Finite Group Databasebeta

← #25019359

Subgroups — #25019359

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582757C211yesmaximal, characteristic
2C2×C22⋊C4×Dic43C211yesmaximal, characteristic
3C22×C43⋊#95C211yesmaximal, characteristic
4#19132853C212yesmaximal, complemented
5#19132850C212yesmaximal, complemented
6#19132820C212yesmaximal, complemented
7#19132819C212yesmaximal, complemented
8#19132818C211yesmaximal, characteristic
9#19132817C211yesmaximal, characteristic
10#19132817C211yesmaximal, characteristic
11C43×C22⋊#95C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2211yescharacteristic
15C22×Dic43⋊C4C2211yescharacteristic
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C4×Dic43C2212yes—
19#14582757—24no—
20C22⋊C4×Dic43C418yescomplemented
21C2×C43⋊#95—24no—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C24×C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C22×C22⋊C4×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C23×Dic43—22no—
39C23×Dic43—24no—
40C23×Dic43—22no—
41C23×Dic43—22no—
42C23×Dic43—42no—
43C23×Dic43—42no—
44C23×Dic43—42no—
45C23×Dic43C2×C414yes—
46C23×Dic43D414yes—
47C23×Dic43Q814yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2312yes—
51C23×Dic43C2312yes—
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C2×Dic43⋊C4—22no—
55C2×Dic43⋊C4—22no—
56C2×Dic43⋊C4—42no—
57C2×Dic43⋊C4—42no—
58C2×C22⋊Dic43—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43C2×C414yes—
64C2×C4×Dic43—42no—
65C2×C4×Dic43—42no—
66C2×C4×Dic43C2×C418yescomplemented
67C43⋊#95—24no—
68C43⋊#95—24no—
69C43⋊#95—24no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C43⋊#95—42no—
77C43⋊#95C2×C418yescomplemented
78C25×C43C2311yescharacteristic
79C23×C4×C43—22no—
80C23×C4×C43—24no—
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—42no—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2312yes—
87C23×C4×C43C2312yes—
88C2×C22⋊C4×C43—22no—
89C2×C22⋊C4×C43—22no—
90C2×C22⋊C4×C43—22no—
91C2×C22⋊C4×C43—22no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43C2×C414yes—
94#95×C43—24no—
95#95×C43—42no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43C22×C412yes—
101C24×C43C2×D412yes—
102C24×C43C2×Q812yes—
103C24×C43#4112yes—
104C24×C43#4112yes—
105C24×C43#4112yes—
106C24×C43#4112yes—
107C24×C43C2411yescharacteristic
108C22×C4×C43—28no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
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—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
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×C43—22no—
131C22×C4×C43—48no—
132C22×C4×C43—48no—
133C22×C4×C43—44no—
134C22×C4×C43—44no—
135C22×C4×C43C22×C414yes—
136C22×C4×C43#4114yes—
137C22×Dic43—28no—
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—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
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—48no—
165C22×Dic43—44no—
166C22×Dic43—44no—
167C22×Dic43—48no—
168C22×Dic43—48no—
169C22×Dic43—48no—
170C22×Dic43—44no—
171C22×Dic43—44no—
172C22×Dic43C4⋊C4116yes—
173C22×Dic43C22×C414yes—
174C22×Dic43C22×C412yes—
175C22×Dic43C22×C412yes—
176C22×Dic43C2×D412yes—
177C22×Dic43C2×D412yes—
178C22×Dic43C2×Q812yes—
179C22×Dic43C2×Q812yes—
180C22×Dic43#4114yes—
181C22⋊C4×C43—28no—
182C22⋊C4×C43—44no—
183C22⋊Dic43—28no—
184C22⋊Dic43—44no—
185Dic43⋊C4—44no—
186Dic43⋊C4—44no—
187C4×Dic43—48no—
188C23×C43—24no—
189C23×C43—24no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—24no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—24no—
196C23×C43—24no—
197C23×C43—24no—
198C23×C43—24no—
199C23×C43—24no—
200C23×C43—24no—
201C23×C43—24no—
202C23×C43—24no—
203C23×C43—24no—
204C23×C43C2×C4⋊C414yes—
205C23×C43#11714yes—
206C23×C43#11714yes—
207C23×C43#12414yes—
208C23×C43#12414yes—
209C23×C43#12514yes—
210C23×C43#12514yes—
211C23×C43C23×C411yescharacteristic
212C23×C43C22×D411yescharacteristic
213C23×C43C22×Q811yescharacteristic
214C23×C43C2×#4112yes—
215C23×C43C2×#4111yescharacteristic
216C23×C43C2×#4111yescharacteristic
217C23×C43C2×#4112yes—
218C23×C43C2×#4111yescharacteristic
219C23×C43C2×#4111yescharacteristic
220C23×C43H(5,𝔽2)12yes—
221C23×C43H(5,𝔽2)12yes—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—416no—
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×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—416no—
262C2×Dic43—416no—
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—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43C2×C4⋊C414yes—
282C2×Dic43C2×C4⋊C414yes—
283#13966—431nomaximal, Sylow
284C22×C43—24no—
285C22×C43—24no—
286C22×C43—28no—
287C22×C43—28no—
288C22×C43—24no—
289C22×C43—24no—
290C22×C43—24no—
291C22×C43—28no—
292C22×C43—28no—
293C22×C43—24no—
294C22×C43#38218yes—
295C22×C43C22×C4⋊C411yescharacteristic
296C22×C43C2×#11711yescharacteristic
297C22×C43C2×#11711yescharacteristic
298C22×C43C4×#4112yes—
299C22×C43#51812yes—
300C22×C43#52511yescharacteristic
301C22×C43#52511yescharacteristic
302C22×C43C2×#12411yescharacteristic
303C22×C43C2×#12411yescharacteristic
304C22×C43C2×#12511yescharacteristic
305C22×C43C2×#12511yescharacteristic
306C22×C43#53312yes—
307C22×C43#53411yescharacteristic
308C22×C43#53411yescharacteristic
309C22×C43#54312yes—
310C22×C43#55112yes—
311C22×C43#55112yes—
312C22×C43#55112yes—
313C22×C43#55112yes—
314C22×C43#55312yes—
315C22×C43#55312yes—
316C22×C43#55312yes—
317C22×C43#55312yes—
318C4×C43—44no—
319C4×C43—44no—
320C4×C43—81no—
321C4×C43—81no—
322Dic43—24no—
323Dic43—24no—
324Dic43—44no—
325Dic43—44no—
326Dic43—81no—
327Dic43—81no—
328C2×#380—431no—
329C2×C4×C22⋊C4—431no—
330C22×#95—431no—
331#1442—432no—
332#1442—432no—
333#1434—432no—
334#1434—432no—
335C22⋊#95—431no—
336C22⋊#95—431no—
337C22⋊#95—431no—
338C22⋊#95D4311yescharacteristic
339C2×C43—28no—
340C2×C43C2×#38211yescharacteristic
341C2×C43#229611yescharacteristic
342C2×C43#231511yescharacteristic
343C2×C43#235312yes—
344C2×C43#235312yes—
345C2×C43#256111yescharacteristic
346C2×C43#256111yescharacteristic
347C2×C43#256912yes—
348C2×C43#256912yes—
349C2×C43#259111yescharacteristic
350C2×C43#259111yescharacteristic
351C24×C4—431no—
352C24×C4—431no—
353C24×C4C2×D4311yescharacteristic
354C22×C4⋊C4—431no—
355C22×C4⋊C4—431no—
356C22×C22⋊C4—431no—
357C22×C22⋊C4—431no—
358C22×C22⋊C4C2×D4311yescharacteristic
359C22×C22⋊C4C2×D4311yescharacteristic
360C22×C42—432no—
361#380—864no—
362C4×C22⋊C4—438no—
363C2×#95—432no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95—432no—
368C2×#95—431no—
369C2×#95—431no—
370C2×#95—432no—
371C2×#95—432no—
372C2×#95—432no—
373C2×#95—432no—
374C2×#95—864no—
375C2×#95C2×D4312yes—
376C2×#95C2×D4312yes—
377C43#1396611yescharacteristic, complemented, Sylow
378C25C22×D4311yescharacteristic
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—42no—
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—434no—
387C23×C4—434no—
388C23×C4—434no—
389C23×C4—432no—
390C23×C4—432no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4—864no—
394C23×C4—862no—
395C23×C4—862no—
396C23×C4—862no—
397C23×C4—1722no—
398C23×C4—1722no—
399C23×C4—1722no—
400C23×C4C22×D4311yescharacteristic
401C23×C4C22×D4311yescharacteristic
402C23×C4C22×D4312yes—
403C23×C4C22×D4312yes—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—1722no—
407C2×C4⋊C4—1722no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—434no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—862no—
416C2×C22⋊C4—862no—
417C2×C22⋊C4—862no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4C4×D4314yes—
420C2×C42—438no—
421C2×C42—1722no—
422C2×C42—1722no—
423#95—24no—
424#95—42no—
425#95—438no—
426#95—864no—
427#95—864no—
428#95—864no—
429#95—864no—
430#95—862no—
431#95—862no—
432#95—864no—
433#95—1722no—
434#95—1722no—
435#95—1722no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24C2×C4×D4312yes—
441C24#1062189812yes—
442C24#1062189812yes—
443C24D4×D4312yes—
444C24#1062190012yes—
445C24#1062190012yes—
446C24Q8×D4312yes—
447C24C23×D4311yescharacteristic
448C22×C4—28no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—4316no—
482C22×C4—434no—
483C22×C4—434no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—868no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—1728no—
512C22×C4—1724no—
513C22×C4—1724no—
514C22×C4—1728no—
515C22×C4—1728no—
516C22×C4—1728no—
517C22×C4—1724no—
518C22×C4—1724no—
519C22×C4C2×C4×D4314yes—
520C22×C4#1062190014yes—
521C4⋊C4—1724no—
522C4⋊C4—1724no—
523C22⋊C4—28no—
524C22⋊C4—44no—
525C22⋊C4—868no—
526C22⋊C4—1724no—
527C42—1728no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—22no—
539C23—22no—
540C23—24no—
541C23—22no—
542C23—22no—
543C23—24no—
544C23C4⋊C4×D4314yes—
545C23#1306328114yes—
546C23#1306328214yes—
547C23#1306331114yes—
548C23#1306331114yes—
549C23#1306331514yes—
550C23#1306331514yes—
551C23C22×C4×D4311yescharacteristic
552C23C2×D4×D4311yescharacteristic
553C23C2×Q8×D4311yescharacteristic
554C23#41×D4312yes—
555C23C2×#1062190011yescharacteristic
556C23C2×#1062190012yes—
557C23C2×#1062190011yescharacteristic
558C23C2×#1062189811yescharacteristic
559C23C2×#1062189811yescharacteristic
560C23#1306337012yes—
561C23#1306337112yes—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—416no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—434no—
588C2×C4—434no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—17216no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—17216no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C22—24no—
624C22—24no—
625C22—24no—
626C22—24no—
627C22—28no—
628C22—24no—
629C22—24no—
630C22—28no—
631C22—28no—
632C22—28no—
633C22#1458276318yes—
634C22C2×C4⋊C4×D4311yescharacteristic
635C22C2×#1306328111yescharacteristic
636C22C2×#1306328211yescharacteristic
637C22C4×#1062190012yes—
638C22#1458337112yes—
639C22#1458340511yescharacteristic
640C22#1458340711yescharacteristic
641C22C2×#1306331111yescharacteristic
642C22C2×#1306331111yescharacteristic
643C22C2×#1306331511yescharacteristic
644C22C2×#1306331511yescharacteristic
645C22#1458345112yes—
646C22#1458345911yescharacteristic
647C22#1458346011yescharacteristic
648C22#1458352412yes—
649C22#1458357212yes—
650C22#1458357312yes—
651C22#1458357512yes—
652C22#1458358012yes—
653C22#1458359212yes—
654C22#1458359512yes—
655C22#1458359812yes—
656C22#1458360112yes—
657C4—44no—
658C4—44no—
659C4—81no—
660C4—81no—
661C4—864no—
662C4—864no—
663C4—3441no—
664C4—3441no—
665C4—1724no—
666C4—1724no—
667C2—28no—
668C2C2×#1458276311yescharacteristic
669C2#1913707411yescharacteristic
670C2#1913720611yescharacteristic
671C2#1913752912yes—
672C2#1913753312yes—
673C2#1913975011yescharacteristic
674C2#1913975211yescharacteristic
675C2#1913981612yes—
676C2#1913982112yes—
677C2#1914007211yescharacteristic
678C2#1914007411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13966
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #19132853C2semidirect
5. #19132850C2semidirect
6. #19132820C2semidirect
7. #19132819C2semidirect
20. C22⋊C4×Dic43C4semidirect
66. C2×C4×Dic43C2×C4semidirect
77. C43⋊#95C2×C4semidirect
377. C43#13966semidirect

Maximal subgroups

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

subgroupindex
C2×#145827572
C2×C22⋊C4×Dic432
C22×C43⋊#952
#191328532
#191328502
#191328202
#191328192
#191328182
#191328172
C43×C22⋊#952
#1396643