Finite Group Databasebeta

← #25104449

Subgroups — #25104449

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#19144383C211yesmaximal, characteristic
2#19143535C211yesmaximal, characteristic, complemented
3#19135539C211yesmaximal, characteristic, complemented
4#19135370C211yesmaximal, characteristic, complemented
5#19135194C211yesmaximal, characteristic, complemented
6#19135194C211yesmaximal, characteristic, complemented
7#19134870C211yesmaximal, characteristic
8#19134870C211yesmaximal, characteristic
9#19134615C211yesmaximal, characteristic
10#19134480C211yesmaximal, characteristic, complemented
11#19134475C211yesmaximal, characteristic, complemented
12#19134467C211yesmaximal, characteristic, complemented
13#19134437C211yesmaximal, characteristic
14#19134430C211yesmaximal, characteristic
15C43×#2875C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583206C411yescharacteristic, complemented
18#14583206C411yescharacteristic, complemented
19#14583199C411yescharacteristic, complemented
20#14583199C411yescharacteristic, complemented
21#14583194C411yescharacteristic, complemented
22#14583189C411yescharacteristic, complemented
23#14583184C411yescharacteristic, complemented
24#14583179C411yescharacteristic, complemented
25#14583027—21no—
26#14583027—21no—
27#14583027—21no—
28#14583027—21no—
29C2×#13063260C2211yescharacteristic
30C2×#13063260C2211yescharacteristic
31#14582935C2211yescharacteristic
32#14582935C2211yescharacteristic
33#14582925C2211yescharacteristic
34#14582925C2211yescharacteristic
35#14582923C2211yescharacteristic
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39#14582895C2211yescharacteristic
40#14582895C2211yescharacteristic
41#14582854C2211yescharacteristic
42#14582854C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582663C2211yescharacteristic
47#14582663C2211yescharacteristic
48#14582660C2211yescharacteristic
49#14582660C2211yescharacteristic
50#14582660C2211yescharacteristic
51#14582660C2211yescharacteristic
52#14582658C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#131×C43C2211yescharacteristic
57C2×#131×C43C2211yescharacteristic
58C4×#41×C43C2211yescharacteristic
59C43×#405—21no—
60C43×#405—21no—
61C43×#405C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C4×M16×C43—21no—
64C4×M16×C43C2211yescharacteristic
65C2×#97×C43—21no—
66C2×#97×C43C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063325C2×C411yescharacteristic
72#13063325C2×C411yescharacteristic
73#13063317C2×C411yescharacteristic
74#13063317C2×C411yescharacteristic
75#13063304—21no—
76#13063304—21no—
77C4×Dic86—21no—
78C4×Dic86—21no—
79#13063284C2311yescharacteristic
80#13063284C2311yescharacteristic
81C2×C4⋊Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063260—22no—
85#13063260—22no—
86#13063258C2×C411yescharacteristic
87#13063258C2×C411yescharacteristic
88#13063258C2×C411yescharacteristic
89#13063258C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91#13063256C2×C411yescharacteristic
92#13063256C2×C411yescharacteristic
93#13063256C2×C411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2×C411yescharacteristic
97C4⋊(C43⋊C8)C2×C411yescharacteristic
98C4⋊(C43⋊C8)C2×C411yescharacteristic
99C4⋊(C43⋊C8)C2×C411yescharacteristic
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104#13063252—22no—
105#13063252—22no—
106#13063249C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063235—21no—
115#13063235—21no—
116#13063235—22no—
117C8×Dic43—21no—
118C8×Dic43—21no—
119C8×Dic43—22no—
120C43⋊#95—21no—
121C2×#41×C43C2311yescharacteristic
122#131×C43—22no—
123#131×C43—22no—
124#131×C43—22no—
125#131×C43Q814yescomplemented
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43C2311yescharacteristic
129C2×M16×C43C2311yescharacteristic
130C22×C8×C43—21no—
131C22×C8×C43—21no—
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C4×Q8×C43C2×C411yescharacteristic
135C4×Q8×C43C2×C411yescharacteristic
136C4×D4×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43C2×C411yescharacteristic
139C4×D4×C43C2×C411yescharacteristic
140#117×C43—21no—
141#117×C43C2311yescharacteristic
142C2×C42×C43—21no—
143C2×C42×C43C2311yescharacteristic
144#97×C43—21no—
145#97×C43—21no—
146#97×C43—21no—
147#97×C43D411yescharacteristic
148#97×C43D411yescharacteristic
149#97×C43D411yescharacteristic
150#97×C43D411yescharacteristic
151C4×C8×C43—21no—
152C4×C8×C43—21no—
153C4×C8×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43C2×Q812yes—
157#41×C43#4112yes—
158C2×Q8×C43C22×C411yescharacteristic
159C2×D4×C43—21no—
160C2×D4×C43C22×C411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43#4111yescharacteristic
165C22×C4×C43#4111yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C22×Dic43—21no—
168C22×Dic43—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171M16×C43—24no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43—24no—
175M16×C43C2×Q812yes—
176M16×C43#4112yes—
177C2×C8×C43—24no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—24no—
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×Q812yes—
188C2×C8×C43#4112yes—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C22×C411yescharacteristic
192C4⋊C4×C43C22×C411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43C22×C411yescharacteristic
200C42×C43C22×C411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2×D411yescharacteristic
203C22⋊Dic43—21no—
204C22⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—42no—
208C4⋊Dic43C22×C411yescharacteristic
209C4⋊Dic43C22×C411yescharacteristic
210C4⋊Dic43C22×C411yescharacteristic
211C4⋊Dic43C22×C411yescharacteristic
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8C22×C411yescharacteristic
233C2×C43⋊C8C22×C411yescharacteristic
234C2×C43⋊C8C22×C411yescharacteristic
235C2×C43⋊C8C22×C411yescharacteristic
236C23×C43—21no—
237C23×C43C2×#4111yescharacteristic
238Q8×C43—21no—
239Q8×C43C4×Q812yes—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—21no—
243D4×C43C4×Q812yes—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—81no—
252C2×C4×C43—81no—
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43C4×D411yescharacteristic
256C2×C4×C43C4×D411yescharacteristic
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×Q811yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273Dic86—81no—
274Dic86—81no—
275C8×C43—22no—
276C8×C43—21no—
277C8×C43—22no—
278C8×C43—21no—
279C8×C43C22⋊Q812yes—
280C8×C43C22⋊Q812yes—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#21629—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43#52911yescharacteristic
295C22×C43#53311yescharacteristic
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—22no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43C2×C4×Q811yescharacteristic
304C4×C43C4×#4111yescharacteristic
305C4×C43C2×C22⋊Q811yescharacteristic
306C4×C43#52511yescharacteristic
307Dic43—42no—
308Dic43—41no—
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312Dic43—81no—
313#3076—431no—
314#2961—431no—
315#2875D4311yescharacteristic
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×C43—42no—
331C2×C43C4×C22⋊Q811yescharacteristic
332C2×C43#295611yescharacteristic
333C2×C43#295711yescharacteristic
334C2×#131C2×D4311yescharacteristic
335C2×#131C2×D4311yescharacteristic
336#533—431no—
337C4×#41C2×D4311yescharacteristic
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—861no—
347#446—861no—
348#446—861no—
349#446—861no—
350C2×#108—431no—
351C2×#108—431no—
352#427—431no—
353#427—431no—
354#424—431no—
355#424—431no—
356#423—431no—
357C2×C4⋊C8—431no—
358C2×#104—431no—
359C2×#104—431no—
360#416—431no—
361#416—431no—
362#405—21no—
363#405—21no—
364#405—431no—
365#405—431no—
366#405C2×D4311yescharacteristic
367#405C2×D4311yescharacteristic
368C4×M16—21no—
369C4×M16C2×D4311yescharacteristic
370C2×#97—21no—
371C2×#97—431no—
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×#41C22×D4311yescharacteristic
387#131—22no—
388#131—22no—
389#131—22no—
390#131Dic8614yescomplemented
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16C22×D4311yescharacteristic
396C2×M16C22×D4311yescharacteristic
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C4⋊Q8—431no—
404C4⋊Q8—431no—
405#125—431no—
406#125—431no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C4×Q8—861no—
410C4×Q8—861no—
411C4×Q8C4×D4311yescharacteristic
412C4×Q8C4×D4311yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C4×D4311yescharacteristic
416C4×D4C4×D4311yescharacteristic
417#117—21no—
418#117—431no—
419#117—431no—
420#117C22×D4311yescharacteristic
421C2×C4⋊C4—861no—
422C2×C42—21no—
423C2×C42—431no—
424C2×C42—431no—
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—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—861no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
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—21no—
459#97—862no—
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—21no—
469C4×C8—862no—
470C4×C8—861no—
471C4×C8—861no—
472#95—861no—
473#41—21no—
474#41—21no—
475#41C2×Dic8612yes—
476#41#1062189812yes—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8C2×C4×D4311yescharacteristic
480C2×D4—21no—
481C2×D4C2×C4×D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4#1062189811yescharacteristic
488C22×C4#1062189811yescharacteristic
489C22×C4C23×D4311yescharacteristic
490M16—24no—
491M16—21no—
492M16—21no—
493M16—24no—
494M16—861no—
495M16—861no—
496M16—861no—
497M16—861no—
498M16C2×Dic8612yes—
499M16#1062189812yes—
500C2×C8—24no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—24no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—431no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8C2×Dic8612yes—
517C2×C8#1062189812yes—
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—431no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4C2×C4×D4311yescharacteristic
536C4⋊C4C2×C4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—21no—
543C42—21no—
544C42—21no—
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—21no—
556C23C2×#1062189811yescharacteristic
557Q8—21no—
558Q8—3441no—
559Q8—3441no—
560Q8C4×Dic8612yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4C4×Dic8612yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
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×C4C22×Dic8611yescharacteristic
591C2×C4C2×#1062189811yescharacteristic
592C2×C4C2×#1062189811yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C8—22no—
595C8—21no—
596C8—22no—
597C8—21no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—1721no—
603C8—1721no—
604C8#1306330412yes—
605C8#1306330412yes—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×C4×C22⋊D4311yescharacteristic
612C22#1458343311yescharacteristic
613C22#1458345611yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—3441no—
622C4—1722no—
623C4—1721no—
624C4—1721no—
625C4—1721no—
626C4—1721no—
627C4C2×C4×Dic8611yescharacteristic
628C4C4×#1062189811yescharacteristic
629C4C2×#1306330411yescharacteristic
630C4#1458341011yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C4×#1306330411yescharacteristic
635C2#1914350211yescharacteristic
636C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2875C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#2875D43
hypocenterC43#21629
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. #19143535C2semidirect
3. #19135539C2semidirect
4. #19135370C2semidirect
5. #19135194C2semidirect
6. #19135194C2semidirect
10. #19134480C2semidirect
11. #19134475C2semidirect
12. #19134467C2semidirect
17. #14583206C4semidirect
18. #14583206C4semidirect
19. #14583199C4semidirect
20. #14583199C4semidirect
21. #14583194C4semidirect
22. #14583189C4semidirect
23. #14583184C4semidirect
24. #14583179C4semidirect
125. #131×C43Q8semidirect
385. C43#21629semidirect
390. #131Dic86semidirect

Maximal subgroups

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

subgroupindex
#191443832
#191435352
#191355392
#191353702
#191351942
#191348702
#191346152
#191344802
#191344752
#191344672
#191344372
#191344302
C43×#28752
#2162943