Finite Group Databasebeta

← #25027953

Subgroups — #25027953

Order 11008.

1770 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063320C211yesmaximal, characteristic
2C2×#14582766C211yesmaximal, characteristic, complemented
3C2×C42×Dic43C211yesmaximal, characteristic, complemented
4#19132833C211yesmaximal, characteristic
5#19132831C212yesmaximal
6#19132831C211yesmaximal, characteristic
7#19132831C212yesmaximal
8#19132829C212yesmaximal, complemented
9#19132827C211yesmaximal, characteristic, complemented
10#19132826C212yesmaximal, complemented
11C43×#1436C211yesmaximal, characteristic, complemented
12C2×#13063320—24no—
13C2×#13063320—24no—
14C2×#13063320C418yescomplemented
15C22×C4⋊Dic43C2211yescharacteristic
16C22×Dic43⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×C4×Dic43C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2212yes—
25C22×C4×Dic43C2211yescharacteristic
26#14582766—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C42×Dic43—24no—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2312yes—
46#13063320—232no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43C2×C414yes—
50C2×Dic43⋊C4—22no—
51C2×Dic43⋊C4—22no—
52C2×Dic43⋊C4C2×C414yes—
53C2×(C2×D43)⋊C4—22no—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4—22no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—24no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4C2×C414yes—
66C2×(C2×D43)⋊C4C2×C414yes—
67C2×(C2×D43)⋊C4C2×C414yes—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—24no—
71C2×C4×Dic43—24no—
72C2×C4×Dic43—24no—
73C2×C4×Dic43—24no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43C2×C414yes—
77C2×C4×Dic43D414yes—
78C2×C4×Dic43D414yes—
79C43⋊#95—22no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2312yes—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43C2×C414yes—
94C2×C42×C43—22no—
95C2×C42×C43—24no—
96#95×C43—22no—
97#95×C43—24no—
98#95×C43—24no—
99C24×C43C2411yescharacteristic
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—22no—
103C23×D43—22no—
104C23×D43—22no—
105C23×D43—22no—
106C23×D43—22no—
107C23×D43—22no—
108C23×D43C22×C412yes—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43#4114yes—
136C22×C4×C43#4114yes—
137C22×C4×C43#4114yes—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43C22×C412yes—
158C22×Dic43C22×C412yes—
159C22×Dic43C22×C412yes—
160C22×Dic43C2×D412yes—
161C22×Dic43C2×D412yes—
162C22×Dic43C2×D412yes—
163C22×Dic43C2×D412yes—
164C22×Dic43#4114yes—
165C22×Dic43#4114yes—
166C22×Dic43#4114yes—
167C4⋊C4×C43—28no—
168C42×C43—28no—
169(C2×D43)⋊C4—28no—
170(C2×D43)⋊C4—28no—
171(C2×D43)⋊C4—28no—
172(C2×D43)⋊C4—48no—
173(C2×D43)⋊C4—48no—
174C4⋊Dic43—28no—
175Dic43⋊C4—28no—
176C4×Dic43—216no—
177C4×Dic43—216no—
178C4×Dic43—28no—
179C4×Dic43C22⋊C4116yescomplemented
180C23×C43C23×C411yescharacteristic
181C23×C43C22×D411yescharacteristic
182C23×C43C22×D411yescharacteristic
183C23×C43C2×#4112yes—
184C23×C43C2×#4112yes—
185C23×C43C2×#4112yes—
186C23×C43C2×#4112yes—
187C23×C43C2×#4112yes—
188C23×C43C2×#4112yes—
189C22×D43—22no—
190C22×D43—24no—
191C22×D43—22no—
192C22×D43—22no—
193C22×D43—24no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—41no—
209C22×D43—41no—
210C2×C4×C43—24no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
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×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43C2×C22⋊C414yes—
238C2×C4×C43#12618yescomplemented
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—42no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43C2×C22⋊C414yes—
266C2×Dic43C2×C22⋊C414yes—
267C2×Dic43#12618yescomplemented
268#14711—431nomaximal, Sylow
269C22×C43C22×C22⋊C411yescharacteristic
270C22×C43C4×#4112yes—
271C22×C43C4×#4111yescharacteristic
272C22×C43C4×#4111yescharacteristic
273C22×C43C4×#4112yes—
274C22×C43#52511yescharacteristic
275C22×C43#52511yescharacteristic
276C22×C43#52512yes—
277C22×C43#52512yes—
278C22×C43C2×#12612yes—
279C22×C43C2×#12612yes—
280C22×C43#52912yes—
281C22×C43#52912yes—
282C22×C43#52912yes—
283C22×C43#52912yes—
284C22×C43#52912yes—
285C22×C43#52912yes—
286C22×C43#53212yes—
287C22×C43#53212yes—
288C22×C43#53211yescharacteristic
289C22×C43#53211yescharacteristic
290C2×D43—44no—
291C2×D43—44no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—82no—
296C2×D43—82no—
297C2×D43—82no—
298C2×D43—82no—
299C4×C43—28no—
300C4×C43—24no—
301C4×C43—42no—
302C4×C43—42no—
303C4×C43—82no—
304Dic43—28no—
305Dic43—24no—
306Dic43—24no—
307Dic43—42no—
308Dic43—82no—
309C22×#126—431no—
310C2×#383—431no—
311C2×C43—431no—
312#1437—431no—
313#1437—431no—
314#1437—432no—
315#1437—432no—
316#1436—432no—
317#1436—432no—
318#1436—431no—
319#1436D4311yescharacteristic, complemented
320C2×C43#229711yescharacteristic
321C2×C43#229711yescharacteristic
322C2×C43#229711yescharacteristic
323C2×C43C4×#12612yes—
324C2×C43C4×#12612yes—
325C2×C43#285212yes—
326C2×C43#285212yes—
327C2×C43#286012yes—
328C2×C43#286012yes—
329D43—82no—
330C2×#126—438no—
331C2×#126—864no—
332C2×#126—864no—
333C22×C4⋊C4—431no—
334C22×C4⋊C4—431no—
335C22×C4⋊C4C2×D4311yescharacteristic
336C22×C22⋊C4—431no—
337C22×C22⋊C4—431no—
338C22×C22⋊C4—431no—
339C22×C22⋊C4—432no—
340C22×C22⋊C4—432no—
341C22×C42—431no—
342C22×C42—432no—
343C22×C42—432no—
344C22×C42—431no—
345C22×C42C2×D4311yescharacteristic
346#383—864no—
347C2×#95—432no—
348C2×#95—432no—
349C2×#95—432no—
350C2×#95—432no—
351C2×#95—432no—
352C2×#95—432no—
353C2×#95—431no—
354C2×#95C2×D4312yes—
355C2×#95C2×D4312yes—
356C2×#95C2×D4311yescharacteristic
357C43—864no—
358C43#1471111yescharacteristic, complemented, Sylow
359C25—431no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—432no—
363C23×C4—431no—
364C23×C4—432no—
365C23×C4C22×D4312yes—
366C23×C4C22×D4311yescharacteristic
367C23×C4C22×D4311yescharacteristic
368C23×C4C22×D4311yescharacteristic
369C23×C4C22×D4312yes—
370#126—8632no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—434no—
374C2×C4⋊C4—434no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4C4×D4314yes—
380C2×C22⋊C4—434no—
381C2×C22⋊C4—434no—
382C2×C22⋊C4—434no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—862no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4—862no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—864no—
390C2×C22⋊C4—864no—
391C2×C22⋊C4—864no—
392C2×C22⋊C4—864no—
393C2×C22⋊C4—864no—
394C2×C22⋊C4—864no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—434no—
398C2×C42—434no—
399C2×C42—434no—
400C2×C42—864no—
401C2×C42—864no—
402C2×C42—864no—
403C2×C42—864no—
404C2×C42—864no—
405C2×C42—864no—
406C2×C42—862no—
407C2×C42—864no—
408#95—24no—
409#95—22no—
410#95—24no—
411#95—864no—
412#95—864no—
413#95—864no—
414#95—864no—
415#95—864no—
416#95—862no—
417#95—864no—
418C24—432no—
419C24—861no—
420C24—861no—
421C24—862no—
422C24—862no—
423C24—862no—
424C24—862no—
425C24—862no—
426C24—862no—
427C24C23×D4311yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—434no—
456C22×C4—434no—
457C22×C4—434no—
458C22×C4—432no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4C2×C4×D4312yes—
479C22×C4C2×C4×D4312yes—
480C22×C4C2×C4×D4312yes—
481C22×C4#1062189814yes—
482C22×C4D4×D4312yes—
483C22×C4D4×D4312yes—
484C22×C4#1062190014yes—
485C22×C4#1062190214yes—
486C4⋊C4—28no—
487C4⋊C4—868no—
488C4⋊C4—868no—
489C22⋊C4—868no—
490C22⋊C4—868no—
491C22⋊C4—868no—
492C22⋊C4—1728no—
493C22⋊C4—1728no—
494C42—28no—
495C42—4316no—
496C42—868no—
497C42—8616no—
498C42—8616no—
499C23—862no—
500C23—864no—
501C23—862no—
502C23—862no—
503C23—864no—
504C23—1721no—
505C23—1721no—
506C23—1722no—
507C23—1722no—
508C23—1722no—
509C23—1722no—
510C23—1722no—
511C23—1722no—
512C23—1722no—
513C23—1722no—
514C23—1722no—
515C23—1722no—
516C23—1722no—
517C23—1722no—
518C23—1721no—
519C23—1721no—
520C23C22×C4×D4311yescharacteristic
521C23C2×D4×D4311yescharacteristic
522C23C2×D4×D4311yescharacteristic
523C23#41×D4312yes—
524C23#41×D4312yes—
525C23#41×D4312yes—
526C23C2×#1062190012yes—
527C23C2×#1062189812yes—
528C23C2×#1062190212yes—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—434no—
557C2×C4—434no—
558C2×C4—438no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—864no—
562C2×C4—864no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—864no—
566C2×C4—864no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—864no—
570C2×C4—864no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—864no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4C22⋊C4×D4314yes—
586C2×C4#1306332018yescomplemented
587C22—3442no—
588C22—3442no—
589C22—3442no—
590C22—3442no—
591C22—1722no—
592C22—1722no—
593C22—1722no—
594C22—1724no—
595C22—1724no—
596C22C2×C22⋊C4×D4311yescharacteristic
597C22C4×#1062190012yes—
598C22#1458336711yescharacteristic
599C22C4×#1062189811yescharacteristic
600C22C4×#1062190212yes—
601C22#1458340511yescharacteristic
602C22#1458340711yescharacteristic
603C22#1458340812yes—
604C22#1458341212yes—
605C22#126×D4312yes—
606C22C2×#1306332012yes—
607C22#1458342612yes—
608C22#1458342712yes—
609C22#1458342912yes—
610C22#1458343412yes—
611C22#1458343512yes—
612C22#1458343612yes—
613C22#1458344412yes—
614C22#1458344612yes—
615C22#1458344811yescharacteristic
616C22#1458345011yescharacteristic
617C4—28no—
618C4—24no—
619C4—42no—
620C4—42no—
621C4—82no—
622C4—868no—
623C4—864no—
624C4—864no—
625C4—3442no—
626C4—1722no—
627C2—3442no—
628C2#1913708011yescharacteristic
629C2#1913708111yescharacteristic
630C2#1913708411yescharacteristic
631C2#1913714512yes—
632C2C4×#1306332012yes—
633C2#1914291212yes—
634C2#1914291312yes—
635C2#1914296112yes—
636C2#1914296312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1436D43
hypocenterC43#14711
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#14582766C2semidirect
3. C2×C42×Dic43C2semidirect
8. #19132829C2semidirect
9. #19132827C2semidirect
10. #19132826C2semidirect
11. C43×#1436C2semidirect
14. C2×#13063320C4semidirect
179. C4×Dic43C22⋊C4semidirect
238. C2×C4×C43#126semidirect
267. C2×Dic43#126semidirect
319. #1436D43semidirect
358. C43#14711semidirect
586. C2×C4#13063320semidirect

Maximal subgroups

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

subgroupindex
C22×#130633202
C2×#145827662
C2×C42×Dic432
#191328332
#191328312
#191328292
#191328272
#191328262
C43×#14362
#1471143