Finite Group Databasebeta

← #25104443

Subgroups — #25104443

Order 11008.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic
2#19143020C211yesmaximal, characteristic
3#19135540C211yesmaximal, characteristic, complemented
4#19135368C211yesmaximal, characteristic, complemented
5#19135191C211yesmaximal, characteristic, complemented
6#19135191C211yesmaximal, characteristic, complemented
7#19134869C211yesmaximal, characteristic
8#19134869C211yesmaximal, characteristic
9#19134612C211yesmaximal, characteristic
10#19134480C211yesmaximal, characteristic, complemented
11#19134475C211yesmaximal, characteristic, complemented
12#19134467C211yesmaximal, characteristic, complemented
13#19134441C211yesmaximal, characteristic
14#19134434C211yesmaximal, characteristic
15C43×#2961C211yesmaximal, characteristic, complemented
16C2×#13063331C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583203C411yescharacteristic, complemented
20#14583203C411yescharacteristic, complemented
21#14583196C411yescharacteristic, complemented
22#14583196C411yescharacteristic, complemented
23#14583191C411yescharacteristic, complemented
24#14583186C411yescharacteristic, complemented
25#14583181C411yescharacteristic, complemented
26#14583176C411yescharacteristic, complemented
27C2×#13063260C2211yescharacteristic
28C2×#13063260C2211yescharacteristic
29#14582935C2211yescharacteristic
30#14582935C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063251C2211yescharacteristic
33C2×#13063251C2211yescharacteristic
34#14582893C2211yescharacteristic
35#14582893C2211yescharacteristic
36#14582856—21no—
37#14582856—21no—
38#14582854C2211yescharacteristic
39#14582854C2211yescharacteristic
40C4×#10621877C2211yescharacteristic
41#14582851—21no—
42C2×#13063235C2211yescharacteristic
43#97×D43—21no—
44C2×C8×Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582663C2211yescharacteristic
47#14582663C2211yescharacteristic
48#14582660C2211yescharacteristic
49#14582660C2211yescharacteristic
50#14582658C2211yescharacteristic
51#14582658C2211yescharacteristic
52#14582658C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#446—21no—
58C43×#446—21no—
59C43×#446—21no—
60C43×#446—21no—
61C43×#424C2211yescharacteristic
62C43×#424C2211yescharacteristic
63C43×#423C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C2×#97×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063331—22no—
69#13063331—22no—
70#13063331—22no—
71#13063331Q814yescomplemented
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C4×Dic86C2×C411yescharacteristic
81C4×Dic86C2×C411yescharacteristic
82C4×D172C2×C411yescharacteristic
83C4×D172C2×C411yescharacteristic
84C4×C22⋊D43—21no—
85C4×C22⋊D43—21no—
86#13063284C2311yescharacteristic
87#13063282—21no—
88C2×C4⋊Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C42×D43—21no—
92#13063260—22no—
93#13063260—22no—
94#13063258C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101#13063256C2×C411yescharacteristic
102C4⋊(C43⋊C8)C2×C411yescharacteristic
103C4⋊(C43⋊C8)C2×C411yescharacteristic
104C4⋊(C43⋊C8)C2×C411yescharacteristic
105C4⋊(C43⋊C8)C2×C411yescharacteristic
106#13063251—22no—
107#13063251—22no—
108#13063248C2×C411yescharacteristic
109#13063248C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113#13063245C2×C411yescharacteristic
114#13063245C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116#13063236—21no—
117#13063235—21no—
118#13063235—21no—
119#13063235—22no—
120C4×C43⋊C8—21no—
121C8×Dic43—21no—
122C8×Dic43—21no—
123C8×Dic43—22no—
124C43⋊#95—21no—
125C2×M16×C43C2311yescharacteristic
126C2×M16×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4⋊Q8×C43C2×C411yescharacteristic
130C4⋊Q8×C43C2×C411yescharacteristic
131#125×C43C2×C411yescharacteristic
132#125×C43C2×C411yescharacteristic
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43—21no—
137#117×C43C2311yescharacteristic
138#117×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C4⋊C8×C43—21no—
141C4⋊C8×C43—21no—
142C4⋊C8×C43—21no—
143C4⋊C8×C43—21no—
144C4⋊C8×C43—21no—
145C4⋊C8×C43—21no—
146#97×C43—21no—
147#97×C43—21no—
148#97×C43D411yescharacteristic
149#97×C43D411yescharacteristic
150#97×C43D411yescharacteristic
151#97×C43D411yescharacteristic
152C4×C8×C43—21no—
153C4×C8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162#10621898—21no—
163#10621898—21no—
164#10621898C2×Q812yes—
165#10621898#4112yes—
166C2×D172C22×C411yescharacteristic
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×Dic86C22×C411yescharacteristic
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×Q812yes—
184C2×C8×C43#4112yes—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C22×C411yescharacteristic
192C4⋊C4×C43C22×C411yescharacteristic
193C4⋊C4×C43C22×C411yescharacteristic
194C4⋊C4×C43C22×C411yescharacteristic
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43C22×C411yescharacteristic
200C42×C43C22×C411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2×D411yescharacteristic
203C22⋊Dic43—21no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—21no—
206C4⋊Dic43—42no—
207C4⋊Dic43C22×C411yescharacteristic
208C4⋊Dic43C22×C411yescharacteristic
209Dic43⋊C4—21no—
210Dic43⋊C4—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877C2×Q812yes—
221#10621877#4112yes—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C22×C411yescharacteristic
229C2×C43⋊C8C22×C411yescharacteristic
230C2×C43⋊C8C22×C411yescharacteristic
231C2×C43⋊C8C22×C411yescharacteristic
232#10621872—24no—
233#10621872—24no—
234C8×D43—24no—
235C8×D43—24no—
236C23×C43C2×#4111yescharacteristic
237C22×D43—21no—
238Q8×C43—81no—
239Q8×C43—81no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C4×D411yescharacteristic
247C2×C4×C43C4×D411yescharacteristic
248C2×C4×C43C4×D411yescharacteristic
249C2×C4×C43C4×D411yescharacteristic
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×Q811yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C22⋊D43—22no—
257C22⋊D43—22no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267D172—21no—
268D172C4×Q812yes—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—81no—
272C4×D43—81no—
273Dic86—21no—
274Dic86C4×Q812yes—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—41no—
278C8×C43—41no—
279C8×C43C22⋊Q812yes—
280C8×C43C22⋊Q812yes—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—22no—
286C43⋊C8—22no—
287#21629—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43#52911yescharacteristic
292C22×C43#53311yescharacteristic
293C2×D43—22no—
294C2×D43—41no—
295C2×D43—41no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43C2×C4×Q811yescharacteristic
305C4×C43C4×#4111yescharacteristic
306C4×C43C2×C22⋊Q811yescharacteristic
307C4×C43#52511yescharacteristic
308Dic43—22no—
309Dic43—42no—
310Dic43—41no—
311Dic43—41no—
312Dic43—81no—
313#3076—431no—
314#2961D4311yescharacteristic, complemented
315#2875—431no—
316#1986—431no—
317#1950—431no—
318#1922—431no—
319#1922—431no—
320#1866—431no—
321#1866—431no—
322#1806—431no—
323#1773—431no—
324#1772—431no—
325#1771—431no—
326#1765—431no—
327#1764—431no—
328C2×C43—21no—
329C2×C43—21no—
330C2×C43C4×C22⋊Q811yescharacteristic
331C2×C43#295611yescharacteristic
332C2×C43#295711yescharacteristic
333D43—42no—
334C2×#131—431no—
335C2×#131—431no—
336#533C2×D4311yescharacteristic
337C4×#41—431no—
338#479—431no—
339#479—431no—
340#478—431no—
341#478—431no—
342#477—431no—
343#476—431no—
344#475—431no—
345#474—431no—
346#446—21no—
347#446—21no—
348#446—21no—
349#446—21no—
350C2×#108—431no—
351C2×#108—431no—
352#427—431no—
353#427—431no—
354#424C2×D4311yescharacteristic
355#424C2×D4311yescharacteristic
356#423C2×D4311yescharacteristic
357C2×C4⋊C8—431no—
358C2×#104—431no—
359C2×#104—431no—
360#416—431no—
361#416—431no—
362#405—431no—
363#405—431no—
364#405—861no—
365#405—861no—
366#405C2×D4311yescharacteristic
367#405C2×D4311yescharacteristic
368C4×M16—431no—
369C4×M16—861no—
370C2×#97—431no—
371C2×#97—861no—
372C2×#97C2×D4311yescharacteristic
373C2×C4×C8—431no—
374C4×C4⋊C4—431no—
375#341—431no—
376#341—431no—
377#339—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339—431no—
382#339—431no—
383#336—431no—
384#336—431no—
385C43#2162911yescharacteristic, complemented, Sylow
386C2×#41—431no—
387#131—434no—
388#131—862no—
389#131—862no—
390#131—862no—
391C2×M16—431no—
392C2×M16—431no—
393C2×M16—861no—
394C2×M16—861no—
395C2×M16C22×D4311yescharacteristic
396C2×M16C22×D4311yescharacteristic
397C22×C8—431no—
398C22×C8—431no—
399C22×C8—861no—
400C22×C8—861no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C4⋊Q8C4×D4311yescharacteristic
404C4⋊Q8C4×D4311yescharacteristic
405#125C4×D4311yescharacteristic
406#125C4×D4311yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—431no—
412C4×Q8—431no—
413C4×D4—431no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4—861no—
417#117—431no—
418#117—861no—
419#117C22×D4311yescharacteristic
420#117C22×D4311yescharacteristic
421C2×C4⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—861no—
425C2×C42C22×D4311yescharacteristic
426#108—862no—
427#108—862no—
428#107—431no—
429#107—431no—
430#107—431no—
431#107—431no—
432#106—431no—
433#106—431no—
434#106—431no—
435#106—431no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—431no—
446#104—862no—
447#104—862no—
448#103—431no—
449#103—431no—
450#103—431no—
451#103—431no—
452#102—431no—
453#102—431no—
454#102—431no—
455#102—431no—
456#97—21no—
457#97—21no—
458#97—862no—
459#97—861no—
460#97—861no—
461#97—861no—
462#97C22⋊D4311yescharacteristic
463#97C22⋊D4311yescharacteristic
464#97C22⋊D4311yescharacteristic
465#97C22⋊D4311yescharacteristic
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—862no—
469C4×C8—861no—
470C4×C8—861no—
471C4×C8—861no—
472#95—861no—
473#41—432no—
474#41—432no—
475#41—861no—
476#41—861no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—431no—
480C2×D4—431no—
481C2×D4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4#1062189811yescharacteristic
488C22×C4#1062189811yescharacteristic
489C22×C4C23×D4311yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—432no—
495M16—432no—
496M16—864no—
497M16—861no—
498M16—861no—
499M16—864no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—431no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—864no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—864no—
516C2×C8Q8×D4312yes—
517C2×C8#1062190212yes—
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—431no—
529C4⋊C4—431no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—1722no—
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C4⋊C4C2×C4×D4311yescharacteristic
536C4⋊C4C2×C4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—21no—
543C42—21no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42C2×C4×D4311yescharacteristic
552C42C2×C4×D4311yescharacteristic
553C42C2×C22⋊D4311yescharacteristic
554C42C2×C22⋊D4311yescharacteristic
555C23—861no—
556C23C2×#1062189811yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—432no—
560Q8—861no—
561D4—432no—
562D4—862no—
563D4—862no—
564D4—861no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—3441no—
578C2×C4—3441no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4C4×C22⋊D4311yescharacteristic
585C2×C4C4×C22⋊D4311yescharacteristic
586C2×C4C4×C22⋊D4311yescharacteristic
587C2×C4C4×C22⋊D4311yescharacteristic
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C22×C22⋊D4311yescharacteristic
590C2×C4C2×Q8×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4C2×#1062190211yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—862no—
603C8—862no—
604C8#1306330112yes—
605C8#1306330112yes—
606C22—21no—
607C22—21no—
608C22—862no—
609C22—1721no—
610C22—1721no—
611C22C2×C4×C22⋊D4311yescharacteristic
612C22#1458343611yescharacteristic
613C22#1458345311yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—862no—
623C4—3441no—
624C4—1722no—
625C4—1721no—
626C4—1721no—
627C4C4×Q8×D4311yescharacteristic
628C4C4×#1062190211yescharacteristic
629C4C2×#1306330111yescharacteristic
630C4#1458340611yescharacteristic
631C2—21no—
632C2—21no—
633C2—1722no—
634C2C4×#1306330111yescharacteristic
635C2#1914350211yescharacteristic
636C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2961C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#2961D43
hypocenterC43#21629
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #19135540C2semidirect
4. #19135368C2semidirect
5. #19135191C2semidirect
6. #19135191C2semidirect
10. #19134480C2semidirect
11. #19134475C2semidirect
12. #19134467C2semidirect
15. C43×#2961C2semidirect
19. #14583203C4semidirect
20. #14583203C4semidirect
21. #14583196C4semidirect
22. #14583196C4semidirect
23. #14583191C4semidirect
24. #14583186C4semidirect
25. #14583181C4semidirect
26. #14583176C4semidirect
71. #13063331Q8semidirect
314. #2961D43semidirect
385. C43#21629semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191430202
#191355402
#191353682
#191351912
#191348692
#191346122
#191344802
#191344752
#191344672
#191344412
#191344342
C43×#29612
#2162943