Finite Group Databasebeta

← #25118446

Subgroups — #25118446

Order 11008.

846 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137695C211yesmaximal, characteristic, complemented
2#19137505C211yesmaximal, characteristic
3#19135561C211yesmaximal, characteristic, complemented
4#19135365C211yesmaximal, characteristic, complemented
5#19135329C211yesmaximal, characteristic, complemented
6#19135324C211yesmaximal, characteristic, complemented
7#19135189C211yesmaximal, characteristic, complemented
8#19135182C211yesmaximal, characteristic, complemented
9#19134858C211yesmaximal, characteristic
10#19134844C211yesmaximal, characteristic
11#19134460C211yesmaximal, characteristic, complemented
12#102×Dic43C211yesmaximal, characteristic
13#102×Dic43C211yesmaximal, characteristic
14C4×#13063246C211yesmaximal, characteristic
15C2×C43×#478C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063246C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×C4×C43⋊C8C2211yescharacteristic
23C2×C8×Dic43C2211yescharacteristic
24C2×C8×Dic43C2211yescharacteristic
25#14582798—21no—
26#14582798C2211yescharacteristic
27#14582798C2211yescharacteristic
28#14582798C2211yescharacteristic
29#14582798C2211yescharacteristic
30#14582785—21no—
31#14582785—21no—
32#14582774—21no—
33#14582774—21no—
34#14582765C2211yescharacteristic
35#14582759—21no—
36C4⋊C4×Dic43—21no—
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C2×C43⋊#95—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#125×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#478C418yescomplemented
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—41no—
67D4×Dic43—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43C2311yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85#13063259—41no—
86#13063257—41no—
87#13063246—22no—
88#13063246Q814yes—
89C4×C43⋊C8—22no—
90C8×Dic43—41no—
91C8×Dic43—41no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×D4×C43C2311yescharacteristic
104C23×C4×C43—21no—
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107#125×C43—22no—
108#125×C43C2×C414yescomplemented
109C4×D4×C43—22no—
110C4×D4×C43C2×C414yes—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#107×C43C2×C414yescomplemented
119#106×C43C2×C414yescomplemented
120C4⋊C8×C43C2×C414yescomplemented
121#102×C43C2×C414yes—
122#102×C43C2×C414yes—
123C24×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43C22×C412yes—
128C2×D4×C43C2×Q812yes—
129C2×D4×C43#4112yes—
130C22×C4×C43—24no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—81no—
135C22×C4×C43—81no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—81no—
148C22×Dic43—81no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43C22×C412yes—
158C2×C8×C43C22×C412yes—
159C4⋊C4×C43—24no—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43C22×C412yes—
165C4⋊C4×C43C22×C412yes—
166C4⋊C4×C43C22×C412yes—
167C22⋊C4×C43—24no—
168C42×C43C22×C412yes—
169C42×C43#4112yes—
170C22⋊Dic43—42no—
171C22⋊Dic43—42no—
172C4⋊Dic43—21no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43—81no—
183C4⋊Dic43—81no—
184C4⋊Dic43—81no—
185C4⋊Dic43C2×Q812yes—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—42no—
191C4×Dic43—81no—
192C4×Dic43—81no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×Q812yes—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43C22×D411yescharacteristic
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—22no—
210D4×C43C4×Q814yes—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—84no—
225C2×C4×C43C4×D412yes—
226C2×C4×C43C4×D412yes—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×Q811yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
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—41no—
254C2×Dic43—41no—
255C2×Dic43—84no—
256C2×Dic43—84no—
257C2×Dic43#13512yes—
258C2×Dic43#13512yes—
259C8×C43—22no—
260C8×C43—22no—
261C43⋊C8—22no—
262C43⋊C8—41no—
263#22966—431nomaximal, Sylow
264C22×C43—24no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43C2×C4×D411yescharacteristic
272C22×C43#54611yescharacteristic
273C22×C43D4×Q811yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43#57611yescharacteristic
277C22×C43#57711yescharacteristic
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43C2×C4×Q811yescharacteristic
284C4×C43#52011yescharacteristic
285C4×C43#55211yescharacteristic
286C4×C43#55411yescharacteristic
287Dic43—22no—
288Dic43—22no—
289Dic43—42no—
290Dic43—41no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295C2×#478D4311yescharacteristic
296#2370—431no—
297#2349—431no—
298#1991—431no—
299#1949—431no—
300#1942—431no—
301#1941—431no—
302#1921—431no—
303#1920—431no—
304#1864—431no—
305#1862—431no—
306C8×C4⋊C4—431no—
307C4×#102—431no—
308C4×#102—431no—
309C4×#102—431no—
310C2×C43—44no—
311C2×C43#236011yescharacteristic
312C2×C43C4×#13511yescharacteristic
313C2×C43#294611yescharacteristic
314C2×C43#329611yescharacteristic
315C2×C43#329711yescharacteristic
316C2×C43#338011yescharacteristic
317C2×C43#338111yescharacteristic
318C2×#125C2×D4311yescharacteristic
319C2×C4×D4—431no—
320C2×C4×D4—431no—
321C2×C4×D4C2×D4311yescharacteristic
322#478Dic4318yescomplemented
323C2×#107—431no—
324C2×#107C2×D4311yescharacteristic
325C2×#106—431no—
326C2×#106C2×D4311yescharacteristic
327C2×C4⋊C8C2×D4311yescharacteristic
328C2×#102—431no—
329C2×#102—431no—
330C2×#102C2×D4311yescharacteristic
331C2×#102C2×D4311yescharacteristic
332C2×C4×C8—431no—
333C2×C4×C8—431no—
334C2×C4×C8—431no—
335#389—431no—
336#389—431no—
337#389—431no—
338#389—431no—
339#389—861no—
340#387—861no—
341#387—861no—
342#385—861no—
343#385—861no—
344#382—431no—
345#380—861no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—861no—
351C2×#95—861no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#336—431no—
361#336—431no—
362C43#2296611yescharacteristic, complemented, Sylow
363C22×D4C22×D4311yescharacteristic
364C23×C4—21no—
365C23×C4—861no—
366C23×C4—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371#125—22no—
372#125C2×Dic4314yescomplemented
373C4×D4—22no—
374C4×D4—862no—
375C4×D4—862no—
376C4×D4—1721no—
377C4×D4—1721no—
378C4×D4C2×Dic4314yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
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—861no—
396C2×C22⋊C4—861no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—861no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403#107—1721no—
404#107C2×Dic4314yescomplemented
405#106—1721no—
406#106C2×Dic4314yescomplemented
407C4⋊C8C2×Dic4314yescomplemented
408#102—434no—
409#102—862no—
410#102C2×Dic4314yes—
411#102C2×Dic4314yes—
412C4×C8—862no—
413C4×C8—1721no—
414C4×C8—1721no—
415#95—431no—
416#95—431no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426C24—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4Q8×D4312yes—
431C2×D4#1062190212yes—
432C2×D4C22×Dic4312yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—81no—
438C22×C4—81no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—3441no—
448C22×C4—3441no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4C23×D4311yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8C22×Dic4312yes—
467C2×C8C22×Dic4312yes—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—432no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—3441no—
484C4⋊C4—3441no—
485C4⋊C4—3441no—
486C4⋊C4—1722no—
487C4⋊C4C22×Dic4312yes—
488C4⋊C4C22×Dic4312yes—
489C4⋊C4C22×Dic4312yes—
490C22⋊C4—24no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—861no—
494C42—861no—
495C42—861no—
496C42—861no—
497C42—3441no—
498C42—3441no—
499C42—1722no—
500C42#1062190012yes—
501C42C22×Dic4312yes—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C2×D4×D4311yescharacteristic
510D4—22no—
511D4—22no—
512D4—22no—
513D4Q8×Dic4314yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—84no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—862no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3444no—
542C2×C4—3444no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4D4×Dic4312yes—
555C2×C4D4×Dic4312yes—
556C2×C4C23×Dic4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4C2×#1062190011yescharacteristic
559C2×C4C2×#1062190211yescharacteristic
560C2×C4#1306337111yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—22no—
563C8—22no—
564C8—862no—
565C8—1721no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22C2×D4×Dic4311yescharacteristic
574C22#1458354011yescharacteristic
575C22#1458356211yescharacteristic
576C22#135×D4311yescharacteristic
577C22#135×D4311yescharacteristic
578C22#1458370311yescharacteristic
579C22#1458370911yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—1721no—
591C4—1722no—
592C4—1721no—
593C4C2×Q8×Dic4311yescharacteristic
594C4#1458338211yescharacteristic
595C4#1458359111yescharacteristic
596C4#1458360711yescharacteristic
597C2—44no—
598C2#1913760411yescharacteristic
599C2#135×Dic4311yescharacteristic
600C2#1914342811yescharacteristic
601C2#1914642711yescharacteristic
602C2#1914644211yescharacteristic
603C2#1914745711yescharacteristic
604C2#1914746511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC2×#478D43
hypocenterC43#22966
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. #19137695C2semidirect
3. #19135561C2semidirect
4. #19135365C2semidirect
5. #19135329C2semidirect
6. #19135324C2semidirect
7. #19135189C2semidirect
8. #19135182C2semidirect
11. #19134460C2semidirect
54. C43×#478C4semidirect
108. #125×C43C2×C4semidirect
118. #107×C43C2×C4semidirect
119. #106×C43C2×C4semidirect
120. C4⋊C8×C43C2×C4semidirect
322. #478Dic43semidirect
362. C43#22966semidirect
372. #125C2×Dic43semidirect
404. #107C2×Dic43semidirect
406. #106C2×Dic43semidirect
407. C4⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191376952
#191375052
#191355612
#191353652
#191353292
#191353242
#191351892
#191351822
#191348582
#191348442
#191344602
#102×Dic432
C4×#130632462
C2×C43×#4782
#2296643