Finite Group Databasebeta

← #25269787

Subgroups — #25269787

Order 11008.

2042 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142901C214yesmaximal, complemented
2#19140567C214yesmaximal, complemented
3#19139821C214yesmaximal, complemented
4#19139816C214yesmaximal, complemented
5#19138318C214yesmaximal, complemented
6#19138316C214yesmaximal, complemented
7#19137209C211yesmaximal, characteristic
8#19137207C211yesmaximal, characteristic
9#19137207C211yesmaximal, characteristic
10C2×#14582757C211yesmaximal, characteristic
11C2×#14582757C211yesmaximal, characteristic
12C2×C22⋊C4×Dic43C211yesmaximal, characteristic
13C43×#2315C211yesmaximal, characteristic
14C24×Dic43C2211yescharacteristic
15C2×#13063315C2214yescomplemented
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2212yes—
22#14582840C2214yescomplemented
23#14582840C2214yescomplemented
24#14582839C2214yescomplemented
25#14582837C2214yescomplemented
26#14582833C2214yescomplemented
27#14582832C2214yescomplemented
28#14582830C2214yescomplemented
29#14582829C2214yescomplemented
30#14582796C2214yescomplemented
31#14582794C2214yescomplemented
32#14582785C2214yescomplemented
33#14582784C2214yescomplemented
34#14582781C2214yescomplemented
35#14582780C2214yescomplemented
36#14582774C2214yes—
37#14582774C2214yes—
38#14582772C2214yes—
39#14582772C2214yes—
40#14582771C2214yes—
41#14582771C2214yes—
42#14582763C2214yescomplemented
43#14582759C2214yes—
44#14582757C2212yes—
45#14582757C2214yes—
46#14582757C2212yes—
47#14582757C2214yes—
48#14582757C2212yes—
49#14582757C2212yes—
50#14582757C2212yes—
51#14582757C2212yes—
52#14582757C2212yes—
53#14582757C2212yes—
54C22⋊C4×Dic43C2212yes—
55C22⋊C4×Dic43C2212yes—
56C22⋊C4×Dic43C2212yes—
57C22⋊C4×Dic43C2212yes—
58C2×C43⋊#95C2212yes—
59C2×C43⋊#95C2212yes—
60C2×C43⋊#95C2212yes—
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C43×#385C2214yes—
65C43×#385C2214yes—
66C43×#380C2214yes—
67C23×Dic43—44no—
68C23×Dic43Q818yes—
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2312yes—
73C23×Dic43C2312yes—
74C23×Dic43C2312yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78#13063315—48no—
79C2×C4⋊Dic43C2314yes—
80C2×C4⋊Dic43C2314yes—
81C2×Dic43⋊C4—44no—
82C2×Dic43⋊C4—44no—
83C2×Dic43⋊C4C2314yes—
84C2×Dic43⋊C4C2314yes—
85C2×Dic43⋊C4C2314yes—
86C2×Dic43⋊C4C2314yes—
87C2×Dic43⋊C4C2314yes—
88C2×Dic43⋊C4C2314yes—
89C2×Dic43⋊C4C2314yes—
90C2×Dic43⋊C4C2314yes—
91C2×C22⋊Dic43—24no—
92C2×C22⋊Dic43—24no—
93C2×C22⋊Dic43—24no—
94C2×C22⋊Dic43C2312yes—
95C2×C22⋊Dic43C2312yes—
96C2×C22⋊Dic43C2312yes—
97C2×C22⋊Dic43C2312yes—
98C2×C22⋊Dic43C2312yes—
99C2×C22⋊Dic43C2312yes—
100C2×C4×Dic43—44no—
101C2×C4×Dic43C2314yes—
102C2×C4×Dic43C2314yes—
103C43⋊#95C2314yes—
104C43⋊#95C2314yes—
105C43⋊#95C2314yes—
106C43⋊#95C2314yes—
107C43⋊#95C2314yes—
108C43⋊#95C2314yes—
109C43⋊#95C2314yes—
110C43⋊#95C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C25×C43C2311yescharacteristic
116C23×C4×C43C2312yes—
117C23×C4×C43C2312yes—
118C23×C4×C43C2312yes—
119C2×C4⋊C4×C43C2314yes—
120C2×C4⋊C4×C43C2314yes—
121C2×C22⋊C4×C43—24no—
122C2×C22⋊C4×C43—24no—
123C2×C22⋊C4×C43—24no—
124C2×C22⋊C4×C43C2312yes—
125C2×C22⋊C4×C43C2312yes—
126C2×C22⋊C4×C43C2312yes—
127C2×C22⋊C4×C43C2312yes—
128C2×C22⋊C4×C43C2312yes—
129C2×C22⋊C4×C43C2312yes—
130#95×C43C2314yes—
131#95×C43C2314yes—
132C24×C43—42no—
133C24×C43—42no—
134C24×C43C2×Q814yes—
135C24×C43#4114yes—
136C24×C43#4114yes—
137C24×C43C2411yescharacteristic
138C24×C43C2411yescharacteristic
139C24×C43C2411yescharacteristic
140C22×C4×C43—24no—
141C22×C4×C43—24no—
142C22×C4×C43—24no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43C2414yes—
150C22×C4×C43C2414yes—
151C22×C4×C43C2414yes—
152C22×Dic43—24no—
153C22×Dic43—24no—
154C22×Dic43—24no—
155C22×Dic43—24no—
156C22×Dic43—24no—
157C22×Dic43—24no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—416no—
168C22×Dic43C2×Q814yes—
169C22×Dic43C2×Q814yes—
170C22×Dic43C2×Q814yes—
171C22×Dic43C2×Q814yes—
172C22×Dic43C2×Q814yes—
173C22×Dic43C2×Q814yes—
174C22×Dic43C2414yes—
175C22×Dic43C2414yes—
176C22×Dic43C2414yes—
177C22×Dic43C2411yescharacteristic
178C22×Dic43C2411yescharacteristic
179C22×Dic43C2411yescharacteristic
180C22×Dic43C2411yescharacteristic
181C4⋊C4×C43—44no—
182C4⋊C4×C43—44no—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—24no—
186C22⋊C4×C43—24no—
187C22⋊C4×C43—24no—
188C22⋊C4×C43—24no—
189C22⋊Dic43—24no—
190C22⋊Dic43—24no—
191C22⋊Dic43—24no—
192C22⋊Dic43—24no—
193C22⋊Dic43—24no—
194C22⋊Dic43—24no—
195C4⋊Dic43—44no—
196C4⋊Dic43—44no—
197Dic43⋊C4—28no—
198Dic43⋊C4—28no—
199Dic43⋊C4—44no—
200Dic43⋊C4—44no—
201Dic43⋊C4—44no—
202Dic43⋊C4—44no—
203Dic43⋊C4—44no—
204Dic43⋊C4—44no—
205C4×Dic43—28no—
206C4×Dic43—44no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—44no—
214C23×C43—44no—
215C23×C43—48no—
216C23×C43—48no—
217C23×C43#125116yescomplemented
218C23×C43C22×Q812yes—
219C23×C43C22×Q812yes—
220C23×C43C22×Q812yes—
221C23×C43C2×#4112yes—
222C23×C43C2×#4112yes—
223C23×C43C2×#4112yes—
224C23×C43C2×#4112yes—
225C23×C43C2×#4112yes—
226C23×C43C2×#4112yes—
227C23×C43C2511yescharacteristic
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—48no—
238C2×C4×C43—84no—
239C2×C4×C43—84no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—28no—
244C2×Dic43—28no—
245C2×Dic43—28no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—44no—
256C2×Dic43—44no—
257C2×Dic43—44no—
258C2×Dic43—48no—
259C2×Dic43—84no—
260C2×Dic43—84no—
261C2×Dic43C22×Q812yes—
262C2×Dic43C22×Q812yes—
263C2×Dic43C22×Q812yes—
264C2×Dic43C22×Q812yes—
265C2×Dic43H(5,𝔽2)14yes—
266#35020—431nomaximal, Sylow
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—24no—
274C22×C43—24no—
275C22×C43—24no—
276C22×C43—24no—
277C22×C43—24no—
278C22×C43—24no—
279C22×C43—416no—
280C22×C43C2×#12514yes—
281C22×C43C2×#12514yes—
282C22×C43C2×#12514yes—
283C22×C43C23×Q811yescharacteristic
284C22×C43C22×#4111yescharacteristic
285C22×C43C22×#4111yescharacteristic
286C22×C43C2×H(5,𝔽2)12yes—
287C22×C43#58512yes—
288C4×C43—44no—
289C4×C43—44no—
290C4×C43—44no—
291Dic43—22no—
292Dic43—22no—
293Dic43—22no—
294Dic43—44no—
295Dic43—44no—
296Dic43—44no—
297Dic43#54314yes—
298#2851—434no—
299#2646—434no—
300#2569—434no—
301#2569—434no—
302#2442—434no—
303#2442—434no—
304#2315—431no—
305#2315—431no—
306#2315—431no—
307#2315D4311yescharacteristic
308C2×#380—431no—
309C2×#380—431no—
310C2×C4×C22⋊C4—431no—
311C2×C43—24no—
312C2×C43—24no—
313C2×C43—24no—
314C2×C43C22×#12511yescharacteristic
315C2×C43C2×#54311yescharacteristic
316C2×C43#345811yescharacteristic
317C2×C43#350512yes—
318C2×C43#350512yes—
319C24×C4—431no—
320C2×#125—434no—
321C22×C4⋊C4—432no—
322C22×C4⋊C4—432no—
323C22×C22⋊C4—431no—
324C22×C22⋊C4—431no—
325C22×C22⋊C4—431no—
326C22×C22⋊C4C2×D4311yescharacteristic
327C22×C22⋊C4C2×D4311yescharacteristic
328C22×C22⋊C4C2×D4311yescharacteristic
329C22×C42—432no—
330#400—434no—
331#400—434no—
332#400—434no—
333#400—434no—
334#398—434no—
335#398—434no—
336#398—434no—
337#398—434no—
338#389—434no—
339#389—434no—
340#387—434no—
341#387—434no—
342#387—434no—
343#387—434no—
344#385—434no—
345#385—434no—
346#385—434no—
347#385—434no—
348#385—434no—
349#385—434no—
350#385C2×D4314yes—
351#385C2×D4314yes—
352#382—434no—
353#380—434no—
354#380—432no—
355#380—432no—
356#380—434no—
357#380—434no—
358#380—432no—
359#380—432no—
360#380—432no—
361#380—432no—
362#380—432no—
363#380—432no—
364#380C2×D4314yes—
365C4×C22⋊C4—432no—
366C4×C22⋊C4—432no—
367C4×C22⋊C4—432no—
368C4×C22⋊C4—432no—
369C2×#95—432no—
370C2×#95—432no—
371C2×#95—432no—
372C43#3502011yescharacteristic, complemented, Sylow
373C25C22×D4311yescharacteristic
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—438no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—432no—
382C23×C4—432no—
383C23×C4—432no—
384C23×C4—1724no—
385C23×C4C22×D4312yes—
386C23×C4C22×D4312yes—
387C23×C4C22×D4312yes—
388#125—1728no—
389C2×C4⋊C4—434no—
390C2×C4⋊C4—434no—
391C2×C4⋊C4—434no—
392C2×C4⋊C4—434no—
393C2×C4⋊C4—434no—
394C2×C4⋊C4—434no—
395C2×C4⋊C4—434no—
396C2×C4⋊C4—434no—
397C2×C4⋊C4—434no—
398C2×C4⋊C4—434no—
399C2×C4⋊C4—1724no—
400C2×C4⋊C4—1724no—
401C2×C4⋊C4C22×D4314yes—
402C2×C4⋊C4C22×D4314yes—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—432no—
407C2×C22⋊C4—432no—
408C2×C22⋊C4—432no—
409C2×C22⋊C4—432no—
410C2×C22⋊C4—432no—
411C2×C22⋊C4—432no—
412C2×C22⋊C4—864no—
413C2×C22⋊C4—864no—
414C2×C22⋊C4—864no—
415C2×C22⋊C4C22×D4312yes—
416C2×C22⋊C4C22×D4312yes—
417C2×C22⋊C4C22×D4312yes—
418C2×C22⋊C4C22×D4312yes—
419C2×C22⋊C4C22×D4312yes—
420C2×C22⋊C4C22×D4312yes—
421C2×C42—434no—
422C2×C42—434no—
423C2×C42—1724no—
424#95—434no—
425#95—434no—
426#95—434no—
427#95—434no—
428#95—434no—
429#95—434no—
430#95—434no—
431#95—434no—
432#95—434no—
433#95—434no—
434#95—434no—
435#95—434no—
436#95C22×D4314yes—
437#95C22×D4314yes—
438C24—42no—
439C24—42no—
440C24#1062189814yes—
441C24#1062190014yes—
442C24Q8×D4314yes—
443C24C23×D4311yescharacteristic
444C24C23×D4311yescharacteristic
445C24C23×D4311yescharacteristic
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—431no—
456C22×C4—434no—
457C22×C4—434no—
458C22×C4—434no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—434no—
463C22×C4—434no—
464C22×C4—434no—
465C22×C4—434no—
466C22×C4—434no—
467C22×C4—434no—
468C22×C4—864no—
469C22×C4—864no—
470C22×C4—864no—
471C22×C4—864no—
472C22×C4—864no—
473C22×C4—864no—
474C22×C4—17216no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4C23×D4314yes—
485C22×C4C23×D4314yes—
486C22×C4C23×D4314yes—
487C4⋊C4—44no—
488C4⋊C4—44no—
489C4⋊C4—868no—
490C4⋊C4—868no—
491C4⋊C4—1724no—
492C4⋊C4—1724no—
493C4⋊C4—1724no—
494C4⋊C4—1724no—
495C4⋊C4—1724no—
496C4⋊C4—1724no—
497C4⋊C4—1724no—
498C4⋊C4—1724no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—864no—
506C22⋊C4—864no—
507C22⋊C4—864no—
508C22⋊C4—864no—
509C22⋊C4—864no—
510C22⋊C4—864no—
511C42—868no—
512C42—1724no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—44no—
520C23—48no—
521C23—48no—
522C23—44no—
523C23#13063315116yescomplemented
524C23C2×Q8×D4312yes—
525C23C2×Q8×D4312yes—
526C23C2×Q8×D4312yes—
527C23C2×#1062190012yes—
528C23C2×#1062190012yes—
529C23C2×#1062190012yes—
530C23C2×#1062189812yes—
531C23C2×#1062189812yes—
532C23C2×#1062189812yes—
533C23C24×D4311yescharacteristic
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—48no—
544C2×C4—84no—
545C2×C4—84no—
546C2×C4—432no—
547C2×C4—434no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—868no—
552C2×C4—868no—
553C2×C4—868no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—864no—
558C2×C4—864no—
559C2×C4—864no—
560C2×C4—864no—
561C2×C4—864no—
562C2×C4—864no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—864no—
566C2×C4—3444no—
567C2×C4—3444no—
568C2×C4—1724no—
569C2×C4—1724no—
570C2×C4—1724no—
571C2×C4—1728no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—24no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—416no—
585C22C2×#1306331514yes—
586C22C2×#1306331514yes—
587C22C2×#1306331514yes—
588C22C22×Q8×D4311yescharacteristic
589C22C22×#1062190011yescharacteristic
590C22C22×#1062189811yescharacteristic
591C22H(5,𝔽2)×D4312yes—
592C22#1458373412yes—
593C4—44no—
594C4—44no—
595C4—44no—
596C4—434no—
597C4—862no—
598C4—862no—
599C4—862no—
600C4—1724no—
601C4—1724no—
602C4—1724no—
603C2—24no—
604C2—24no—
605C2—24no—
606C2C22×#1306331511yescharacteristic
607C2#543×D4311yescharacteristic
608C2#1914799711yescharacteristic
609C2#1914842512yes—
610C2#1914843212yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2315C2
prime radicalC25×C43C23
hypercenter#2315D43
hypocenterC43#35020
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
1. #19142901C2semidirect
2. #19140567C2semidirect
3. #19139821C2semidirect
4. #19139816C2semidirect
5. #19138318C2semidirect
6. #19138316C2semidirect
15. C2×#13063315C22semidirect
22. #14582840C22semidirect
23. #14582840C22semidirect
24. #14582839C22semidirect
25. #14582837C22semidirect
26. #14582833C22semidirect
27. #14582832C22semidirect
28. #14582830C22semidirect
29. #14582829C22semidirect
30. #14582796C22semidirect
31. #14582794C22semidirect
32. #14582785C22semidirect
33. #14582784C22semidirect
34. #14582781C22semidirect
35. #14582780C22semidirect
42. #14582763C22semidirect
217. C23×C43#125semidirect
372. C43#35020semidirect
523. C23#13063315semidirect

Maximal subgroups

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

subgroupindex
#191429012
#191405672
#191398212
#191398162
#191383182
#191383162
#191372092
#191372072
C2×#145827572
C2×C22⋊C4×Dic432
C43×#23152
#3502043