Finite Group Databasebeta

← #25066683

Subgroups — #25066683

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144649C211yesmaximal, characteristic
2#19143703C211yesmaximal, characteristic, complemented
3#19133471C211yesmaximal, characteristic, complemented
4#19133457C211yesmaximal, characteristic, complemented
5#19133436C211yesmaximal, characteristic, complemented
6#19133422C211yesmaximal, characteristic, complemented
7#19133417C211yesmaximal, characteristic, complemented
8#19133407C211yesmaximal, characteristic, complemented
9C8×#10621883C211yesmaximal, characteristic, complemented
10C8×#10621882C211yesmaximal, characteristic, complemented
11#19133381C211yesmaximal, characteristic, complemented
12#19133027C211yesmaximal, characteristic, complemented
13#19132994C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#2981C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583220C411yescharacteristic
18#14583220C411yescharacteristic
19#14583191C411yescharacteristic
20#14583186C411yescharacteristic
21#14583096C411yescharacteristic
22#14583091C411yescharacteristic
23#14583042C411yescharacteristic
24#14583042C411yescharacteristic
25C8×Dic86C2211yescharacteristic
26C8×Dic86C2211yescharacteristic
27C4×#10621883C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31C8×D172C2211yescharacteristic
32C8×D172C2211yescharacteristic
33(C22⋊D43)⋊C8—21no—
34(C22⋊D43)⋊C8—21no—
35#14582952C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582951—21no—
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39C4⋊C8×D43—21no—
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44#14582629C2211yescharacteristic
45#14582629C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48D4⋊(C43⋊C8)C2211yescharacteristic
49D4⋊(C43⋊C8)C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582620C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#436C2211yescharacteristic
58C43×#436C2211yescharacteristic
59C43×#435—21no—
60C43×#435—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#432C2211yescharacteristic
64C43×#431C2211yescharacteristic
65C43×#408—21no—
66C43×#408—21no—
67C2×#10621898C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C4×Dic86C2×C411yescharacteristic
76C4×Dic86C2311yescharacteristic
77C4×D172C2×C411yescharacteristic
78C4×D172C2311yescharacteristic
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81#13063284C2×C411yescharacteristic
82#13063282—21no—
83C42×D43—21no—
84#13063258C2×C411yescharacteristic
85#13063258C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2×C411yescharacteristic
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95Dic43⋊C8—21no—
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063246C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102#13063245C2×C411yescharacteristic
103#13063245C2×C411yescharacteristic
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106C22⋊(C43⋊C8)C2×C411yescharacteristic
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109C4×C43⋊C8C2311yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C8×Dic43—21no—
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C22×C8×C43—21no—
119C22×C8×C43—21no—
120C4⋊Q8×C43C2×C411yescharacteristic
121#127×C43C2×C411yescharacteristic
122#124×C43—21no—
123#121×C43—21no—
124#121×C43C2×C411yescharacteristic
125#121×C43C2×C411yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43D411yescharacteristic
140C22⋊C8×C43D411yescharacteristic
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C411yescharacteristic
152C2×D4×C43C22×C411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C2×C22⋊D43—21no—
159#10621898—22no—
160#10621898—22no—
161C2×D172C22×C411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×Dic86C22×C411yescharacteristic
166M16×C43—81no—
167M16×C43—81no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—81no—
171C2×C8×C43—81no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43C22×C411yescharacteristic
178C4⋊C4×C43C22×C411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C42×C43C22×C411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—21no—
188#10621883—22no—
189#10621883—22no—
190#10621882—22no—
191#10621882—22no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194C4⋊Dic43C22×C411yescharacteristic
195C4⋊Dic43C22×C411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
210C8×D43—81no—
211C8×D43—81no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C4×D411yescharacteristic
215C22×D43—21no—
216Q8×C43—81no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—81no—
222D4×C43—81no—
223D4×C43—81no—
224D4×C43—81no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—24no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246D172—21no—
247D172#13112yes—
248C4×D43—24no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—81no—
252Dic86—21no—
253Dic86#13112yes—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17920—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4×D411yescharacteristic
279C2×D43—22no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43C2×#13111yescharacteristic
289C4×C43C2×#13111yescharacteristic
290C4×C43#57611yescharacteristic
291C4×C43#57711yescharacteristic
292Dic43—22no—
293Dic43—41no—
294Dic43—41no—
295#3106—431no—
296#2988—431no—
297#2981D4311yescharacteristic, complemented
298#1588—431no—
299#1586—431no—
300#1583—431no—
301#1581—431no—
302#1580—431no—
303SD16⋊C8—431no—
304C8×SD16—431no—
305C8×D8—431no—
306#1573—431no—
307#1488—431no—
308#1480—431no—
309#1454—431no—
310C2×C43—41no—
311C2×C43—81no—
312C2×C43—81no—
313C2×C43#292911yescharacteristic
314C2×C43#294611yescharacteristic
315C2×C43#295711yescharacteristic
316D43—42no—
317#532C2×D4311yescharacteristic
318C4×#41—431no—
319#482—431no—
320#482—431no—
321#477—431no—
322#476—431no—
323#460—431no—
324#459—431no—
325#449—431no—
326#449—431no—
327C8×Q8—431no—
328C8×Q8—431no—
329C4×SD16—431no—
330C4×SD16—431no—
331C4×D8—431no—
332C4×D8—431no—
333#436C2×D4311yescharacteristic
334#436C2×D4311yescharacteristic
335#435—21no—
336#435—21no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—861no—
340C8×D4—861no—
341C8×D4C2×D4311yescharacteristic
342C8×D4C2×D4311yescharacteristic
343#432C2×D4311yescharacteristic
344#431—431no—
345#431—431no—
346#431—861no—
347#431C2×D4311yescharacteristic
348C2×C4⋊C8—431no—
349C2×C4⋊C8—861no—
350#408—21no—
351#408—21no—
352#335—431no—
353#335—431no—
354#334—431no—
355#334—431no—
356Q8⋊C8—431no—
357Q8⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364#322—431no—
365#322—431no—
366#322—431no—
367C82—431no—
368C43#1792011yescharacteristic, complemented, Sylow
369C2×#41—21no—
370C2×#41—431no—
371C2×SD16—431no—
372C2×SD16—431no—
373C2×D8—431no—
374C2×D8—431no—
375C2×M16—21no—
376C2×M16—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8C4×D4311yescharacteristic
383#127C4×D4311yescharacteristic
384#124—21no—
385#121—21no—
386#121C4×D4311yescharacteristic
387#121C4×D4311yescharacteristic
388C4×Q8—431no—
389C4×Q8—431no—
390C4×D4—21no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4C22×D4311yescharacteristic
396C4×D4C22×D4311yescharacteristic
397#117—431no—
398#117—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—431no—
402#107—431no—
403#106—431no—
404#106—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8C22⋊D4311yescharacteristic
414C4⋊C8C22⋊D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417#103—431no—
418#103—431no—
419#102—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102—431no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—431no—
431C22⋊C8—431no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8C22⋊D4311yescharacteristic
436C22⋊C8C22⋊D4311yescharacteristic
437#97—21no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446#41—81no—
447#41—81no—
448#41—862no—
449#41—862no—
450C2×Q8—21no—
451C2×Q8—431no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—431no—
457C2×D4—861no—
458C2×D4C2×C4×D4311yescharacteristic
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4#1062189811yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468SD16—862no—
469SD16—862no—
470D8—862no—
471D8—862no—
472M16—81no—
473M16—81no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—3441no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8C2×C22⋊D4311yescharacteristic
490C2×C8C2×C22⋊D4311yescharacteristic
491C2×C8C2×C22⋊D4311yescharacteristic
492C2×C8C2×C22⋊D4311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×C4×D4311yescharacteristic
499C4⋊C4C2×C4×D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C42—861no—
508C42—861no—
509C42—861no—
510C42C2×C4×D4311yescharacteristic
511C42#1062189811yescharacteristic
512C42C2×C22⋊D4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—861no—
517C23C4×C22⋊D4311yescharacteristic
518Q8—81no—
519Q8—432no—
520Q8—861no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—432no—
530D4—864no—
531D4—861no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—864no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—3441no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4C4×C22⋊D4311yescharacteristic
551C2×C4C4×C22⋊D4311yescharacteristic
552C2×C4C4×C22⋊D4311yescharacteristic
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4C22×C22⋊D4311yescharacteristic
555C2×C4C2×#1062189811yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—861no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—1721no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—862no—
580C22—1721no—
581C22—1721no—
582C22C2×C4×C22⋊D4311yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—862no—
590C4—1721no—
591C4—1721no—
592C4#131×D4311yescharacteristic
593C4#131×D4311yescharacteristic
594C4#1458370211yescharacteristic
595C4#1458371011yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—1722no—
600C2#1914328711yescharacteristic
601C2#1914342711yescharacteristic
602C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2981C2
socleC22×C43C2×C4×D4
prime radical#19144649C2
cosocleC42×C43C24
hypercenter#2981D43
hypocenterC43#17920
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #19143703C2semidirect
3. #19133471C2semidirect
4. #19133457C2semidirect
5. #19133436C2semidirect
6. #19133422C2semidirect
7. #19133417C2semidirect
8. #19133407C2semidirect
9. C8×#10621883C2semidirect
10. C8×#10621882C2semidirect
11. #19133381C2semidirect
12. #19133027C2semidirect
13. #19132994C2semidirect
14. #19132895C2semidirect
15. C43×#2981C2semidirect
297. #2981D43semidirect
368. C43#17920semidirect

Maximal subgroups

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

subgroupindex
#191446492
#191437032
#191334712
#191334572
#191334362
#191334222
#191334172
#191334072
C8×#106218832
C8×#106218822
#191333812
#191330272
#191329942
#191328952
C43×#29812
#1792043