Finite Group Databasebeta

← #25156602

Subgroups — #25156602

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583112C211yesmaximal, characteristic
2C2×D8×Dic43C211yesmaximal, characteristic
3#19138380C211yesmaximal, characteristic, complemented
4#19137505C211yesmaximal, characteristic, complemented
5#19136142C211yesmaximal, characteristic, complemented
6#19136085C211yesmaximal, characteristic, complemented
7#19136008C211yesmaximal, characteristic, complemented
8#19135835C211yesmaximal, characteristic, complemented
9#19135272C211yesmaximal, characteristic, complemented
10#19135153C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134927C211yesmaximal, characteristic, complemented
13#19134858C211yesmaximal, characteristic, complemented
14#19134858C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21#14583112—24no—
22D8×Dic43—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582824—21no—
34#14582824—21no—
35#14582805C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582774—21no—
41#14582774—21no—
42#14582774—21no—
43#14582765C2211yescharacteristic
44#14582760—21no—
45#14582759—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47C2×C43⋊#95—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063312—22no—
71#13063312—41no—
72D4×Dic43—22no—
73D4×Dic43—22no—
74D4×Dic43—22no—
75D4×Dic43—41no—
76D4×Dic43—41no—
77D4×Dic43—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43D411yescharacteristic
82C2×C4⋊Dic43D411yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063257—41no—
95Dic43⋊C8—22no—
96#13063250—22no—
97#13063250—41no—
98#13063248—22no—
99#13063246—22no—
100#13063246—22no—
101#13063246—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C2×D8×C43—22no—
118C2×D8×C43—22no—
119C2×D8×C43D414yes—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#102×C43—22no—
131#102×C43—22no—
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×C43C2×D412yes—
143C2×D4×C43C2×D412yes—
144C2×D4×C43#4112yes—
145C2×D4×C43#4112yes—
146C22×C4×C43—24no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—81no—
150C22×C4×C43—81no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—81no—
165C22×Dic43—81no—
166C22×Dic43—81no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177D8×C43—28no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43C2×D412yes—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43#4112yes—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—42no—
190C22⋊C4×C43—81no—
191C42×C43—21no—
192C42×C43—21no—
193C22⋊Dic43—42no—
194C22⋊Dic43—42no—
195C22⋊Dic43—42no—
196C22⋊Dic43—42no—
197C22⋊Dic43—42no—
198#10621883—44no—
199C4⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—41no—
207C4⋊Dic43—81no—
208C4⋊Dic43—81no—
209C4⋊Dic43—81no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
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×C43—41no—
233C23×C43—41no—
234C23×C43C22×D411yescharacteristic
235D4×C43—22no—
236D4×C43—22no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43#12314yes—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—84no—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—84no—
286C2×Dic43—84no—
287C2×Dic43—84no—
288C2×Dic43#13512yes—
289Dic86—41no—
290Dic86—41no—
291Dic86—41no—
292Dic86—41no—
293C8×C43—22no—
294C8×C43—41no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297#26160—431nomaximal, Sylow
298C22×C43—24no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43#52511yescharacteristic
313C22×C43D4211yescharacteristic
314C22×C43#54811yescharacteristic
315C22×C43C2×#13511yescharacteristic
316C22×C43#57511yescharacteristic
317C22×C43#57611yescharacteristic
318C22×C43#57711yescharacteristic
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—42no—
322C4×C43—81no—
323C4×C43C2×#12311yescharacteristic
324C4×C43#53911yescharacteristic
325C4×C43#54711yescharacteristic
326C4×C43#55311yescharacteristic
327Dic43—22no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
331Dic43—81no—
332Dic43—81no—
333Dic43—81no—
334Dic43—81no—
335C2×#463—431no—
336C2×C4×D8—431no—
337#2447—431no—
338#2349—431no—
339#2097—431no—
340#2086—431no—
341#2073—431no—
342#2042—431no—
343#1933—431no—
344#1916—431no—
345#1879D4311yescharacteristic
346#1877—431no—
347#1877—431no—
348#1864—431no—
349#1864—431no—
350C2×C43—44no—
351C2×C43—82no—
352C2×C43#244311yescharacteristic
353C2×C43#310211yescharacteristic
354C2×C43#311811yescharacteristic
355C2×C43#326711yescharacteristic
356C2×C43#328011yescharacteristic
357C2×C43#336011yescharacteristic
358C2×C43#337011yescharacteristic
359C22×SD16—431no—
360C22×D8C2×D4311yescharacteristic
361C2×#124—431no—
362C2×C4×D4—431no—
363C2×C4×D4—431no—
364C2×C4×D4—431no—
365C2×C4×D4C2×D4311yescharacteristic
366#463—864no—
367C4×D8—864no—
368C2×#107—431no—
369C2×#106—431no—
370C2×C4⋊C8—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102C2×D4311yescharacteristic
378C2×#102C2×D4311yescharacteristic
379C2×C4×C8—431no—
380#397—861no—
381#397—861no—
382#391—431no—
383#391—431no—
384#390C2×D4311yescharacteristic
385#389—431no—
386#389—431no—
387#389—431no—
388#385—861no—
389#385—861no—
390#385—861no—
391#382—431no—
392#381—861no—
393#380—861no—
394C4×C4⋊C4—431no—
395C2×#95—861no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400#336—431no—
401#336—431no—
402#336—431no—
403#336C2×D4311yescharacteristic
404C43#2616011yescharacteristic, complemented, Sylow
405C22×Q8—431no—
406C22×D4C22×D4311yescharacteristic
407C22×D4C22×D4311yescharacteristic
408C23×C4—21no—
409C23×C4—861no—
410C23×C4—861no—
411C23×C4—861no—
412C2×SD16—862no—
413C2×SD16—862no—
414C2×SD16—862no—
415C2×D8—22no—
416C2×D8—22no—
417C2×D8D17214yes—
418C22×C8—431no—
419C22×C8—431no—
420C22×C8C22×D4311yescharacteristic
421C22×C8C22×D4311yescharacteristic
422#124—862no—
423#124—1721no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—1721no—
430C4×D4—1721no—
431C4×D4—1721no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42C22×D4311yescharacteristic
453#107—862no—
454#106—1721no—
455C4⋊C8—862no—
456#103—862no—
457#103—862no—
458#103—1721no—
459#102—22no—
460#102—22no—
461#102—862no—
462#102—862no—
463#102—862no—
464C4×C8—862no—
465#95—431no—
466#95—431no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—21no—
477C24—21no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
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×D4C2×D17212yes—
493C2×D4C2×D17212yes—
494C2×D4#1062190012yes—
495C2×D4#1062190012yes—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—3441no—
510C22×C4—3441no—
511C22×C4—3441no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4—1722no—
517C22×C4—1722no—
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4C23×D4311yescharacteristic
521SD16—1724no—
522D8—28no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8C2×D17212yes—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—862no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—3441no—
546C4⋊C4—3441no—
547C4⋊C4—3441no—
548C4⋊C4—1721no—
549C4⋊C4#1062190012yes—
550C22⋊C4—24no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C22⋊C4—1722no—
558C42—21no—
559C42—21no—
560C42—861no—
561C42—861no—
562C42—861no—
563C42—861no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C2×D4×D4311yescharacteristic
579Q8—1721no—
580Q8—1721no—
581Q8—1721no—
582Q8—1721no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4—22no—
588D4—41no—
589D4—41no—
590D4#1306330914yes—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—84no—
604C2×C4—432no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—3444no—
617C2×C4—3444no—
618C2×C4—3444no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4C22×D17211yescharacteristic
632C2×C4C2×#1062190011yescharacteristic
633C2×C4C2×#1062190011yescharacteristic
634C2×C4C2×#1062190011yescharacteristic
635C2×C4#1306337111yescharacteristic
636C2×C4#1306337211yescharacteristic
637C8—22no—
638C8—41no—
639C8—1721no—
640C8—1721no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22#1458340511yescharacteristic
656C22D4×D17211yescharacteristic
657C22#1458355511yescharacteristic
658C22#135×D4311yescharacteristic
659C22#1458369511yescharacteristic
660C22#1458370011yescharacteristic
661C22#1458370911yescharacteristic
662C4—41no—
663C4—42no—
664C4—41no—
665C4—81no—
666C4—862no—
667C4—3441no—
668C4—3441no—
669C4—3441no—
670C4—3441no—
671C4—1721no—
672C4—1721no—
673C4—1721no—
674C4C2×#1306330911yescharacteristic
675C4#1458349311yescharacteristic
676C4#1458355311yescharacteristic
677C4#1458360111yescharacteristic
678C2—44no—
679C2—82no—
680C2#1913832811yescharacteristic
681C2#1914460611yescharacteristic
682C2#1914477211yescharacteristic
683C2#1914612211yescharacteristic
684C2#1914628111yescharacteristic
685C2#1914723911yescharacteristic
686C2#1914734111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#1879D43
hypocenterC43#26160
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
3. #19138380C2semidirect
4. #19137505C2semidirect
5. #19136142C2semidirect
6. #19136085C2semidirect
7. #19136008C2semidirect
8. #19135835C2semidirect
9. #19135272C2semidirect
10. #19135153C2semidirect
11. #19134929C2semidirect
12. #19134927C2semidirect
13. #19134858C2semidirect
14. #19134858C2semidirect
404. C43#26160semidirect

Maximal subgroups

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

subgroupindex
C2×#145831122
C2×D8×Dic432
#191383802
#191375052
#191361422
#191360852
#191360082
#191358352
#191352722
#191351532
#191349292
#191349272
#191348582
C43×#18792
#2616043