Finite Group Databasebeta

← #25135408

Subgroups — #25135408

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582957C211yesmaximal, characteristic
2#19140393C211yesmaximal, characteristic
3#19137181C211yesmaximal, characteristic
4#19135988C211yesmaximal, characteristic, complemented
5#19135974C211yesmaximal, characteristic, complemented
6#19135915C211yesmaximal, characteristic, complemented
7#19135915C211yesmaximal, characteristic, complemented
8#19135467C211yesmaximal, characteristic, complemented
9#19135457C211yesmaximal, characteristic, complemented
10#19135282C211yesmaximal, characteristic, complemented
11#19135268C211yesmaximal, characteristic, complemented
12#19134908C211yesmaximal, characteristic
13#19134796C211yesmaximal, characteristic
14#19134530C211yesmaximal, characteristic
15C2×C43×#451C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18#14582957—24no—
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582838—21no—
33#14582829—21no—
34#14582827—21no—
35#14582827—21no—
36#14582806—21no—
37#14582806—21no—
38#14582806C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582806C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582806C2211yescharacteristic
43#14582806C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582762—21no—
47#14582762—21no—
48#14582759C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54C22×Q16×C43C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C43×#451—24no—
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063284—22no—
64#13063284—22no—
65#13063284—41no—
66#13063284—41no—
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43D411yescharacteristic
78C2×C22⋊Dic43D411yescharacteristic
79C2×C4×Dic43—21no—
80C2×C4×Dic43C2311yescharacteristic
81C2×C4×Dic43C2311yescharacteristic
82#13063259—41no—
83#13063257—41no—
84Dic43⋊C8—22no—
85Dic43⋊C8—22no—
86#13063249—22no—
87#13063249—22no—
88#13063249—41no—
89#13063249—41no—
90#13063249—41no—
91#13063249—41no—
92C22⋊(C43⋊C8)—22no—
93#13063235—22no—
94C8×Dic43—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×Q8×C43—22no—
111C22×Q8×C43—22no—
112C22×Q8×C43—21no—
113C22×Q8×C43—22no—
114C22×Q8×C43—22no—
115C22×Q8×C43—41no—
116C22×Q8×C43—41no—
117C22×Q8×C43C2311yescharacteristic
118C22×Q8×C43C2311yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C23×C4×C43C2311yescharacteristic
122C2×Q16×C43—22no—
123C2×Q16×C43—22no—
124C2×Q16×C43—22no—
125C2×Q16×C43—22no—
126C2×Q16×C43—41no—
127C2×Q16×C43—41no—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22⋊Q8×C43—22no—
131C22⋊Q8×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135#103×C43—22no—
136#103×C43—22no—
137C22⋊C8×C43D414yes—
138C24×C43C2×D411yescharacteristic
139C2×Q8×C43—24no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—44no—
157C2×Q8×C43—44no—
158C2×Q8×C43—44no—
159C2×Q8×C43—44no—
160C2×Q8×C43—42no—
161C2×Q8×C43—42no—
162C2×Q8×C43#4112yes—
163C2×Q8×C43#4112yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—24no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43C2×D412yes—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43#4112yes—
178C22×C4×C43C2411yescharacteristic
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187Q16×C43—44no—
188Q16×C43—44no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×D412yes—
194C2×C8×C43C2×D412yes—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—42no—
198C22⋊C4×C43—42no—
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—42no—
202C22⋊Dic43—81no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213Dic43⋊C4—81no—
214Dic43⋊C4—81no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—42no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43#12112yes—
233C23×C43C22×D411yescharacteristic
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—48no—
239Q8×C43—41no—
240Q8×C43—41no—
241Q8×C43—41no—
242Q8×C43—41no—
243Q8×C43—41no—
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—48no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43#12112yes—
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C8×C43—22no—
298C8×C43—22no—
299C43⋊C8—41no—
300C43⋊C8—41no—
301#24514—431nomaximal, Sylow
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43C2×#12111yescharacteristic
310C22×C43#52511yescharacteristic
311C22×C43#53511yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57811yescharacteristic
314C22×C43#57811yescharacteristic
315C22×C43#57811yescharacteristic
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43#54611yescharacteristic
322C4×C43#54611yescharacteristic
323C4×C43#55111yescharacteristic
324C4×C43#55111yescharacteristic
325Dic43—41no—
326Dic43—41no—
327Dic43—41no—
328Dic43—41no—
329Dic43—81no—
330Dic43—81no—
331Dic43—81no—
332Dic43—81no—
333C2×#451D4311yescharacteristic
334C2×#433—431no—
335#2625—431no—
336#2310—431no—
337#2068—431no—
338#2066—431no—
339#2056—431no—
340#2056—431no—
341#1971—431no—
342#1969—431no—
343#1935—431no—
344#1933—431no—
345#1873—431no—
346#1854—431no—
347#1787—431no—
348C2×C43—42no—
349C2×C43#241111yescharacteristic
350C2×C43#305911yescharacteristic
351C2×C43#306311yescharacteristic
352C2×C43#312111yescharacteristic
353C2×C43#312711yescharacteristic
354C2×C43#322311yescharacteristic
355C2×C43#322511yescharacteristic
356C23×Q8C2×D4311yescharacteristic
357C22×Q16C2×D4311yescharacteristic
358C22×Q16C2×D4311yescharacteristic
359C2×C22⋊Q8C2×D4311yescharacteristic
360C2×#117—431no—
361C2×#117—431no—
362#451—24no—
363#433—864no—
364C2×#107—431no—
365C2×#106—431no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103C2×D4311yescharacteristic
375C2×#103C2×D4311yescharacteristic
376C2×C22⋊C8—431no—
377C2×C22⋊C8C2×D4311yescharacteristic
378C2×#97—431no—
379C2×C4×C8—431no—
380#400—861no—
381#398—861no—
382#397—861no—
383#397—861no—
384#391—431no—
385#391—431no—
386#391—431no—
387#391—431no—
388#391—431no—
389#391—431no—
390#391—861no—
391#391—861no—
392#389—431no—
393#389—431no—
394#381—861no—
395#381—861no—
396#380—431no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401C43#2451411yescharacteristic, complemented, Sylow
402C22×Q8—22no—
403C22×Q8—22no—
404C22×Q8—21no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—41no—
408C22×Q8—41no—
409C22×Q8C22×D4311yescharacteristic
410C22×Q8C22×D4311yescharacteristic
411C22×Q8C22×D4311yescharacteristic
412C23×C4—21no—
413C23×C4C22×D4311yescharacteristic
414C2×Q16—22no—
415C2×Q16—22no—
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16—41no—
419C2×Q16—41no—
420C22×C8—431no—
421C22×C8—431no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426#117—862no—
427#117—862no—
428#117—1721no—
429#117—1721no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—431no—
442C2×C22⋊C4—431no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—861no—
448#107—1721no—
449#106—1721no—
450C4⋊C8—862no—
451C4⋊C8—862no—
452#103—22no—
453#103—22no—
454#103—862no—
455#103—862no—
456#103—1721no—
457#103—1721no—
458#103—1721no—
459#103—1721no—
460C22⋊C8—862no—
461C22⋊C8C22⋊D4314yes—
462#97—862no—
463C4×C8—862no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24D4×D4311yescharacteristic
480C2×Q8—24no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8#1062190012yes—
504C2×Q8#1062190012yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4D4×D4311yescharacteristic
525C22×C4#1062190012yes—
526C22×C4C2×C22⋊D4312yes—
527C22×C4C23×D4311yescharacteristic
528Q16—44no—
529Q16—44no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8C2×C22⋊D4312yes—
541C2×C8C2×C22⋊D4312yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—42no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—3441no—
556C4⋊C4—3441no—
557C22⋊C4—42no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—3441no—
561C22⋊C4—1722no—
562C42—861no—
563C42—861no—
564C42—861no—
565C42—861no—
566C42—1722no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#1306329612yes—
574C23C2×D4×D4311yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—22no—
578Q8—22no—
579Q8—48no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—48no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4#1306329612yes—
632C2×C4C22×C22⋊D4311yescharacteristic
633C2×C4C2×#1062190011yescharacteristic
634C2×C4C2×#1062190011yescharacteristic
635C2×C4C2×#1062190011yescharacteristic
636C2×C4#1306337011yescharacteristic
637C2×C4#1306337011yescharacteristic
638C8—22no—
639C8—22no—
640C8—1721no—
641C8—1721no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#1306329611yescharacteristic
650C22#1458340511yescharacteristic
651C22#1458346411yescharacteristic
652C22#1458370811yescharacteristic
653C22#1458371211yescharacteristic
654C22#1458371211yescharacteristic
655C22#1458371511yescharacteristic
656C4—22no—
657C4—42no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—3441no—
662C4—3441no—
663C4—3441no—
664C4—3441no—
665C4—1721no—
666C4—1721no—
667C4—1721no—
668C4—1721no—
669C4#1458354311yescharacteristic
670C4#1458354311yescharacteristic
671C4#1458358011yescharacteristic
672C4#1458358011yescharacteristic
673C2—42no—
674C2#1913797611yescharacteristic
675C2#1914424611yescharacteristic
676C2#1914428011yescharacteristic
677C2#1914482511yescharacteristic
678C2#1914488911yescharacteristic
679C2#1914567411yescharacteristic
680C2#1914571011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC2×#451D43
hypocenterC43#24514
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
4. #19135988C2semidirect
5. #19135974C2semidirect
6. #19135915C2semidirect
7. #19135915C2semidirect
8. #19135467C2semidirect
9. #19135457C2semidirect
10. #19135282C2semidirect
11. #19135268C2semidirect
401. C43#24514semidirect

Maximal subgroups

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

subgroupindex
C2×#145829572
#191403932
#191371812
#191359882
#191359742
#191359152
#191354672
#191354572
#191352822
#191352682
#191349082
#191347962
#191345302
C2×C43×#4512
#2451443