Finite Group Databasebeta

← #25118682

Subgroups — #25118682

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic
2#19143160C211yesmaximal, characteristic
3#19135577C211yesmaximal, characteristic, complemented
4#19135370C211yesmaximal, characteristic, complemented
5#19135345C211yesmaximal, characteristic, complemented
6#19135340C211yesmaximal, characteristic, complemented
7#19135194C211yesmaximal, characteristic, complemented
8#19135194C211yesmaximal, characteristic, complemented
9#19134869C211yesmaximal, characteristic
10#19134869C211yesmaximal, characteristic
11#19134454C211yesmaximal, characteristic, complemented
12#19134441C211yesmaximal, characteristic
13#19134434C211yesmaximal, characteristic
14#19134408C211yesmaximal, characteristic
15C43×#2962C211yesmaximal, 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
31#14582925C2211yescharacteristic
32#14582925C2211yescharacteristic
33#14582924—21no—
34#14582924—21no—
35#14582923C2211yescharacteristic
36#14582921—21no—
37C2×C4⋊(C43⋊C8)C2211yescharacteristic
38C4⋊C8×D43—21no—
39C2×#13063251C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582893C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582745C2211yescharacteristic
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—
60C8×Q8×C43—21no—
61C43×#424C2211yescharacteristic
62C43×#424C2211yescharacteristic
63C2×C4⋊C8×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063331—22no—
69#13063331—22no—
70#13063331—41no—
71#13063331—41no—
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×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C42×D43—21no—
91#13063260—41no—
92#13063260—41no—
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2×C411yescharacteristic
104C4⋊(C43⋊C8)C2×C411yescharacteristic
105C4⋊(C43⋊C8)C2×C411yescharacteristic
106C4⋊(C43⋊C8)C2×C411yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063251—22no—
112#13063251Q814yescomplemented
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115#13063248C2×C411yescharacteristic
116#13063248C2×C411yescharacteristic
117#13063245C2×C411yescharacteristic
118#13063245C2×C411yescharacteristic
119#13063245C2×C411yescharacteristic
120#13063245C2×C411yescharacteristic
121#13063235—41no—
122C8×Dic43—41no—
123C43⋊#95—21no—
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×C43D411yescharacteristic
145C4⋊C8×C43D411yescharacteristic
146C4⋊C8×C43D411yescharacteristic
147C4⋊C8×C43D411yescharacteristic
148#97×C43—21no—
149#97×C43—21no—
150#97×C43—21no—
151C4×C8×C43—21no—
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×C43C2×Q812yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
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⋊Dic43C22×C411yescharacteristic
207C4⋊Dic43C22×C411yescharacteristic
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43C2×Q812yes—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C22×C411yescharacteristic
228C2×C43⋊C8C22×C411yescharacteristic
229C2×C43⋊C8C22×C411yescharacteristic
230C2×C43⋊C8C22×C411yescharacteristic
231#10621872—42no—
232#10621872—42no—
233C8×D43—42no—
234C8×D43—42no—
235C23×C43C2×#4111yescharacteristic
236C22×D43—21no—
237Q8×C43—42no—
238Q8×C43—81no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C4×D411yescharacteristic
246C2×C4×C43C4×D411yescharacteristic
247C2×C4×C43C4×D411yescharacteristic
248C2×C4×C43C4×D411yescharacteristic
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×Q811yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C22⋊D43—22no—
256C22⋊D43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266D172—21no—
267D172C4×Q812yes—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—42no—
271C4×D43—81no—
272Dic86—21no—
273Dic86C4×Q812yes—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—22no—
279C8×C43—41no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#22984—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43C2×C4×D411yescharacteristic
290C22×C43#55211yescharacteristic
291C22×C43#55411yescharacteristic
292C2×D43—22no—
293C2×D43—41no—
294C2×D43—41no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43C2×C4×Q811yescharacteristic
304C4×C43#52011yescharacteristic
305C4×C43#54611yescharacteristic
306C4×C43D4×Q811yescharacteristic
307Dic43—22no—
308Dic43—42no—
309Dic43—41no—
310Dic43—41no—
311Dic43—81no—
312#3076—431no—
313#2962D4311yescharacteristic, complemented
314#2906—431no—
315#1995—431no—
316#1950—431no—
317#1946—431no—
318#1945—431no—
319#1922—431no—
320#1922—431no—
321#1866—431no—
322#1866—431no—
323#1768—431no—
324#1765—431no—
325#1764—431no—
326#1759—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43#236011yescharacteristic
330C2×C43#295511yescharacteristic
331C2×C43#295711yescharacteristic
332D43—42no—
333C2×#131—431no—
334C2×#131—431no—
335#533C2×D4311yescharacteristic
336C4×#41—431no—
337#479—431no—
338#479—431no—
339#478—431no—
340#478—431no—
341#477—431no—
342#476—431no—
343#475—431no—
344#474—431no—
345#446—21no—
346#446—21no—
347#446—21no—
348C8×Q8—21no—
349C2×#108—431no—
350C2×#108—431no—
351#427—431no—
352#427—431no—
353#424—431no—
354#424—431no—
355#424—861no—
356#424—861no—
357#424C2×D4311yescharacteristic
358#424C2×D4311yescharacteristic
359#423—431no—
360#423—861no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—861no—
363C2×C4⋊C8C2×D4311yescharacteristic
364C2×#104—431no—
365C2×#104—431no—
366#416—431no—
367#416—431no—
368#405C2×D4311yescharacteristic
369#405C2×D4311yescharacteristic
370C4×M16C2×D4311yescharacteristic
371C2×#97—431no—
372C2×C4×C8—431no—
373#376—431no—
374#341—431no—
375#341—431no—
376#339—431no—
377#339—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339—431no—
382#336—431no—
383#336—431no—
384C43#2298411yescharacteristic, complemented, Sylow
385C2×#41—431no—
386#131—862no—
387#131—862no—
388#131—1721no—
389#131—1721no—
390C2×M16—431no—
391C2×M16—431no—
392C2×M16—861no—
393C2×M16—861no—
394C2×M16C22×D4311yescharacteristic
395C2×M16C22×D4311yescharacteristic
396C22×C8—431no—
397C22×C8—431no—
398C22×C8—861no—
399C22×C8—861no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4⋊Q8C4×D4311yescharacteristic
403C4⋊Q8C4×D4311yescharacteristic
404#125C4×D4311yescharacteristic
405#125C4×D4311yescharacteristic
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—431no—
411C4×Q8—431no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416#117—431no—
417#117—861no—
418#117C22×D4311yescharacteristic
419#117C22×D4311yescharacteristic
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#108—1721no—
425#108—1721no—
426#107—431no—
427#107—431no—
428#107—431no—
429#107—431no—
430#106—431no—
431#106—431no—
432#106—431no—
433#106—431no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8C22⋊D4311yescharacteristic
449C4⋊C8C22⋊D4311yescharacteristic
450C4⋊C8C22⋊D4311yescharacteristic
451C4⋊C8C22⋊D4311yescharacteristic
452#104—434no—
453#104—862no—
454#103—431no—
455#103—431no—
456#103—431no—
457#103—431no—
458#102—431no—
459#102—431no—
460#102—431no—
461#102—431no—
462#97—21no—
463#97—21no—
464#97—21no—
465#97—1721no—
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—1721no—
470#95—861no—
471#95—861no—
472#41—432no—
473#41—432no—
474#41—861no—
475#41—861no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—431no—
479C2×D4—431no—
480C2×D4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4#1062189811yescharacteristic
487C22×C4#1062189811yescharacteristic
488C22×C4C23×D4311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496M16—1722no—
497M16—1722no—
498M16Q8×D4312yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—1722no—
516C2×C8—1722no—
517C2×C8C2×C22⋊D4311yescharacteristic
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C2×C8C2×C22⋊D4311yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—431no—
528C4⋊C4—431no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4C2×C4×D4311yescharacteristic
532C4⋊C4C2×C4×D4311yescharacteristic
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C42—21no—
541C42—21no—
542C42—432no—
543C42—861no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42C2×C4×D4311yescharacteristic
550C42C2×C4×D4311yescharacteristic
551C42C2×C22⋊D4311yescharacteristic
552C42C2×C22⋊D4311yescharacteristic
553C23—861no—
554C23C2×#1062189811yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—432no—
558Q8—861no—
559D4—432no—
560D4—862no—
561D4—862no—
562D4—861no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—861no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—3441no—
576C2×C4—1722no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4C4×C22⋊D4311yescharacteristic
583C2×C4C4×C22⋊D4311yescharacteristic
584C2×C4C4×C22⋊D4311yescharacteristic
585C2×C4C4×C22⋊D4311yescharacteristic
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C22×C22⋊D4311yescharacteristic
588C2×C4C2×Q8×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#1306337111yescharacteristic
591C2×C4#1306337311yescharacteristic
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—1721no—
603C8—1721no—
604C22—21no—
605C22—21no—
606C22—862no—
607C22—1721no—
608C22—1721no—
609C22C2×C4×C22⋊D4311yescharacteristic
610C22#1458359011yescharacteristic
611C22#1458360911yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—862no—
621C4—3441no—
622C4—1722no—
623C4—1721no—
624C4—1721no—
625C4C4×Q8×D4311yescharacteristic
626C4#1458338111yescharacteristic
627C4#1458353711yescharacteristic
628C4Q8×C22⋊D4311yescharacteristic
629C2—21no—
630C2—21no—
631C2—1722no—
632C2#1913759611yescharacteristic
633C2#1914349611yescharacteristic
634C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2962C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#2962D43
hypocenterC43#22984
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #19135577C2semidirect
4. #19135370C2semidirect
5. #19135345C2semidirect
6. #19135340C2semidirect
7. #19135194C2semidirect
8. #19135194C2semidirect
11. #19134454C2semidirect
15. C43×#2962C2semidirect
19. #14583203C4semidirect
20. #14583203C4semidirect
21. #14583196C4semidirect
22. #14583196C4semidirect
23. #14583191C4semidirect
24. #14583186C4semidirect
25. #14583181C4semidirect
26. #14583176C4semidirect
112. #13063251Q8semidirect
313. #2962D43semidirect
384. C43#22984semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191431602
#191355772
#191353702
#191353452
#191353402
#191351942
#191348692
#191344542
#191344412
#191344342
#191344082
C43×#29622
#2298443