Finite Group Databasebeta

← #25159477

Subgroups — #25159477

Order 11008.

860 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583201C211yesmaximal, characteristic, complemented
2C2×#14582939C211yesmaximal, characteristic, complemented
3#19138313C211yesmaximal, characteristic, complemented
4#19137637C211yesmaximal, characteristic
5#19136114C211yesmaximal, characteristic, complemented
6#19136099C211yesmaximal, characteristic, complemented
7#19135965C211yesmaximal, characteristic, complemented
8#19135936C211yesmaximal, characteristic, complemented
9#19135362C211yesmaximal, characteristic, complemented
10#19135169C211yesmaximal, characteristic, complemented
11#19135034C211yesmaximal, characteristic
12#19134840C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134777C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14583201—24no—
21#14582939—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32#14582838—21no—
33#14582832—21no—
34#14582802—21no—
35#14582802C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582792—21no—
40#14582779—21no—
41#14582772—21no—
42#14582764C2211yescharacteristic
43#14582759—21no—
44#14582759C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C22⋊C4×Dic43—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C23×Dic43—21no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063316—22no—
68#13063316—41no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71#13063284—22no—
72#13063284—41no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43D411yescharacteristic
88C2×C22⋊Dic43D411yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063259—41no—
94#13063258—22no—
95#13063258D414yescomplemented
96#13063257—22no—
97#13063256—22no—
98#13063256—22no—
99Dic43⋊C8—22no—
100Dic43⋊C8—22no—
101#13063246—22no—
102#13063246—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×D4×C43—21no—
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43—21no—
115C23×C4×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118#121×C43—22no—
119#121×C43Q814yes—
120C2×C4⋊C4×C43—22no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—41no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127#102×C43—22no—
128#102×C43—41no—
129C22⋊C8×C43—22no—
130C24×C43—21no—
131C24×C43C2×D411yescharacteristic
132C2×D4×C43—21no—
133C2×D4×C43—24no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—81no—
139C2×D4×C43—81no—
140C2×D4×C43C2×Q812yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—81no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×Q812yes—
153C22×C4×C43#4112yes—
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—81no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43C2×D412yes—
178C4⋊C4×C43C2×Q812yes—
179C22⋊C4×C43—24no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—42no—
183C22⋊Dic43—42no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—81no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—42no—
195C4⋊Dic43—81no—
196C4⋊Dic43—81no—
197C4⋊Dic43C2×D412yes—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—42no—
205C4×Dic43—81no—
206#10621877—28no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C2×D412yes—
212C2×C43⋊C8#4112yes—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—22no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C22⋊Q812yes—
227C23×C43C22×D411yescharacteristic
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—84no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—84no—
249C2×C4×C43C22⋊Q812yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×Q811yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—84no—
281C8×C43—41no—
282C8×C43—41no—
283C43⋊C8—22no—
284C43⋊C8—22no—
285#26363—431nomaximal, Sylow
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43C2×C22⋊Q811yescharacteristic
301C22×C43D4211yescharacteristic
302C22×C43#54711yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—81no—
311C4×C43#52511yescharacteristic
312C4×C43#53911yescharacteristic
313C4×C43D4×Q811yescharacteristic
314C4×C43#55411yescharacteristic
315Dic43—41no—
316Dic43—41no—
317Dic43—41no—
318Dic43—41no—
319Dic43—42no—
320Dic43—81no—
321Dic43—81no—
322Dic43—81no—
323C2×#478—431no—
324C2×#428—431no—
325#2442—431no—
326#2363—431no—
327#2092—431no—
328#2088—431no—
329#2065—431no—
330#2059—431no—
331#1949—431no—
332#1918—431no—
333#1895—431no—
334#1874D4311yescharacteristic
335#1862—431no—
336#1854—431no—
337#1851—431no—
338C2×C43—42no—
339C2×C43—82no—
340C2×C43#244911yescharacteristic
341C2×C43#308011yescharacteristic
342C2×C43#308111yescharacteristic
343C2×C43#327111yescharacteristic
344C2×C43#327311yescharacteristic
345C2×C43#334811yescharacteristic
346C2×C43#335511yescharacteristic
347C22×M16—431no—
348C2×#125—431no—
349C2×#121C2×D4311yescharacteristic
350C2×C4×D4—431no—
351C2×#117—431no—
352C22×C4⋊C4C2×D4311yescharacteristic
353#478—864no—
354#428—864no—
355C2×#107—431no—
356C2×#107—431no—
357C2×#107—431no—
358C2×#106—431no—
359C2×#106—431no—
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102C2×D4311yescharacteristic
366C2×#102C2×D4311yescharacteristic
367C2×C22⋊C8C2×D4311yescharacteristic
368#400—861no—
369#398—861no—
370#390—431no—
371#390—861no—
372#389—431no—
373#389—431no—
374#389—431no—
375#388—861no—
376#386—861no—
377#385—861no—
378#382—431no—
379#380—431no—
380#380—861no—
381C4×C4⋊C4—431no—
382C4×C22⋊C4—431no—
383C4×C22⋊C4—861no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#340C2×D4311yescharacteristic
390#336—431no—
391#336—431no—
392C43#2636311yescharacteristic, complemented, Sylow
393C22×D4—21no—
394C22×D4C22×D4311yescharacteristic
395C23×C4—21no—
396C23×C4—861no—
397C23×C4C22×D4311yescharacteristic
398C2×M16—862no—
399C2×M16—862no—
400C2×M16—862no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405#125—862no—
406#125—1721no—
407#121—22no—
408#121Dic8614yes—
409C4×D4—862no—
410C4×D4—1721no—
411#117—862no—
412#117—1721no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440#107—434no—
441#107—862no—
442#107—1721no—
443#106—862no—
444#106—862no—
445#106—862no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448#102—22no—
449#102—41no—
450#102—862no—
451#102—862no—
452C22⋊C8—22no—
453#95—431no—
454#95—431no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—21no—
463C24D4×D4311yescharacteristic
464C2×D4—24no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×Dic8612yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—3441no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4C2×Dic8612yes—
495C22×C4D4×D4311yescharacteristic
496C22×C4#1062190012yes—
497C22×C4C23×D4311yescharacteristic
498M16—868no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—432no—
506C2×C8—432no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—432no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—3441no—
525C4⋊C4—3441no—
526C4⋊C4—3441no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4C2×Dic8612yes—
530C4⋊C4D4×D4312yes—
531C22⋊C4—24no—
532C22⋊C4—3441no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C22⋊C4—1722no—
539C42—861no—
540C42—861no—
541C42—861no—
542C42—861no—
543C42—3441no—
544C42—1722no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23#1306330212yes—
559C23C2×D4×D4311yescharacteristic
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—84no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—3444no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4#1306330212yes—
607C2×C4C2×D4×D4311yescharacteristic
608C2×C4C22×Dic8611yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4C2×#1062190011yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337211yescharacteristic
613C8—41no—
614C8—41no—
615C8—862no—
616C8—862no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×#1306330211yescharacteristic
632C22#1458353111yescharacteristic
633C22#1458354711yescharacteristic
634C22#1458369511yescharacteristic
635C22#1458369811yescharacteristic
636C22#1458370011yescharacteristic
637C22#1458370511yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—3441no—
643C4—3441no—
644C4—3441no—
645C4—1721no—
646C4—1721no—
647C4—1721no—
648C4—1721no—
649C4—1722no—
650C4#1458340911yescharacteristic
651C4#1458349411yescharacteristic
652C4D4×Dic8611yescharacteristic
653C4#1458360811yescharacteristic
654C2—42no—
655C2—82no—
656C2#1913840811yescharacteristic
657C2#1914441511yescharacteristic
658C2#1914442211yescharacteristic
659C2#1914618311yescharacteristic
660C2#1914620611yescharacteristic
661C2#1914711311yescharacteristic
662C2#1914720111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#1874D43
hypocenterC43#26363
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#14583201C2semidirect
2. C2×#14582939C2semidirect
3. #19138313C2semidirect
5. #19136114C2semidirect
6. #19136099C2semidirect
7. #19135965C2semidirect
8. #19135936C2semidirect
9. #19135362C2semidirect
10. #19135169C2semidirect
12. #19134840C2semidirect
13. #19134796C2semidirect
14. #19134777C2semidirect
95. #13063258D4semidirect
392. C43#26363semidirect

Maximal subgroups

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

subgroupindex
C2×#145832012
C2×#145829392
#191383132
#191376372
#191361142
#191360992
#191359652
#191359362
#191353622
#191351692
#191350342
#191348402
#191347962
#191347772
C43×#18742
#2636343