Finite Group Databasebeta

← #25103855

Subgroups — #25103855

Order 11008.

900 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137290C211yesmaximal, characteristic
2#19136952C211yesmaximal, characteristic, complemented
3#19135224C211yesmaximal, characteristic, complemented
4#19135217C211yesmaximal, characteristic, complemented
5#19135182C211yesmaximal, characteristic, complemented
6#19135175C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic
8#19134796C211yesmaximal, characteristic, complemented
9#19134681C211yesmaximal, characteristic, complemented
10#19134495C211yesmaximal, characteristic, complemented
11#106×Dic43C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#481C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063235C2211yescharacteristic
25C2×C8×Dic43C2211yescharacteristic
26#14582802—21no—
27#14582802C2211yescharacteristic
28#14582798C2211yescharacteristic
29#14582792—21no—
30#14582779—21no—
31#14582774—21no—
32#14582759C2211yescharacteristic
33C4⋊C4×Dic43—21no—
34C4⋊C4×Dic43—21no—
35C4⋊C4×Dic43C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×C22⋊Dic43—21no—
41C4×C22⋊Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C43×#481C418yescomplemented
55C2×#106×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63D4×Dic43—22no—
64D4×Dic43—22no—
65#13063284—22no—
66#13063284—22no—
67#13063284—22no—
68#13063284—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43D411yescharacteristic
82C2×C22⋊Dic43D411yescharacteristic
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063257—22no—
93#13063246—22no—
94#13063246—22no—
95C22⋊(C43⋊C8)—22no—
96#13063235—22no—
97C8×Dic43—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×D4×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111#121×C43—22no—
112#121×C43C2×C414yes—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43C2×C414yescomplemented
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120#106×C43C2×C414yescomplemented
121#106×C43C2×C414yescomplemented
122#102×C43C2×C414yes—
123#102×C43C2×C414yes—
124C22⋊C8×C43C2×C414yescomplemented
125C24×C43—21no—
126C24×C43C2×D411yescharacteristic
127C2×D4×C43—21no—
128C2×D4×C43—24no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—81no—
134C2×D4×C43—81no—
135C2×D4×C43C22×C412yes—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—24no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43C22×C412yes—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—42no—
155C22×Dic43—81no—
156C22×Dic43—81no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43C22×C412yes—
166C2×C8×C43C22×C412yes—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C22×C412yes—
172C4⋊C4×C43C22×C412yes—
173C4⋊C4×C43C22×C412yes—
174C22⋊C4×C43—24no—
175C22⋊Dic43—24no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—42no—
179C22⋊Dic43—81no—
180C22⋊Dic43—81no—
181C22⋊Dic43—81no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—81no—
191C4⋊Dic43#4112yes—
192C4⋊Dic43#4112yes—
193C4×Dic43—24no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—81no—
197C4×Dic43—81no—
198C4×Dic43—81no—
199C4×Dic43—81no—
200C4×Dic43—81no—
201C4×Dic43#4112yes—
202C4×Dic43#4112yes—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—22no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C4×D412yes—
223C23×C43C22×D411yescharacteristic
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—84no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—84no—
245C2×C4×C43C4×D412yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—84no—
275C2×Dic43#12312yes—
276C2×Dic43#12312yes—
277C8×C43—22no—
278C8×C43—22no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#21584—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43C2×#12311yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43#57611yescharacteristic
300C22×C43#57711yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57711yescharacteristic
303C4×C43—22no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43C4×#4111yescharacteristic
308C4×C43C4×#4111yescharacteristic
309C4×C43#52911yescharacteristic
310C4×C43#52911yescharacteristic
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—42no—
316Dic43—42no—
317Dic43—81no—
318Dic43—81no—
319C2×#481D4311yescharacteristic
320#2324—431no—
321#2274—431no—
322#1926—431no—
323#1925—431no—
324#1920—431no—
325#1919—431no—
326#1875—431no—
327#1854—431no—
328#1823—431no—
329#1776—431no—
330C4×#106—431no—
331#1762—431no—
332C4×#102—431no—
333#1750—431no—
334C2×C43—42no—
335C2×C43—82no—
336C2×C43C4×#12311yescharacteristic
337C2×C43#294611yescharacteristic
338C2×C43#294911yescharacteristic
339C2×C43#309611yescharacteristic
340C2×C43#309911yescharacteristic
341C2×C43#311911yescharacteristic
342C2×C43#312511yescharacteristic
343C2×#121C2×D4311yescharacteristic
344C2×C4×D4—431no—
345C2×#117—431no—
346C2×#117—431no—
347C22×C4⋊C4C2×D4311yescharacteristic
348#481Dic4318yescomplemented
349C2×#107—431no—
350C2×#106—431no—
351C2×#106C2×D4311yescharacteristic
352C2×#106C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102—431no—
355C2×#102C2×D4311yescharacteristic
356C2×#102C2×D4311yescharacteristic
357C2×C22⋊C8—431no—
358C2×C22⋊C8C2×D4311yescharacteristic
359C2×#97—431no—
360C2×C4×C8—431no—
361#390—431no—
362#390—861no—
363#389—431no—
364#388—861no—
365#386—861no—
366#385—861no—
367#380—431no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—861no—
374C4×C4⋊C4—861no—
375C4×C22⋊C4—861no—
376C4×C22⋊C4—861no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336—431no—
386#336—431no—
387C43#2158411yescharacteristic, complemented, Sylow
388C22×D4—21no—
389C22×D4C22×D4311yescharacteristic
390C23×C4—21no—
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#121—22no—
398#121C2×Dic4314yes—
399C4×D4—862no—
400C4×D4—862no—
401#117—862no—
402#117—862no—
403#117—862no—
404#117—862no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C2×Dic4314yescomplemented
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—431no—
420C2×C22⋊C4—431no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42—861no—
434#107—862no—
435#106—862no—
436#106C2×Dic4314yescomplemented
437#106C2×Dic4314yescomplemented
438#102—862no—
439#102—862no—
440#102C2×Dic4314yes—
441#102C2×Dic4314yes—
442C22⋊C8—862no—
443C22⋊C8C2×Dic4314yescomplemented
444#97—862no—
445C4×C8—862no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453C24—21no—
454C24D4×D4311yescharacteristic
455C2×D4—24no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4C22×Dic4312yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—3441no—
483C22×C4—3441no—
484C22×C4—1722no—
485C22×C4D4×D4311yescharacteristic
486C22×C4#1062190012yes—
487C22×C4C22×Dic4312yes—
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8C22×Dic4312yes—
500C2×C8C22×Dic4312yes—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—432no—
506C4⋊C4—432no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—3441no—
516C4⋊C4C22×Dic4312yes—
517C4⋊C4C22×Dic4312yes—
518C4⋊C4C22×Dic4312yes—
519C22⋊C4—24no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—864no—
523C22⋊C4—3441no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—1722no—
527C42—432no—
528C42—432no—
529C42—864no—
530C42—861no—
531C42—861no—
532C42—3441no—
533C42—3441no—
534C42—3441no—
535C42—3441no—
536C42—3441no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23D4×Dic4312yes—
551C23C2×D4×D4311yescharacteristic
552D4—22no—
553D4—22no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4D4×Dic4312yes—
599C2×C4C23×Dic4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4C2×#1062190011yescharacteristic
605C8—22no—
606C8—22no—
607C8—1721no—
608C8—1721no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22C2×D4×Dic4311yescharacteristic
624C22#123×D4311yescharacteristic
625C22#1458340711yescharacteristic
626C22#1458370311yescharacteristic
627C22#1458370511yescharacteristic
628C22#1458370511yescharacteristic
629C22#1458370911yescharacteristic
630C4—22no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—862no—
635C4—862no—
636C4—3441no—
637C4—3441no—
638C4—1722no—
639C4—1721no—
640C4—1721no—
641C4—1722no—
642C4#41×Dic4311yescharacteristic
643C4#41×Dic4311yescharacteristic
644C4#1458342611yescharacteristic
645C4#1458342611yescharacteristic
646C2—42no—
647C2—82no—
648C2#123×Dic4311yescharacteristic
649C2#1914342811yescharacteristic
650C2#1914345511yescharacteristic
651C2#1914455211yescharacteristic
652C2#1914458511yescharacteristic
653C2#1914478911yescharacteristic
654C2#1914487511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#481C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#481D43
hypocenterC43#21584
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. #19136952C2semidirect
3. #19135224C2semidirect
4. #19135217C2semidirect
5. #19135182C2semidirect
6. #19135175C2semidirect
8. #19134796C2semidirect
9. #19134681C2semidirect
10. #19134495C2semidirect
11. #106×Dic43C2semidirect
12. #19134422C2semidirect
13. #102×Dic43C2semidirect
14. #19134363C2semidirect
54. C43×#481C4semidirect
115. C2×C4⋊C4×C43C2×C4semidirect
120. #106×C43C2×C4semidirect
121. #106×C43C2×C4semidirect
124. C22⋊C8×C43C2×C4semidirect
348. #481Dic43semidirect
387. C43#21584semidirect
414. C2×C4⋊C4C2×Dic43semidirect
436. #106C2×Dic43semidirect
437. #106C2×Dic43semidirect
443. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191372902
#191369522
#191352242
#191352172
#191351822
#191351752
#191349182
#191347962
#191346812
#191344952
#106×Dic432
#191344222
#102×Dic432
#191343632
C2×C43×#4812
#2158443