Finite Group Databasebeta

← #25104320

Subgroups — #25104320

Order 11008.

868 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
1C2×#14583198C211yesmaximal, characteristic
2#19137332C211yesmaximal, characteristic, complemented
3#19136955C211yesmaximal, characteristic
4#19135549C211yesmaximal, characteristic, complemented
5#19135350C211yesmaximal, characteristic, complemented
6#19135185C211yesmaximal, characteristic, complemented
7#19135182C211yesmaximal, characteristic, complemented
8#19134843C211yesmaximal, characteristic
9#19134839C211yesmaximal, characteristic
10#19134594C211yesmaximal, characteristic
11C4×#13063258C211yesmaximal, characteristic, complemented
12#19134455C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic
14C4×#13063245C211yesmaximal, characteristic
15C43×#1776C211yesmaximal, characteristic, complemented
16C2×#13063316C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14583198C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582797—21no—
32#14582796—21no—
33#14582795C2211yescharacteristic
34#14582783—21no—
35#14582782—21no—
36#14582768C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×(C2×D43)⋊C4—21no—
41C4×(C2×D43)⋊C4—21no—
42#14582746—21no—
43#14582745C2211yescharacteristic
44#95×D43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063316—22no—
67#13063316C2×C414yescomplemented
68C4×D172—22no—
69C4×D172Q814yes—
70#13063287—22no—
71#13063287—22no—
72#13063287—22no—
73#13063287C2×C414yes—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—22no—
92#13063258C2×C414yescomplemented
93Dic43⋊C8—22no—
94Dic43⋊C8C2×C414yescomplemented
95#13063247—22no—
96#13063247C2×C414yes—
97#13063245—22no—
98#13063245C2×C414yes—
99C4×C43⋊C8—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#107×C43—22no—
119#106×C43C2×C414yescomplemented
120#97×C43—22no—
121#95×C43—21no—
122#95×C43—21no—
123C23×D43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172C22×C412yes—
142C2×D172C2×Q812yes—
143C2×D172#4112yes—
144C2×C4×D43—24no—
145C2×C4×D43—24no—
146C2×C4×D43—24no—
147C2×C4×D43—81no—
148C2×C4×D43—81no—
149C2×C4×D43—81no—
150C2×C4×D43—81no—
151C2×C4×D43—81no—
152C2×C4×D43—81no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43C22×C412yes—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43C22×C412yes—
165C4⋊C4×C43C22×C412yes—
166C4⋊C4×C43#4112yes—
167C42×C43—81no—
168C42×C43—81no—
169C42×C43C2×Q812yes—
170C42×C43#4112yes—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—24no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—24no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—81no—
180C4⋊Dic43C22×C412yes—
181C4⋊Dic43C2×Q812yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—81no—
184Dic43⋊C4—81no—
185Dic43⋊C4—81no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—81no—
189C4×Dic43—81no—
190C4×Dic43—81no—
191C4×Dic43C22×C412yes—
192C4×Dic43#4112yes—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
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×C43—41no—
223C2×C4×C43C22⋊Q812yes—
224C2×C4×C43C22⋊Q812yes—
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C22×Q811yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43C4×D412yes—
251C2×Dic43C4×D412yes—
252D172—22no—
253D172—22no—
254D172—22no—
255D172C4×Q814yes—
256C4×D43—84no—
257C4×D43—84no—
258C4×D43—84no—
259C8×C43—22no—
260C8×C43—41no—
261C43⋊C8—22no—
262C43⋊C8—41no—
263#21620—431nomaximal, Sylow
264C22×C43C2×C4×D411yescharacteristic
265C22×C43C2×C22⋊Q811yescharacteristic
266C22×C43#52511yescharacteristic
267C22×C43#57611yescharacteristic
268C22×C43#57611yescharacteristic
269C22×C43#57711yescharacteristic
270C22×C43#57811yescharacteristic
271C2×D43—24no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43—81no—
284C4×C43C2×C4×Q811yescharacteristic
285C4×C43C4×#4111yescharacteristic
286C4×C43#52911yescharacteristic
287C4×C43#53311yescharacteristic
288Dic43—22no—
289Dic43—22no—
290Dic43—42no—
291Dic43—41no—
292Dic43—41no—
293Dic43—42no—
294Dic43—81no—
295C2×#478—431no—
296#2330—431no—
297#2275—431no—
298#1989—431no—
299#1947—431no—
300#1921—431no—
301#1920—431no—
302#1862—431no—
303#1862—431no—
304#1802—431no—
305#1776D4311yescharacteristic, complemented
306C4×#107—431no—
307#1768—431no—
308#1762—431no—
309C4×#102—431no—
310C2×C43C4×C22⋊Q811yescharacteristic
311C2×C43#294611yescharacteristic
312C2×C43#295111yescharacteristic
313C2×C43#308111yescharacteristic
314C2×C43#308311yescharacteristic
315C2×C43#312011yescharacteristic
316C2×C43#312211yescharacteristic
317D43—44no—
318C2×#125—431no—
319C2×C4×D4—431no—
320C2×C4×D4—431no—
321C2×C4×D4—431no—
322#478—438no—
323C2×#107—431no—
324C2×#107—431no—
325C2×#107C2×D4311yescharacteristic
326C2×#106C2×D4311yescharacteristic
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#97C2×D4311yescharacteristic
334C2×C4×C8—431no—
335#389—431no—
336#389—431no—
337#389—861no—
338#389—861no—
339#387—861no—
340#387—861no—
341#384—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4C2×D4311yescharacteristic
346C4×C4⋊C4C2×D4311yescharacteristic
347C4×C22⋊C4—861no—
348C4×C22⋊C4—861no—
349C4×C22⋊C4—861no—
350#376—431no—
351C2×#95—861no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340C2×D4311yescharacteristic
359#340C2×D4311yescharacteristic
360#336—431no—
361#336—431no—
362C43#2162011yescharacteristic, complemented, Sylow
363C22×D4—431no—
364C23×C4—861no—
365C23×C4—861no—
366C23×C4—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371#125—434no—
372#125—862no—
373C4×D4—434no—
374C4×D4—434no—
375C4×D4—862no—
376C4×D4—862no—
377C4×D4—862no—
378C4×D4—862no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—861no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403#107—22no—
404#107—434no—
405#107—862no—
406#106C4×D4314yescomplemented
407C4⋊C8—434no—
408C4⋊C8—862no—
409#102—434no—
410#102—434no—
411#102—862no—
412#102—862no—
413#97—22no—
414C4×C8—862no—
415#95—21no—
416#95—21no—
417#95—431no—
418#95—431no—
419#95—431no—
420#95—431no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426C24—861no—
427C2×D4—432no—
428C2×D4—432no—
429C2×D4—432no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—864no—
442C22×C4—864no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—864no—
446C22×C4—861no—
447C22×C4—3441no—
448C22×C4—3441no—
449C22×C4—3441no—
450C22×C4—3441no—
451C22×C4—3441no—
452C22×C4—3441no—
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4C23×D4311yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—432no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8C2×C4×D4312yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—864no—
476C4⋊C4—864no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—3441no—
484C4⋊C4—3441no—
485C4⋊C4C2×C4×D4312yes—
486C4⋊C4C2×C4×D4312yes—
487C4⋊C4#1062189812yes—
488C22⋊C4—864no—
489C22⋊C4—864no—
490C22⋊C4—864no—
491C42—81no—
492C42—81no—
493C42—432no—
494C42—432no—
495C42—861no—
496C42—861no—
497C42—3441no—
498C42—3441no—
499C42—3441no—
500C42#1062189812yes—
501C42Q8×D4312yes—
502C23—862no—
503C23—862no—
504C23—862no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23C2×D4×D4311yescharacteristic
510D4—434no—
511D4—862no—
512D4—862no—
513D4—862no—
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—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—3444no—
545C2×C4—3444no—
546C2×C4—3444no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4#1306330312yes—
555C2×C4#1306330312yes—
556C2×C4C22×C4×D4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4#41×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4C2×#1062189811yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C8—22no—
563C8—41no—
564C8—862no—
565C8—1721no—
566C22—864no—
567C22—1722no—
568C22—1722no—
569C22—1722no—
570C22—1722no—
571C22—1722no—
572C22—1722no—
573C22C4×D4×D4311yescharacteristic
574C22C2×#1306330311yescharacteristic
575C22#1458340811yescharacteristic
576C22#1458370311yescharacteristic
577C22#1458370311yescharacteristic
578C22#1458370811yescharacteristic
579C22#1458371511yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—81no—
586C4—862no—
587C4—862no—
588C4—3441no—
589C4—1722no—
590C4—1721no—
591C4—1721no—
592C4—1722no—
593C4C4×Q8×D4311yescharacteristic
594C4C4×#1062189811yescharacteristic
595C4#1458342711yescharacteristic
596C4#1458345311yescharacteristic
597C2—1724no—
598C2C4×#1306330311yescharacteristic
599C2#1914342611yescharacteristic
600C2#1914346711yescharacteristic
601C2#1914442411yescharacteristic
602C2#1914444511yescharacteristic
603C2#1914480711yescharacteristic
604C2#1914483711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1776C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1776D43
hypocenterC43#21620
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
2. #19137332C2semidirect
4. #19135549C2semidirect
5. #19135350C2semidirect
6. #19135185C2semidirect
7. #19135182C2semidirect
11. C4×#13063258C2semidirect
12. #19134455C2semidirect
15. C43×#1776C2semidirect
20. #14583198C4semidirect
67. #13063316C2×C4semidirect
92. #13063258C2×C4semidirect
94. Dic43⋊C8C2×C4semidirect
119. #106×C43C2×C4semidirect
305. #1776D43semidirect
362. C43#21620semidirect
406. #106C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831982
#191373322
#191369552
#191355492
#191353502
#191351852
#191351822
#191348432
#191348392
#191345942
C4×#130632582
#191344552
#191344212
C4×#130632452
C43×#17762
#2162043