Finite Group Databasebeta

← #25104585

Subgroups — #25104585

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583252C211yesmaximal, characteristic
2#19137154C211yesmaximal, characteristic, complemented
3#19137142C211yesmaximal, characteristic
4#19135558C211yesmaximal, characteristic, complemented
5#19135405C211yesmaximal, characteristic
6#19135281C211yesmaximal, characteristic
7#19135271C211yesmaximal, characteristic, complemented
8#19135270C211yesmaximal, characteristic, complemented
9#19134724C211yesmaximal, characteristic, complemented
10#19134414C211yesmaximal, characteristic, complemented
11#19134414C211yesmaximal, characteristic, complemented
12#102×Dic43C211yesmaximal, characteristic
13#102×Dic43C211yesmaximal, characteristic
14C4×C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20#14583252C418yescomplemented
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582787—21no—
35#14582787—21no—
36#14582784—21no—
37#14582780—21no—
38#14582764C2211yescharacteristic
39#14582764C2211yescharacteristic
40C4⋊C4×Dic43—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43#14582750—21no—
44C22⋊C4×Dic43—21no—
45C22⋊C4×Dic43—21no—
46C42×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063316—22no—
65#13063316C2×C414yescomplemented
66#13063312—22no—
67#13063312C2×C414yes—
68#13063290—22no—
69#13063290—22no—
70D4×Dic43—22no—
71D4×Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063250—22no—
92#13063250C2×C414yescomplemented
93#13063248—22no—
94#13063248C2×C414yescomplemented
95#13063246—22no—
96#13063246C2×C414yes—
97C4×C43⋊C8—22no—
98C8×Dic43—22no—
99C8×Dic43—22no—
100C8×Dic43—22no—
101C8×Dic43C2×C414yescomplemented
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×D4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43C2×C414yes—
123C4×C8×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C22×C412yes—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C22×C412yes—
160C2×C8×C43#4112yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43C22×C412yes—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C42×C43—21no—
171C42×C43—21no—
172C22⋊Dic43—24no—
173C22⋊Dic43—24no—
174C22⋊Dic43—42no—
175C4⋊Dic43—21no—
176C4⋊Dic43—24no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43C22×C412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—22no—
189C4×Dic43—42no—
190C4×Dic43—42no—
191C4×Dic43—42no—
192C4×Dic43C22×C412yes—
193C4×Dic43#4112yes—
194C4×Dic43#4112yes—
195C4×Dic43#4112yes—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C22×C412yes—
201C2×C43⋊C8#4112yes—
202C23×C43—22no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43C22×D411yescharacteristic
210D4×C43—22no—
211D4×C43—22no—
212D4×C43—41no—
213D4×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43#13512yes—
228C2×C4×C43#13512yes—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—84no—
254C2×Dic43C4×D412yes—
255C2×Dic43C4×D412yes—
256C2×Dic43#12412yes—
257C2×Dic43#12412yes—
258C2×Dic43#13512yes—
259C2×Dic43#13512yes—
260Dic86—22no—
261Dic86—22no—
262Dic86—41no—
263Dic86—41no—
264C8×C43—22no—
265C8×C43—22no—
266C43⋊C8—22no—
267C43⋊C8—22no—
268C4×#488—431nomaximal, Sylow
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×C4×D411yescharacteristic
277C22×C43C2×#12411yescharacteristic
278C22×C43#53211yescharacteristic
279C22×C43C2×#13511yescharacteristic
280C22×C43C2×#13511yescharacteristic
281C22×C43C2×#13511yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43C4×#4111yescharacteristic
289C4×C43C4×#4111yescharacteristic
290C4×C43#52911yescharacteristic
291C4×C43#52911yescharacteristic
292Dic43—22no—
293Dic43—22no—
294Dic43—22no—
295Dic43—42no—
296Dic43—42no—
297Dic43—81no—
298Dic43—81no—
299Dic43#48814yescomplemented
300C2×#488—431no—
301C4×#125—431no—
302C4×#124—431no—
303#1991—431no—
304#1958—431no—
305#1934—431no—
306#1934D4311yescharacteristic
307#1933—431no—
308#1933—431no—
309#1835—431no—
310C4×#103—431no—
311C4×#103—431no—
312C4×#102—431no—
313C4×#102—431no—
314C42×C8—431no—
315C2×C43—82no—
316C2×C43C4×#12411yescharacteristic
317C2×C43C4×#13511yescharacteristic
318C2×C43C4×#13511yescharacteristic
319C2×C43C2×#48811yescharacteristic
320C2×C43#313111yescharacteristic
321C2×C43#316811yescharacteristic
322C2×C43#316811yescharacteristic
323C2×#125—431no—
324C2×#124—431no—
325C2×C4×Q8—431no—
326C2×C4×D4—431no—
327#488—438no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#103—431no—
331C2×#103—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×#102C2×D4311yescharacteristic
335C2×#102C2×D4311yescharacteristic
336C2×C4×C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8—431no—
339C2×C4×C8—431no—
340C2×C4×C8—431no—
341C2×C4×C8C2×D4311yescharacteristic
342#391—431no—
343#390C2×D4311yescharacteristic
344#389—431no—
345#389C2×D4311yescharacteristic
346#388—861no—
347#388—861no—
348#387—861no—
349#387—861no—
350#382—431no—
351#382—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—861no—
355C4×C4⋊C4—861no—
356C4×C22⋊C4—861no—
357C4×C22⋊C4—861no—
358C43—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340C2×D4311yescharacteristic
366#340C2×D4311yescharacteristic
367C43C4×#48811yescharacteristic, complemented, Sylow
368C22×Q8—431no—
369C22×D4C22×D4311yescharacteristic
370C23×C4—861no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375#125—434no—
376#125—862no—
377#124—434no—
378#124—862no—
379C4×Q8—862no—
380C4×Q8—862no—
381C4×D4—862no—
382C4×D4—862no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42—861no—
408C2×C42C22×D4311yescharacteristic
409#103—434no—
410#103—434no—
411#103—862no—
412#103—862no—
413#102—22no—
414#102—434no—
415#102—862no—
416#102C4×D4314yes—
417C4×C8—22no—
418C4×C8—434no—
419C4×C8—862no—
420C4×C8—862no—
421C4×C8—862no—
422C4×C8—862no—
423#95—21no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433C24—21no—
434C2×Q8—432no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×C4×D4312yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4—1722no—
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4C23×D4311yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8C2×C4×D4312yes—
474C2×C8#1062190012yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—432no—
482C4⋊C4—864no—
483C4⋊C4—864no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1722no—
490C4⋊C4—1722no—
491C4⋊C4C2×C4×D4312yes—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—864no—
495C22⋊C4—864no—
496C22⋊C4—1722no—
497C42—21no—
498C42—21no—
499C42—432no—
500C42—432no—
501C42—432no—
502C42—432no—
503C42—862no—
504C42—862no—
505C42—862no—
506C42—862no—
507C42—1722no—
508C42—1722no—
509C42—1722no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C2×D4×D4311yescharacteristic
518Q8—862no—
519Q8—862no—
520Q8—1721no—
521Q8—1721no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—432no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—3444no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4#1306334412yes—
565C2×C4#1306334612yes—
566C2×C4C22×C4×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062190011yescharacteristic
572C8—22no—
573C8—22no—
574C8—862no—
575C8—862no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C4×D4×D4311yescharacteristic
584C22#124×D4311yescharacteristic
585C22#1458344411yescharacteristic
586C22#135×D4311yescharacteristic
587C22#135×D4311yescharacteristic
588C22C2×#1306334411yescharacteristic
589C22C2×#1306334611yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—434no—
596C4—862no—
597C4—862no—
598C4—862no—
599C4—3441no—
600C4—3441no—
601C4—1722no—
602C4—1722no—
603C4C4×#1062190011yescharacteristic
604C4#1458336711yescharacteristic
605C4#1458342611yescharacteristic
606C4#1458343211yescharacteristic
607C2—82no—
608C2#1913713611yescharacteristic
609C2C4×#1306334411yescharacteristic
610C2C4×#1306334611yescharacteristic
611C2#488×D4311yescharacteristic
612C2#1914491411yescharacteristic
613C2#1914515811yescharacteristic
614C2#1914516011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1934D43
hypocenterC43C4×#488
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #19137154C2semidirect
4. #19135558C2semidirect
7. #19135271C2semidirect
8. #19135270C2semidirect
9. #19134724C2semidirect
10. #19134414C2semidirect
11. #19134414C2semidirect
14. C4×C8×Dic43C2semidirect
20. #14583252C4semidirect
65. #13063316C2×C4semidirect
92. #13063250C2×C4semidirect
94. #13063248C2×C4semidirect
101. C8×Dic43C2×C4semidirect
299. Dic43#488semidirect
367. C43C4×#488semidirect

Maximal subgroups

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

subgroupindex
C2×#145832522
#191371542
#191371422
#191355582
#191354052
#191352812
#191352712
#191352702
#191347242
#191344142
#102×Dic432
C4×C8×Dic432
C43×#19342
C4×#48843