Finite Group Databasebeta

← #25025777

Subgroups — #25025777

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582792C212yesmaximal, complemented
2#19132863C212yesmaximal, complemented
3#19132840C212yesmaximal, complemented
4#19132836C211yesmaximal, characteristic
5#19132836C211yesmaximal, characteristic
6#19132832C212yesmaximal, complemented
7#19132824C212yesmaximal, complemented
8#19132818C212yesmaximal, complemented
9C22×#123×C43C211yesmaximal, characteristic
10C22×C4⋊Dic43C2212yes—
11C22×C22⋊Dic43C2212yes—
12C22×C22⋊Dic43C2212yes—
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2212yes—
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C4×Dic43C2212yes—
17#14582792—28no—
18C2×C43⋊#95C2212yes—
19C2×C43⋊#95C2212yes—
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C23×D4×C43C2211yescharacteristic
28C24×C4×C43C2211yescharacteristic
29C2×#123×C43—28no—
30C2×#123×C43C418yescomplemented
31C22×C4⋊C4×C43C2212yes—
32C22×C22⋊C4×C43C2212yes—
33C22×C22⋊C4×C43C2211yescharacteristic
34C23×Dic43C2312yes—
35C23×Dic43C2312yes—
36C23×Dic43C2312yes—
37C23×Dic43C2312yes—
38C2×C4⋊Dic43—24no—
39C2×C4⋊Dic43—24no—
40C2×C4⋊Dic43—42no—
41C2×C22⋊Dic43—24no—
42C2×C22⋊Dic43—24no—
43C2×C22⋊Dic43—24no—
44C2×C22⋊Dic43—24no—
45C2×C22⋊Dic43—24no—
46C2×C22⋊Dic43—24no—
47C2×C22⋊Dic43—42no—
48C2×C22⋊Dic43—42no—
49C2×C22⋊Dic43—41no—
50C2×C22⋊Dic43—42no—
51C2×C22⋊Dic43—42no—
52C2×C22⋊Dic43—41no—
53C2×C22⋊Dic43—42no—
54C2×C4×Dic43—24no—
55C2×C4×Dic43—24no—
56C2×C4×Dic43—42no—
57C43⋊#95—24no—
58C43⋊#95—24no—
59C43⋊#95—41no—
60C43⋊#95—42no—
61C43⋊#95—42no—
62C43⋊#95—42no—
63C43⋊#95—42no—
64C43⋊#95—41no—
65C43⋊#95—42no—
66C25×C43C2311yescharacteristic
67C25×C43C2311yescharacteristic
68C22×D4×C43—24no—
69C22×D4×C43—42no—
70C22×D4×C43—41no—
71C22×D4×C43—41no—
72C22×D4×C43C2×C414yes—
73C23×C4×C43—24no—
74C23×C4×C43—42no—
75C23×C4×C43—41no—
76C23×C4×C43—41no—
77C23×C4×C43C2×C414yes—
78C23×C4×C43C2312yes—
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2312yes—
81#123×C43—232no—
82C2×C4⋊C4×C43—24no—
83C2×C4⋊C4×C43—24no—
84C2×C4⋊C4×C43C2×C418yes—
85C2×C22⋊C4×C43—24no—
86C2×C22⋊C4×C43—24no—
87C2×C22⋊C4×C43C2×C418yes—
88C2×C22⋊C4×C43C2×C414yes—
89C2×C22⋊C4×C43D418yes—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—21no—
94C24×C43—21no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—21no—
102C24×C43—21no—
103C24×C43—22no—
104C24×C43—22no—
105C24×C43C22×C412yes—
106C24×C43C22×C412yes—
107C24×C43C2×D414yes—
108C24×C43C2411yescharacteristic
109C2×D4×C43—28no—
110C2×D4×C43—44no—
111C2×D4×C43—44no—
112C2×D4×C43—48no—
113C2×D4×C43—48no—
114C22×C4×C43—28no—
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—21no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—44no—
130C22×C4×C43—44no—
131C22×C4×C43—48no—
132C22×C4×C43—48no—
133C22×C4×C43C22×C414yes—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C22×C414yes—
136C22×C4×C43C2×D414yes—
137C22×C4×C43C2×D414yes—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
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×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43#4114yes—
165C22×Dic43#4114yes—
166C4⋊C4×C43—216no—
167C22⋊C4×C43—216no—
168C22⋊C4×C43C22⋊C4116yescomplemented
169C22⋊Dic43—48no—
170C22⋊Dic43—48no—
171C22⋊Dic43—44no—
172C22⋊Dic43—48no—
173C22⋊Dic43—44no—
174C4⋊Dic43—48no—
175C4×Dic43—48no—
176C23×C43—24no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—24no—
180C23×C43—24no—
181C23×C43—24no—
182C23×C43—24no—
183C23×C43—24no—
184C23×C43—24no—
185C23×C43—24no—
186C23×C43—22no—
187C23×C43—24no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—24no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—41no—
196C23×C43—42no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—42no—
200C23×C43—41no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—41no—
212C23×C43—42no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—42no—
216C23×C43—41no—
217C23×C43C2×C22⋊C414yes—
218C23×C43C23×C411yescharacteristic
219C23×C43C22×D412yes—
220C23×C43C2×#4112yes—
221C23×C43C2×#4112yes—
222C23×C43H(5,𝔽2)12yes—
223C23×C43H(5,𝔽2)11yescharacteristic
224C23×C43H(5,𝔽2)11yescharacteristic
225C23×C43H(5,𝔽2)12yes—
226C23×C432−1+412yes—
227D4×C43—416no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
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—22no—
239C2×C4×C43—22no—
240C2×C4×C43—416no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43C2×C22⋊C418yes—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276#14506—431nomaximal, Sylow
277C22×C43—24no—
278C22×C43—28no—
279C22×C43—44no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—44no—
283C22×C43—44no—
284C22×C43—44no—
285C22×C43—44no—
286C22×C43—42no—
287C22×C43—44no—
288C22×C43—44no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43C4×#4112yes—
297C22×C43#51811yescharacteristic
298C22×C43#51811yescharacteristic
299C22×C43#52012yes—
300C22×C43#53512yes—
301C22×C43#53512yes—
302C22×C43#53812yes—
303C22×C43#53912yes—
304C22×C43#54012yes—
305C22×C43#54212yes—
306C22×C43#54612yes—
307C22×C43#54612yes—
308C22×C43#54712yes—
309C22×C43#54712yes—
310C22×C43#55111yescharacteristic
311C22×C43#55312yes—
312C22×C43#55911yescharacteristic
313C22×C43#56011yescharacteristic
314C22×C43#56212yes—
315C22×C43#56311yescharacteristic
316C4×C43—28no—
317C4×C43—44no—
318C4×C43—42no—
319Dic43—44no—
320Dic43—44no—
321Dic43—82no—
322Dic43—82no—
323C22×#123D4311yescharacteristic
324C2×#388—432no—
325#1445—432no—
326#1439—432no—
327#1438—431no—
328#1438—431no—
329#1437—432no—
330C4⋊#95—432no—
331C22⋊#95—432no—
332C2×C43—44no—
333C2×C43—82no—
334C2×C43#230911yescharacteristic
335C2×C43#233512yes—
336C2×C43#233912yes—
337C2×C43#237411yescharacteristic
338C2×C43#237611yescharacteristic
339C2×C43#270312yes—
340C2×C43#270612yes—
341C2×C43#271012yes—
342C2×C43#271812yes—
343C23×D4C2×D4311yescharacteristic
344C24×C4C2×D4311yescharacteristic
345C2×#123—28no—
346C2×#123Dic4318yescomplemented
347C22×C4⋊C4—432no—
348C22×C4⋊C4C2×D4312yes—
349C22×C22⋊C4—432no—
350C22×C22⋊C4—432no—
351C22×C22⋊C4—431no—
352C22×C22⋊C4—432no—
353C22×C22⋊C4—431no—
354C22×C22⋊C4C2×D4312yes—
355C22×C22⋊C4C2×D4311yescharacteristic
356C22×C42—432no—
357#388—868no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95—432no—
361C2×#95—432no—
362C2×#95—432no—
363C2×#95—432no—
364C2×#95—431no—
365C2×#95—432no—
366C2×#95—431no—
367C43#1450611yescharacteristic, complemented, Sylow
368C25C22×D4311yescharacteristic
369C25C22×D4311yescharacteristic
370C22×D4—24no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4—42no—
374C22×D4C2×Dic4314yes—
375C23×C4—24no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4—42no—
379C23×C4—432no—
380C23×C4—432no—
381C23×C4—432no—
382C23×C4—432no—
383C23×C4C2×Dic4314yes—
384C23×C4C22×D4312yes—
385C23×C4C22×D4311yescharacteristic
386C23×C4C22×D4312yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—864no—
392C2×C4⋊C4—1722no—
393C2×C4⋊C4C2×Dic4318yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—864no—
397C2×C22⋊C4—864no—
398C2×C22⋊C4—864no—
399C2×C22⋊C4—864no—
400C2×C22⋊C4—864no—
401C2×C22⋊C4—864no—
402C2×C22⋊C4—1721no—
403C2×C22⋊C4—1722no—
404C2×C22⋊C4—1722no—
405C2×C22⋊C4—1722no—
406C2×C22⋊C4—1722no—
407C2×C22⋊C4—1721no—
408C2×C22⋊C4—1722no—
409C2×C22⋊C4C2×Dic4318yes—
410C2×C22⋊C4C2×Dic4314yes—
411C2×C22⋊C4C22⋊D4318yes—
412C2×C42—864no—
413C2×C42—864no—
414C2×C42—1722no—
415#95—864no—
416#95—864no—
417#95—1722no—
418#95—1722no—
419#95—1722no—
420#95—1722no—
421#95—1721no—
422#95—1722no—
423#95—1721no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24C22×Dic4312yes—
440C24C22×Dic4312yes—
441C24C2×C22⋊D4314yes—
442C24C23×D4311yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—434no—
468C22×C4—434no—
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×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4C22×Dic4314yes—
496C22×C4C22×Dic4312yes—
497C22×C4C22×Dic4314yes—
498C22×C4C2×C22⋊D4314yes—
499C22×C4C2×C22⋊D4314yes—
500C4⋊C4—216no—
501C4⋊C4—1728no—
502C22⋊C4—216no—
503C22⋊C4—1724no—
504C22⋊C4—1728no—
505C22⋊C4—1728no—
506C22⋊C4—1728no—
507C22⋊C4—1724no—
508C22⋊C4C22⋊Dic43116yescomplemented
509C42—1728no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—41no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—41no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23C2×C22⋊Dic4314yes—
552C23C23×Dic4311yescharacteristic
553C23C22×C22⋊D4312yes—
554C23#41×D4312yes—
555C23#41×D4312yes—
556C23#1306337011yescharacteristic
557C23#1306337011yescharacteristic
558C23#1306337012yes—
559C23#1306337112yes—
560C23#1306337212yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—416no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—864no—
582C2×C4—864no—
583C2×C4—864no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4C2×C22⋊Dic4318yes—
610C22—28no—
611C22—24no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊Dic4311yescharacteristic
629C22#41×Dic4312yes—
630C22#1458337411yescharacteristic
631C22#1458337411yescharacteristic
632C22#1458338212yes—
633C22#1458346612yes—
634C22#1458346612yes—
635C22#1458348512yes—
636C22#1458349212yes—
637C22#1458350112yes—
638C22#1458351712yes—
639C22#1458353712yes—
640C22#1458353712yes—
641C22#1458354812yes—
642C22#1458354812yes—
643C22#1458357711yescharacteristic
644C22#1458359412yes—
645C22#1458363311yescharacteristic
646C22#1458363911yescharacteristic
647C22#1458364612yes—
648C22#1458365211yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—3442no—
653C4—3442no—
654C4—1724no—
655C4—1724no—
656C2—44no—
657C2—82no—
658C2#1913717711yescharacteristic
659C2#1913738912yes—
660C2#1913742512yes—
661C2#1913773111yescharacteristic
662C2#1913774311yescharacteristic
663C2#1914123212yes—
664C2#1914127712yes—
665C2#1914133312yes—
666C2#1914144112yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC22×#123×C43C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC22×#123D43
hypocenterC43#14506
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14582792C2semidirect
2. #19132863C2semidirect
3. #19132840C2semidirect
6. #19132832C2semidirect
7. #19132824C2semidirect
8. #19132818C2semidirect
30. C2×#123×C43C4semidirect
168. C22⋊C4×C43C22⋊C4semidirect
346. C2×#123Dic43semidirect
367. C43#14506semidirect
508. C22⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
#191328632
#191328402
#191328362
#191328322
#191328242
#191328182
C22×#123×C432
#1450643