Finite Group Databasebeta

← #25146135

Subgroups — #25146135

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583112C211yesmaximal, characteristic
2C2×#14583023C211yesmaximal, characteristic, complemented
3#19140080C211yesmaximal, characteristic, complemented
4#19139951C211yesmaximal, characteristic, complemented
5#19135989C211yesmaximal, characteristic, complemented
6#19135965C211yesmaximal, characteristic, complemented
7#19135911C211yesmaximal, characteristic, complemented
8#19135462C211yesmaximal, characteristic
9#19135448C211yesmaximal, characteristic, complemented
10#19135405C211yesmaximal, characteristic, complemented
11#19135366C211yesmaximal, characteristic, complemented
12#19135281C211yesmaximal, characteristic, complemented
13#19135272C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2054C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20#14583112—24no—
21#14583023—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582835—21no—
36#14582827—21no—
37#14582811—21no—
38#14582811—21no—
39#14582805C2211yescharacteristic
40#14582804C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582798C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582792—21no—
46#14582787—21no—
47#14582774—21no—
48#14582771—21no—
49#14582764C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063312—22no—
70#13063312—22no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73D4×Dic43—22no—
74D4×Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43D411yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063259—41no—
94#13063256—41no—
95Dic43⋊C8—22no—
96Dic43⋊C8D414yes—
97#13063250—22no—
98#13063250—41no—
99#13063248—22no—
100#13063246—22no—
101#13063246—22no—
102#13063246—22no—
103C4×C43⋊C8—22no—
104C8×Dic43—22no—
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×D4×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C2×D8×C43—22no—
118C2×D8×C43—22no—
119C2×D8×C43—41no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130#102×C43—22no—
131#102×C43—41no—
132C24×C43—21no—
133C24×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43#4112yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—42no—
156C22×Dic43—81no—
157C22×Dic43—81no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C2×Dic86—22no—
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171D8×C43—44no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D412yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—81no—
185C22⋊C4×C43—81no—
186C42×C43—21no—
187C42×C43—21no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195#10621883—44no—
196C4⋊Dic43—22no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—81no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—81no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—81no—
210C4×Dic43C2×D412yes—
211C4×Dic43#4112yes—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C2×D412yes—
217C2×C43⋊C8#4112yes—
218C23×C43—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43C22×D411yescharacteristic
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43#13512yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
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—41no—
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—
281C2×Dic43#12112yes—
282C2×Dic43#12112yes—
283C2×Dic43#13512yes—
284Dic86—28no—
285Dic86—41no—
286Dic86—41no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293#25296—431nomaximal, Sylow
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43C2×#12111yescharacteristic
309C22×C43#54811yescharacteristic
310C22×C43#55011yescharacteristic
311C22×C43C2×#13511yescharacteristic
312C22×C43C2×#13511yescharacteristic
313C22×C43#57611yescharacteristic
314C22×C43#57711yescharacteristic
315C4×C43—22no—
316C4×C43—41no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43#52911yescharacteristic
320C4×C43#54211yescharacteristic
321C4×C43#54611yescharacteristic
322C4×C43#54811yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—22no—
326Dic43—41no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330Dic43—81no—
331C2×#463—431no—
332C2×C8×Q8—431no—
333#2592—431no—
334#2580—431no—
335#2068—431no—
336#2065—431no—
337#2055—431no—
338#2054D4311yescharacteristic
339#1970—431no—
340#1968—431no—
341#1958—431no—
342#1949—431no—
343#1934—431no—
344#1933—431no—
345C4×#102—431no—
346C2×C43—82no—
347C2×C43—161no—
348C2×C43#242611yescharacteristic
349C2×C43#305011yescharacteristic
350C2×C43#306211yescharacteristic
351C2×C43#336011yescharacteristic
352C2×C43#336111yescharacteristic
353C2×C43#339411yescharacteristic
354C2×C43#339611yescharacteristic
355C22×SD16—431no—
356C22×D8C2×D4311yescharacteristic
357C2×#124—431no—
358C2×C4×Q8—431no—
359C2×C4×D4—431no—
360#463—864no—
361C8×Q8—864no—
362C2×#107—431no—
363C2×#106—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×C4⋊C8C2×D4311yescharacteristic
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102C2×D4311yescharacteristic
374C2×#102C2×D4311yescharacteristic
375C2×C4×C8—431no—
376C2×C4×C8—431no—
377C2×C4×C8—431no—
378#399—861no—
379#397—861no—
380#393—861no—
381#393—861no—
382#391—431no—
383#391—431no—
384#390—431no—
385#390—431no—
386#390C2×D4311yescharacteristic
387#390C2×D4311yescharacteristic
388#389—431no—
389#389—431no—
390#388—861no—
391#388—861no—
392#385—861no—
393#385—861no—
394#382—431no—
395C4×C4⋊C4—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400C43#2529611yescharacteristic, complemented, Sylow
401C22×Q8—431no—
402C22×Q8—431no—
403C22×D4C22×D4311yescharacteristic
404C22×D4C22×D4311yescharacteristic
405C23×C4—861no—
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16—1721no—
409C2×D8—22no—
410C2×D8—22no—
411C2×D8—41no—
412C22×C8—431no—
413C22×C8—431no—
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416#124—862no—
417#124—862no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×D4—862no—
421C4×D4—862no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—861no—
446C2×C42C22×D4311yescharacteristic
447#107—1721no—
448#106—1721no—
449C4⋊C8—22no—
450C4⋊C8—434no—
451C4⋊C8—862no—
452#103—862no—
453#103—862no—
454#103—1721no—
455#102—22no—
456#102—41no—
457#102—862no—
458#102—862no—
459#102—862no—
460C4×C8—862no—
461C4×C8—862no—
462C4×C8—862no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—21no—
473C24—21no—
474C2×Q8—862no—
475C2×Q8—862no—
476C2×Q8—862no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4#1062190012yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—3441no—
506C22×C4—3441no—
507C22×C4—1722no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—1724no—
512D8—44no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—432no—
519C2×C8—432no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8D4×D4312yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—3441no—
539C4⋊C4—3441no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4—3441no—
545C22⋊C4—3441no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C22⋊C4—1722no—
550C22⋊C4—1722no—
551C42—21no—
552C42—21no—
553C42—432no—
554C42—432no—
555C42—861no—
556C42—861no—
557C42—3441no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C2×D4×D4311yescharacteristic
573Q8—868no—
574Q8—1721no—
575Q8—1721no—
576Q8—1721no—
577Q8—1721no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—41no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—432no—
598C2×C4—432no—
599C2×C4—432no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—3444no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4#1306334412yes—
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4C2×#1062190011yescharacteristic
627C2×C4#1306337011yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—22no—
630C8—41no—
631C8—862no—
632C8—862no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22#121×D4311yescharacteristic
648C22#1458355511yescharacteristic
649C22#1458356711yescharacteristic
650C22#135×D4311yescharacteristic
651C22C2×#1306334411yescharacteristic
652C22#1458370311yescharacteristic
653C22#1458370911yescharacteristic
654C4—22no—
655C4—41no—
656C4—81no—
657C4—81no—
658C4—862no—
659C4—862no—
660C4—862no—
661C4—3441no—
662C4—3441no—
663C4—3441no—
664C4—3441no—
665C4—1721no—
666C4#1458342611yescharacteristic
667C4#1458351711yescharacteristic
668C4#1458353611yescharacteristic
669C4#1458355711yescharacteristic
670C2—82no—
671C2—161no—
672C2#1913815411yescharacteristic
673C2#1914417411yescharacteristic
674C2#1914427211yescharacteristic
675C2#1914723911yescharacteristic
676C2#1914725911yescharacteristic
677C2#1914759511yescharacteristic
678C2#1914760211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2054C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#2054D43
hypocenterC43#25296
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2054

Complements

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

NH ≅ G/Ntype
2. C2×#14583023C2semidirect
3. #19140080C2semidirect
4. #19139951C2semidirect
5. #19135989C2semidirect
6. #19135965C2semidirect
7. #19135911C2semidirect
9. #19135448C2semidirect
10. #19135405C2semidirect
11. #19135366C2semidirect
12. #19135281C2semidirect
13. #19135272C2semidirect
14. #102×Dic43C2semidirect
400. C43#25296semidirect

Maximal subgroups

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

subgroupindex
C2×#145831122
C2×#145830232
#191400802
#191399512
#191359892
#191359652
#191359112
#191354622
#191354482
#191354052
#191353662
#191352812
#191352722
#102×Dic432
C43×#20542
#2529643