Finite Group Databasebeta

← #25101978

Subgroups — #25101978

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583431C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C4×M16×D43C211yesmaximal, characteristic, complemented
4#19135586C212yesmaximal, complemented
5#19135441C212yesmaximal, complemented
6#19135062C212yesmaximal, complemented
7#19135055C212yesmaximal
8C4×#13063243C211yesmaximal, characteristic, complemented
9C4×#13063243C211yesmaximal, characteristic, complemented
10C4×#13063242C211yesmaximal, characteristic, complemented
11C4×#100×C43C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583431—21no—
14#14583431—21no—
15#14583431—21no—
16#14583431—21no—
17#14583431—21no—
18#14583431—21no—
19#14583431—21no—
20#14583431—21no—
21C2×#13063318C412yes—
22C2×#13063316C2211yescharacteristic
23C2×#13063312C2211yescharacteristic
24C2×#13063307C412yes—
25C2×#13063305C2211yescharacteristic
26C2×#13063296C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×C4×C22⋊D43C412yes—
29C2×#13063284C412yes—
30C2×C42×D43C2211yescharacteristic
31#14582954—21no—
32#14582954—21no—
33#14582950—21no—
34#14582950—21no—
35#14582922C2212yes—
36C2×#13063243C2212yes—
37C2×#13063243C2212yes—
38C2×#13063242C2212yes—
39#14582862C2212yes—
40C4×#10621877C2211yescharacteristic
41C4×#10621877C2211yescharacteristic
42#14582851—21no—
43M16×Dic43C2212yes—
44C4×#10621872—21no—
45#97×D43—21no—
46C4×C8×D43—21no—
47#14582668C2212yes—
48#14582667C2212yes—
49#14582667C2212yes—
50C2×C4×D4×C43C2211yescharacteristic
51C2×#100×C43C2212yes—
52C4×M16×C43C2211yescharacteristic
53C4×M16×C43C2211yescharacteristic
54C43×#343C2212yes—
55C22×Dic86C2311yescharacteristic
56C22×C22⋊D43C2×C412yes—
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C2×#10621877C2312yes—
61C2×#10621877C2312yes—
62C2×#10621872—22no—
63M16×D43—24no—
64M16×D43—24no—
65C2×C8×D43—22no—
66#13063318—22no—
67#13063318—22no—
68#13063318—22no—
69#13063318—22no—
70#13063316—21no—
71#13063316—21no—
72#13063316—21no—
73#13063316—21no—
74#13063312—21no—
75#13063312—21no—
76#13063312—21no—
77#13063312—21no—
78#13063307—22no—
79#13063307—22no—
80#13063307—22no—
81#13063307—22no—
82#13063305—21no—
83#13063305—21no—
84#13063305—21no—
85#13063305—21no—
86#13063296—21no—
87#13063296—21no—
88#13063296—21no—
89#13063296—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86—21no—
93C4×Dic86—21no—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96C4×C22⋊D43—22no—
97C4×C22⋊D43—22no—
98#13063284—22no—
99#13063284—22no—
100#13063284—22no—
101#13063284—22no—
102C2×C4⋊Dic43C2×C412yes—
103C2×C4⋊Dic43C2×C412yes—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4C2×C412yes—
106C2×Dic43⋊C4C2×C412yes—
107C2×C22⋊Dic43C2×C412yes—
108C2×C22⋊Dic43C2×C412yes—
109C2×C22⋊Dic43C2×C412yes—
110C2×(C2×D43)⋊C4C2×C412yes—
111C2×C4×Dic43C2×C412yes—
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119C42×D43D411yescharacteristic
120C42×D43D411yescharacteristic
121C42×D43D411yescharacteristic
122C42×D43D411yescharacteristic
123Dic43⋊C8—22no—
124Dic43⋊C8—22no—
125#13063243—24no—
126#13063243—24no—
127#13063242—24no—
128(C2×D43)⋊C8—22no—
129(C2×D43)⋊C8—22no—
130#13063236—21no—
131#13063236—21no—
132#13063235—22no—
133C4×C43⋊C8—21no—
134C4×C43⋊C8—21no—
135C8×Dic43—22no—
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43C2×C412yes—
138C2×M16×C43C2312yes—
139C2×M16×C43C2312yes—
140C4×D4×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43C2×C412yes—
146C2×C42×C43C2311yescharacteristic
147#100×C43—24no—
148#97×C43—21no—
149#97×C43—21no—
150C4×C8×C43—21no—
151C4×C8×C43—21no—
152C24×C43C22×C412yes—
153C23×D43C22×C411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—44no—
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C412yes—
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—44no—
168C22×Dic43C22×C412yes—
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C412yes—
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C411yescharacteristic
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22⋊C411yescharacteristic
180C2×C4×D43C22⋊C411yescharacteristic
181C2×C4×D43C22⋊C411yescharacteristic
182C2×C4×D43C22⋊C411yescharacteristic
183C2×C4×D43C22⋊C411yescharacteristic
184C2×C4×D43C22⋊C411yescharacteristic
185C2×C4×D43C2×D411yescharacteristic
186C2×C4×D43C2×D411yescharacteristic
187C2×C4×D43C2×D411yescharacteristic
188C2×C4×D43C2×D411yescharacteristic
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—22no—
192C2×Dic86—22no—
193M16×C43—22no—
194M16×C43—22no—
195M16×C43—22no—
196M16×C43#4114yes—
197C2×C8×C43—22no—
198C2×C8×C43—22no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206C42×C43C2×D411yescharacteristic
207C22⋊Dic43—22no—
208C22⋊Dic43—22no—
209C22⋊Dic43—22no—
210C22⋊Dic43—22no—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213(C2×D43)⋊C4—22no—
214(C2×D43)⋊C4—22no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—22no—
218C4⋊Dic43—22no—
219C4⋊Dic43—22no—
220C4⋊Dic43—22no—
221Dic43⋊C4—22no—
222Dic43⋊C4—22no—
223Dic43⋊C4—22no—
224Dic43⋊C4—22no—
225C4×Dic43—22no—
226C4×Dic43—22no—
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22⋊C411yescharacteristic
234C4×Dic43C22⋊C411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237C4×Dic43C2×D411yescharacteristic
238C4×Dic43C2×D411yescharacteristic
239#10621877—22no—
240#10621877—22no—
241#10621877—22no—
242#10621877#4114yes—
243C2×C43⋊C8—22no—
244C2×C43⋊C8—22no—
245#10621872—28no—
246C8×D43—28no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—42no—
251C23×C43—42no—
252C23×C43C23×C411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—22no—
256C22×D43—41no—
257C22×D43C2×C22⋊C411yescharacteristic
258C22×D43C2×C22⋊C411yescharacteristic
259D4×C43—42no—
260D4×C43—42no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—41no—
264C2×C4×C43—44no—
265C2×C4×C43—44no—
266C2×C4×C43—42no—
267C2×C4×C43C2×C22⋊C411yescharacteristic
268C2×C4×C43C2×C22⋊C411yescharacteristic
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43C2×C22⋊C411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C2×#4112yes—
274C2×C4×C43C2×#4112yes—
275C22⋊D43—44no—
276C22⋊D43—44no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—42no—
286C2×Dic43C2×C22⋊C411yescharacteristic
287C2×Dic43C2×C22⋊C411yescharacteristic
288C2×Dic43C2×C22⋊C411yescharacteristic
289C2×Dic43C2×C22⋊C411yescharacteristic
290C2×Dic43C2×C22⋊C411yescharacteristic
291C2×Dic43C2×C22⋊C411yescharacteristic
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—22no—
299C4×D43—22no—
300C4×D43—41no—
301C4×D43—41no—
302C4×D43—41no—
303C4×D43—41no—
304Dic86—42no—
305Dic86—42no—
306C8×C43—24no—
307C8×C43—42no—
308C43⋊C8—24no—
309C43⋊C8—42no—
310#21426—431nomaximal, Sylow
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43—42no—
316C22×C43—82no—
317C22×C43—82no—
318C22×C43C22×C22⋊C411yescharacteristic
319C22×C43C4×#4111yescharacteristic
320C22×C43C4×#4111yescharacteristic
321C2×D43—21no—
322C2×D43—21no—
323C2×D43—21no—
324C2×D43—21no—
325C2×D43—21no—
326C2×D43—42no—
327C2×D43—42no—
328C2×D43#41312yes—
329C4×C43—21no—
330C4×C43—21no—
331C4×C43—21no—
332C4×C43—42no—
333C4×C43#41312yes—
334C4×C43#52512yes—
335C4×C43#53212yes—
336Dic43—21no—
337Dic43—21no—
338Dic43—21no—
339Dic43—21no—
340Dic43—21no—
341Dic43—21no—
342Dic43—42no—
343Dic43—42no—
344C2×#529—431no—
345#2920—431no—
346C2×C4×M16—431no—
347#1998—432no—
348#1967—432no—
349#1901—432no—
350#1900—432no—
351C4×#101—431no—
352C4×#101—431no—
353C4×#100—431no—
354C4×#100D4311yescharacteristic, complemented
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—82no—
358C2×C43#229711yescharacteristic
359C2×C43C2×#41311yescharacteristic
360C2×C43C2×#41311yescharacteristic
361D43—22no—
362D43—41no—
363C22×M16—432no—
364#529—861no—
365#529—861no—
366#529—861no—
367#529—861no—
368#529—861no—
369#529—861no—
370#529—861no—
371#529—861no—
372C2×#126—432no—
373C2×#125—431no—
374C2×#124—431no—
375C2×#123—432no—
376C2×C22⋊Q8—431no—
377C2×#121—431no—
378C2×C4×Q8—431no—
379C2×C4×D4—432no—
380C2×C4×D4C2×D4311yescharacteristic
381C2×#117—432no—
382C22×C42—431no—
383#432—861no—
384#432—861no—
385#431—861no—
386#431—861no—
387#423—432no—
388C2×#101—432no—
389C2×#101—432no—
390C2×#100—432no—
391C2×#100C2×D4312yes—
392#407—432no—
393C4×M16—432no—
394C4×M16—431no—
395C4×M16—431no—
396C4×M16—861no—
397C4×M16—861no—
398C4×M16C2×D4311yescharacteristic
399C4×M16C2×D4311yescharacteristic
400C2×#97—861no—
401C2×C4×C8—861no—
402#343—432no—
403#343—432no—
404#343—432no—
405#343C2×D4312yes—
406C43#2142611yescharacteristic, complemented, Sylow
407C22×Q8—431no—
408C22×D4—432no—
409C22×D4C22×D4311yescharacteristic
410C23×C4—431no—
411C23×C4—431no—
412C23×C4—431no—
413C23×C4C4×D4312yes—
414C2×M16—432no—
415C2×M16—432no—
416C2×M16—862no—
417C2×M16—864no—
418C2×M16—864no—
419C2×M16C22×D4312yes—
420C2×M16C22×D4312yes—
421C22×C8—862no—
422#126—862no—
423#126—862no—
424#126—862no—
425#126—862no—
426#125—861no—
427#125—861no—
428#125—861no—
429#125—861no—
430#124—861no—
431#124—861no—
432#124—861no—
433#124—861no—
434#123—862no—
435#123—862no—
436#123—862no—
437#123—862no—
438C22⋊Q8—861no—
439C22⋊Q8—861no—
440C22⋊Q8—861no—
441C22⋊Q8—861no—
442#121—861no—
443#121—861no—
444#121—861no—
445#121—861no—
446C4×Q8—861no—
447C4×Q8—861no—
448C4×Q8—861no—
449C4×Q8—861no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—862no—
455C4×D4—862no—
456C4×D4—862no—
457C4×D4—862no—
458#117—862no—
459#117—862no—
460#117—862no—
461#117—862no—
462C2×C4⋊C4—432no—
463C2×C4⋊C4—432no—
464C2×C4⋊C4—432no—
465C2×C4⋊C4—432no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4C22×D4311yescharacteristic
468C2×C22⋊C4—432no—
469C2×C22⋊C4—432no—
470C2×C22⋊C4—432no—
471C2×C22⋊C4—432no—
472C2×C22⋊C4C4×D4312yes—
473C2×C42—431no—
474C2×C42—431no—
475C2×C42—431no—
476C2×C42—431no—
477C2×C42—431no—
478C2×C42—431no—
479C2×C42—431no—
480C2×C42—431no—
481C2×C42—431no—
482C2×C42—431no—
483C2×C42—431no—
484C2×C42—432no—
485C2×C42C22×D4311yescharacteristic
486C4⋊C8—862no—
487C4⋊C8—862no—
488#101—864no—
489#101—864no—
490#100—24no—
491#100—864no—
492C22⋊C8—862no—
493C22⋊C8—862no—
494#97—21no—
495#97—21no—
496#97—862no—
497#97—861no—
498#97—861no—
499C4×C8—21no—
500C4×C8—21no—
501C4×C8—862no—
502C4×C8—861no—
503C4×C8—861no—
504C24—431no—
505C24C2×C4×D4312yes—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—862no—
509C2×Q8—862no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—862no—
515C2×D4—862no—
516C2×D4—1724no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—44no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—431no—
527C22×C4—431no—
528C22×C4—431no—
529C22×C4—431no—
530C22×C4—431no—
531C22×C4—431no—
532C22×C4—431no—
533C22×C4—431no—
534C22×C4—431no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—1722no—
540C22×C4—1722no—
541C22×C4C2×C4×D4311yescharacteristic
542C22×C4C2×C4×D4312yes—
543C22×C4C2×C4×D4311yescharacteristic
544C22×C4C23×D4311yescharacteristic
545M16—22no—
546M16—22no—
547M16—22no—
548M16—434no—
549M16—868no—
550M16—862no—
551M16—862no—
552M16—862no—
553M16#1062189814yes—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—868no—
557C2×C8—862no—
558C2×C8—862no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—862no—
562C4⋊C4—862no—
563C4⋊C4—862no—
564C4⋊C4—862no—
565C4⋊C4—862no—
566C4⋊C4—862no—
567C4⋊C4—862no—
568C4⋊C4—862no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—862no—
574C22⋊C4—862no—
575C22⋊C4—862no—
576C22⋊C4—862no—
577C22⋊C4—862no—
578C22⋊C4—862no—
579C22⋊C4—862no—
580C22⋊C4—862no—
581C42—431no—
582C42—431no—
583C42—431no—
584C42—431no—
585C42—431no—
586C42—431no—
587C42—431no—
588C42—431no—
589C42—431no—
590C42—431no—
591C42—431no—
592C42—431no—
593C42—862no—
594C42—862no—
595C42D4×D4311yescharacteristic
596C42D4×D4311yescharacteristic
597C42D4×D4311yescharacteristic
598C42D4×D4311yescharacteristic
599C23—22no—
600C23—22no—
601C23—22no—
602C23—42no—
603C23—42no—
604C23—431no—
605C23—431no—
606C23—862no—
607C23—861no—
608C23—861no—
609C23—1721no—
610C23C22×C4×D4311yescharacteristic
611Q8—1722no—
612Q8—1722no—
613D4—42no—
614D4—42no—
615D4—1724no—
616D4—1724no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—41no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—42no—
623C2×C4—431no—
624C2×C4—431no—
625C2×C4—431no—
626C2×C4—431no—
627C2×C4—431no—
628C2×C4—431no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1722no—
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4C22⋊C4×D4311yescharacteristic
652C2×C4C22⋊C4×D4311yescharacteristic
653C2×C4C22⋊C4×D4311yescharacteristic
654C2×C4C2×D4×D4311yescharacteristic
655C2×C4C2×D4×D4311yescharacteristic
656C2×C4#41×D4312yes—
657C2×C4C2×#1062189812yes—
658C8—24no—
659C8—42no—
660C8—864no—
661C8—1722no—
662C22—21no—
663C22—21no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—82no—
668C22—82no—
669C22—432no—
670C22—861no—
671C22—861no—
672C22—861no—
673C22—861no—
674C22—861no—
675C22—1722no—
676C22—1722no—
677C22C2×C22⋊C4×D4311yescharacteristic
678C22#1458336711yescharacteristic
679C22C4×#1062189811yescharacteristic
680C4—21no—
681C4—21no—
682C4—21no—
683C4—42no—
684C4—861no—
685C4—861no—
686C4—861no—
687C4—861no—
688C4—861no—
689C4—861no—
690C4—1722no—
691C4—1722no—
692C4#1458288012yes—
693C4#1458340812yes—
694C4#1458344612yes—
695C2—21no—
696C2—21no—
697C2—82no—
698C2—862no—
699C2—1721no—
700C2#1913708111yescharacteristic
701C2#413×D4311yescharacteristic
702C2C2×#1458288011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43#21426
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. C4×M16×D43C2semidirect
4. #19135586C2semidirect
5. #19135441C2semidirect
6. #19135062C2semidirect
8. C4×#13063243C2semidirect
9. C4×#13063243C2semidirect
10. C4×#13063242C2semidirect
11. C4×#100×C43C2semidirect
354. C4×#100D43semidirect
406. C43#21426semidirect

Maximal subgroups

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

subgroupindex
C2×#145834312
#191432262
C4×M16×D432
#191355862
#191354412
#191350622
#191350552
C4×#130632432
C4×#130632422
C4×#100×C432
#2142643