Finite Group Databasebeta

← #25146421

Subgroups — #25146421

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144981C211yesmaximal, characteristic
2#19144400C211yesmaximal, characteristic, complemented
3#19143538C211yesmaximal, characteristic, complemented
4#19135960C211yesmaximal, characteristic, complemented
5#19135953C211yesmaximal, characteristic
6#19135860C211yesmaximal, characteristic, complemented
7#19135853C211yesmaximal, characteristic
8#19135511C211yesmaximal, characteristic, complemented
9#19135500C211yesmaximal, characteristic
10#19135445C211yesmaximal, characteristic
11#19135371C211yesmaximal, characteristic, complemented
12#19135254C211yesmaximal, characteristic
13#19135247C211yesmaximal, characteristic, complemented
14C4×#13063244C211yesmaximal, characteristic, complemented
15C2×C43×#464C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583258—21no—
18#14583258—21no—
19#14583253—21no—
20#14583253—21no—
21#14583206—21no—
22#14583206—21no—
23#14583194—21no—
24#14583184—21no—
25#14583028—21no—
26#14583028—21no—
27#14583026—21no—
28#14583023—21no—
29C2×#13063261C2211yescharacteristic
30C2×#13063261C2211yescharacteristic
31#14582939C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582925C2211yescharacteristic
34#14582925C2211yescharacteristic
35#14582923C2211yescharacteristic
36#14582908C2211yescharacteristic
37#14582908C2211yescharacteristic
38#14582908C2211yescharacteristic
39#14582908C2211yescharacteristic
40#14582904C2211yescharacteristic
41#14582904C2211yescharacteristic
42C2×#13063244C2211yescharacteristic
43C2×#13063244C2211yescharacteristic
44C2×#13063244C2211yescharacteristic
45C2×#13063244C2211yescharacteristic
46C2×#13063242C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48#14582854C2211yescharacteristic
49#14582854C2211yescharacteristic
50C4×#10621877C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C22×SD16×C43C2211yescharacteristic
58C2×#124×C43C2211yescharacteristic
59C2×C4×Q8×C43C2211yescharacteristic
60C43×#464—21no—
61C43×#464—21no—
62C43×#464—21no—
63C43×#464—21no—
64C2×C4⋊C8×C43C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73#13063325D411yescharacteristic
74#13063325D411yescharacteristic
75#13063317D411yescharacteristic
76#13063317D411yescharacteristic
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063284C2311yescharacteristic
82#13063284C2311yescharacteristic
83#13063261—41no—
84#13063261—41no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91Dic43⋊C8—21no—
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94Dic43⋊C8—21no—
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063244—22no—
108#13063244—22no—
109#13063244—22no—
110#13063244—41no—
111#13063242—22no—
112#13063242—41no—
113#13063236—21no—
114#13063236—21no—
115#13063235—21no—
116#13063235—21no—
117C4×C43⋊C8—21no—
118C4×C43⋊C8—21no—
119C8×Dic43—21no—
120C8×Dic43—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123C22×D4×C43C2311yescharacteristic
124C2×Q16×C43—22no—
125C2×Q16×C43—21no—
126C2×Q16×C43—21no—
127C2×Q16×C43—41no—
128C2×SD16×C43—22no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—41no—
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134#124×C43—21no—
135#124×C43—21no—
136#124×C43—21no—
137#124×C43—21no—
138C4×Q8×C43—21no—
139C4×Q8×C43—21no—
140C4×Q8×C43—21no—
141C4×Q8×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C42×C43—21no—
147C2×C42×C43C2311yescharacteristic
148C4⋊C8×C43D411yescharacteristic
149C4⋊C8×C43D411yescharacteristic
150C4⋊C8×C43D411yescharacteristic
151C4⋊C8×C43D411yescharacteristic
152#103×C43—21no—
153#103×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156C24×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43#4112yes—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43#4111yescharacteristic
179C22×C4×C43#4111yescharacteristic
180C22×C4×C43C2411yescharacteristic
181C2×Dic86—21no—
182C2×Dic86—21no—
183Q16×C43—42no—
184Q16×C43—42no—
185SD16×C43—42no—
186SD16×C43—42no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C42×C43—41no—
204C42×C43—41no—
205C42×C43C2×D411yescharacteristic
206C42×C43C2×D411yescharacteristic
207C42×C43C2×D411yescharacteristic
208C42×C43C2×D411yescharacteristic
209C22⋊Dic43—21no—
210C22⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43C2×D411yescharacteristic
214C4⋊Dic43C2×D411yescharacteristic
215C4⋊Dic43C2×D411yescharacteristic
216C4⋊Dic43C2×D411yescharacteristic
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220Dic43⋊C4—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877#4112yes—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—81no—
245C23×C43—81no—
246C23×C43C2×#4111yescharacteristic
247Q8×C43—22no—
248Q8×C43—22no—
249Q8×C43—41no—
250Q8×C43—41no—
251Q8×C43—41no—
252Q8×C43—41no—
253Q8×C43—41no—
254Q8×C43—41no—
255D4×C43—41no—
256D4×C43—41no—
257D4×C43—41no—
258D4×C43—41no—
259C2×C4×C43—22no—
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—41no—
267C2×C4×C43—41no—
268C2×C4×C43—81no—
269C2×C4×C43#12111yescharacteristic
270C2×C4×C43#12111yescharacteristic
271C2×C4×C43#12111yescharacteristic
272C2×C4×C43#12111yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43H(5,𝔽2)11yescharacteristic
278C2×C4×C432−1+411yescharacteristic
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283Dic86—42no—
284Dic86—81no—
285C8×C43—21no—
286C8×C43—21no—
287C8×C43—21no—
288C8×C43—21no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295#25317—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—161no—
302C22×C43—161no—
303C22×C43C2×#12111yescharacteristic
304C22×C43#52911yescharacteristic
305C22×C43#54211yescharacteristic
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43#54611yescharacteristic
314C4×C43#54811yescharacteristic
315C4×C43#54811yescharacteristic
316C4×C43#55011yescharacteristic
317Dic43—41no—
318Dic43—41no—
319Dic43—41no—
320Dic43—41no—
321#3140—431no—
322#3078—431no—
323C2×#464D4311yescharacteristic
324#2962—431no—
325#2064—431no—
326#2063—431no—
327#2047—431no—
328#2046—431no—
329#1979—431no—
330#1977—431no—
331#1967—431no—
332#1950—431no—
333#1931—431no—
334#1930—431no—
335C4×#101—431no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—161no—
339C2×C43#242611yescharacteristic
340C2×C43#306711yescharacteristic
341C2×C43#306911yescharacteristic
342C22×Q16C2×D4311yescharacteristic
343C22×SD16C2×D4311yescharacteristic
344#533—431no—
345C2×#124C2×D4311yescharacteristic
346C2×C4×Q8C2×D4311yescharacteristic
347#489—861no—
348#489—861no—
349#488—861no—
350#488—861no—
351#479—861no—
352#479—861no—
353#477—861no—
354#475—861no—
355#464—21no—
356#464—21no—
357#464—21no—
358#464—21no—
359#446—861no—
360#446—861no—
361#446—861no—
362C8×Q8—861no—
363C2×#108—431no—
364C2×#108—431no—
365#428—431no—
366#428—431no—
367#424—431no—
368#424—431no—
369#423—431no—
370C2×C4⋊C8C2×D4311yescharacteristic
371#419—431no—
372#419—431no—
373#419—431no—
374#419—431no—
375#418—431no—
376#418—431no—
377C2×#103C2×D4311yescharacteristic
378C2×#102C2×D4311yescharacteristic
379C2×#101—431no—
380C2×#101—431no—
381C2×#101—431no—
382C2×#101—431no—
383C2×#100—431no—
384C2×#100—431no—
385#405—431no—
386#405—431no—
387C4×M16—431no—
388C4×M16—431no—
389#343—431no—
390#343—431no—
391#341—431no—
392#341—431no—
393C43#2531711yescharacteristic, complemented, Sylow
394C22×Q8C22×D4311yescharacteristic
395C22×Q8C22×D4311yescharacteristic
396C22×D4C22×D4311yescharacteristic
397C2×Q16—22no—
398C2×Q16—21no—
399C2×Q16—21no—
400C2×Q16—41no—
401C2×SD16—22no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—41no—
405C2×M16—431no—
406C2×M16—431no—
407C2×M16—431no—
408C2×M16—431no—
409C2×M16—431no—
410C2×M16—431no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413C4⋊Q8—431no—
414C4⋊Q8—431no—
415#125—431no—
416#125—431no—
417#124—21no—
418#124—21no—
419#124—21no—
420#124—21no—
421C22⋊Q8—861no—
422C22⋊Q8—861no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—861no—
428C4×Q8—861no—
429#117—431no—
430#117—431no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—21no—
436C2×C42C22×D4311yescharacteristic
437#108—1721no—
438#108—1721no—
439#107—861no—
440#107—861no—
441#106—861no—
442#106—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8C22⋊D4311yescharacteristic
450C4⋊C8C22⋊D4311yescharacteristic
451C4⋊C8C22⋊D4311yescharacteristic
452C4⋊C8C22⋊D4311yescharacteristic
453#103—21no—
454#103—21no—
455#103—861no—
456#103—861no—
457#103—861no—
458#103—861no—
459#103—861no—
460#103—861no—
461#103—861no—
462#103—861no—
463#102—21no—
464#102—21no—
465#102—861no—
466#102—861no—
467#102—861no—
468#102—861no—
469#101—862no—
470#101—862no—
471#101—862no—
472#101—1721no—
473#100—862no—
474#100—1721no—
475#97—861no—
476#97—861no—
477#97—861no—
478#97—861no—
479C4×C8—861no—
480C4×C8—861no—
481C4×C8—861no—
482C4×C8—861no—
483C24—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—861no—
496C2×Q8—861no—
497C2×Q8#1062190012yes—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4#1062190011yescharacteristic
508C22×C4#1062190011yescharacteristic
509C22×C4C23×D4311yescharacteristic
510Q16—42no—
511Q16—42no—
512SD16—42no—
513SD16—42no—
514M16—432no—
515M16—861no—
516M16—861no—
517M16—861no—
518M16—861no—
519M16—861no—
520M16—861no—
521M16—861no—
522M16—861no—
523M16—861no—
524M16—861no—
525M16—861no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8C2×C22⋊D4311yescharacteristic
537C2×C8C2×C22⋊D4311yescharacteristic
538C2×C8C2×C22⋊D4311yescharacteristic
539C2×C8C2×C22⋊D4311yescharacteristic
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—431no—
545C4⋊C4—431no—
546C4⋊C4—431no—
547C4⋊C4—431no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—861no—
559C22⋊C4—861no—
560C42—41no—
561C42—41no—
562C42—861no—
563C42—861no—
564C42D4×D4311yescharacteristic
565C42D4×D4311yescharacteristic
566C42C2×C22⋊D4311yescharacteristic
567C42C2×C22⋊D4311yescharacteristic
568C23—41no—
569C23—41no—
570C23—41no—
571C23—81no—
572C23—81no—
573C23C2×#1062190011yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—3441no—
583Q8—1722no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—81no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4#1306329611yescharacteristic
603C2×C4#1306329611yescharacteristic
604C2×C4#1306329611yescharacteristic
605C2×C4#1306329611yescharacteristic
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4C22×C22⋊D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062190011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337211yescharacteristic
612C8—21no—
613C8—21no—
614C8—21no—
615C8—21no—
616C8—862no—
617C8—1721no—
618C8—1721no—
619C8—1721no—
620C8—1721no—
621C8—1721no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22C2×#1306329611yescharacteristic
630C22#1458343011yescharacteristic
631C22#1458351611yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—1721no—
640C4—1721no—
641C4—1721no—
642C4—1721no—
643C4#1458354311yescharacteristic
644C4#1458355511yescharacteristic
645C4#1458355611yescharacteristic
646C4#1458356711yescharacteristic
647C2—21no—
648C2—21no—
649C2—161no—
650C2#1913815711yescharacteristic
651C2#1914431111yescharacteristic
652C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#464C2
socleC22×C43C2×#121
prime radicalC22×D4×C43C23
hypercenterC2×#464D43
hypocenterC43#25317
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. #19144400C2semidirect
3. #19143538C2semidirect
4. #19135960C2semidirect
6. #19135860C2semidirect
8. #19135511C2semidirect
11. #19135371C2semidirect
13. #19135247C2semidirect
14. C4×#13063244C2semidirect
393. C43#25317semidirect

Maximal subgroups

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

subgroupindex
#191449812
#191444002
#191435382
#191359602
#191359532
#191358602
#191358532
#191355112
#191355002
#191354452
#191353712
#191352542
#191352472
C4×#130632442
C2×C43×#4642
#2531743