Finite Group Databasebeta

← #25100353

Subgroups — #25100353

Order 11008.

1598 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583476C211yesmaximal, characteristic
2C2×#14582871C214yesmaximal, complemented
3#19137212C211yesmaximal, characteristic, complemented
4#19136950C211yesmaximal, characteristic, complemented
5#19135432C211yesmaximal, characteristic, complemented
6#19135431C211yesmaximal, characteristic, complemented
7#19135430C211yesmaximal, characteristic, complemented
8#19135429C214yesmaximal, complemented
9C43×#1964C211yesmaximal, characteristic, complemented
10C22×#10621900C2212yes—
11#14583476—22no—
12#14583476—22no—
13#14583476—22no—
14#14583476—22no—
15C2×#13063303C412yescomplemented
16C2×#13063302C412yescomplemented
17C2×#13063299C2211yescharacteristic
18C2×#13063298C412yescomplemented
19C2×#13063297C412yescomplemented
20C2×#13063297C2212yes—
21C2×#13063281C2212yes—
22C2×#13063281C2212yes—
23C22×Dic43⋊C4C2211yescharacteristic
24#14582871—216no—
25C2×#13063240C2214yes—
26C2×#13063239C2214yes—
27C2×#13063239C2214yes—
28#14582796—22no—
29#14582794—22no—
30#14582759C2211yescharacteristic
31#14582757C2212yes—
32C4×Dic43⋊C4—22no—
33#14582750—22no—
34C22⋊C4×Dic43C2212yes—
35C4×C22⋊Dic43C2211yescharacteristic
36C2×#121×C43C2211yescharacteristic
37C2×#99×C43C2214yes—
38C43×#380C2211yescharacteristic
39C4×C22⋊C4×C43C2211yescharacteristic
40C2×#10621900—28no—
41C2×#10621900—24no—
42C2×#10621900—24no—
43C2×#10621900—28no—
44C22×Dic86C2×C412yes—
45C22×D172C2×C411yescharacteristic
46C22×C22⋊D43C2×C412yes—
47C22×C22⋊D43C2×C412yes—
48C22×C22⋊D43C2312yes—
49C23×Dic43C2×C412yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2311yescharacteristic
52C22×C4×D43C2×C412yes—
53#13063303—24no—
54#13063303—24no—
55#13063302—24no—
56#13063302—24no—
57#13063299—21no—
58#13063299—21no—
59#13063299—21no—
60#13063299—21no—
61#13063298—24no—
62#13063298—24no—
63#13063297—24no—
64#13063297—24no—
65#13063297—24no—
66#13063297—24no—
67#13063281—24no—
68#13063281—28no—
69#13063281D418yescomplemented
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2×C411yescharacteristic
72C2×Dic43⋊C4—22no—
73C2×Dic43⋊C4—22no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4C2×C412yes—
76C2×Dic43⋊C4C2×C412yes—
77C2×Dic43⋊C4C2×C412yes—
78C2×Dic43⋊C4D412yes—
79C2×Dic43⋊C4D412yes—
80C2×Dic43⋊C4D412yes—
81C2×Dic43⋊C4D412yes—
82C2×C22⋊Dic43C2×C412yes—
83C2×C22⋊Dic43C2312yes—
84C2×C22⋊Dic43C2312yes—
85C2×(C2×D43)⋊C4C2×C412yes—
86C2×(C2×D43)⋊C4C2×C412yes—
87C2×C4×Dic43—22no—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—22no—
91#13063240—28no—
92#13063239—28no—
93#13063239—28no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×D4×C43C2×C411yescharacteristic
99C22×D4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101#121×C43—21no—
102#121×C43—21no—
103#121×C43—21no—
104#121×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2×C411yescharacteristic
107C2×C22⋊C4×C43C2×C412yes—
108C2×C22⋊C4×C43C2312yes—
109C2×C22⋊C4×C43C2312yes—
110C2×C42×C43—21no—
111#99×C43—28no—
112#95×C43—21no—
113#95×C43—21no—
114C24×C43C22×C412yes—
115C24×C43C2411yescharacteristic
116C23×D43C22×C412yes—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—24no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—24no—
123C2×D4×C43—81no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—81no—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C22×C411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—24no—
136C2×C22⋊D43—28no—
137C2×C22⋊D43—24no—
138C2×C22⋊D43—22no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43—24no—
141C2×C22⋊D43—82no—
142C22×Dic43—24no—
143C22×Dic43—28no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—81no—
147C22×Dic43C22×C412yes—
148C22×Dic43C22×C412yes—
149C22×Dic43C22×C412yes—
150C22×Dic43C2×D412yes—
151C22×Dic43C2×D412yes—
152C22×Dic43C2×D412yes—
153C22×Dic43C2×D412yes—
154C22×Dic43C2×D414yes—
155C22×Dic43#4114yes—
156#10621900—48no—
157#10621900—48no—
158#10621900—48no—
159#10621900—48no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—81no—
163C2×C4×D43—24no—
164C2×C4×D43—28no—
165C2×Dic86—24no—
166C2×Dic86—28no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—81no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43C2×D414yes—
175C42×C43—81no—
176C22⋊Dic43—24no—
177C22⋊Dic43—24no—
178C22⋊Dic43—22no—
179C22⋊Dic43C2×D414yes—
180(C2×D43)⋊C4—22no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—24no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—81no—
186Dic43⋊C4—24no—
187Dic43⋊C4—28no—
188Dic43⋊C4—44no—
189Dic43⋊C4—82no—
190Dic43⋊C4C22⋊C414yes—
191Dic43⋊C4C22⋊C414yes—
192Dic43⋊C4C22⋊C414yes—
193Dic43⋊C4C22⋊C414yes—
194C4×Dic43—28no—
195C4×Dic43—44no—
196C4×Dic43—82no—
197C4×Dic43—81no—
198C23×C43—22no—
199C23×C43—24no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43C23×C411yescharacteristic
205C23×C43C22×D411yescharacteristic
206C23×C43C22×D411yescharacteristic
207C23×C43C22×D412yes—
208C23×C43C2×#4112yes—
209C22×D43—22no—
210C22×D43—24no—
211C22×D43—42no—
212C22×D43—42no—
213D4×C43—44no—
214D4×C43—42no—
215D4×C43—42no—
216D4×C43—81no—
217D4×C43—81no—
218C2×C4×C43—22no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43C2×C22⋊C411yescharacteristic
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C22⋊D43—44no—
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—48no—
240C22⋊D43—84no—
241C2×Dic43—22no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—48no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43C2×C22⋊C414yes—
254C2×Dic43C2×C22⋊C414yes—
255C2×Dic43C4×D418yes—
256C2×Dic43#12114yes—
257C2×Dic43#12114yes—
258C2×Dic43#12414yes—
259C2×Dic43#12714yes—
260D172—81no—
261D172—81no—
262C4×D43—48no—
263Dic86—48no—
264#21214—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—84no—
277C22×C43C22×C22⋊C411yescharacteristic
278C22×C43C2×C4×D412yes—
279C22×C43C2×#12112yes—
280C22×C43C2×#12411yescharacteristic
281C22×C43C2×#12711yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—84no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—44no—
291C4×C43—42no—
292C4×C43—82no—
293Dic43—24no—
294Dic43—44no—
295Dic43—42no—
296Dic43—82no—
297Dic43#39018yes—
298C2×#537—431no—
299C2×#410—434no—
300#2316—431no—
301#2274—431no—
302#1964—434no—
303#1964—431no—
304#1964—431no—
305#1964—431no—
306#1964D4311yescharacteristic, complemented
307C2×C43—22no—
308C2×C43—21no—
309C2×C43—22no—
310C2×C43—21no—
311C2×C43—82no—
312C2×C43C2×#39011yescharacteristic
313C2×C43#288311yescharacteristic
314C2×C43#288411yescharacteristic
315D43—82no—
316C22×#41—432no—
317#537—862no—
318#537—862no—
319#537—862no—
320#537—862no—
321C2×C22⋊Q8—432no—
322C2×C22⋊Q8—432no—
323C2×#121—432no—
324C2×#121—432no—
325C2×#121—431no—
326C2×#121—432no—
327C2×#121C2×D4311yescharacteristic
328C2×#117—432no—
329C2×#117—432no—
330C22×C4⋊C4—431no—
331#410—8616no—
332C2×#99—434no—
333C2×#99—434no—
334C2×#99—434no—
335C2×#99C2×D4314yes—
336#389—862no—
337#389—862no—
338#380—431no—
339#380—432no—
340#380C2×D4311yescharacteristic
341C4×C4⋊C4—862no—
342C4×C4⋊C4—862no—
343C4×C22⋊C4—431no—
344C4×C22⋊C4—432no—
345C4×C22⋊C4C2×D4311yescharacteristic
346C43#2121411yescharacteristic, complemented, Sylow
347C2×#41—864no—
348C2×#41—864no—
349C2×#41—868no—
350C2×#41—868no—
351C22×Q8—432no—
352C22×D4—432no—
353C22×D4—432no—
354C22×D4—432no—
355C22×D4—431no—
356C22×D4C4×D4311yescharacteristic
357C22×D4C22×D4312yes—
358C23×C4—431no—
359C23×C4—431no—
360C23×C4—432no—
361C23×C4—432no—
362C23×C4C22×D4311yescharacteristic
363C22⋊Q8—864no—
364C22⋊Q8—864no—
365C22⋊Q8—864no—
366C22⋊Q8—864no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—864no—
372#121—864no—
373#121—864no—
374#121—864no—
375#121—864no—
376#121—864no—
377#121—861no—
378#121—861no—
379#121—861no—
380#121—861no—
381#117—438no—
382#117—864no—
383#117—868no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—432no—
386C2×C4⋊C4—432no—
387C2×C4⋊C4—432no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—432no—
390C2×C4⋊C4—432no—
391C2×C4⋊C4—432no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—862no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4C4×D4311yescharacteristic
398C2×C22⋊C4—432no—
399C2×C22⋊C4—432no—
400C2×C22⋊C4—432no—
401C2×C22⋊C4—432no—
402C2×C22⋊C4—432no—
403C2×C22⋊C4C4×D4312yes—
404C2×C22⋊C4C22×D4312yes—
405C2×C22⋊C4C22×D4312yes—
406C2×C42—21no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—861no—
410C2×C42—862no—
411#99—28no—
412#99—868no—
413#99—868no—
414#99—868no—
415#95—21no—
416#95—21no—
417#95—862no—
418#95—862no—
419#95—861no—
420#95—861no—
421C24—432no—
422C24C2×C4×D4312yes—
423C24C23×D4311yescharacteristic
424#41—1728no—
425#41—1728no—
426#41—1728no—
427#41—1728no—
428C2×Q8—864no—
429C2×Q8—868no—
430C2×D4—24no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—24no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—81no—
437C2×D4—864no—
438C2×D4—864no—
439C2×D4—868no—
440C2×D4—864no—
441C2×D4—862no—
442C2×D4—862no—
443C2×D4—864no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—3441no—
447C2×D4—3442no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—81no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—434no—
455C22×C4—434no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—864no—
461C22×C4—868no—
462C22×C4—864no—
463C22×C4—868no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—3441no—
467C22×C4C2×C4×D4312yes—
468C22×C4C2×C4×D4311yescharacteristic
469C22×C4C2×C4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—81no—
477C4⋊C4—434no—
478C4⋊C4—434no—
479C4⋊C4—434no—
480C4⋊C4—434no—
481C4⋊C4—864no—
482C4⋊C4—868no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—3442no—
486C4⋊C4—3441no—
487C4⋊C4—1724no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—24no—
492C22⋊C4—434no—
493C22⋊C4—864no—
494C22⋊C4—864no—
495C22⋊C4—862no—
496C22⋊C4—862no—
497C22⋊C4—862no—
498C22⋊C4—864no—
499C22⋊C4D4×D4314yes—
500C42—81no—
501C42—868no—
502C42—3441no—
503C42—3442no—
504C42—1724no—
505C23—22no—
506C23—24no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—864no—
512C23—862no—
513C23—1722no—
514C23—1722no—
515C23C22×C4×D4311yescharacteristic
516C23C2×D4×D4311yescharacteristic
517C23C2×D4×D4311yescharacteristic
518C23C2×D4×D4312yes—
519C23#41×D4312yes—
520Q8—1728no—
521D4—44no—
522D4—42no—
523D4—42no—
524D4—81no—
525D4—81no—
526D4—3441no—
527D4—3441no—
528D4—3444no—
529D4—1728no—
530D4—1724no—
531D4—1722no—
532D4—1722no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—434no—
548C2×C4—438no—
549C2×C4—434no—
550C2×C4—434no—
551C2×C4—434no—
552C2×C4—434no—
553C2×C4—434no—
554C2×C4—862no—
555C2×C4—864no—
556C2×C4—864no—
557C2×C4—1728no—
558C2×C4—1728no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4C22⋊C4×D4311yescharacteristic
568C2×C4C22⋊C4×D4311yescharacteristic
569C2×C4C22⋊C4×D4311yescharacteristic
570C2×C4C22⋊C4×D4311yescharacteristic
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—84no—
583C22—3444no—
584C22—1722no—
585C22—1722no—
586C22—1722no—
587C22C2×C22⋊C4×D4311yescharacteristic
588C22C4×D4×D4312yes—
589C22#121×D4312yes—
590C22#124×D4311yescharacteristic
591C22#127×D4311yescharacteristic
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—44no—
597C4—42no—
598C4—82no—
599C4—438no—
600C4—864no—
601C4—3442no—
602C4—1724no—
603C4—1722no—
604C2—22no—
605C2—21no—
606C2—22no—
607C2—21no—
608C2—82no—
609C2—3442no—
610C2#390×D4311yescharacteristic
611C2#1914305311yescharacteristic
612C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1964C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583476C2
cosocleC24×C43C24
hypercenter#1964D43
hypocenterC43#21214
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. C2×#14582871C2semidirect
3. #19137212C2semidirect
4. #19136950C2semidirect
5. #19135432C2semidirect
6. #19135431C2semidirect
7. #19135430C2semidirect
8. #19135429C2semidirect
9. C43×#1964C2semidirect
15. C2×#13063303C4semidirect
16. C2×#13063302C4semidirect
18. C2×#13063298C4semidirect
19. C2×#13063297C4semidirect
69. #13063281D4semidirect
306. #1964D43semidirect
346. C43#21214semidirect

Maximal subgroups

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

subgroupindex
C2×#145834762
C2×#145828712
#191372122
#191369502
#191354322
#191354312
#191354302
#191354292
C43×#19642
#2121443