Finite Group Databasebeta

← #25140469

Subgroups — #25140469

Order 11008.

932 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×#14583054C211yesmaximal, characteristic
2C2×C4×#10621885C211yesmaximal, characteristic, complemented
3C22⋊C4×Dic86C211yesmaximal, characteristic
4#19136146C211yesmaximal, characteristic, complemented
5#19136021C211yesmaximal, characteristic
6#19135917C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic
8#19135270C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic
10#19134939C211yesmaximal, characteristic, complemented
11#19134936C211yesmaximal, characteristic, complemented
12#19134862C211yesmaximal, characteristic, complemented
13#19134607C211yesmaximal, characteristic, complemented
14#19134529C211yesmaximal, characteristic
15C43×#2421C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21#14583054—24no—
22C4×#10621885—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582803—21no—
40#14582803—21no—
41#14582759C2211yescharacteristic
42#14582757—21no—
43C22⋊C4×Dic43—21no—
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C22⋊Q8×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#400—21no—
53C43×#397—21no—
54C43×#391C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#388—21no—
57C43×#387—21no—
58C43×#382C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C23×Dic43—21no—
71C2×#10621885—22no—
72C2×#10621885—22no—
73C2×#10621885—22no—
74C2×#10621885—22no—
75C2×#10621885—41no—
76C2×#10621885D414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—41no—
84C4×Dic86—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92#13063258—22no—
93#13063256—41no—
94C4⋊(C43⋊C8)—41no—
95#13063249—22no—
96#13063249—41no—
97#13063248—22no—
98#13063248—22no—
99#13063248—22no—
100#13063248—22no—
101#13063248—22no—
102#13063248—41no—
103C22⋊(C43⋊C8)—22no—
104C22⋊(C43⋊C8)—41no—
105C4×C43⋊C8—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×Q8×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—41no—
115C4×Q8×C43—22no—
116C4×Q8×C43—41no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C2×D412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—24no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—24no—
176C2×Dic86—21no—
177C2×Dic86—44no—
178C2×Dic86—44no—
179C2×Dic86—44no—
180C2×Dic86—42no—
181C2×Dic86—42no—
182C2×Dic86—44no—
183C2×Dic86C2×D412yes—
184C2×Dic86#4112yes—
185C2×Dic86#4112yes—
186C2×Dic86#4112yes—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—42no—
194C4⋊C4×C43—42no—
195C4⋊C4×C43—42no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—42no—
199C22⋊C4×C43—42no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—42no—
205C22⋊Dic43—42no—
206#10621885—28no—
207#10621885—44no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214C4×Dic43—42no—
215C4×Dic43—42no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×D412yes—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43#13512yes—
235C23×C43C22×D411yescharacteristic
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
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×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43#13712yes—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—48no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290Dic86—22no—
291Dic86—22no—
292Dic86—22no—
293Dic86—22no—
294Dic86—22no—
295Dic86—48no—
296Dic86—41no—
297Dic86—41no—
298Dic86#12314yes—
299C43⋊C8—22no—
300C43⋊C8—41no—
301C43⋊C8—41no—
302C43⋊C8—41no—
303#24902—431nomaximal, Sylow
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43#52511yescharacteristic
312C22×C43D4211yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C22×C43C2×#13711yescharacteristic
316C22×C43#57811yescharacteristic
317C22×C43#57811yescharacteristic
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—42no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43C2×#12311yescharacteristic
328C4×C43#53811yescharacteristic
329C4×C43#54611yescharacteristic
330C4×C43#55111yescharacteristic
331Dic43—24no—
332Dic43—42no—
333Dic43—81no—
334Dic43—81no—
335C2×#451—431no—
336C2×C4×Q16—431no—
337#2421D4311yescharacteristic
338Q8×C22⋊C4—431no—
339#2097—431no—
340#2075—431no—
341#2056—431no—
342#2035—431no—
343#1933—431no—
344#1923—431no—
345#1878—431no—
346#1878—431no—
347#1865—431no—
348#1805—431no—
349#1787—431no—
350C2×C43—42no—
351C2×C43#241811yescharacteristic
352C2×C43#310811yescharacteristic
353C2×C43#312711yescharacteristic
354C2×C43#327011yescharacteristic
355C2×C43#328511yescharacteristic
356C2×C43#330011yescharacteristic
357C2×C43#332811yescharacteristic
358C23×Q8—431no—
359C22×Q16—431no—
360C22×Q16—431no—
361C2×C22⋊Q8C2×D4311yescharacteristic
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×C4×Q8C2×D4311yescharacteristic
365#451—864no—
366C4×Q16—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×C22⋊C8—431no—
379C2×C22⋊C8—431no—
380C2×C4×C8—431no—
381#400—21no—
382#397—21no—
383#391—431no—
384#391—431no—
385#391—861no—
386#391—861no—
387#391C2×D4311yescharacteristic
388#389C2×D4311yescharacteristic
389#388—21no—
390#387—21no—
391#382C2×D4311yescharacteristic
392#380—431no—
393#380—861no—
394#380C2×D4311yescharacteristic
395C4×C22⋊C4—861no—
396C4×C22⋊C4C2×D4311yescharacteristic
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#336—431no—
402#336—431no—
403C43#2490211yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×Q8—431no—
406C22×Q8—862no—
407C22×Q8—862no—
408C22×Q8—862no—
409C22×Q8—862no—
410C22×Q8—861no—
411C22×Q8—1721no—
412C22×Q8—1721no—
413C22×Q8C22×D4311yescharacteristic
414C23×C4—861no—
415C23×C4C22×D4311yescharacteristic
416C2×Q16—434no—
417C2×Q16—862no—
418C2×Q16—862no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—1721no—
422C22×C8—431no—
423C22×C8—431no—
424C22×C8—431no—
425C22×C8—431no—
426C22⋊Q8—22no—
427C22⋊Q8—41no—
428C4×Q8—22no—
429C4×Q8—41no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—1721no—
433C4×Q8—1721no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4C22⋊D4311yescharacteristic
448C2×C22⋊C4C22⋊D4311yescharacteristic
449C2×C42—21no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454#107—862no—
455#106—1721no—
456C4⋊C8—1721no—
457#103—862no—
458#103—862no—
459#103—862no—
460#103—862no—
461#103—862no—
462#103—862no—
463#103—1721no—
464#103—1721no—
465C22⋊C8—862no—
466C22⋊C8—1721no—
467C4×C8—862no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95C22⋊D4311yescharacteristic
480#95C22⋊D4311yescharacteristic
481C24C2×C22⋊D4311yescharacteristic
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—432no—
488C2×Q8—432no—
489C2×Q8—432no—
490C2×Q8—432no—
491C2×Q8—864no—
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—1722no—
501C2×Q8—1722no—
502C2×Q8—1724no—
503C2×Q8—1724no—
504C2×Q8—1724no—
505C2×Q8—1724no—
506C2×Q8D4×D4312yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—861no—
518C22×C4—864no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4C2×C22⋊D4311yescharacteristic
525C22×C4C2×C22⋊D4311yescharacteristic
526C22×C4C2×C22⋊D4311yescharacteristic
527C22×C4C2×C22⋊D4311yescharacteristic
528C22×C4C2×C22⋊D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530Q16—868no—
531Q16—1724no—
532C2×C8—432no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—1722no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—42no—
569C42—1722no—
570C42—1722no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23#1306334512yes—
578C23C22×C22⋊D4311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—434no—
584Q8—862no—
585Q8—862no—
586Q8—862no—
587Q8—862no—
588Q8—862no—
589Q8—1728no—
590Q8—1721no—
591Q8—1721no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
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—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—1728no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4#1306335512yes—
636C2×C4C2×D4×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4#41×D4311yescharacteristic
639C2×C4#41×D4311yescharacteristic
640C2×C4#1306337011yescharacteristic
641C2×C4#1306337111yescharacteristic
642C8—862no—
643C8—1721no—
644C8—1721no—
645C8—1721no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22#1458340611yescharacteristic
654C22D4×C22⋊D4311yescharacteristic
655C22#1458353711yescharacteristic
656C22C2×#1306334511yescharacteristic
657C22C2×#1306335511yescharacteristic
658C22#1458371411yescharacteristic
659C22#1458371411yescharacteristic
660C4—22no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—864no—
670C4—3441no—
671C4—3441no—
672C4—1722no—
673C4#123×D4311yescharacteristic
674C4#1458348511yescharacteristic
675C4#1458354111yescharacteristic
676C4#1458357711yescharacteristic
677C2—42no—
678C2#1913805411yescharacteristic
679C2#1914467111yescharacteristic
680C2#1914489011yescharacteristic
681C2#1914616111yescharacteristic
682C2#1914633211yescharacteristic
683C2#1914647611yescharacteristic
684C2#1914687211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2421C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2421D43
hypocenterC43#24902
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2421

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621885C2semidirect
4. #19136146C2semidirect
6. #19135917C2semidirect
8. #19135270C2semidirect
10. #19134939C2semidirect
11. #19134936C2semidirect
12. #19134862C2semidirect
13. #19134607C2semidirect
403. C43#24902semidirect

Maximal subgroups

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

subgroupindex
C2×#145830542
C2×C4×#106218852
C22⋊C4×Dic862
#191361462
#191360212
#191359172
#191357882
#191352702
#191352032
#191349392
#191349362
#191348622
#191346072
#191345292
C43×#24212
#2490243