Finite Group Databasebeta

← #25256739

Subgroups — #25256739

Order 11008.

2542 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2#19137549C214yesmaximal, complemented
3#19137541C214yesmaximal, complemented
4#19137523C214yesmaximal, complemented
5#19137519C214yesmaximal, complemented
6#19137205C211yesmaximal, characteristic, complemented
7#19137204C211yesmaximal, characteristic, complemented
8#19137203C211yesmaximal, characteristic, complemented
9#19137184C212yesmaximal
10#19137001C211yesmaximal, characteristic, complemented
11#19136999C212yesmaximal, complemented
12#19136997C212yesmaximal, complemented
13#384×D43C211yesmaximal, characteristic, complemented
14#19136949C212yesmaximal, complemented
15C43×#2314C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583367C4116yescomplemented
18C2×#13063290C2212yes—
19C2×#13063287C2212yes—
20C2×(C22⋊D43)⋊C4C2212yes—
21C2×(C22⋊D43)⋊C4C2212yes—
22C2×#13063283C2212yes—
23C2×#13063282C2214yes—
24C2×#13063282C2211yescharacteristic
25C2×#13063282C2211yescharacteristic
26C2×#13063281C2214yes—
27C2×C4⋊C4×D43C2212yes—
28C2×C4⋊C4×D43C2214yes—
29C22×C4×Dic43C2211yescharacteristic
30C2×C42×D43C2211yescharacteristic
31C2×C42×D43C2211yescharacteristic
32#14582803C2214yes—
33#14582799C2214yes—
34#14582792C2214yes—
35#14582791C2214yes—
36#14582789C2214yes—
37#14582786C2214yes—
38#14582785C2214yes—
39#14582780C2214yes—
40#14582777C2214yes—
41#14582775C2214yes—
42#14582769C2211yescharacteristic
43#14582768C2214yes—
44#14582768C2212yes—
45#14582768C2212yes—
46#14582765C2211yescharacteristic
47#14582763C2214yes—
48#14582763C2214yes—
49#14582759C2212yes—
50#14582758C2214yes—
51#14582758C2214yes—
52#14582757C2214yes—
53#14582756C2212yes—
54#14582756C2212yes—
55C4⋊C4×Dic43C2212yes—
56C4⋊C4×Dic43C2212yes—
57C4×Dic43⋊C4C2214yes—
58C4×Dic43⋊C4C2214yes—
59C4×C4⋊Dic43C2212yes—
60#14582750C2214yes—
61#14582750C2214yes—
62#14582750C2214yes—
63C4×(C2×D43)⋊C4C2214yes—
64#14582746C2214yes—
65C2×#117×C43C2211yescharacteristic
66C43×#388C2214yes—
67C43×#387C2214yes—
68C43×#384C2211yescharacteristic
69C43×#382C2211yescharacteristic
70C43×#380C2212yes—
71C4×C4⋊C4×C43C2212yes—
72C2×#10621898—24no—
73C2×#10621898—24no—
74C2×#10621898C2×C418yes—
75C22×Dic86C2311yescharacteristic
76C22×D172C2311yescharacteristic
77C22×C22⋊D43C2311yescharacteristic
78C22×C22⋊D43C2311yescharacteristic
79C23×Dic43C2312yes—
80C22×C4×D43C2312yes—
81C22×C4×D43C2312yes—
82C22×C4×D43C2311yescharacteristic
83C22×C4×D43C2314yes—
84C22×C4×D43C2311yescharacteristic
85#13063290C2×C4116yescomplemented
86#13063287C2×C4116yes—
87(C22⋊D43)⋊C4C2×C4116yes—
88(C22⋊D43)⋊C4C2×C4116yescomplemented
89#13063283—28no—
90#13063282—48no—
91#13063282C2×C418yes—
92#13063282C2×C418yescomplemented
93#13063281—48no—
94C2×C4⋊Dic43C2312yes—
95C2×C4⋊Dic43C2312yes—
96C2×C4⋊Dic43C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2312yes—
103C2×Dic43⋊C4C2312yes—
104C4⋊C4×D43—28no—
105C4⋊C4×D43—48no—
106C2×C22⋊Dic43C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2312yes—
111C2×(C2×D43)⋊C4C2312yes—
112C2×C4×Dic43C2×C418yescomplemented
113C2×C4×Dic43C2314yes—
114C2×C4×Dic43C2314yes—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C2×C4×Dic43C2311yescharacteristic
118C2×C4×Dic43C2312yes—
119C2×C4×Dic43C2312yes—
120C2×C4×Dic43C2311yescharacteristic
121C2×C4×Dic43C2312yes—
122C42×D43C2×C418yes—
123C42×D43C2×C418yescomplemented
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C23×C4×C43C2311yescharacteristic
132#117×C43C2×C418yescomplemented
133C2×C4⋊C4×C43C2312yes—
134C2×C4⋊C4×C43C2312yes—
135C2×C4⋊C4×C43C2314yes—
136C2×C4⋊C4×C43C2312yes—
137C2×C22⋊C4×C43C2314yes—
138C2×C22⋊C4×C43C2312yes—
139C2×C42×C43C2314yes—
140C2×C42×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142#95×C43C2314yes—
143#95×C43C2314yes—
144#95×C43C2314yes—
145C24×C43C2411yescharacteristic
146C23×D43C2411yescharacteristic
147C23×D43C2411yescharacteristic
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43C22×C414yes—
151C22×C4×C43C2414yes—
152C22×C4×C43C2414yes—
153C22×C4×C43C2411yescharacteristic
154C22×C4×C43C2412yes—
155C22×C4×C43C2412yes—
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43C22×C414yes—
162C2×C22⋊D43C22×C414yes—
163C22×Dic43—24no—
164C22×Dic43—24no—
165C22×Dic43C22×C418yes—
166C22×Dic43C2414yes—
167C22×Dic43C2414yes—
168C22×Dic43C2411yescharacteristic
169C22×Dic43C2412yes—
170C22×Dic43C2411yescharacteristic
171C22×Dic43C2412yes—
172#10621898—232no—
173C2×D172—22no—
174C2×D172—22no—
175C2×D172C22×C414yes—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—24no—
181C2×C4×D43—24no—
182C2×C4×D43—28no—
183C2×C4×D43—44no—
184C2×C4×D43—44no—
185C2×C4×D43C22×C418yes—
186C2×C4×D43C22×C414yes—
187C2×C4×D43C22×C418yes—
188C2×C4×D43C22×C414yes—
189C2×C4×D43#4114yes—
190C2×C4×D43#4114yes—
191C2×Dic86—22no—
192C2×Dic86—22no—
193C2×Dic86C22×C414yes—
194C4⋊C4×C43—24no—
195C4⋊C4×C43—24no—
196C4⋊C4×C43—44no—
197C4⋊C4×C43C22×C418yes—
198C22⋊C4×C43—44no—
199C22⋊C4×C43C22×C418yes—
200C42×C43—44no—
201C42×C43C22×C414yes—
202C42×C43C22×C414yes—
203C22⋊Dic43—44no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—44no—
206(C2×D43)⋊C4—44no—
207(C2×D43)⋊C4C22×C418yes—
208(C2×D43)⋊C4C22×C418yes—
209C4⋊Dic43—24no—
210C4⋊Dic43—24no—
211C4⋊Dic43—44no—
212Dic43⋊C4—28no—
213Dic43⋊C4—28no—
214Dic43⋊C4—28no—
215Dic43⋊C4—28no—
216Dic43⋊C4—28no—
217Dic43⋊C4C22×C418yes—
218Dic43⋊C4C22×C418yes—
219C4×Dic43—28no—
220C4×Dic43—44no—
221C4×Dic43—44no—
222C4×Dic43—44no—
223C4×Dic43C22×C414yes—
224C4×Dic43C22×C418yes—
225C4×Dic43C22×C418yes—
226C4×Dic43C22×C414yes—
227C4×Dic43C22×C418yes—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—22no—
231C23×C43—22no—
232C23×C43C23×C412yes—
233C23×C43C2511yescharacteristic
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—22no—
239C22×D43—22no—
240C22×D43C23×C412yes—
241C22×D43C23×C412yes—
242C22×D43C2×#4112yes—
243C22×D43C2×#4112yes—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—28no—
251C2×C4×C43—24no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—24no—
255C2×C4×C43—24no—
256C2×C4×C43—24no—
257C2×C4×C43C23×C412yes—
258C2×C4×C43C23×C414yes—
259C2×C4×C43C23×C414yes—
260C2×C4×C43C23×C412yes—
261C2×C4×C43C2×#4112yes—
262C2×C4×C43C2×#4112yes—
263C22⋊D43—28no—
264C22⋊D43—28no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—216no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—24no—
275C2×Dic43—24no—
276C2×Dic43C23×C414yes—
277C2×Dic43C23×C412yes—
278C2×Dic43C23×C412yes—
279C2×Dic43C23×C414yes—
280C2×Dic43C2×#4112yes—
281C2×Dic43C2×#4112yes—
282C2×Dic43H(5,𝔽2)14yes—
283C2×Dic432−1+414yes—
284D172—28no—
285C4×D43—28no—
286C4×D43—216no—
287C4×D43—216no—
288C4×D43—88no—
289C4×D43#117116yescomplemented
290Dic86—28no—
291#34188—431nomaximal, Sylow
292C22×C43—22no—
293C22×C43—24no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—42no—
297C22×C43C24×C411yescharacteristic
298C22×C43C22×#4111yescharacteristic
299C22×C43C22×#4111yescharacteristic
300C22×C43C2×H(5,𝔽2)12yes—
301C22×C43C2×2−1+412yes—
302C2×D43—24no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—24no—
306C2×D43—22no—
307C2×D43—24no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—42no—
311C2×D43C2×#11714yes—
312C4×C43—22no—
313C4×C43—24no—
314C4×C43—24no—
315C4×C43—44no—
316C4×C43—44no—
317C4×C43C2×#11714yes—
318Dic43—22no—
319Dic43—24no—
320Dic43—44no—
321Dic43—44no—
322Dic43C2×#11714yes—
323Dic43#52018yes—
324C2×C4×#41—431no—
325#2355—434no—
326#2354—434no—
327#2352—434no—
328#2352—434no—
329#2314—431no—
330#2314—431no—
331#2314—431no—
332#2314D4311yescharacteristic, complemented
333#2311—432no—
334#2285—431no—
335#2285—432no—
336#2285—432no—
337C2×#384—431no—
338#2274—432no—
339C2×C43—42no—
340C2×C43C22×#11711yescharacteristic
341C2×C43C2×#52012yes—
342C2×C43#350811yescharacteristic
343C2×C43#350911yescharacteristic
344C2×C43#351112yes—
345D43—24no—
346D43—42no—
347C22×#41—431no—
348C4×#41—4316no—
349C2×C4×Q8—432no—
350C2×C4×D4—432no—
351C2×C4×D4—432no—
352C2×C4×D4—432no—
353C2×#117—432no—
354C2×#117—434no—
355C2×#117—431no—
356C2×#117—431no—
357C2×#117—434no—
358C2×#117C2×D4311yescharacteristic
359C22×C4⋊C4—432no—
360C22×C4⋊C4—434no—
361C22×C42—431no—
362C22×C42—431no—
363C22×C42—431no—
364#391—434no—
365#390—434no—
366#388—434no—
367#388—434no—
368#388—434no—
369#388C2×D4314yes—
370#387—434no—
371#387—434no—
372#387—434no—
373#387C2×D4314yes—
374#386—434no—
375#386—434no—
376#384—434no—
377#384—432no—
378#384—432no—
379#384—431no—
380#384C2×D4311yescharacteristic
381#382—431no—
382#382—434no—
383#382—434no—
384#382C2×D4311yescharacteristic
385#380—432no—
386#380—432no—
387#380—432no—
388#380—434no—
389#380—434no—
390#380—434no—
391#380C2×D4312yes—
392C4×C4⋊C4—432no—
393C4×C4⋊C4—432no—
394C4×C4⋊C4—432no—
395C4×C4⋊C4—434no—
396C4×C4⋊C4—434no—
397C4×C4⋊C4—434no—
398C4×C4⋊C4—434no—
399C4×C4⋊C4—434no—
400C4×C4⋊C4C2×D4312yes—
401C4×C22⋊C4—434no—
402C4×C22⋊C4—434no—
403C43#3418811yescharacteristic, complemented, Sylow
404C2×#41—438no—
405C2×#41—864no—
406C2×#41—864no—
407C22×Q8—431no—
408C22×D4—431no—
409C22×D4—431no—
410C22×D4—431no—
411C23×C4—431no—
412C23×C4—432no—
413C23×C4—432no—
414C23×C4—432no—
415C23×C4—431no—
416C23×C4—434no—
417C23×C4C22×D4311yescharacteristic
418C4×Q8—4316no—
419C4×D4—4316no—
420C4×D4—4316no—
421C4×D4—4316no—
422#117—438no—
423#117—438no—
424#117—868no—
425#117—1728no—
426#117—1728no—
427#117C4×D4318yescomplemented
428C2×C4⋊C4—432no—
429C2×C4⋊C4—432no—
430C2×C4⋊C4—434no—
431C2×C4⋊C4—434no—
432C2×C4⋊C4—434no—
433C2×C4⋊C4—432no—
434C2×C4⋊C4—434no—
435C2×C4⋊C4—432no—
436C2×C4⋊C4—434no—
437C2×C4⋊C4—434no—
438C2×C4⋊C4—868no—
439C2×C4⋊C4—1728no—
440C2×C4⋊C4C22×D4312yes—
441C2×C4⋊C4C22×D4312yes—
442C2×C4⋊C4C22×D4314yes—
443C2×C4⋊C4C22×D4312yes—
444C2×C22⋊C4—432no—
445C2×C22⋊C4—432no—
446C2×C22⋊C4—434no—
447C2×C22⋊C4—434no—
448C2×C22⋊C4—434no—
449C2×C22⋊C4—434no—
450C2×C22⋊C4C22×D4314yes—
451C2×C22⋊C4C22×D4312yes—
452C2×C42—438no—
453C2×C42—431no—
454C2×C42—432no—
455C2×C42—432no—
456C2×C42—432no—
457C2×C42—431no—
458C2×C42—438no—
459C2×C42—438no—
460C2×C42—434no—
461C2×C42—434no—
462C2×C42—434no—
463C2×C42—434no—
464C2×C42C22×D4314yes—
465C2×C42C22×D4311yescharacteristic
466C2×C42C22×D4311yescharacteristic
467#95—434no—
468#95—434no—
469#95—434no—
470#95—434no—
471#95—434no—
472#95—434no—
473#95—434no—
474#95C22×D4314yes—
475#95C22×D4314yes—
476#95C22×D4314yes—
477C24—431no—
478C24—431no—
479C24C23×D4311yescharacteristic
480#41—8632no—
481C2×Q8—434no—
482C2×Q8—862no—
483C2×Q8—862no—
484C2×D4—434no—
485C2×D4—434no—
486C2×D4—434no—
487C2×D4—862no—
488C2×D4—862no—
489C2×D4—862no—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4—862no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—431no—
496C22×C4—432no—
497C22×C4—434no—
498C22×C4—434no—
499C22×C4—434no—
500C22×C4—438no—
501C22×C4—431no—
502C22×C4—432no—
503C22×C4—434no—
504C22×C4—438no—
505C22×C4—438no—
506C22×C4—434no—
507C22×C4—434no—
508C22×C4—864no—
509C22×C4—864no—
510C22×C4—864no—
511C22×C4—864no—
512C22×C4—868no—
513C22×C4—864no—
514C22×C4—864no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—1724no—
518C22×C4—1724no—
519C22×C4C2×C4×D4314yes—
520C22×C4C23×D4314yes—
521C22×C4C23×D4314yes—
522C22×C4C23×D4311yescharacteristic
523C22×C4C23×D4312yes—
524C22×C4C23×D4312yes—
525C22×C4C23×D4311yescharacteristic
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—44no—
529C4⋊C4—438no—
530C4⋊C4—438no—
531C4⋊C4—868no—
532C4⋊C4—868no—
533C4⋊C4—868no—
534C4⋊C4—868no—
535C4⋊C4—868no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—1724no—
539C4⋊C4C2×C4×D4318yes—
540C22⋊C4—44no—
541C22⋊C4—438no—
542C22⋊C4—438no—
543C22⋊C4—868no—
544C22⋊C4—1724no—
545C22⋊C4—1724no—
546C22⋊C4—1724no—
547C22⋊C4C2×C4×D4318yes—
548C42—44no—
549C42—434no—
550C42—434no—
551C42—438no—
552C42—438no—
553C42—438no—
554C42—868no—
555C42—1724no—
556C42—1724no—
557C42—1724no—
558C42C2×C4×D4314yes—
559C42C2×C4×D4314yes—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—22no—
564C23—432no—
565C23—432no—
566C23—432no—
567C23—432no—
568C23—862no—
569C23—862no—
570C23—861no—
571C23—861no—
572C23—862no—
573C23—862no—
574C23C22×C4×D4312yes—
575C23C24×D4311yescharacteristic
576Q8—868no—
577D4—868no—
578D4—868no—
579D4—868no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—28no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—434no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—434no—
598C2×C4—434no—
599C2×C4—4316no—
600C2×C4—434no—
601C2×C4—432no—
602C2×C4—8616no—
603C2×C4—8616no—
604C2×C4—8616no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—868no—
610C2×C4—864no—
611C2×C4—864no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—864no—
615C2×C4—864no—
616C2×C4—3448no—
617C2×C4C22×C4×D4312yes—
618C2×C4C22×C4×D4314yes—
619C2×C4C22×C4×D4314yes—
620C2×C4C22×C4×D4312yes—
621C2×C4#41×D4312yes—
622C2×C4#41×D4312yes—
623C22—24no—
624C22—22no—
625C22—41no—
626C22—41no—
627C22—42no—
628C22—434no—
629C22—864no—
630C22—862no—
631C22—862no—
632C22—864no—
633C22—864no—
634C22—862no—
635C22—1721no—
636C22—1721no—
637C22—1722no—
638C22C23×C4×D4311yescharacteristic
639C22C2×#41×D4311yescharacteristic
640C22C2×#41×D4311yescharacteristic
641C22H(5,𝔽2)×D4312yes—
642C222−1+4×D4312yes—
643C4—24no—
644C4—24no—
645C4—22no—
646C4—44no—
647C4—44no—
648C4—438no—
649C4—434no—
650C4—864no—
651C4—862no—
652C4—1724no—
653C4—1724no—
654C4#117×D4314yes—
655C2—42no—
656C2—864no—
657C2—1722no—
658C2C2×#117×D4311yescharacteristic
659C2#520×D4312yes—
660C2#1914846711yescharacteristic
661C2#1914847711yescharacteristic
662C2#1914850012yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2314C2
socle, cosocleC23×C43C25
prime radicalC22×#10621898C22
hypercenter#2314D43
hypocenterC43#34188
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #19137549C2semidirect
3. #19137541C2semidirect
4. #19137523C2semidirect
5. #19137519C2semidirect
6. #19137205C2semidirect
7. #19137204C2semidirect
8. #19137203C2semidirect
10. #19137001C2semidirect
11. #19136999C2semidirect
12. #19136997C2semidirect
13. #384×D43C2semidirect
14. #19136949C2semidirect
15. C43×#2314C2semidirect
17. #14583367C4semidirect
85. #13063290C2×C4semidirect
88. (C22⋊D43)⋊C4C2×C4semidirect
92. #13063282C2×C4semidirect
112. C2×C4×Dic43C2×C4semidirect
123. C42×D43C2×C4semidirect
132. #117×C43C2×C4semidirect
289. C4×D43#117semidirect
332. #2314D43semidirect
403. C43#34188semidirect
427. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
#191375492
#191375412
#191375232
#191375192
#191372052
#191372042
#191372032
#191371842
#191370012
#191369992
#191369972
#384×D432
#191369492
C43×#23142
#3418843