Finite Group Databasebeta

← #25002016

Subgroups — #25002016

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×#13063239C212yesmaximal
3C2×#14582666C211yesmaximal, characteristic, complemented
4#19132817C212yesmaximal, complemented
5C2×C43×#342C211yesmaximal, characteristic, complemented
6C23×C22⋊D43C2211yescharacteristic
7C24×Dic43C2211yescharacteristic
8C23×C4×D43C411yescharacteristic, complemented
9C2×(C22⋊D43)⋊C4—24no—
10C2×(C22⋊D43)⋊C4—24no—
11C2×(C22⋊D43)⋊C4—22no—
12C2×(C22⋊D43)⋊C4—22no—
13C22×Dic43⋊C4C411yescharacteristic, complemented
14C22×C22⋊Dic43C2212yes—
15C22×(C2×D43)⋊C4C411yescharacteristic, complemented
16C22×C4×Dic43C411yescharacteristic, complemented
17C2×#13063239—24no—
18C2×#13063239—24no—
19C2×#13063239C418yescomplemented
20C2×C43⋊#95—24no—
21#14582666—22no—
22C22×C22⋊C4×C43C2212yes—
23C22×C22⋊C4×C43C2211yescharacteristic
24C43×#342—22no—
25C24×D43C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C22⋊D43—22no—
28C22×C22⋊D43—21no—
29C22×C22⋊D43—22no—
30C22×C22⋊D43—21no—
31C22×C22⋊D43—21no—
32C22×C22⋊D43C2×C414yes—
33C22×C22⋊D43D414yes—
34C22×C22⋊D43D412yes—
35C22×C22⋊D43Q812yes—
36C23×Dic43—21no—
37C23×Dic43—22no—
38C23×Dic43—21no—
39C23×Dic43—22no—
40C23×Dic43—44no—
41C23×Dic43C2×C411yescharacteristic
42C23×Dic43C2×C411yescharacteristic
43C23×Dic43C2×C411yescharacteristic
44C23×Dic43D414yes—
45C22×C4×D43—22no—
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43—44no—
49(C22⋊D43)⋊C4—216no—
50(C22⋊D43)⋊C4—216no—
51C2×Dic43⋊C4—22no—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—22no—
54C2×C22⋊Dic43—22no—
55C2×C22⋊Dic43—22no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—22no—
59C2×C22⋊Dic43C2×C414yescomplemented
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×C4×Dic43—22no—
64C2×C4×Dic43—22no—
65C2×C4×Dic43—22no—
66#13063239—216no—
67C43⋊#95—48no—
68C25×C43C2311yescharacteristic
69C23×C4×C43—22no—
70C23×C4×C43C2×C411yescharacteristic
71C23×C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43—22no—
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43C2×C414yescomplemented
80C2×C22⋊C4×C43D412yes—
81C2×C22⋊C4×C43D412yes—
82C24×C43—42no—
83C24×C43—42no—
84C24×C43C22×C411yescharacteristic
85C24×C43C22×C412yes—
86C24×C43C2×D412yes—
87C24×C43C2×D412yes—
88C24×C43C2×D411yescharacteristic
89C24×C43C2×D411yescharacteristic
90C24×C43C2×D411yescharacteristic
91C24×C43C2×Q811yescharacteristic
92C24×C43#4112yes—
93C24×C43#4111yescharacteristic
94C24×C43#4111yescharacteristic
95C23×D43—21no—
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—21no—
99C23×D43—42no—
100C23×D43—42no—
101C23×D43C4212yes—
102C23×D43C22⋊C412yes—
103C23×D43C4⋊C412yes—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—24no—
109C22×C4×C43—42no—
110C22×C4×C43—42no—
111C22×C4×C43—44no—
112C22×C4×C43—44no—
113C22×C4×C43—42no—
114C22×C4×C43—42no—
115C22×C4×C43C22⋊C412yes—
116C22×C4×C43C22⋊C412yes—
117C2×C22⋊D43—24no—
118C2×C22⋊D43—24no—
119C2×C22⋊D43—24no—
120C2×C22⋊D43—24no—
121C2×C22⋊D43—24no—
122C2×C22⋊D43—24no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43—24no—
125C2×C22⋊D43—22no—
126C2×C22⋊D43—22no—
127C2×C22⋊D43—24no—
128C2×C22⋊D43—22no—
129C2×C22⋊D43—24no—
130C2×C22⋊D43—24no—
131C2×C22⋊D43C22⋊C418yes—
132C2×C22⋊D43C4⋊C418yes—
133C22×Dic43—24no—
134C22×Dic43—28no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—24no—
144C22×Dic43—24no—
145C22×Dic43—24no—
146C22×Dic43—42no—
147C22×Dic43—44no—
148C22×Dic43—44no—
149C22×Dic43—44no—
150C22×Dic43—44no—
151C22×Dic43—48no—
152C22×Dic43—44no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43C4212yes—
156C22×Dic43C22⋊C412yes—
157C22×Dic43C22⋊C412yes—
158C22×Dic43C22⋊C412yes—
159C22×Dic43C4⋊C412yes—
160C2×C4×D43—28no—
161C2×C4×D43—48no—
162C2×C4×D43—44no—
163C2×C4×D43—48no—
164C2×C4×D43—44no—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—42no—
170C22⋊C4×C43—42no—
171C22⋊Dic43—24no—
172C22⋊Dic43—24no—
173C22⋊Dic43—42no—
174C22⋊Dic43—42no—
175(C2×D43)⋊C4—28no—
176Dic43⋊C4—28no—
177C4×Dic43—28no—
178C23×C43—24no—
179C23×C43—22no—
180C23×C43—24no—
181C23×C43—22no—
182C23×C43—41no—
183C23×C43—42no—
184C23×C43—41no—
185C23×C43—44no—
186C23×C43—41no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—41no—
190C23×C43—42no—
191C23×C43—44no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43C2×C4211yescharacteristic
195C23×C43C2×C22⋊C411yescharacteristic
196C23×C43C2×C22⋊C412yes—
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43C2×C22⋊C411yescharacteristic
199C23×C43C2×C4⋊C411yescharacteristic
200C23×C43C2×C4⋊C412yes—
201C23×C43#11711yescharacteristic
202C23×C43#11711yescharacteristic
203C23×C43C4×D412yes—
204C23×C43C4×D412yes—
205C23×C43C4×D412yes—
206C23×C43C4×D412yes—
207C23×C43#12012yes—
208C23×C43#12012yes—
209C23×C43#12111yescharacteristic
210C23×C43#12112yes—
211C23×C43#12111yescharacteristic
212C23×C43C22⋊Q811yescharacteristic
213C23×C43C22⋊Q812yes—
214C23×C43C22⋊Q811yescharacteristic
215C23×C43#12312yes—
216C23×C43#12312yes—
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—42no—
224C22×D43—44no—
225C22×D43—44no—
226C22×D43—42no—
227C22×D43—42no—
228C22×D43—42no—
229C22×D43—42no—
230C22×D43—44no—
231C22×D43—42no—
232C22×D43—44no—
233C22×D43#9514yescomplemented
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—48no—
243C2×C4×C43—44no—
244C2×C4×C43—84no—
245C2×C4×C43—82no—
246C2×C4×C43—82no—
247C22⋊D43—28no—
248C22⋊D43—28no—
249C22⋊D43—28no—
250C22⋊D43—28no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—24no—
263C2×Dic43—48no—
264C2×Dic43—48no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—48no—
268C2×Dic43—44no—
269C2×Dic43—84no—
270C2×Dic43—82no—
271C2×Dic43—82no—
272C2×Dic43#9514yescomplemented
273C2×Dic43#9914yescomplemented
274C4×D43—416no—
275#10761—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—24no—
279C22×C43—24no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—24no—
283C22×C43—24no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43C2×#9511yescharacteristic
303C22×C43C4×C22⋊C411yescharacteristic
304C22×C43C4×C22⋊C411yescharacteristic
305C22×C43#37911yescharacteristic
306C22×C43#38011yescharacteristic
307C22×C43#38011yescharacteristic
308C22×C43#38111yescharacteristic
309C22×C43#38512yes—
310C22×C43#38512yes—
311C22×C43#38612yes—
312C22×C43#38612yes—
313C22×C43C2×#9912yes—
314C22×C43#41012yes—
315C2×D43—24no—
316C2×D43—44no—
317C2×D43—44no—
318C2×D43—44no—
319C2×D43—44no—
320C2×D43—44no—
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—44no—
324C4×C43—42no—
325C4×C43—42no—
326C4×C43—84no—
327Dic43—24no—
328Dic43—24no—
329Dic43—42no—
330Dic43—84no—
331C22×C4×D4—431no—
332C22×#99—432no—
333C2×#342—431no—
334C2×#342D4311yescharacteristic, complemented
335C22⋊#95—432no—
336C2×C43—22no—
337C2×C43—22no—
338C2×C43—21no—
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—21no—
342C2×C43—22no—
343C2×C43—22no—
344C2×C43C22⋊#9511yescharacteristic
345C2×C43C4×#9912yes—
346C2×C43#178111yescharacteristic
347C2×C43#178211yescharacteristic
348C2×C43#179912yes—
349D43—44no—
350C23×D4—431no—
351C24×C4—431no—
352C24×C4—431no—
353C2×C4×D4—864no—
354C2×C4×D4—864no—
355C2×C4×D4—862no—
356C2×C4×D4—862no—
357C22×C4⋊C4—431no—
358C22×C22⋊C4—432no—
359C22×C22⋊C4—431no—
360C22×C22⋊C4C2×D4312yes—
361C22×C22⋊C4C2×D4311yescharacteristic
362C22×C42—431no—
363C2×#99—438no—
364C2×#99—864no—
365C2×#99—864no—
366C2×#95—864no—
367#342—22no—
368#342—862no—
369C43#1076111yescharacteristic, complemented, Sylow
370C25—431no—
371C25C22×D4311yescharacteristic
372C22×D4—434no—
373C22×D4—434no—
374C22×D4—432no—
375C22×D4—432no—
376C22×D4—861no—
377C22×D4—862no—
378C22×D4—862no—
379C22×D4—861no—
380C22×D4—861no—
381C22×D4—861no—
382C23×C4—22no—
383C23×C4—431no—
384C23×C4—431no—
385C23×C4—434no—
386C23×C4—431no—
387C23×C4—862no—
388C23×C4—862no—
389C23×C4—861no—
390C23×C4—862no—
391C23×C4—861no—
392C23×C4—862no—
393C23×C4—862no—
394C23×C4—1724no—
395C23×C4—1724no—
396C23×C4C4×D4311yescharacteristic
397C23×C4C4×D4311yescharacteristic
398C4×D4—8616no—
399C4×D4—8616no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—862no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—434no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—862no—
416C2×C22⋊C4—862no—
417C2×C22⋊C4—862no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4C4×D4314yescomplemented
420C2×C22⋊C4D17212yes—
421C2×C22⋊C4C22⋊D4312yes—
422C2×C42—862no—
423C2×C42—862no—
424C2×C42—862no—
425#99—8616no—
426#95—1728no—
427C24—42no—
428C24—42no—
429C24—432no—
430C24—432no—
431C24—432no—
432C24—861no—
433C24—861no—
434C24—861no—
435C24—861no—
436C24—1722no—
437C24—1722no—
438C24C2×C4×D4311yescharacteristic
439C24C2×C4×D4312yes—
440C24C2×D17211yescharacteristic
441C24#1062189812yes—
442C24D4×D4312yes—
443C24D4×D4312yes—
444C24D4×D4311yescharacteristic
445C24#1062190011yescharacteristic
446C24Q8×D4311yescharacteristic
447C24#1062190211yescharacteristic
448C24C2×C22⋊D4311yescharacteristic
449C2×D4—438no—
450C2×D4—438no—
451C2×D4—864no—
452C2×D4—864no—
453C2×D4—864no—
454C2×D4—864no—
455C2×D4—864no—
456C2×D4—864no—
457C2×D4—862no—
458C2×D4—864no—
459C2×D4—862no—
460C2×D4—862no—
461C2×D4—864no—
462C2×D4—862no—
463C2×D4—864no—
464C2×D4—864no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—868no—
482C22×C4—864no—
483C22×C4—868no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—864no—
493C22×C4—864no—
494C22×C4—864no—
495C22×C4—1724no—
496C22×C4—1728no—
497C22×C4—1724no—
498C22×C4—1728no—
499C22×C4—1724no—
500C22×C4—1722no—
501C22×C4—1724no—
502C22×C4—1728no—
503C22×C4—1724no—
504C22×C4—1724no—
505C22×C4—1724no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4(C2×D43)⋊C412yes—
509C22×C4(C2×D43)⋊C412yes—
510C4⋊C4—868no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—868no—
518C22⋊C4—864no—
519C22⋊C4—864no—
520C22⋊C4—1722no—
521C22⋊C4—1722no—
522C42—868no—
523C23—24no—
524C23—22no—
525C23—24no—
526C23—22no—
527C23—41no—
528C23—42no—
529C23—41no—
530C23—44no—
531C23—41no—
532C23—44no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—41no—
539C23—434no—
540C23—862no—
541C23—862no—
542C23—862no—
543C23—862no—
544C23—862no—
545C23—862no—
546C23—1722no—
547C23—1722no—
548C23—1724no—
549C23—1724no—
550C23—1722no—
551C23—1722no—
552C23—1724no—
553C23—1724no—
554C23—1722no—
555C23—1722no—
556C23C42×D4311yescharacteristic
557C23C22⋊C4×D4311yescharacteristic
558C23C22⋊C4×D4312yes—
559C23C22⋊C4×D4311yescharacteristic
560C23C2×(C2×D43)⋊C411yescharacteristic
561C23C4⋊C4×D4311yescharacteristic
562C23C4⋊C4×D4312yes—
563C23#1306328211yescharacteristic
564C23#1306328311yescharacteristic
565C23(C22⋊D43)⋊C412yes—
566C23C4×C22⋊D4312yes—
567C23#1306328712yes—
568C23C4×D17212yes—
569C23#1306329312yes—
570C23#1306329512yes—
571C23#1306329611yescharacteristic
572C23#1306329812yes—
573C23#1306330011yescharacteristic
574C23#1306330111yescharacteristic
575C23#1306330312yes—
576C23#1306330511yescharacteristic
577C23#1306330712yes—
578C23#1306331012yes—
579D4—868no—
580D4—868no—
581D4—868no—
582D4—868no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—48no—
592C2×C4—44no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—84no—
596C2×C4—434no—
597C2×C4—434no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—864no—
609C2×C4—862no—
610C2×C4—3442no—
611C2×C4—3442no—
612C2×C4—3444no—
613C2×C4—17216no—
614C2×C4—1728no—
615C2×C4—1728no—
616C2×C4—1728no—
617C2×C4—1724no—
618C2×C4—1722no—
619C2×C4—1722no—
620C22—21no—
621C22—21no—
622C22—22no—
623C22—22no—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—22no—
628C22—24no—
629C22—22no—
630C22—22no—
631C22—24no—
632C22—24no—
633C22—24no—
634C22—22no—
635C22—22no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—42no—
645C22—42no—
646C22—864no—
647C22—1724no—
648C22—1724no—
649C22—1724no—
650C22—1724no—
651C22—1722no—
652C22—1722no—
653C22—1724no—
654C22—1724no—
655C22#95×D4311yescharacteristic
656C22#1458274611yescharacteristic
657C22C4×(C2×D43)⋊C411yescharacteristic
658C22#1458275411yescharacteristic
659C22#1458275611yescharacteristic
660C22#1458275811yescharacteristic
661C22#1458276111yescharacteristic
662C22#1458277012yes—
663C22#1458277312yes—
664C22#1458277512yes—
665C22#1458277712yes—
666C22#99×D4312yes—
667C22#1458287112yes—
668C4—42no—
669C4—42no—
670C4—84no—
671C4—864no—
672C4—864no—
673C4—3444no—
674C4—1722no—
675C2—22no—
676C2—22no—
677C2—21no—
678C2—21no—
679C2—21no—
680C2—21no—
681C2—22no—
682C2—22no—
683C2—1724no—
684C2(C2×D43)⋊#9511yescharacteristic
685C2#1913438212yes—
686C2#1913450811yescharacteristic
687C2#1913451111yescharacteristic
688C2#1913458212yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#10761
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×#14582666C2semidirect
4. #19132817C2semidirect
5. C2×C43×#342C2semidirect
8. C23×C4×D43C4semidirect
13. C22×Dic43⋊C4C4semidirect
15. C22×(C2×D43)⋊C4C4semidirect
16. C22×C4×Dic43C4semidirect
19. C2×#13063239C4semidirect
59. C2×C22⋊Dic43C2×C4semidirect
79. C2×C22⋊C4×C43C2×C4semidirect
233. C22×D43#95semidirect
272. C2×Dic43#95semidirect
273. C2×Dic43#99semidirect
334. C2×#342D43semidirect
369. C43#10761semidirect
419. C2×C22⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C22×#130632392
C2×#145826662
#191328172
C2×C43×#3422
#1076143