Finite Group Databasebeta

← #25131406

Subgroups — #25131406

Order 11008.

1050 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×#14583624C211yesmaximal, characteristic
2C2×#14583108C211yesmaximal, characteristic
3C2×#14582991C211yesmaximal, characteristic
4#19139967C211yesmaximal, characteristic
5#19135839C211yesmaximal, characteristic
6#19135696C211yesmaximal, characteristic
7#19135695C211yesmaximal, characteristic
8#19135529C211yesmaximal, characteristic
9#19135395C211yesmaximal, characteristic
10#19134935C211yesmaximal, characteristic
11#19134934C211yesmaximal, characteristic
12#19134848C211yesmaximal, characteristic
13#19134847C211yesmaximal, characteristic
14#19134598C211yesmaximal, characteristic
15C43×#2043C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19#14583624—24no—
20#14583624—24no—
21C2×#13063323C2211yescharacteristic
22C2×#13063323C2211yescharacteristic
23C2×#13063316—21no—
24C2×#13063315—21no—
25C2×#13063315—21no—
26C2×Q8×Dic43C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×Dic86C2211yescharacteristic
30C2×#13063290—21no—
31C2×#13063290C2211yescharacteristic
32#14583108—24no—
33#14582991—24no—
34C2×#13063258C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×C8×Dic43C2211yescharacteristic
43#14582833—21no—
44#14582830—21no—
45#14582805C2211yescharacteristic
46#14582804C2211yescharacteristic
47#14582803—21no—
48#14582795C2211yescharacteristic
49#14582794—21no—
50#14582768C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86D411yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×Dic86C2311yescharacteristic
66C2×Dic172—22no—
67C2×Dic172—22no—
68C2×Dic172—41no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885—22no—
72C2×#10621885—22no—
73C2×#10621885—22no—
74C2×#10621885—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063323—22no—
78#13063323—22no—
79#13063323—22no—
80#13063323D414yes—
81#13063316—28no—
82#13063315—28no—
83#13063315—28no—
84Q8×Dic43—22no—
85Q8×Dic43—22no—
86Q8×Dic43—22no—
87Q8×Dic43D414yes—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×Dic86—22no—
92#13063290—28no—
93#13063290—22no—
94#13063290—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43D411yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4D411yescharacteristic
110C2×Dic43⋊C4D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117#13063258—22no—
118Dic43⋊C8—22no—
119#13063250—22no—
120#13063250—41no—
121#13063249—22no—
122#13063249—41no—
123#13063248—22no—
124#13063248—22no—
125C8×Dic43—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C4⋊Q8×C43—22no—
136C4⋊Q8×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#103×C43—22no—
144#103×C43—22no—
145#103×C43—41no—
146#103×C43—41no—
147#95×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43C2×D412yes—
159C2×Q8×C43C2×D412yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86Q1614yescomplemented
188C2×Dic86C2×D412yes—
189C2×Dic86#4112yes—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C4⋊C4×C43—24no—
197C4⋊C4×C43—24no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—81no—
203C42×C43—21no—
204C42×C43—21no—
205#10621885—28no—
206#10621885—44no—
207C4⋊Dic43—24no—
208C4⋊Dic43—21no—
209C4⋊Dic43—24no—
210C4⋊Dic43—22no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43C2×D412yes—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—24no—
218Dic43⋊C4—24no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221Dic43⋊C4—42no—
222Dic43⋊C4—42no—
223Dic43⋊C4—81no—
224Dic43⋊C4—81no—
225C4×Dic43—24no—
226C4×Dic43—24no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—24no—
230C4×Dic43—42no—
231C4×Dic43C2×D412yes—
232C4×Dic43C2×D412yes—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8#4112yes—
239Dic172—44no—
240C23×C43C22×D411yescharacteristic
241Q8×C43—22no—
242Q8×C43—22no—
243Q8×C43—22no—
244Q8×C43—22no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248Q8×C43—41no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43C2×Q1612yes—
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C432−1+411yescharacteristic
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—21no—
280C2×Dic43—22no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43#12012yes—
293C2×Dic43#12012yes—
294C2×Dic43C2×Q1612yes—
295C2×Dic43C2×Q1612yes—
296C2×Dic43#13712yes—
297Dic86—28no—
298Dic86—22no—
299Dic86—22no—
300Dic86—22no—
301Dic86—22no—
302Dic86—41no—
303Dic86—41no—
304Dic86—41no—
305Dic86—41no—
306C8×C43—41no—
307C8×C43—41no—
308C43⋊C8—22no—
309C43⋊C8—41no—
310#24191—431nomaximal, Sylow
311C22×C43C2×#12011yescharacteristic
312C22×C43#54811yescharacteristic
313C22×C43#55011yescharacteristic
314C22×C43C22×Q1611yescharacteristic
315C22×C43C2×#13711yescharacteristic
316C22×C43#57711yescharacteristic
317C22×C43#57811yescharacteristic
318C4×C43—22no—
319C4×C43—42no—
320C4×C43—42no—
321C4×C43—41no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43#52511yescharacteristic
325C4×C43#53711yescharacteristic
326C4×C43#54611yescharacteristic
327C4×C43#54711yescharacteristic
328Dic43—22no—
329Dic43—22no—
330Dic43—42no—
331Dic43—42no—
332Dic43—41no—
333Dic43—42no—
334Dic43—81no—
335Dic43#45114yes—
336C2×#557—431no—
337C2×#462—431no—
338C2×C4×Q16—431no—
339#2582—431no—
340#2043—431no—
341#2043D4311yescharacteristic
342#2016—431no—
343#2016—431no—
344#1984—431no—
345#1956—431no—
346#1878—431no—
347#1878—431no—
348#1863—431no—
349#1863—431no—
350#1803—431no—
351C2×C43#240711yescharacteristic
352C2×C43C2×#45111yescharacteristic
353C2×C43#301311yescharacteristic
354C2×C43#336311yescharacteristic
355C2×C43#337411yescharacteristic
356C2×C43#339511yescharacteristic
357C2×C43#340011yescharacteristic
358C22×Q16—431no—
359C22×Q16—431no—
360C22×Q16—431no—
361#557—864no—
362#557—864no—
363C2×C4⋊Q8—431no—
364C2×C4⋊Q8—431no—
365C2×C4⋊Q8C2×D4311yescharacteristic
366C2×#125—861no—
367C2×#125—861no—
368C2×#125—861no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×C4×Q8—431no—
372C2×C4×Q8—431no—
373C2×C4×Q8—431no—
374C2×C4×Q8—861no—
375#462—864no—
376C4×Q16—864no—
377C2×#107—431no—
378C2×C4⋊C8—431no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103C2×D4311yescharacteristic
386C2×#103C2×D4311yescharacteristic
387C2×#103C2×D4311yescharacteristic
388C2×#103C2×D4311yescharacteristic
389C2×C4×C8—431no—
390#398—861no—
391#398—861no—
392#391—431no—
393#391—431no—
394#391—861no—
395#389—431no—
396#389—861no—
397#389C2×D4311yescharacteristic
398#384—431no—
399#340—431no—
400#340—431no—
401#336—431no—
402#336—431no—
403#336—431no—
404#336C2×D4311yescharacteristic
405C43#2419111yescharacteristic, complemented, Sylow
406C22×Q8—431no—
407C22×Q8—431no—
408C22×Q8—431no—
409C22×Q8C22×D4311yescharacteristic
410C22×Q8C22×D4311yescharacteristic
411C2×Q16—862no—
412C2×Q16—862no—
413C2×Q16—862no—
414C2×Q16—862no—
415C2×Q16—862no—
416C2×Q16—862no—
417C2×Q16—862no—
418C2×Q16—1721no—
419C2×Q16—1721no—
420C22×C8—431no—
421C22×C8—431no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C4⋊Q8—22no—
425C4⋊Q8—22no—
426C4⋊Q8—434no—
427C4⋊Q8—862no—
428C4⋊Q8—862no—
429C4⋊Q8—862no—
430#125—868no—
431#125—868no—
432#125—868no—
433C4×Q8—434no—
434C4×Q8—862no—
435C4×Q8—862no—
436C4×Q8—862no—
437C4×Q8—862no—
438C4×Q8—862no—
439C4×Q8—862no—
440C4×Q8—862no—
441C4×Q8—868no—
442C4×Q8—862no—
443C4×Q8—862no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4—861no—
461C2×C4⋊C4—861no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4C22×D4311yescharacteristic
464C2×C4⋊C4C22×D4311yescharacteristic
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—861no—
468C2×C42—861no—
469C2×C42—861no—
470C2×C42—861no—
471C2×C42C22×D4311yescharacteristic
472#107—862no—
473C4⋊C8—862no—
474#103—22no—
475#103—22no—
476#103—41no—
477#103—41no—
478#103—862no—
479#103—862no—
480#103—862no—
481#103—862no—
482#103—1721no—
483#103—1721no—
484C4×C8—862no—
485#95—21no—
486#95—861no—
487#95—861no—
488#95—861no—
489#95—861no—
490#95—861no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—434no—
502C2×Q8—432no—
503C2×Q8—432no—
504C2×Q8—862no—
505C2×Q8—862no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—861no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×Q8D4×D4312yes—
517C2×Q8D4×D4312yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4D4×D4311yescharacteristic
531C22×C4D4×D4311yescharacteristic
532C22×C4C23×D4311yescharacteristic
533Q16—868no—
534Q16—1724no—
535Q16—1724no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—432no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—81no—
555C4⋊C4—432no—
556C4⋊C4—862no—
557C4⋊C4—862no—
558C4⋊C4—862no—
559C4⋊C4—864no—
560C4⋊C4—864no—
561C4⋊C4—864no—
562C4⋊C4—864no—
563C4⋊C4—864no—
564C4⋊C4—864no—
565C4⋊C4—864no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—3441no—
570C4⋊C4—3441no—
571C4⋊C4—1722no—
572C4⋊C4—1722no—
573C42—21no—
574C42—21no—
575C42—432no—
576C42—432no—
577C42—864no—
578C42—864no—
579C42—864no—
580C42—861no—
581C42—861no—
582C42—1722no—
583C23C2×D4×D4311yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—868no—
593Q8—862no—
594Q8—862no—
595Q8—862no—
596Q8—862no—
597Q8—1721no—
598Q8—1721no—
599Q8—1721no—
600Q8—1721no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—432no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—432no—
622C2×C4—432no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—861no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4Q16×D4312yes—
643C2×C4C2×D4×D4311yescharacteristic
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#1306337011yescharacteristic
648C2×C4#1306337211yescharacteristic
649C8—41no—
650C8—41no—
651C8—862no—
652C8—1721no—
653C22#120×D4311yescharacteristic
654C22#1458355711yescharacteristic
655C22#1458356711yescharacteristic
656C22C2×Q16×D4311yescharacteristic
657C22#137×D4311yescharacteristic
658C22#1458370511yescharacteristic
659C22#1458371511yescharacteristic
660C4—22no—
661C4—42no—
662C4—42no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—434no—
667C4—862no—
668C4—862no—
669C4—3441no—
670C4—1722no—
671C4—1722no—
672C4—1721no—
673C4—1722no—
674C4#1458340711yescharacteristic
675C4#1458347611yescharacteristic
676C4#1458353811yescharacteristic
677C4#1458354711yescharacteristic
678C2#1913793511yescharacteristic
679C2#451×D4311yescharacteristic
680C2#1914390511yescharacteristic
681C2#1914727011yescharacteristic
682C2#1914739511yescharacteristic
683C2#1914759711yescharacteristic
684C2#1914764311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2043C2
socle, prime radicalC23×C43C22×D4
hypercenter#2043D43
hypocenterC43#24191
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
187. C2×Dic86Q16semidirect
405. C43#24191semidirect

Maximal subgroups

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

subgroupindex
C2×#145836242
C2×#145831082
C2×#145829912
#191399672
#191358392
#191356962
#191356952
#191355292
#191353952
#191349352
#191349342
#191348482
#191348472
#191345982
C43×#20432
#2419143