Finite Group Databasebeta

← #25018821

Subgroups — #25018821

Order 11008.

3526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D43)⋊C4C211yesmaximal, characteristic
2C2×#14582762C211yesmaximal, characteristic, complemented
3C2×#14582757C211yesmaximal, characteristic, complemented
4C2×#14582754C211yesmaximal, characteristic
5C2×#14582754C211yesmaximal, characteristic
6C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
7#19132839C214yesmaximal, complemented
8#19132831C214yesmaximal, complemented
9C2×C43×#381C211yesmaximal, characteristic, complemented
10C25×D43C2211yescharacteristic
11C24×Dic43C2211yescharacteristic
12C22×Dic43⋊C4C2212yescomplemented
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×(C2×D43)⋊C4—24no—
16C22×(C2×D43)⋊C4—24no—
17C22×(C2×D43)⋊C4C418yescomplemented
18C22×(C2×D43)⋊C4C2214yes—
19C22×(C2×D43)⋊C4C2214yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×C4×Dic43C2212yescomplemented
23#14582762—24no—
24#14582757—24no—
25#14582754—24no—
26#14582754—24no—
27C22⋊C4×Dic43—24no—
28C2×C43⋊#95C2212yescomplemented
29C2×C43⋊#95C2212yescomplemented
30C2×C43⋊#95C2214yescomplemented
31C24×C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C43×#381—24no—
35C2×#95×C43C2214yescomplemented
36C24×D43—22no—
37C24×D43—22no—
38C24×D43—28no—
39C24×D43—22no—
40C24×D43—22no—
41C24×D43—22no—
42C24×D43—22no—
43C24×D43—44no—
44C24×D43C2×C414yes—
45C24×D43C2312yes—
46C23×Dic43—44no—
47C23×Dic43C2×C414yes—
48C23×Dic43D414yes—
49C23×Dic43D414yes—
50C23×Dic43C2312yes—
51C23×Dic43C2312yes—
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—44no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43D414yes—
62C2×(C2×D43)⋊C4—232no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—24no—
67C2×(C2×D43)⋊C4—28no—
68C2×(C2×D43)⋊C4—28no—
69C2×(C2×D43)⋊C4—28no—
70C2×(C2×D43)⋊C4—28no—
71C2×(C2×D43)⋊C4—44no—
72C2×(C2×D43)⋊C4—44no—
73C2×(C2×D43)⋊C4C2×C418yes—
74C2×(C2×D43)⋊C4C2×C418yes—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—44no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—28no—
80C25×C43C2311yescharacteristic
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—22no—
86C23×C4×C43—22no—
87C23×C4×C43C2×C414yes—
88C23×C4×C43C2312yes—
89C23×C4×C43C2312yes—
90C23×C4×C43C2312yes—
91C2×C22⋊C4×C43—22no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—22no—
96C2×C22⋊C4×C43D414yes—
97#95×C43—28no—
98C24×C43—24no—
99C24×C43—24no—
100C24×C43C22×C412yes—
101C24×C43C2×D412yes—
102C24×C43C2×D412yes—
103C24×C43C2×D412yes—
104C24×C43C2×D412yes—
105C24×C43#4112yes—
106C24×C43#4112yes—
107C24×C43C2411yescharacteristic
108C23×D43—216no—
109C23×D43—216no—
110C23×D43—28no—
111C23×D43—22no—
112C23×D43—22no—
113C23×D43—22no—
114C23×D43—22no—
115C23×D43—24no—
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—24no—
119C23×D43—24no—
120C23×D43—216no—
121C23×D43—28no—
122C23×D43—28no—
123C23×D43—48no—
124C23×D43—416no—
125C23×D43—416no—
126C23×D43—416no—
127C23×D43—416no—
128C23×D43—48no—
129C23×D43—48no—
130C23×D43—44no—
131C23×D43—44no—
132C23×D43—44no—
133C23×D43—44no—
134C23×D43C22×C414yes—
135C23×D43#4118yes—
136C22×C4×C43—28no—
137C22×C4×C43—28no—
138C22×C4×C43—28no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—24no—
151C22×C4×C43—24no—
152C22×C4×C43—24no—
153C22×C4×C43—24no—
154C22×C4×C43—44no—
155C22×C4×C43—44no—
156C22×C4×C43—44no—
157C22×C4×C43—44no—
158C22×C4×C43C22×C414yes—
159C22×C4×C43C2×D414yes—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—24no—
165C22×Dic43—22no—
166C22×Dic43—24no—
167C22×Dic43—24no—
168C22×Dic43—24no—
169C22×Dic43—24no—
170C22×Dic43—24no—
171C22×Dic43—48no—
172C22×Dic43—48no—
173C22×Dic43—48no—
174C22×Dic43C22⋊C4116yescomplemented
175C22×Dic43C22×C412yes—
176C22×Dic43C22×C412yes—
177C22×Dic43C2×D414yes—
178C22×Dic43C2×D412yes—
179C22×Dic43C2×D412yes—
180C22×Dic43C2×D412yes—
181C22×Dic43C2×D412yes—
182C22⋊C4×C43—28no—
183C22⋊C4×C43—44no—
184C22⋊Dic43—28no—
185C22⋊Dic43—44no—
186(C2×D43)⋊C4—216no—
187(C2×D43)⋊C4—216no—
188(C2×D43)⋊C4—416no—
189(C2×D43)⋊C4—416no—
190Dic43⋊C4—48no—
191C4×Dic43—48no—
192C23×C43—24no—
193C23×C43—24no—
194C23×C43—24no—
195C23×C43—24no—
196C23×C43—24no—
197C23×C43—24no—
198C23×C43—28no—
199C23×C43—28no—
200C23×C43—28no—
201C23×C43—28no—
202C23×C43C2×C22⋊C414yes—
203C23×C43C4×D414yes—
204C23×C43C4×D414yes—
205C23×C43#12114yes—
206C23×C43#12114yes—
207C23×C43#12414yes—
208C23×C43#12714yes—
209C23×C43C23×C411yescharacteristic
210C23×C43C22×D411yescharacteristic
211C23×C43C22×D411yescharacteristic
212C23×C43C22×D411yescharacteristic
213C23×C43C22×D411yescharacteristic
214C23×C43C2×#4114yes—
215C23×C43C2×#4111yescharacteristic
216C23×C43C2×#4111yescharacteristic
217C23×C43H(5,𝔽2)14yes—
218C22×D43—232no—
219C22×D43—24no—
220C22×D43—24no—
221C22×D43—24no—
222C22×D43—24no—
223C22×D43—24no—
224C22×D43—24no—
225C22×D43—28no—
226C22×D43—28no—
227C22×D43—28no—
228C22×D43—28no—
229C22×D43—28no—
230C22×D43—28no—
231C22×D43—432no—
232C22×D43—432no—
233C22×D43—432no—
234C22×D43—416no—
235C22×D43—432no—
236C22×D43—432no—
237C22×D43—432no—
238C22×D43—42no—
239C22×D43—42no—
240C22×D43—42no—
241C22×D43—42no—
242C22×D43—44no—
243C22×D43—44no—
244C22×D43—44no—
245C22×D43—44no—
246C22×D43—44no—
247C22×D43—44no—
248C22×D43—416no—
249C22×D43#11718yes—
250C2×C4×C43—24no—
251C2×C4×C43—24no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—28no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—44no—
262C2×C4×C43—416no—
263C2×C4×C43—42no—
264C2×C4×C43—42no—
265C2×C4×C43—42no—
266C2×C4×C43—44no—
267C2×C4×C43—44no—
268C2×Dic43—24no—
269C2×Dic43—24no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—24no—
275C2×Dic43—28no—
276C2×Dic43—416no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—44no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—44no—
284C2×Dic43—44no—
285C2×Dic43C2×C22⋊C414yes—
286C2×Dic43C2×C22⋊C414yes—
287#13903—431nomaximal, Sylow
288C22×C43—28no—
289C22×C43—24no—
290C22×C43—28no—
291C22×C43—28no—
292C22×C43—28no—
293C22×C43—28no—
294C22×C43—24no—
295C22×C43—28no—
296C22×C43#39018yes—
297C22×C43C22×C22⋊C411yescharacteristic
298C22×C43C2×#11712yes—
299C22×C43C2×C4×D411yescharacteristic
300C22×C43C2×C4×D411yescharacteristic
301C22×C43#51812yes—
302C22×C43C2×#12111yescharacteristic
303C22×C43C2×#12111yescharacteristic
304C22×C43#52512yes—
305C22×C43#52512yes—
306C22×C43C2×#12411yescharacteristic
307C22×C43C2×#12711yescharacteristic
308C22×C43#53412yes—
309C22×C43#53412yes—
310C22×C43#54614yes—
311C22×C43#54614yes—
312C22×C43#55114yes—
313C22×C43#55114yes—
314C2×D43—28no—
315C2×D43—28no—
316C2×D43—28no—
317C2×D43—464no—
318C2×D43—48no—
319C2×D43—44no—
320C2×D43—44no—
321C2×D43—44no—
322C2×D43—48no—
323C2×D43—48no—
324C2×D43—48no—
325C2×D43—44no—
326C4×C43—44no—
327C4×C43—44no—
328C4×C43—82no—
329Dic43—24no—
330Dic43—24no—
331Dic43—44no—
332Dic43—82no—
333C23×C22⋊C4—431no—
334C2×#381—431no—
335C2×#381D4311yescharacteristic, complemented
336C2×#380—431no—
337C2×#379—431no—
338C2×#379—431no—
339C2×C4×C22⋊C4—431no—
340#1439—434no—
341#1437—434no—
342C2×C43—28no—
343C2×C43#228011yescharacteristic
344C2×C43C2×#39011yescharacteristic
345C2×C43#230811yescharacteristic
346C2×C43#234212yes—
347C2×C43#234212yes—
348C2×C43#253412yes—
349C2×C43#253412yes—
350C2×C43#253912yes—
351C2×C43#256112yes—
352D43—48no—
353C26—431no—
354C24×C4—431no—
355C24×C4C2×D4311yescharacteristic
356C22×C4⋊C4—432no—
357C22×C22⋊C4—431no—
358C22×C22⋊C4—432no—
359C22×C22⋊C4—432no—
360C22×C22⋊C4—438no—
361C22×C22⋊C4—431no—
362C22×C22⋊C4—434no—
363C22×C22⋊C4—434no—
364C22×C22⋊C4—864no—
365C22×C22⋊C4—864no—
366C22×C22⋊C4C2×D4311yescharacteristic
367C22×C22⋊C4C2×D4311yescharacteristic
368C22×C42—432no—
369#381—24no—
370#381—864no—
371#380—864no—
372#379—864no—
373#379—864no—
374C4×C22⋊C4—864no—
375C2×#95—432no—
376C2×#95—434no—
377C2×#95—432no—
378C2×#95C2×D4314yescomplemented
379C43#1390311yescharacteristic, complemented, Sylow
380C25—432no—
381C25—434no—
382C25—868no—
383C25—862no—
384C25—862no—
385C25—862no—
386C25—862no—
387C25—862no—
388C25—862no—
389C25—1724no—
390C25C22×D4311yescharacteristic
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—431no—
398C23×C4—431no—
399C23×C4—434no—
400C23×C4—434no—
401C23×C4—434no—
402C23×C4—432no—
403C23×C4—432no—
404C23×C4—1724no—
405C23×C4C4×D4314yes—
406C23×C4C22×D4312yes—
407C23×C4C22×D4312yes—
408C23×C4C22×D4312yes—
409C2×C4⋊C4—864no—
410C2×C4⋊C4—1724no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—434no—
417C2×C22⋊C4—438no—
418C2×C22⋊C4—438no—
419C2×C22⋊C4—8632no—
420C2×C22⋊C4—864no—
421C2×C22⋊C4—864no—
422C2×C22⋊C4—864no—
423C2×C22⋊C4—864no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—868no—
427C2×C22⋊C4—868no—
428C2×C22⋊C4—868no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—862no—
431C2×C22⋊C4—862no—
432C2×C22⋊C4—868no—
433C2×C22⋊C4—1724no—
434C2×C22⋊C4—1724no—
435C2×C22⋊C4C22⋊D4314yes—
436C2×C42—864no—
437C2×C42—1724no—
438#95—28no—
439#95—864no—
440#95—864no—
441#95—868no—
442C24—24no—
443C24—24no—
444C24—434no—
445C24—438no—
446C24—8616no—
447C24—8616no—
448C24—8616no—
449C24—868no—
450C24—862no—
451C24—862no—
452C24—862no—
453C24—862no—
454C24—864no—
455C24—862no—
456C24—862no—
457C24—864no—
458C24—864no—
459C24—868no—
460C24—868no—
461C24—1728no—
462C24—17216no—
463C24—17216no—
464C24—17216no—
465C24—17216no—
466C24—1728no—
467C24—1728no—
468C24—1724no—
469C24—1724no—
470C24—1724no—
471C24—1724no—
472C24C2×C4×D4312yes—
473C24#1062189812yes—
474C24D4×D4312yes—
475C24D4×D4312yes—
476C24D4×D4312yes—
477C24#1062190012yes—
478C24C2×C22⋊D4312yes—
479C24C23×D4311yescharacteristic
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—432no—
503C22×C4—432no—
504C22×C4—432no—
505C22×C4—432no—
506C22×C4—432no—
507C22×C4—432no—
508C22×C4—4316no—
509C22×C4—434no—
510C22×C4—864no—
511C22×C4—864no—
512C22×C4—862no—
513C22×C4—864no—
514C22×C4—862no—
515C22×C4—864no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—864no—
520C22×C4—864no—
521C22×C4—1728no—
522C22×C4—1728no—
523C22×C4—1728no—
524C22×C4C2×C4×D4314yes—
525C22×C4C2×C22⋊D4314yes—
526C4⋊C4—1728no—
527C22⋊C4—28no—
528C22⋊C4—44no—
529C22⋊C4—8616no—
530C22⋊C4—8616no—
531C22⋊C4—868no—
532C22⋊C4—17216no—
533C22⋊C4—17216no—
534C22⋊C4—1724no—
535C42—1728no—
536C23—28no—
537C23—28no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—28no—
545C23—28no—
546C23—438no—
547C23—8632no—
548C23—868no—
549C23—868no—
550C23—864no—
551C23—864no—
552C23—864no—
553C23—864no—
554C23—864no—
555C23—864no—
556C23—868no—
557C23—868no—
558C23—868no—
559C23—868no—
560C23—17232no—
561C23—17232no—
562C23—17216no—
563C23—17232no—
564C23—17232no—
565C23—17232no—
566C23—17232no—
567C23—17216no—
568C23—1724no—
569C23—1724no—
570C23—1722no—
571C23—1722no—
572C23—1722no—
573C23—1722no—
574C23—1724no—
575C23—1724no—
576C23—1724no—
577C23—1724no—
578C23C22⋊C4×D4314yes—
579C23(C22⋊D43)⋊C414yes—
580C23C4×C22⋊D4314yes—
581C23#1306329714yes—
582C23#1306329814yes—
583C23#1306331114yes—
584C23#1306332114yes—
585C23C22×C4×D4311yescharacteristic
586C23C2×D4×D4311yescharacteristic
587C23C2×D4×D4311yescharacteristic
588C23C2×D4×D4311yescharacteristic
589C23C22×C22⋊D4311yescharacteristic
590C23#41×D4314yes—
591C23C2×#1062190011yescharacteristic
592C23C2×#1062189811yescharacteristic
593C23#1306337114yes—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—28no—
599C2×C4—416no—
600C2×C4—44no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—44no—
612C2×C4—434no—
613C2×C4—434no—
614C2×C4—864no—
615C2×C4—864no—
616C2×C4—864no—
617C2×C4—864no—
618C2×C4—864no—
619C2×C4—864no—
620C2×C4—864no—
621C2×C4—868no—
622C2×C4—17216no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1724no—
627C2×C4—1724no—
628C2×C4—1724no—
629C2×C4—1722no—
630C2×C4—1722no—
631C22—24no—
632C22—28no—
633C22—28no—
634C22—28no—
635C22—28no—
636C22—28no—
637C22—28no—
638C22—24no—
639C22—868no—
640C22—868no—
641C22—868no—
642C22—17264no—
643C22—1724no—
644C22—1724no—
645C22—1728no—
646C22—1724no—
647C22—1728no—
648C22—1724no—
649C22—1728no—
650C22—1728no—
651C22#1458279918yes—
652C22C2×C22⋊C4×D4311yescharacteristic
653C22#117×D4312yes—
654C22C2×(C22⋊D43)⋊C411yescharacteristic
655C22C2×C4×C22⋊D4311yescharacteristic
656C22#1458337312yes—
657C22C2×#1306329711yescharacteristic
658C22C2×#1306329811yescharacteristic
659C22#1458340712yes—
660C22#1458340712yes—
661C22C2×#1306331111yescharacteristic
662C22C2×#1306332111yescharacteristic
663C22#1458346012yes—
664C22#1458346012yes—
665C22#1458353714yes—
666C22#1458354114yes—
667C22#1458357214yes—
668C22#1458357314yes—
669C4—44no—
670C4—44no—
671C4—82no—
672C4—864no—
673C4—864no—
674C4—3442no—
675C4—1724no—
676C2—28no—
677C2—1728no—
678C2#1913697511yescharacteristic
679C2C2×#1458279911yescharacteristic
680C2#1913717211yescharacteristic
681C2#1913743712yes—
682C2#1913744512yes—
683C2#1913948412yes—
684C2#1913949012yes—
685C2#1913952512yes—
686C2#1913975212yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#381C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenterC2×#381D43
hypocenterC43#13903
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C2×#14582762C2semidirect
3. C2×#14582757C2semidirect
6. C2×C22⋊C4×Dic43C2semidirect
7. #19132839C2semidirect
8. #19132831C2semidirect
9. C2×C43×#381C2semidirect
12. C22×Dic43⋊C4C22semidirect
17. C22×(C2×D43)⋊C4C4semidirect
22. C22×C4×Dic43C22semidirect
28. C2×C43⋊#95C22semidirect
29. C2×C43⋊#95C22semidirect
30. C2×C43⋊#95C22semidirect
35. C2×#95×C43C22semidirect
174. C22×Dic43C22⋊C4semidirect
335. C2×#381D43semidirect
378. C2×#95C2×D43semidirect
379. C43#13903semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D43)⋊C42
C2×#145827622
C2×#145827572
C2×#145827542
C2×C22⋊C4×Dic432
#191328392
#191328312
C2×C43×#3812
#1390343