Finite Group Databasebeta

← #25153560

Subgroups — #25153560

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583626C211yesmaximal, characteristic, complemented
2C2×#14583257C211yesmaximal, characteristic
3C2×#14583120C211yesmaximal, characteristic
4#19140080C211yesmaximal, characteristic
5#19135745C211yesmaximal, characteristic, complemented
6#19135743C211yesmaximal, characteristic, complemented
7#19135739C211yesmaximal, characteristic
8#19135541C211yesmaximal, characteristic, complemented
9#19135533C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134947C211yesmaximal, characteristic
12#19134937C211yesmaximal, characteristic, complemented
13#19134935C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#2025C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18#14583626—24no—
19#14583626—24no—
20C2×#13063324—21no—
21C2×#13063324C2211yescharacteristic
22C2×#13063316C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063315—21no—
25C2×#13063312C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×#13063290—21no—
29C2×#13063290C2211yescharacteristic
30C2×#13063290C2211yescharacteristic
31#14583257—24no—
32#14583120—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41#14582827—21no—
42#14582811—21no—
43#14582805C2211yescharacteristic
44#14582804C2211yescharacteristic
45#14582802C2211yescharacteristic
46#14582792—21no—
47#14582787—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×Dic86C2311yescharacteristic
66C22×Dic86C2311yescharacteristic
67C2×Dic172—22no—
68C2×Dic172—22no—
69C2×Dic172—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324—28no—
76#13063324—22no—
77#13063324D414yes—
78#13063316—22no—
79#13063316—22no—
80#13063315—28no—
81#13063315—28no—
82#13063312—22no—
83#13063312—22no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88#13063290—28no—
89#13063290—22no—
90#13063290—22no—
91#13063290—22no—
92#13063290D414yes—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C2×Dic43⋊C4D411yescharacteristic
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114Dic43⋊C8—22no—
115#13063250—22no—
116#13063250—22no—
117#13063248—22no—
118#13063248—22no—
119#13063248—22no—
120#13063246—22no—
121#13063235—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×D4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#125×C43—22no—
131#125×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43C2311yescharacteristic
140#102×C43—22no—
141#102×C43—22no—
142C24×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—24no—
167C2×Dic86—22no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—41no—
175C2×Dic86—41no—
176C2×Dic86—42no—
177C2×Dic86—42no—
178C2×Dic86C2×D412yes—
179C2×Dic86#4112yes—
180C2×Dic86#4112yes—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C4⋊C4×C43—24no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C2×D412yes—
194C4⋊C4×C43C2×D412yes—
195C22⋊C4×C43—42no—
196C22⋊C4×C43—81no—
197C42×C43—21no—
198C42×C43—21no—
199C22⋊Dic43—42no—
200C22⋊Dic43—42no—
201C22⋊Dic43—42no—
202C22⋊Dic43—81no—
203#10621883—44no—
204C4⋊Dic43—24no—
205C4⋊Dic43—21no—
206C4⋊Dic43—22no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43C2×D412yes—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217C4×Dic43—24no—
218C4×Dic43—24no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—24no—
222C4×Dic43—81no—
223C4×Dic43C2×D412yes—
224C4×Dic43C2×D412yes—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231Dic172—44no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C22×D411yescharacteristic
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43#12012yes—
288C2×Dic43#12012yes—
289Dic86—22no—
290Dic86—22no—
291Dic86—22no—
292Dic86—44no—
293Dic86—48no—
294Dic86—41no—
295Dic86—41no—
296Dic86—41no—
297Dic86—41no—
298Dic86#12414yes—
299C8×C43—41no—
300C8×C43—41no—
301C43⋊C8—41no—
302C43⋊C8—41no—
303#25941—431nomaximal, Sylow
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43C2×#12011yescharacteristic
312C22×C43#54811yescharacteristic
313C22×C43#54811yescharacteristic
314C22×C43#57511yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57711yescharacteristic
317C22×C43#57811yescharacteristic
318C4×C43—41no—
319C4×C43—42no—
320C4×C43—41no—
321C4×C43—42no—
322C4×C43—81no—
323C4×C43C2×#12411yescharacteristic
324C4×C43#53611yescharacteristic
325C4×C43#54811yescharacteristic
326C4×C43#54811yescharacteristic
327Dic43—24no—
328Dic43—22no—
329Dic43—22no—
330Dic43—41no—
331Dic43—42no—
332Dic43—41no—
333Dic43—81no—
334Dic43—81no—
335C2×#557—431no—
336C2×#489—431no—
337C2×#464—431no—
338#2592—431no—
339#2026—431no—
340#2026—431no—
341#2025—431no—
342#2025D4311yescharacteristic
343#1987—431no—
344#1985—431no—
345#1880—431no—
346#1880—431no—
347#1878—431no—
348#1878—431no—
349#1763—431no—
350C2×C43—161no—
351C2×C43#243611yescharacteristic
352C2×C43#300511yescharacteristic
353C2×C43#301311yescharacteristic
354C2×C43#337111yescharacteristic
355C2×C43#337111yescharacteristic
356C2×C43#337711yescharacteristic
357C2×C43#337711yescharacteristic
358C22×Q16—431no—
359C22×SD16—431no—
360#557—864no—
361#557—864no—
362C2×C4⋊Q8—431no—
363C2×C4⋊Q8—861no—
364C2×#125—431no—
365C2×#125—861no—
366C2×#125—861no—
367C2×#125C2×D4311yescharacteristic
368C2×#124—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×C4×Q8—431no—
372C2×C4×Q8—431no—
373C2×C4×Q8—861no—
374#489—864no—
375#464—864no—
376C2×C4⋊C8—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#102—431no—
383C2×#102C2×D4311yescharacteristic
384C2×#102C2×D4311yescharacteristic
385C2×#97—431no—
386#397—861no—
387#393—861no—
388#391—431no—
389#391—431no—
390#390—431no—
391#390C2×D4311yescharacteristic
392#388—861no—
393#388—861no—
394C4×C4⋊C4—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400#340C2×D4311yescharacteristic
401#336—431no—
402#336—431no—
403#336—431no—
404#336C2×D4311yescharacteristic
405C43#2594111yescharacteristic, complemented, Sylow
406C22×Q8—431no—
407C22×Q8—431no—
408C22×Q8—431no—
409C22×Q8—861no—
410C22×D4C22×D4311yescharacteristic
411C2×Q16—862no—
412C2×Q16—862no—
413C2×Q16—862no—
414C2×SD16—862no—
415C2×SD16—862no—
416C2×SD16—862no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421C4⋊Q8—434no—
422C4⋊Q8—862no—
423C4⋊Q8—868no—
424#125—22no—
425#125—22no—
426#125—862no—
427#125—868no—
428#125—868no—
429#125—862no—
430#124—862no—
431#124—862no—
432C4×Q8—434no—
433C4×Q8—862no—
434C4×Q8—862no—
435C4×Q8—862no—
436C4×Q8—862no—
437C4×Q8—862no—
438C4×Q8—862no—
439C4×Q8—868no—
440C4×Q8—862no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C4⋊C4C22×D4311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—861no—
466C2×C42—861no—
467C2×C42—861no—
468C2×C42—861no—
469C2×C42C22×D4311yescharacteristic
470C4⋊C8—862no—
471#103—862no—
472#103—862no—
473#103—862no—
474#103—862no—
475#103—862no—
476#102—22no—
477#102—22no—
478#102—862no—
479#97—862no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95—861no—
485C24—21no—
486C2×Q8—432no—
487C2×Q8—432no—
488C2×Q8—432no—
489C2×Q8—864no—
490C2×Q8—862no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—1721no—
501C2×Q8—1721no—
502C2×Q8—1722no—
503C2×Q8—1722no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4D4×D4311yescharacteristic
522C22×C4D4×D4311yescharacteristic
523C22×C4C23×D4311yescharacteristic
524Q16—1724no—
525SD16—1724no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—432no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—864no—
549C4⋊C4—864no—
550C4⋊C4—864no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—864no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4D4×D4312yes—
558C4⋊C4D4×D4312yes—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—3441no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—432no—
568C42—432no—
569C42—864no—
570C42—864no—
571C42—864no—
572C42—861no—
573C42—861no—
574C42—3441no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C2×D4×D4311yescharacteristic
583Q8—434no—
584Q8—862no—
585Q8—862no—
586Q8—862no—
587Q8—1724no—
588Q8—1728no—
589Q8—1721no—
590Q8—1721no—
591Q8—1721no—
592Q8—1721no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—432no—
613C2×C4—432no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—862no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4C2×D4×D4311yescharacteristic
637C2×C4C2×D4×D4311yescharacteristic
638C2×C4#41×D4311yescharacteristic
639C2×C4#41×D4311yescharacteristic
640C2×C4#1306337211yescharacteristic
641C2×C4#1306337311yescharacteristic
642C8—41no—
643C8—41no—
644C8—1721no—
645C8—1721no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22#120×D4311yescharacteristic
654C22#1458355711yescharacteristic
655C22#1458355911yescharacteristic
656C22#1458369511yescharacteristic
657C22#1458369611yescharacteristic
658C22#1458370911yescharacteristic
659C22#1458371311yescharacteristic
660C4—41no—
661C4—42no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—862no—
666C4—864no—
667C4—862no—
668C4—3441no—
669C4—3441no—
670C4—1721no—
671C4—1722no—
672C4—1721no—
673C4#124×D4311yescharacteristic
674C4#1458347211yescharacteristic
675C4#1458355711yescharacteristic
676C4#1458355911yescharacteristic
677C2—161no—
678C2#1913824811yescharacteristic
679C2#1914383311yescharacteristic
680C2#1914390811yescharacteristic
681C2#1914735811yescharacteristic
682C2#1914736111yescharacteristic
683C2#1914744011yescharacteristic
684C2#1914744311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2025C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2025D43
hypocenterC43#25941
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×#14583626C2semidirect
5. #19135745C2semidirect
6. #19135743C2semidirect
8. #19135541C2semidirect
9. #19135533C2semidirect
12. #19134937C2semidirect
13. #19134935C2semidirect
14. #19134424C2semidirect
405. C43#25941semidirect

Maximal subgroups

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

subgroupindex
C2×#145836262
C2×#145832572
C2×#145831202
#191400802
#191357452
#191357432
#191357392
#191355412
#191355332
#191349532
#191349472
#191349372
#191349352
#191344242
C43×#20252
#2594143