Finite Group Databasebeta

← #25269498

Subgroups — #25269498

Order 11008.

2322 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583494C212yesmaximal, complemented
2#19142921C212yesmaximal, complemented
3#19142894C212yesmaximal, complemented
4#19140709C211yesmaximal, characteristic, complemented
5#19140339C212yesmaximal, complemented
6#19139680C214yesmaximal, complemented
7#19139656C214yesmaximal, complemented
8#19139263C214yesmaximal, complemented
9#19138557C214yesmaximal, complemented
10#19137300C212yesmaximal, complemented
11#121×Dic43C212yesmaximal, complemented
12C2×#14582750C211yesmaximal, characteristic, complemented
13C43×#2656C211yesmaximal, characteristic
14#14583494—216no—
15C2×#13063318C2214yes—
16C2×#13063315C2214yes—
17C2×#13063312C2212yes—
18C2×#13063306C2214yes—
19C2×#13063306C2214yes—
20C2×#13063304C2212yes—
21C2×#13063302C2214yes—
22C2×D4×Dic43C2214yes—
23C2×D4×Dic43C2212yes—
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29#14582831C2214yes—
30#14582830C2214yes—
31#14582822C2214yes—
32#14582822C2214yes—
33#14582820C2214yes—
34#14582813C2214yes—
35#14582804C2212yes—
36#14582802C2212yes—
37#14582802C2212yes—
38#14582802C2212yes—
39#14582802C2212yes—
40#14582798C2212yes—
41#14582795C2212yes—
42#14582795C2212yes—
43#14582793C2214yes—
44#14582793C2214yes—
45#14582792C2214yes—
46#14582792C2214yes—
47#14582787C2214yes—
48#14582787C2214yes—
49#14582785C2214yes—
50#14582779C2214yes—
51#14582779C2214yes—
52#14582779C2214yes—
53#14582774C2214yes—
54#14582764C2212yes—
55#14582759C2212yes—
56#14582759C2212yes—
57C4⋊C4×Dic43C2212yes—
58#14582750C2214yes—
59#14582750C2214yes—
60C22⋊C4×Dic43C2214yes—
61C2×C43⋊#95C2211yescharacteristic
62C2×#121×C43C2212yes—
63C2×#121×C43C2212yes—
64C2×#121×C43C2212yes—
65C43×#399C2214yes—
66C43×#392C2214yes—
67C2×#95×C43C2211yescharacteristic
68C22×Dic86C2312yes—
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2314yes—
73C23×Dic43C2311yescharacteristic
74#13063318—216no—
75#13063315—216no—
76#13063312—44no—
77#13063306—216no—
78#13063306—216no—
79#13063304—28no—
80#13063302—216no—
81D4×Dic43—216no—
82D4×Dic43—44no—
83C2×C4⋊Dic43C2314yes—
84C2×C4⋊Dic43C2312yes—
85C2×C4⋊Dic43C2312yes—
86C2×C4⋊Dic43C2312yes—
87C2×C4⋊Dic43C2312yes—
88C2×C4⋊Dic43C2312yes—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4D418yescomplemented
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2314yes—
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×C22⋊Dic43C2314yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×C22⋊Dic43C2314yes—
100C2×C22⋊Dic43C2314yes—
101C2×C22⋊Dic43C2314yes—
102C2×C22⋊Dic43C2314yes—
103C2×C22⋊Dic43C2314yes—
104C2×C4×Dic43—24no—
105C2×C4×Dic43—42no—
106C2×C4×Dic43—42no—
107C2×C4×Dic43C2314yes—
108C2×C4×Dic43C2312yes—
109C2×C4×Dic43C2312yes—
110C2×C4×Dic43C2312yes—
111C2×C4×Dic43C2312yes—
112C2×C4×Dic43C2312yes—
113C2×C4×Dic43C2312yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C22×D4×C43C2314yes—
122C22×D4×C43C2312yes—
123C22×D4×C43C2312yes—
124C22×D4×C43C2312yes—
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128#121×C43—28no—
129#121×C43—28no—
130#121×C43—28no—
131C2×C4⋊C4×C43C2312yes—
132C2×C4⋊C4×C43C2312yes—
133C2×C4⋊C4×C43C2312yes—
134C2×C22⋊C4×C43C2314yes—
135C2×C22⋊C4×C43C2314yes—
136C2×C22⋊C4×C43C2314yes—
137#95×C43C2314yes—
138C24×C43C2414yes—
139C24×C43C2411yescharacteristic
140C2×D4×C43—24no—
141C2×D4×C43—24no—
142C2×D4×C43—24no—
143C2×D4×C43—28no—
144C2×D4×C43—28no—
145C2×D4×C43—28no—
146C2×D4×C43—42no—
147C2×D4×C43—42no—
148C2×D4×C43—42no—
149C2×D4×C43—42no—
150C2×D4×C43—42no—
151C2×D4×C43—42no—
152C22×C4×C43—41no—
153C22×C4×C43—41no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43C2×D414yes—
159C22×C4×C43#4114yes—
160C22×C4×C43#4114yes—
161C22×C4×C43C2414yes—
162C22×C4×C43C2412yes—
163C22×C4×C43C2412yes—
164C22×C4×C43C2412yes—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—28no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—41no—
173C22×Dic43—41no—
174C22×Dic43—41no—
175C22×Dic43—41no—
176C22×Dic43—44no—
177C22×Dic43—44no—
178C22×Dic43C2×D414yes—
179C22×Dic43C2×D414yes—
180C22×Dic43C2412yes—
181C22×Dic43C2414yes—
182C22×Dic43C2414yes—
183C22×Dic43C2412yes—
184C22×Dic43C2412yes—
185C22×Dic43C2411yescharacteristic
186C22×Dic43C2411yescharacteristic
187C2×Dic86—24no—
188C2×Dic86—42no—
189C2×Dic86—42no—
190C4⋊C4×C43—24no—
191C4⋊C4×C43—24no—
192C4⋊C4×C43—24no—
193C22⋊C4×C43—28no—
194C22⋊C4×C43—28no—
195C22⋊C4×C43—28no—
196C22⋊Dic43—28no—
197C22⋊Dic43—28no—
198C22⋊Dic43—28no—
199C22⋊Dic43—28no—
200C22⋊Dic43—28no—
201C22⋊Dic43—28no—
202C22⋊Dic43—44no—
203C22⋊Dic43—44no—
204C4⋊Dic43—24no—
205C4⋊Dic43—28no—
206C4⋊Dic43—42no—
207C4⋊Dic43—42no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210Dic43⋊C4—28no—
211Dic43⋊C4—28no—
212Dic43⋊C4—28no—
213Dic43⋊C4—28no—
214Dic43⋊C4C2×D4116yes—
215C4×Dic43—24no—
216C4×Dic43—24no—
217C4×Dic43—28no—
218C4×Dic43—24no—
219C4×Dic43—24no—
220C4×Dic43—42no—
221C4×Dic43—42no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—24no—
227C23×C43—24no—
228C23×C43—24no—
229C23×C43—24no—
230C23×C43—24no—
231C23×C43—24no—
232C23×C43—24no—
233C23×C43C22×D412yes—
234C23×C43C2×#4112yes—
235C23×C43C2×#4112yes—
236C23×C43C2511yescharacteristic
237D4×C43—48no—
238D4×C43—416no—
239D4×C43—84no—
240D4×C43—84no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—24no—
248C2×C4×C43—24no—
249C2×C4×C43—24no—
250C2×C4×C43—44no—
251C2×C4×C43—44no—
252C2×C4×C43—44no—
253C2×C4×C43C22×D414yes—
254C2×C4×C43C2×#4114yes—
255C2×C4×C43C2×#4114yes—
256C2×Dic43—28no—
257C2×Dic43—28no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—24no—
267C2×Dic43—24no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—22no—
275C2×Dic43—44no—
276C2×Dic43—44no—
277C2×Dic43—88no—
278C2×Dic43C22×D414yes—
279C2×Dic43C22×D414yes—
280C2×Dic43H(5,𝔽2)12yes—
281C2×Dic432−1+412yes—
282Dic86—84no—
283#35004—431nomaximal, Sylow
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—44no—
291C22×C43—44no—
292C22×C43—44no—
293C22×C43—44no—
294C22×C43—44no—
295C22×C43—44no—
296C22×C43—44no—
297C22×C43#53214yes—
298C22×C43C23×D411yescharacteristic
299C22×C43C22×#4111yescharacteristic
300C22×C43C22×#4111yescharacteristic
301C22×C43C2×H(5,𝔽2)11yescharacteristic
302C22×C43C2×2−1+411yescharacteristic
303C22×C43#58511yescharacteristic
304C22×C43#58511yescharacteristic
305C4×C43—24no—
306C4×C43—24no—
307C4×C43—24no—
308C4×C43—44no—
309Dic43—24no—
310Dic43—22no—
311Dic43—22no—
312Dic43—24no—
313Dic43—42no—
314Dic43—44no—
315Dic43—44no—
316C2×#539—432no—
317#2854—432no—
318#2850—432no—
319#2659—431no—
320#2656D4311yescharacteristic
321#2618—432no—
322#2556—434no—
323#2554—434no—
324#2519—434no—
325#2461—434no—
326#2325—432no—
327C4×#121—432no—
328C2×C4×C4⋊C4—431no—
329C2×C43—24no—
330C2×C43—84no—
331C2×C43C2×#53211yescharacteristic
332C2×C43#345911yescharacteristic
333C2×C43#346111yescharacteristic
334C2×C43#349111yescharacteristic
335C2×C43#349211yescharacteristic
336C2×C43#349611yescharacteristic
337C2×C43#349711yescharacteristic
338#539—8616no—
339C2×#126—434no—
340C2×#125—434no—
341C2×#124—432no—
342C2×#123—434no—
343C2×#123—434no—
344C2×C22⋊Q8—432no—
345C2×C22⋊Q8—434no—
346C2×#121C2×D4312yes—
347C2×#121C2×D4312yes—
348C2×#121C2×D4312yes—
349C2×C4×D4—434no—
350C2×C4×D4—432no—
351C22×C4⋊C4—431no—
352C22×C4⋊C4—431no—
353C22×C42—431no—
354C22×C42—431no—
355C22×C42—431no—
356#399C2×D4314yes—
357#398—434no—
358#398—434no—
359#396—434no—
360#396—434no—
361#395—434no—
362#394—434no—
363#392C2×D4314yes—
364#391—432no—
365#390—432no—
366#390—432no—
367#390—432no—
368#390—432no—
369#389—432no—
370#389—432no—
371#389—432no—
372#388—434no—
373#388—434no—
374#388—434no—
375#388—434no—
376#388—434no—
377#388—434no—
378#387—434no—
379#386—434no—
380#386—434no—
381#386—434no—
382#385—434no—
383#382—432no—
384#380—432no—
385#380—432no—
386C4×C4⋊C4—432no—
387C4×C4⋊C4—434no—
388C4×C4⋊C4—434no—
389C4×C22⋊C4—434no—
390C2×#95—431no—
391C2×#95C2×D4311yescharacteristic
392C43#3500411yescharacteristic, complemented, Sylow
393C22×Q8—432no—
394C22×D4C22×D4314yes—
395C22×D4C22×D4312yes—
396C22×D4C22×D4312yes—
397C22×D4C22×D4312yes—
398C23×C4—431no—
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—434no—
403C23×C4C22×D4311yescharacteristic
404C23×C4C22×D4311yescharacteristic
405C23×C4C22×D4311yescharacteristic
406#126—8616no—
407#125—8616no—
408#124—1724no—
409#123—8616no—
410#123—8616no—
411C22⋊Q8—8616no—
412C22⋊Q8—868no—
413#121—28no—
414#121—28no—
415#121—28no—
416C4×D4—8616no—
417C4×D4—1724no—
418C2×C4⋊C4—438no—
419C2×C4⋊C4—434no—
420C2×C4⋊C4—434no—
421C2×C4⋊C4—434no—
422C2×C4⋊C4—434no—
423C2×C4⋊C4—434no—
424C2×C4⋊C4—432no—
425C2×C4⋊C4—434no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—432no—
428C2×C4⋊C4—432no—
429C2×C4⋊C4—432no—
430C2×C4⋊C4—864no—
431C2×C4⋊C4C22×D4312yes—
432C2×C4⋊C4C22×D4312yes—
433C2×C4⋊C4C22×D4312yes—
434C2×C22⋊C4—434no—
435C2×C22⋊C4—434no—
436C2×C22⋊C4—434no—
437C2×C22⋊C4—434no—
438C2×C22⋊C4—434no—
439C2×C22⋊C4—434no—
440C2×C22⋊C4—434no—
441C2×C22⋊C4—434no—
442C2×C22⋊C4C22×D4314yes—
443C2×C22⋊C4C22×D4314yes—
444C2×C22⋊C4C22×D4314yes—
445C2×C42—434no—
446C2×C42—432no—
447C2×C42—432no—
448C2×C42—432no—
449C2×C42—432no—
450C2×C42—432no—
451C2×C42—432no—
452C2×C42—864no—
453C2×C42—1722no—
454C2×C42—1722no—
455#95—434no—
456#95—434no—
457#95—434no—
458#95—434no—
459#95—434no—
460#95—434no—
461#95—434no—
462#95C22×D4314yes—
463C24C23×D4314yes—
464C24C23×D4311yescharacteristic
465C2×Q8—864no—
466C2×Q8—1722no—
467C2×Q8—1722no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—434no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—434no—
492C22×C4—432no—
493C22×C4—434no—
494C22×C4—434no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—868no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—1724no—
503C22×C4—1724no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4D4×D4314yes—
509C22×C4#1062190014yes—
510C22×C4#1062190014yes—
511C22×C4C23×D4314yes—
512C22×C4C23×D4312yes—
513C22×C4C23×D4312yes—
514C22×C4C23×D4312yes—
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—4316no—
519C4⋊C4—868no—
520C4⋊C4—868no—
521C4⋊C4—868no—
522C4⋊C4—868no—
523C4⋊C4—864no—
524C4⋊C4—868no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C22⋊C4—28no—
530C22⋊C4—28no—
531C22⋊C4—28no—
532C22⋊C4—868no—
533C22⋊C4—868no—
534C22⋊C4—868no—
535C22⋊C4—868no—
536C22⋊C4—868no—
537C22⋊C4—868no—
538C22⋊C4—1724no—
539C22⋊C4—1724no—
540C42—864no—
541C42—864no—
542C42—868no—
543C42—864no—
544C42—864no—
545C42—1722no—
546C42—1722no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23C2×D4×D4312yes—
559C23C2×#1062190012yes—
560C23C2×#1062190012yes—
561C23C24×D4311yescharacteristic
562Q8—3444no—
563D4—48no—
564D4—416no—
565D4—84no—
566D4—84no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—434no—
580C2×C4—434no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—868no—
584C2×C4—868no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—862no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—3448no—
603C2×C4—1724no—
604C2×C4—1724no—
605C2×C4C2×D4×D4314yes—
606C2×C4C2×#1062190014yes—
607C2×C4C2×#1062190014yes—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22#1458344714yes—
622C22C22×D4×D4311yescharacteristic
623C22C22×#1062190011yescharacteristic
624C22C22×#1062190011yescharacteristic
625C22H(5,𝔽2)×D4311yescharacteristic
626C222−1+4×D4311yescharacteristic
627C22#1458373411yescharacteristic
628C22#1458373411yescharacteristic
629C4—24no—
630C4—24no—
631C4—24no—
632C4—44no—
633C4—862no—
634C4—862no—
635C4—864no—
636C4—864no—
637C4—1724no—
638C4—1724no—
639C4—1722no—
640C2—24no—
641C2—84no—
642C2C2×#1458344711yescharacteristic
643C2#1914800111yescharacteristic
644C2#1914802311yescharacteristic
645C2#1914829211yescharacteristic
646C2#1914830211yescharacteristic
647C2#1914835611yescharacteristic
648C2#1914836411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
Fitting, prime radicalC43×#2656C2
hypercenter#2656D43
hypocenterC43#35004
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2656

Complements

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

NH ≅ G/Ntype
1. C2×#14583494C2semidirect
2. #19142921C2semidirect
3. #19142894C2semidirect
4. #19140709C2semidirect
5. #19140339C2semidirect
6. #19139680C2semidirect
7. #19139656C2semidirect
8. #19139263C2semidirect
9. #19138557C2semidirect
10. #19137300C2semidirect
11. #121×Dic43C2semidirect
12. C2×#14582750C2semidirect
90. C2×Dic43⋊C4D4semidirect
392. C43#35004semidirect

Maximal subgroups

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

subgroupindex
C2×#145834942
#191429212
#191428942
#191407092
#191403392
#191396802
#191396562
#191392632
#191385572
#191373002
#121×Dic432
C2×#145827502
C43×#26562
#3500443