Finite Group Databasebeta

← #25146431

Subgroups — #25146431

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#19144396C211yesmaximal, characteristic, complemented
2C2×#14583118C211yesmaximal, characteristic
3#19143544C211yesmaximal, characteristic, complemented
4#19135962C211yesmaximal, characteristic, complemented
5#19135955C211yesmaximal, characteristic
6#19135862C211yesmaximal, characteristic, complemented
7#19135857C211yesmaximal, characteristic
8#19135509C211yesmaximal, characteristic, complemented
9#19135501C211yesmaximal, characteristic
10#19135445C211yesmaximal, characteristic
11#19135370C211yesmaximal, characteristic, complemented
12#19135260C211yesmaximal, characteristic
13#19135253C211yesmaximal, characteristic, complemented
14C4×#13063243C211yesmaximal, characteristic, complemented
15C43×#3140C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583203—21no—
20#14583203—21no—
21#14583191—21no—
22#14583181—21no—
23#14583118—21no—
24#14583118—21no—
25#14583118—21no—
26#14583118—21no—
27#14583030—21no—
28#14583030—21no—
29#14583030—21no—
30Q8×C43⋊C8—21no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582942C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582926C2211yescharacteristic
36#14582926C2211yescharacteristic
37#14582923C2211yescharacteristic
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39#14582907C2211yescharacteristic
40#14582907C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063244C2211yescharacteristic
44C2×#13063244C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48C2×#13063242C2211yescharacteristic
49#14582855C2211yescharacteristic
50#14582855C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C2×#124×C43C2211yescharacteristic
58C43×#489—21no—
59C43×#489—21no—
60C43×#488—21no—
61C43×#488—21no—
62C43×#419C2211yescharacteristic
63C43×#419C2211yescharacteristic
64C43×#418C2211yescharacteristic
65C43×#418C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68C2×#10621885—22no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—41no—
72C2×#10621883—22no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75C2×#10621883—41no—
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×C4×Dic43—21no—
89#13063260—41no—
90#13063260—41no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)D411yescharacteristic
102C4⋊(C43⋊C8)D411yescharacteristic
103C4⋊(C43⋊C8)D411yescharacteristic
104C4⋊(C43⋊C8)D411yescharacteristic
105#13063249—21no—
106#13063249—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248—21no—
110#13063248—21no—
111#13063246—21no—
112#13063246—21no—
113#13063244—22no—
114#13063244—41no—
115#13063243—22no—
116#13063243—22no—
117#13063242—22no—
118#13063242—41no—
119#13063236—21no—
120#13063236—21no—
121#13063236—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8—21no—
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C4⋊Q8×C43D411yescharacteristic
130C4⋊Q8×C43D411yescharacteristic
131#125×C43D411yescharacteristic
132#125×C43D411yescharacteristic
133#124×C43—21no—
134#124×C43—21no—
135#124×C43—21no—
136#124×C43—21no—
137C22⋊Q8×C43—21no—
138C22⋊Q8×C43—21no—
139C4×Q8×C43—21no—
140C4×Q8×C43—21no—
141#117×C43C2311yescharacteristic
142#117×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C42×C43C2311yescharacteristic
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#103×C43—21no—
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#97×C43—21no—
155C4×C8×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×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43#4111yescharacteristic
173C22×C4×C43#4111yescharacteristic
174C22×C4×C43C2411yescharacteristic
175C22×Dic43—21no—
176C22×Dic43—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86#4112yes—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—21no—
186M16×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43C2×D411yescharacteristic
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C42×C43C2×D411yescharacteristic
211#10621885—42no—
212#10621885—42no—
213#10621883—42no—
214#10621883—42no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217Dic43⋊C4—41no—
218Dic43⋊C4—41no—
219C4×Dic43—41no—
220C4×Dic43—41no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877#4112yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8C2×D411yescharacteristic
238C2×C43⋊C8C2×D411yescharacteristic
239C2×C43⋊C8C2×D411yescharacteristic
240C2×C43⋊C8C2×D411yescharacteristic
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—81no—
245C23×C43—81no—
246C23×C43C2×#4111yescharacteristic
247Q8×C43—42no—
248Q8×C43—41no—
249Q8×C43—41no—
250Q8×C43—41no—
251Q8×C43—41no—
252Q8×C43—81no—
253D4×C43—41no—
254D4×C43—41no—
255D4×C43—41no—
256D4×C43—41no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43#12111yescharacteristic
267C2×C4×C43#12111yescharacteristic
268C2×C4×C43#12111yescharacteristic
269C2×C4×C43#12111yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C2×C4×C432−1+411yescharacteristic
276C2×Dic43—22no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—81no—
281Dic86—22no—
282Dic86—22no—
283Dic86—41no—
284Dic86—41no—
285C8×C43—41no—
286C8×C43—41no—
287C43⋊C8—21no—
288C43⋊C8—21no—
289C43⋊C8—21no—
290C43⋊C8—21no—
291C43⋊C8—22no—
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—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43#54611yescharacteristic
316C4×C43#54811yescharacteristic
317C4×C43#54811yescharacteristic
318C4×C43#55011yescharacteristic
319Dic43—42no—
320Dic43—81no—
321#3140D4311yescharacteristic
322#3078—431no—
323C2×#464—431no—
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×Q16—431no—
343C22×SD16—431no—
344#533C2×D4311yescharacteristic
345C2×#124C2×D4311yescharacteristic
346C2×C4×Q8—431no—
347#489—21no—
348#489—21no—
349#488—21no—
350#488—21no—
351#479—861no—
352#479—861no—
353#477—861no—
354#475—861no—
355#464—861no—
356#464—861no—
357#464—861no—
358#464—861no—
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⋊C8—431no—
371#419—431no—
372#419—431no—
373#419C2×D4311yescharacteristic
374#419C2×D4311yescharacteristic
375#418C2×D4311yescharacteristic
376#418C2×D4311yescharacteristic
377C2×#103—431no—
378C2×#102—431no—
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×M16C2×D4311yescharacteristic
389#343—431no—
390#343—431no—
391#341—431no—
392#341—431no—
393C43#2531711yescharacteristic, complemented, Sylow
394C22×Q8—431no—
395C22×Q8C22×D4311yescharacteristic
396C22×D4C22×D4311yescharacteristic
397C2×Q16—861no—
398C2×Q16—861no—
399C2×Q16—862no—
400C2×Q16—1721no—
401C2×SD16—861no—
402C2×SD16—861no—
403C2×SD16—862no—
404C2×SD16—1721no—
405C2×M16—431no—
406C2×M16—431no—
407C2×M16—431no—
408C2×M16—431no—
409C2×M16C22×D4311yescharacteristic
410C2×M16C22×D4311yescharacteristic
411C22×C8—431no—
412C22×C8—431no—
413C4⋊Q8C22⋊D4311yescharacteristic
414C4⋊Q8C22⋊D4311yescharacteristic
415#125C22⋊D4311yescharacteristic
416#125C22⋊D4311yescharacteristic
417#124—21no—
418#124—21no—
419#124—21no—
420#124—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—861no—
426C4×Q8—861no—
427C4×Q8—861no—
428C4×Q8—861no—
429#117C22×D4311yescharacteristic
430#117C22×D4311yescharacteristic
431C2×C4⋊C4—431no—
432C2×C4⋊C4—861no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—861no—
436C2×C42C22×D4311yescharacteristic
437#108—1721no—
438#108—1721no—
439#107—861no—
440#107—861no—
441#106—861no—
442#106—861no—
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—431no—
446C4⋊C8—431no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8—861no—
452C4⋊C8—861no—
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
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—21no—
466#102—21no—
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—21no—
476#97—861no—
477#97—861no—
478#97—861no—
479C4×C8—21no—
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—432no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C22×C4—21no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4#1062190011yescharacteristic
508C22×C4#1062190011yescharacteristic
509C22×C4C23×D4311yescharacteristic
510Q16—1722no—
511Q16—1722no—
512SD16—1722no—
513SD16—1722no—
514M16—21no—
515M16—21no—
516M16—21no—
517M16—21no—
518M16—432no—
519M16—861no—
520M16—861no—
521M16—861no—
522M16—861no—
523M16—861no—
524M16—861no—
525M16—861no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—431no—
529C2×C8—431no—
530C2×C8—431no—
531C2×C8—431no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—1721no—
549C4⋊C4—1721no—
550C4⋊C4C2×C22⋊D4311yescharacteristic
551C4⋊C4C2×C22⋊D4311yescharacteristic
552C4⋊C4C2×C22⋊D4311yescharacteristic
553C4⋊C4C2×C22⋊D4311yescharacteristic
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C42—21no—
561C42—21no—
562C42—1721no—
563C42—1721no—
564C42D4×D4311yescharacteristic
565C42D4×D4311yescharacteristic
566C42C2×C22⋊D4311yescharacteristic
567C42C2×C22⋊D4311yescharacteristic
568C23—41no—
569C23—41no—
570C23—41no—
571C23—81no—
572C23—81no—
573C23C2×#1062190011yescharacteristic
574Q8—42no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—81no—
580Q8—862no—
581Q8—862no—
582Q8—1721no—
583Q8—1721no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—862no—
598C2×C4—3441no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4#1306329711yescharacteristic
603C2×C4#1306329711yescharacteristic
604C2×C4#1306329711yescharacteristic
605C2×C4#1306329711yescharacteristic
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4C22×C22⋊D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#1306337111yescharacteristic
611C2×C4#1306337211yescharacteristic
612C8—41no—
613C8—41no—
614C8—862no—
615C8—861no—
616C8—861no—
617C8—861no—
618C8—861no—
619C8—1721no—
620C8—1721no—
621C8—1721no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22C2×#1306329711yescharacteristic
630C22#1458342811yescharacteristic
631C22#1458351811yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—3441no—
642C4—1722no—
643C4#1458354211yescharacteristic
644C4#1458355611yescharacteristic
645C4#1458355711yescharacteristic
646C4#1458356811yescharacteristic
647C2—21no—
648C2—21no—
649C2—161no—
650C2#1913816411yescharacteristic
651C2#1914431211yescharacteristic
652C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3140C2
socleC22×C43C2×#121
prime radicalC22×D4×C43C23
hypercenter#3140D43
hypocenterC43#25317
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3140

Complements

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

NH ≅ G/Ntype
1. #19144396C2semidirect
3. #19143544C2semidirect
4. #19135962C2semidirect
6. #19135862C2semidirect
8. #19135509C2semidirect
11. #19135370C2semidirect
13. #19135253C2semidirect
14. C4×#13063243C2semidirect
393. C43#25317semidirect

Maximal subgroups

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

subgroupindex
#191443962
C2×#145831182
#191435442
#191359622
#191359552
#191358622
#191358572
#191355092
#191355012
#191354452
#191353702
#191352602
#191352532
C4×#130632432
C43×#31402
#2531743