Finite Group Databasebeta

← #25020255

Subgroups — #25020255

Order 11008.

2222 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582780C212yesmaximal, complemented
2C2×#14582772C211yesmaximal, characteristic
3C2×C4×C22⋊Dic43C211yesmaximal, characteristic
4#19132854C212yesmaximal, complemented
5#19132845C212yesmaximal, complemented
6#19132827C212yesmaximal, complemented
7#19132818C211yesmaximal, characteristic
8#19132818C211yesmaximal, characteristic
9#19132818C211yesmaximal, characteristic
10#19132818C211yesmaximal, characteristic
11C23×C4⋊C4×C43C211yesmaximal, characteristic
12C22×Dic43⋊C4C2212yes—
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C4×Dic43C2211yescharacteristic
18C22×C4×Dic43C2211yescharacteristic
19#14582780—28no—
20#14582772C418yescomplemented
21C4×C22⋊Dic43—24no—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C24×C4×C43C2211yescharacteristic
34C24×C4×C43C2211yescharacteristic
35C24×C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43—24no—
37C22×C4⋊C4×C43—28no—
38C22×C4⋊C4×C43C2212yes—
39C22×C4⋊C4×C43C2212yes—
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C2×Dic43⋊C4—24no—
47C2×Dic43⋊C4—24no—
48C2×Dic43⋊C4C2×C418yescomplemented
49C2×C22⋊Dic43—22no—
50C2×C22⋊Dic43—22no—
51C2×C22⋊Dic43—22no—
52C2×C22⋊Dic43—22no—
53C2×C22⋊Dic43—22no—
54C2×C22⋊Dic43—22no—
55C2×C22⋊Dic43—22no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43C2×C414yes—
59C2×C22⋊Dic43C2×C414yes—
60C2×C22⋊Dic43Q814yes—
61C2×C4×Dic43—22no—
62C2×C4×Dic43—22no—
63C2×C4×Dic43—24no—
64C2×C4×Dic43—42no—
65C43⋊#95—22no—
66C43⋊#95—22no—
67C43⋊#95—24no—
68C43⋊#95—24no—
69C43⋊#95—24no—
70C43⋊#95—24no—
71C43⋊#95—24no—
72C43⋊#95—42no—
73C43⋊#95—42no—
74C43⋊#95—42no—
75C43⋊#95C2×C418yescomplemented
76C25×C43C2311yescharacteristic
77C23×C4×C43—22no—
78C23×C4×C43—22no—
79C23×C4×C43—24no—
80C23×C4×C43—24no—
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—24no—
85C23×C4×C43—24no—
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—42no—
89C23×C4×C43—42no—
90C23×C4×C43C2×C414yes—
91C23×C4×C43D414yes—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43—232no—
97C2×C4⋊C4×C43—24no—
98C2×C4⋊C4×C43—24no—
99C2×C4⋊C4×C43—24no—
100C2×C4⋊C4×C43—24no—
101C2×C4⋊C4×C43—24no—
102C2×C4⋊C4×C43D418yes—
103C24×C43—22no—
104C24×C43—22no—
105C24×C43—22no—
106C24×C43—22no—
107C24×C43C22×C412yes—
108C24×C43C2×D412yes—
109C24×C43C2×Q812yes—
110C24×C43#4112yes—
111C24×C43#4112yes—
112C24×C43#4112yes—
113C24×C43#4112yes—
114C24×C43C2411yescharacteristic
115C22×C4×C43—28no—
116C22×C4×C43—28no—
117C22×C4×C43—216no—
118C22×C4×C43—216no—
119C22×C4×C43—28no—
120C22×C4×C43—28no—
121C22×C4×C43—28no—
122C22×C4×C43—28no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—44no—
141C22×C4×C43—48no—
142C22×C4×C43—48no—
143C22×C4×C43—48no—
144C22×C4×C43—48no—
145C22×C4×C43—44no—
146C22×C4×C43—44no—
147C22×C4×C43C22×C414yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D414yes—
150C22×C4×C43C2×D414yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D414yes—
153C22×C4×C43#4114yes—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—22no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43C22×C412yes—
184C22×Dic43C22×C414yes—
185C22×Dic43C22×C412yes—
186C22×Dic43C2×Q812yes—
187C22×Dic43C2×Q812yes—
188C4⋊C4×C43—216no—
189C4⋊C4×C43—216no—
190C22⋊Dic43—28no—
191C22⋊Dic43—28no—
192C22⋊Dic43—28no—
193C22⋊Dic43—44no—
194Dic43⋊C4—216no—
195C4×Dic43—44no—
196C4×Dic43—44no—
197C23×C43—24no—
198C23×C43—24no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—24no—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43—24no—
205C23×C43—24no—
206C23×C43—24no—
207C23×C43—24no—
208C23×C43—24no—
209C23×C43—24no—
210C23×C43—24no—
211C23×C43—24no—
212C23×C43—24no—
213C23×C43#11714yes—
214C23×C43C4×D414yes—
215C23×C43C4×Q814yes—
216C23×C43C22⋊Q814yes—
217C23×C43#12314yes—
218C23×C43#12514yes—
219C23×C43#12614yes—
220C23×C43C23×C411yescharacteristic
221C23×C43C22×D411yescharacteristic
222C23×C43C22×D412yes—
223C23×C43C22×Q811yescharacteristic
224C23×C43C2×#4111yescharacteristic
225C23×C43C2×#4111yescharacteristic
226C23×C43C2×#4111yescharacteristic
227C23×C43C2×#4112yes—
228C23×C43C2×#4111yescharacteristic
229C23×C43H(5,𝔽2)12yes—
230C23×C432−1+412yes—
231C2×C4×C43—232no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—24no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—22no—
243C2×C4×C43—24no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—24no—
247C2×C4×C43—24no—
248C2×C4×C43—416no—
249C2×C4×C43—416no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43C4×D418yes—
257C2×C4×C43#12014yes—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—24no—
264C2×Dic43—24no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—24no—
268C2×Dic43—24no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—42no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—42no—
288C2×Dic43—42no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—42no—
292#14039—431nomaximal, Sylow
293C22×C43—24no—
294C22×C43—24no—
295C22×C43—28no—
296C22×C43—28no—
297C22×C43—24no—
298C22×C43—24no—
299C22×C43—28no—
300C22×C43—28no—
301C22×C43—24no—
302C22×C43—24no—
303C22×C43#38718yescomplemented
304C22×C43C2×#11711yescharacteristic
305C22×C43C2×C4×D411yescharacteristic
306C22×C43C2×C4×D412yes—
307C22×C43C2×C4×Q811yescharacteristic
308C22×C43#52012yes—
309C22×C43C2×#12011yescharacteristic
310C22×C43C2×C22⋊Q811yescharacteristic
311C22×C43C2×#12311yescharacteristic
312C22×C43#52511yescharacteristic
313C22×C43#52512yes—
314C22×C43C2×#12511yescharacteristic
315C22×C43C2×#12611yescharacteristic
316C22×C43#53411yescharacteristic
317C22×C43#53611yescharacteristic
318C22×C43#53912yes—
319C22×C43#54612yes—
320C22×C43#54612yes—
321C22×C43#54812yes—
322C22×C43D4×Q812yes—
323C22×C43#55212yes—
324C22×C43#55212yes—
325C22×C43#55312yes—
326C22×C43#55412yes—
327C4×C43—24no—
328C4×C43—28no—
329C4×C43—42no—
330C4×C43—44no—
331Dic43—42no—
332Dic43—42no—
333Dic43—44no—
334Dic43—42no—
335Dic43—42no—
336Dic43—82no—
337C23×C4⋊C4D4311yescharacteristic
338C2×#387—432no—
339C2×#385—431no—
340C2×C4×C22⋊C4—431no—
341#1442—432no—
342#1441—432no—
343#1436—432no—
344C22⋊#95—431no—
345C22⋊#95—431no—
346C22⋊#95—431no—
347C22⋊#95—431no—
348C2×C43—28no—
349C2×C43C2×#38711yescharacteristic
350C2×C43C4×#12011yescharacteristic
351C2×C43#232211yescharacteristic
352C2×C43#235212yes—
353C2×C43#236012yes—
354C2×C43#240511yescharacteristic
355C2×C43#240911yescharacteristic
356C2×C43#247312yes—
357C2×C43#248112yes—
358C2×C43#248411yescharacteristic
359C2×C43#257911yescharacteristic
360C24×C4C2×D4311yescharacteristic
361C24×C4C2×D4311yescharacteristic
362C24×C4C2×D4311yescharacteristic
363C22×C4⋊C4—24no—
364C22×C4⋊C4—28no—
365C22×C4⋊C4—432no—
366C22×C4⋊C4C2×D4312yes—
367C22×C4⋊C4C2×D4312yes—
368C22×C22⋊C4—431no—
369C22×C22⋊C4—431no—
370C22×C22⋊C4—431no—
371C22×C22⋊C4—431no—
372C22×C42—431no—
373C22×C42—431no—
374#387—868no—
375#385—438no—
376C4×C22⋊C4—864no—
377C2×#95—432no—
378C2×#95—432no—
379C2×#95—432no—
380C2×#95—432no—
381C2×#95—432no—
382C2×#95—432no—
383C2×#95—431no—
384C2×#95—431no—
385C2×#95—432no—
386C2×#95—432no—
387C2×#95—432no—
388C43#1403911yescharacteristic, complemented, Sylow
389C25C22×D4311yescharacteristic
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—431no—
404C23×C4—432no—
405C23×C4—431no—
406C23×C4—431no—
407C23×C4—431no—
408C23×C4—432no—
409C23×C4C4×D4314yes—
410C23×C4C22⋊D4314yes—
411C23×C4C22×D4311yescharacteristic
412C23×C4C22×D4312yes—
413C23×C4C22×D4312yes—
414C23×C4C22×D4311yescharacteristic
415C2×C4⋊C4—232no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—438no—
422C2×C4⋊C4—864no—
423C2×C4⋊C4—864no—
424C2×C4⋊C4C22⋊D4318yes—
425C2×C22⋊C4—434no—
426C2×C22⋊C4—434no—
427C2×C22⋊C4—434no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—862no—
431C2×C22⋊C4—862no—
432C2×C22⋊C4—862no—
433C2×C22⋊C4—862no—
434C2×C22⋊C4—862no—
435C2×C22⋊C4—862no—
436C2×C22⋊C4—862no—
437C2×C42—862no—
438C2×C42—862no—
439C2×C42—864no—
440C2×C42—1722no—
441#95—438no—
442#95—864no—
443#95—862no—
444#95—862no—
445#95—864no—
446#95—864no—
447#95—864no—
448#95—864no—
449#95—1722no—
450#95—1722no—
451#95—1722no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24C2×C4×D4312yes—
457C24#1062189812yes—
458C24#1062190012yes—
459C24#1062190012yes—
460C24Q8×D4312yes—
461C24#1062190212yes—
462C24C2×C22⋊D4312yes—
463C24C23×D4311yescharacteristic
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—216no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—44no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—432no—
497C22×C4—434no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—432no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4C2×C4×D4314yes—
531C22×C4#1062189814yes—
532C22×C4C2×C22⋊D4312yes—
533C22×C4C2×C22⋊D4314yes—
534C22×C4C2×C22⋊D4314yes—
535C22×C4C2×C22⋊D4314yes—
536C22×C4C2×C22⋊D4312yes—
537C4⋊C4—216no—
538C4⋊C4—216no—
539C4⋊C4—8616no—
540C22⋊C4—868no—
541C22⋊C4—868no—
542C22⋊C4—868no—
543C22⋊C4—1724no—
544C42—1724no—
545C42—1724no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—22no—
555C23—24no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23#1306328314yes—
563C23C4×C22⋊D4314yes—
564C23#1306329014yes—
565C23#1306330114yes—
566C23#1306330614yes—
567C23#1306331514yes—
568C23#1306332014yes—
569C23C22×C4×D4311yescharacteristic
570C23C22×C22⋊D4312yes—
571C23C22×C22⋊D4311yescharacteristic
572C23C2×Q8×D4311yescharacteristic
573C23C2×#1062190011yescharacteristic
574C23C2×#1062190011yescharacteristic
575C23C2×#1062189812yes—
576C23C2×#1062189811yescharacteristic
577C23C2×#1062190211yescharacteristic
578C23#1306337012yes—
579C23#1306337312yes—
580C2×C4—232no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—416no—
598C2×C4—416no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—864no—
606C2×C4—864no—
607C2×C4—864no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—864no—
611C2×C4—864no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1722no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1722no—
638C2×C4—1722no—
639C2×C4C4×C22⋊D4318yes—
640C2×C4#1306329414yes—
641C22—28no—
642C22—28no—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—28no—
649C22—24no—
650C22—28no—
651C22#1458278018yescomplemented
652C22C2×#1306328311yescharacteristic
653C22C2×C4×C22⋊D4312yes—
654C22C2×C4×C22⋊D4311yescharacteristic
655C22C2×#1306329011yescharacteristic
656C22#1458338012yes—
657C22C2×#1306329411yescharacteristic
658C22C2×#1306330111yescharacteristic
659C22C2×#1306330611yescharacteristic
660C22#1458341012yes—
661C22#1458341011yescharacteristic
662C22C2×#1306331511yescharacteristic
663C22C2×#1306332011yescharacteristic
664C22#1458345811yescharacteristic
665C22#1458347311yescharacteristic
666C22#1458349612yes—
667C22#1458354312yes—
668C22#1458354312yes—
669C22#1458356012yes—
670C22Q8×C22⋊D4312yes—
671C22#1458358412yes—
672C22#1458358412yes—
673C22#1458359712yes—
674C22#1458360412yes—
675C4—28no—
676C4—24no—
677C4—42no—
678C4—44no—
679C4—3442no—
680C4—1722no—
681C4—1722no—
682C4—1722no—
683C4—1722no—
684C4—1724no—
685C2—28no—
686C2C2×#1458278011yescharacteristic
687C2C4×#1306329411yescharacteristic
688C2#1913726411yescharacteristic
689C2#1913752012yes—
690C2#1913760012yes—
691C2#1913791811yescharacteristic
692C2#1913795411yescharacteristic
693C2#1913873012yes—
694C2#1913885012yes—
695C2#1913888211yescharacteristic
696C2#1913994211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC23×C4⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC23×C4⋊C4D43
hypocenterC43#14039
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14582780C2semidirect
4. #19132854C2semidirect
5. #19132845C2semidirect
6. #19132827C2semidirect
20. #14582772C4semidirect
48. C2×Dic43⋊C4C2×C4semidirect
75. C43⋊#95C2×C4semidirect
303. C22×C43#387semidirect
388. C43#14039semidirect
651. C22#14582780semidirect

Maximal subgroups

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

subgroupindex
C2×#145827802
C2×#145827722
C2×C4×C22⋊Dic432
#191328542
#191328452
#191328272
#191328182
C23×C4⋊C4×C432
#1403943