—862no—
410C4×Q8—1721no—
411C4×Q8—1721no—
412C4×D4—1721no—
413C4×D4—1721no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42C22×D4311yescharacteristic
442#107—1721no—
443#106—1721no—
444#103—862no—
445#103—862no—
446#103—1721no—
447#102—22no—
448#102—22no—
449#102—1721no—
450#102—1721no—
451#102—1721no—
452C4×C8—22no—
453C4×C8—862no—
454#95—21no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—21no—
462C24—861no—
463C2×Q8—432no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4#1062189812yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—1724no—
498D8—1724no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8#1062190012yes—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—864no—
528C22⋊C4—864no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C42—21no—
537C42—21no—
538C42—862no—
539C42—862no—
540C42—862no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42—861no—
545C42—1721no—
546C42—1722no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23C2×D4×D4311yescharacteristic
562Q8—862no—
563Q8—862no—
564Q8—1721no—
565Q8—1721no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—1721no—
571D4—1721no—
572D4—1721no—
573D4—1721no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—3444no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4#1306334612yes—
610C2×C4#1306334912yes—
611C2×C4#41×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4C2×#1062190011yescharacteristic
614C2×C4C2×#1062189811yescharacteristic
615C2×C4#1306337111yescharacteristic
616C2×C4#1306337111yescharacteristic
617C8—22no—
618C8—41no—
619C8—862no—
620C8—1721no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22#1458340811yescharacteristic
636C22#1458344411yescharacteristic
637C22#1458346711yescharacteristic
638C22#135×D4311yescharacteristic
639C22C2×#1306334611yescharacteristic
640C22C2×#1306334911yescharacteristic
641C22#1458369611yescharacteristic
642C4—22no—
643C4—22no—
644C4—81no—
645C4—81no—
646C4—81no—
647C4—862no—
648C4—3441no—
649C4—3441no—
650C4—1721no—
651C4—1722no—
652C4—1721no—
653C4—1721no—
654C4#1458357211yescharacteristic
655C4#1458357311yescharacteristic
656C4#1458359511yescharacteristic
657C4#1458360011yescharacteristic
658C2—82no—
659C2—6881no—
660C2#1914022011yescharacteristic
661C2#1914461711yescharacteristic
662C2#1914465111yescharacteristic
663C2#1914515811yescharacteristic
664C2#1914528811yescharacteristic
665C2#1914552911yescharacteristic
666C2#1914556111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#1934D43
hypocenterC43#29497
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
1. #19142963C2semidirect
2. #19137142C2semidirect
3. #19136081C2semidirect
4. #19136012C2semidirect
5. #19135834C2semidirect
8. #19135449C2semidirect
9. #19135270C2semidirect
10. #19134951C2semidirect
12. #19134858C2semidirect
13. #19134850C2semidirect
14. #19134340C2semidirect
15. C43×#1934C2semidirect
333. #1934D43semidirect
392. C43#29497semidirect

Maximal subgroups

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

subgroupindex
#191429632
#191371422
#191360812
#191360122
#191358342
#191356742
#191354602
#191354492
#191352702
#191349512
#191349412
#191348582
#191348502
#191343402
C43×#19342
#2949743