Finite Group Databasebeta

← #25103870

Subgroups — #25103870

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137279C211yesmaximal, characteristic
2#19136952C211yesmaximal, characteristic
3#19135238C211yesmaximal, characteristic, complemented
4#19135231C211yesmaximal, characteristic, complemented
5#19135189C211yesmaximal, characteristic, complemented
6#19135168C211yesmaximal, characteristic, complemented
7#19134908C211yesmaximal, characteristic
8#19134796C211yesmaximal, characteristic
9#19134681C211yesmaximal, characteristic
10#19134494C211yesmaximal, characteristic, complemented
11#107×Dic43C211yesmaximal, characteristic, complemented
12#19134427C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic
15C2×C43×#484C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063235C2211yescharacteristic
25C2×C8×Dic43C2211yescharacteristic
26#14582806C2211yescharacteristic
27#14582798—21no—
28#14582798C2211yescharacteristic
29#14582792—21no—
30#14582792—21no—
31#14582785—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×C22⋊Q8×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C43×#484C418yescomplemented
55C2×#107×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62Q8×Dic43—22no—
63Q8×Dic43—22no—
64#13063284—22no—
65#13063284—22no—
66#13063284—22no—
67#13063284—22no—
68C2×C4⋊Dic43—21no—
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⋊Dic43D411yescharacteristic
79C2×C22⋊Dic43D411yescharacteristic
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063257—22no—
91#13063249—22no—
92#13063249—22no—
93C22⋊(C43⋊C8)—22no—
94#13063235—22no—
95C8×Dic43—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×Q8×C43C2311yescharacteristic
106C23×C4×C43—21no—
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22⋊Q8×C43—22no—
111C22⋊Q8×C43C2×C414yes—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43C2×C414yes—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120#107×C43C2×C414yes—
121#107×C43C2×C414yes—
122#103×C43C2×C414yes—
123#103×C43C2×C414yes—
124C22⋊C8×C43C2×C414yes—
125C24×C43C2×D411yescharacteristic
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—24no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—81no—
142C22×C4×C43—81no—
143C22×C4×C43C22×C412yes—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43#4112yes—
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C22×C412yes—
160C2×C8×C43C22×C412yes—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C22×C412yes—
167C4⋊C4×C43C22×C412yes—
168C4⋊C4×C43C22×C412yes—
169C22⋊C4×C43—24no—
170C22⋊Dic43—24no—
171C22⋊Dic43—22no—
172C22⋊Dic43—22no—
173C22⋊Dic43—81no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43—81no—
184C4⋊Dic43#4112yes—
185C4⋊Dic43#4112yes—
186C4×Dic43—24no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—42no—
190C4×Dic43—81no—
191C4×Dic43—81no—
192C4×Dic43—81no—
193C4×Dic43—81no—
194C4×Dic43—81no—
195C4×Dic43#4112yes—
196C4×Dic43#4112yes—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43C4×D412yes—
210C23×C43C22×D411yescharacteristic
211Q8×C43—22no—
212Q8×C43—22no—
213Q8×C43—41no—
214Q8×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—84no—
234C2×C4×C43C4×D412yes—
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43#12312yes—
264C2×Dic43#12312yes—
265C8×C43—22no—
266C8×C43—22no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#21585—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43C2×C4×D411yescharacteristic
278C22×C43C2×#12311yescharacteristic
279C22×C43#52511yescharacteristic
280C22×C43#57611yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57811yescharacteristic
283C22×C43#57811yescharacteristic
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—42no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43C4×#4111yescharacteristic
290C4×C43C4×#4111yescharacteristic
291C4×C43#52911yescharacteristic
292C4×C43#52911yescharacteristic
293Dic43—22no—
294Dic43—22no—
295Dic43—41no—
296Dic43—41no—
297Dic43—42no—
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301C2×#484D4311yescharacteristic
302#2323—431no—
303#2274—431no—
304#1928—431no—
305#1927—431no—
306#1921—431no—
307#1918—431no—
308#1873—431no—
309#1854—431no—
310#1823—431no—
311#1776—431no—
312C4×#107—431no—
313#1763—431no—
314C4×#103—431no—
315#1750—431no—
316C2×C43—42no—
317C2×C43C4×#12311yescharacteristic
318C2×C43#294611yescharacteristic
319C2×C43#295011yescharacteristic
320C2×C43#309711yescharacteristic
321C2×C43#309811yescharacteristic
322C2×C43#312011yescharacteristic
323C2×C43#312411yescharacteristic
324C2×C22⋊Q8C2×D4311yescharacteristic
325C2×C4×Q8—431no—
326C2×#117—431no—
327C2×#117—431no—
328C22×C4⋊C4C2×D4311yescharacteristic
329#484Dic4318yescomplemented
330C2×#107—431no—
331C2×#107C2×D4311yescharacteristic
332C2×#107C2×D4311yescharacteristic
333C2×#106—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#103C2×D4311yescharacteristic
337C2×#103C2×D4311yescharacteristic
338C2×C22⋊C8—431no—
339C2×C22⋊C8C2×D4311yescharacteristic
340C2×#97—431no—
341C2×C4×C8—431no—
342#391—431no—
343#389—431no—
344#389—861no—
345#388—861no—
346#388—861no—
347#387—861no—
348#380—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—431no—
351C4×C4⋊C4—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—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#336—431no—
367#336—431no—
368C43#2158511yescharacteristic, complemented, Sylow
369C22×Q8C22×D4311yescharacteristic
370C23×C4—21no—
371C23×C4C22×D4311yescharacteristic
372C22×C8—431no—
373C22×C8—431no—
374C22×C8C22×D4311yescharacteristic
375C22×C8C22×D4311yescharacteristic
376C22⋊Q8—22no—
377C22⋊Q8C2×Dic4314yes—
378C4×Q8—862no—
379C4×Q8—862no—
380#117—862no—
381#117—862no—
382#117—862no—
383#117—862no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4C2×Dic4314yes—
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—431no—
401C2×C22⋊C4—431no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C42—431no—
405C2×C42—431no—
406C2×C42—861no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413#107—862no—
414#107C2×Dic4314yes—
415#107C2×Dic4314yes—
416#106—862no—
417#103—862no—
418#103—862no—
419#103C2×Dic4314yes—
420#103C2×Dic4314yes—
421C22⋊C8—862no—
422C22⋊C8C2×Dic4314yes—
423#97—862no—
424C4×C8—862no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24D4×D4311yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C22×Dic4312yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4D4×D4311yescharacteristic
461C22×C4#1062190012yes—
462C22×C4C22×Dic4312yes—
463C22×C4C23×D4311yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8C22×Dic4312yes—
475C2×C8C22×Dic4312yes—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—432no—
482C4⋊C4—432no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—3441no—
492C4⋊C4—1722no—
493C4⋊C4C22×Dic4312yes—
494C4⋊C4C22×Dic4312yes—
495C4⋊C4C22×Dic4312yes—
496C22⋊C4—24no—
497C22⋊C4—862no—
498C22⋊C4—862no—
499C22⋊C4—864no—
500C22⋊C4—3441no—
501C42—432no—
502C42—432no—
503C42—864no—
504C42—861no—
505C42—861no—
506C42—3441no—
507C42—3441no—
508C42—3441no—
509C42—3441no—
510C42—3441no—
511C42—1722no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23D4×Dic4312yes—
519C23C2×D4×D4311yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—84no—
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—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4D4×Dic4312yes—
568C2×C4C23×Dic4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4#41×D4311yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C2×C4C2×#1062190011yescharacteristic
574C8—22no—
575C8—22no—
576C8—1721no—
577C8—1721no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×D4×Dic4311yescharacteristic
586C22#123×D4311yescharacteristic
587C22#1458340711yescharacteristic
588C22#1458370311yescharacteristic
589C22#1458370911yescharacteristic
590C22#1458371211yescharacteristic
591C22#1458371211yescharacteristic
592C4—22no—
593C4—42no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—862no—
598C4—862no—
599C4—3441no—
600C4—3441no—
601C4—1722no—
602C4—1721no—
603C4—1721no—
604C4—1722no—
605C4#41×Dic4311yescharacteristic
606C4#41×Dic4311yescharacteristic
607C4#1458342611yescharacteristic
608C4#1458342611yescharacteristic
609C2—42no—
610C2#123×Dic4311yescharacteristic
611C2#1914342811yescharacteristic
612C2#1914346311yescharacteristic
613C2#1914456311yescharacteristic
614C2#1914457411yescharacteristic
615C2#1914480411yescharacteristic
616C2#1914486011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#484C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#484D43
hypocenterC43#21585
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #19135238C2semidirect
4. #19135231C2semidirect
5. #19135189C2semidirect
6. #19135168C2semidirect
10. #19134494C2semidirect
11. #107×Dic43C2semidirect
12. #19134427C2semidirect
13. #103×Dic43C2semidirect
54. C43×#484C4semidirect
329. #484Dic43semidirect
368. C43#21585semidirect

Maximal subgroups

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

subgroupindex
#191372792
#191369522
#191352382
#191352312
#191351892
#191351682
#191349082
#191347962
#191346812
#191344942
#107×Dic432
#191344272
#103×Dic432
#191343632
C2×C43×#4842
#2158543