Finite Group Databasebeta

← #25101446

Subgroups — #25101446

Order 11008.

870 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582949C211yesmaximal, characteristic
2#19136990C211yesmaximal, characteristic
3#117×Dic43C211yesmaximal, characteristic
4#19135366C211yesmaximal, characteristic, complemented
5#19135364C211yesmaximal, characteristic, complemented
6#19135362C211yesmaximal, characteristic, complemented
7#19135360C211yesmaximal, characteristic, complemented
8#19134796C211yesmaximal, characteristic
9#19134794C211yesmaximal, characteristic
10#19134792C211yesmaximal, characteristic
11#107×Dic43C211yesmaximal, characteristic, complemented
12#19134487C211yesmaximal, characteristic, complemented
13#106×Dic43C211yesmaximal, characteristic, complemented
14#19134483C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C22×C4×Dic43C2211yescharacteristic
18#14582949C418yescomplemented
19C2×#13063259C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582766—21no—
31#14582764C2211yescharacteristic
32#14582764C2211yescharacteristic
33#14582760—21no—
34#14582759C2211yescharacteristic
35C4⋊C4×Dic43C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42C22⋊C4×Dic43—21no—
43C22⋊C4×Dic43—21no—
44#14582745—21no—
45#14582744—21no—
46C42×Dic43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C23×Dic43D411yescharacteristic
61C23×Dic43D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063284—22no—
65#13063284—22no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2×C414yes—
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43Q814yes—
83C2×C4×Dic43C2311yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85#13063259—22no—
86#13063258—22no—
87#13063258—22no—
88#13063257—22no—
89#13063256—22no—
90#13063256—22no—
91Dic43⋊C8C2×C414yes—
92Dic43⋊C8C2×C414yes—
93C22⋊(C43⋊C8)C2×C414yes—
94C8×Dic43C2×C414yes—
95C8×Dic43C2×C414yes—
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—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110#117×C43—22no—
111#117×C43—22no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43—21no—
119#107×C43—22no—
120#106×C43—22no—
121C22⋊C8×C43C2×C414yes—
122#95×C43—21no—
123C24×C43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×Q812yes—
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—41no—
143C22×Dic43—41no—
144C22×Dic43C4⋊C414yes—
145C22×Dic43C4⋊C414yes—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43C22×C412yes—
155C2×C8×C43C22×C412yes—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43#4112yes—
163C4⋊C4×C43#4112yes—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—42no—
166C42×C43—24no—
167C22⋊Dic43—24no—
168C22⋊Dic43—42no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43#4112yes—
176C4⋊Dic43#4112yes—
177C4×Dic43—24no—
178C4×Dic43—42no—
179C4×Dic43—42no—
180C4×Dic43—42no—
181C4×Dic43—42no—
182C4×Dic43—42no—
183C4×Dic43—42no—
184C4×Dic43C4⋊C414yes—
185C4×Dic43C4⋊C414yes—
186C4×Dic43C22×C412yes—
187C4×Dic43C22×C412yes—
188C4×Dic43C2×Q812yes—
189C4×Dic43C2×Q812yes—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8C22×C412yes—
195C2×C43⋊C8C22×C412yes—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43C2×C4⋊C412yes—
203C23×C43C22×D411yescharacteristic
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C2×C4⋊C412yes—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×Q811yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—28no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—44no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43C2×C4⋊C412yes—
250C2×Dic43C2×C4⋊C412yes—
251C2×Dic43C2×C4⋊C412yes—
252C2×Dic43C2×C4⋊C412yes—
253C2×Dic43#13512yes—
254C2×Dic43#13512yes—
255C8×C43—22no—
256C8×C43—22no—
257C43⋊C8—22no—
258C43⋊C8—22no—
259#21360—431nomaximal, Sylow
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43C22×C4⋊C411yescharacteristic
268C22×C43#52511yescharacteristic
269C22×C43#52511yescharacteristic
270C22×C43C2×#13511yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57511yescharacteristic
274C4×C43—22no—
275C4×C43—42no—
276C4×C43—42no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C4×#4111yescharacteristic
280C4×C43C4×#4111yescharacteristic
281C4×C43#53311yescharacteristic
282C4×C43#53311yescharacteristic
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—42no—
287Dic43—42no—
288Dic43—81no—
289Dic43—81no—
290Dic43#42714yes—
291C2×#431—431no—
292#2283—431no—
293C4×#117—431no—
294#1949—431no—
295#1949—431no—
296#1949—431no—
297#1949—431no—
298#1854—431no—
299#1854—431no—
300#1854—431no—
301#1854D4311yescharacteristic
302C4×#107—431no—
303C4×#107—431no—
304C4×#106—431no—
305C4×#106—431no—
306C2×C43—42no—
307C2×C43#229611yescharacteristic
308C2×C43C2×#42711yescharacteristic
309C2×C43#291111yescharacteristic
310C2×C43#310211yescharacteristic
311C2×C43#310211yescharacteristic
312C2×C43#310211yescharacteristic
313C2×C43#310211yescharacteristic
314C2×#117—431no—
315C2×#117C2×D4311yescharacteristic
316C22×C42—431no—
317#431—438no—
318C2×#107—431no—
319C2×#107—431no—
320C2×#107—431no—
321C2×#107C2×D4311yescharacteristic
322C2×#106—431no—
323C2×#106—431no—
324C2×#106—431no—
325C2×#106C2×D4311yescharacteristic
326C2×C4⋊C8—431no—
327C2×C4⋊C8—431no—
328C2×C22⋊C8—431no—
329C2×C22⋊C8C2×D4311yescharacteristic
330C2×C4×C8—431no—
331C2×C4×C8—431no—
332#383—861no—
333#382—431no—
334#382—431no—
335#381—861no—
336#380—431no—
337#380C2×D4311yescharacteristic
338C4×C4⋊C4—431no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—431no—
344C4×C22⋊C4—861no—
345C4×C22⋊C4—861no—
346C4×C22⋊C4—861no—
347#376—861no—
348#376—861no—
349C43—861no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340C2×D4311yescharacteristic
357#340C2×D4311yescharacteristic
358C43#2136011yescharacteristic, complemented, Sylow
359C23×C4—431no—
360C23×C4—431no—
361C23×C4C22×D4311yescharacteristic
362C22×C8—431no—
363C22×C8—431no—
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366#117—22no—
367#117—22no—
368#117—862no—
369#117—862no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C42—21no—
383C2×C42—434no—
384C2×C42—431no—
385C2×C42—431no—
386C2×C42—434no—
387C2×C42—431no—
388C2×C42—431no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42—861no—
396#107—22no—
397#107—862no—
398#107—862no—
399#107—862no—
400#106—22no—
401#106—862no—
402#106—862no—
403#106—862no—
404C4⋊C8—434no—
405C4⋊C8—434no—
406C22⋊C8—434no—
407C22⋊C8C4×D4314yes—
408C4×C8—434no—
409C4×C8—434no—
410#95—21no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422C24D4×D4311yescharacteristic
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—431no—
432C22×C4—434no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—434no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4C2×C4×D4312yes—
446C22×C4D4×D4311yescharacteristic
447C22×C4Q8×D4312yes—
448C22×C4C23×D4311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—432no—
454C2×C8—432no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8C2×C4×D4312yes—
460C2×C8C2×C4×D4312yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—432no—
468C4⋊C4—432no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4#1062190012yes—
476C4⋊C4#1062190012yes—
477C22⋊C4—24no—
478C22⋊C4—42no—
479C22⋊C4—864no—
480C22⋊C4—1722no—
481C42—24no—
482C42—434no—
483C42—434no—
484C42—432no—
485C42—432no—
486C42—432no—
487C42—432no—
488C42—864no—
489C42—1722no—
490C42—1722no—
491C42—1722no—
492C42—1722no—
493C42—1722no—
494C42—1722no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23C4⋊C4×D4312yes—
502C23C2×D4×D4311yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—432no—
526C2×C4—432no—
527C2×C4—868no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—1724no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4C4⋊C4×D4312yes—
548C2×C4C22×C4×D4311yescharacteristic
549C2×C4C2×Q8×D4311yescharacteristic
550C2×C4#41×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C2×C4C2×#1062190011yescharacteristic
553C2×C4C2×#1062190011yescharacteristic
554C8—22no—
555C8—22no—
556C8—862no—
557C8—862no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22C2×C4⋊C4×D4311yescharacteristic
566C22#1458340511yescharacteristic
567C22#1458340711yescharacteristic
568C22#135×D4311yescharacteristic
569C22#135×D4311yescharacteristic
570C22#1458369511yescharacteristic
571C22#1458369811yescharacteristic
572C4—22no—
573C4—42no—
574C4—42no—
575C4—81no—
576C4—81no—
577C4—434no—
578C4—862no—
579C4—862no—
580C4—862no—
581C4—3441no—
582C4—3441no—
583C4—1722no—
584C4—1722no—
585C4C4×#1062190011yescharacteristic
586C4C4×#1062190011yescharacteristic
587C4#1458345111yescharacteristic
588C4#1458345111yescharacteristic
589C2—42no—
590C2#1913707411yescharacteristic
591C2#427×D4311yescharacteristic
592C2#1914318211yescharacteristic
593C2#1914460611yescharacteristic
594C2#1914460811yescharacteristic
595C2#1914461411yescharacteristic
596C2#1914461611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#21360
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #19135366C2semidirect
5. #19135364C2semidirect
6. #19135362C2semidirect
7. #19135360C2semidirect
11. #107×Dic43C2semidirect
12. #19134487C2semidirect
13. #106×Dic43C2semidirect
14. #19134483C2semidirect
18. #14582949C4semidirect
358. C43#21360semidirect

Maximal subgroups

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

subgroupindex
C2×#145829492
#191369902
#117×Dic432
#191353662
#191353642
#191353622
#191353602
#191347962
#191347942
#191347922
#107×Dic432
#191344872
#106×Dic432
#191344832
C43×#18542
#2136043