Finite Group Databasebeta

← #25027355

Subgroups — #25027355

Order 11008.

1586 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582816C211yesmaximal, characteristic
2C2×#14582790C212yesmaximal, complemented
3#19132850C212yesmaximal, complemented
4#19132848C211yesmaximal, characteristic, complemented
5#19132841C212yesmaximal, complemented
6#19132839C212yesmaximal, complemented
7#19132837C212yesmaximal, complemented
8#19132835C212yesmaximal
9C43×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D172C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×Dic43⋊C4C2212yes—
13C22×(C2×D43)⋊C4C2212yes—
14C22×(C2×D43)⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19#14582816C418yescomplemented
20#14582790—28no—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C4⋊C4×C43C2211yescharacteristic
30C22×C42×C43C2211yescharacteristic
31C2×#95×C43C2212yes—
32C2×#95×C43C2212yes—
33C24×D43C2312yes—
34C22×D172—42no—
35C22×D172—41no—
36C22×D172—41no—
37C22×D172—42no—
38C22×D172C2×C414yes—
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C2×C4⋊Dic43—42no—
43C2×C4⋊Dic43—41no—
44C2×Dic43⋊C4—24no—
45C2×Dic43⋊C4—42no—
46C2×Dic43⋊C4—42no—
47C2×(C2×D43)⋊C4—24no—
48C2×(C2×D43)⋊C4—24no—
49C2×(C2×D43)⋊C4—24no—
50C2×(C2×D43)⋊C4—24no—
51C2×(C2×D43)⋊C4—42no—
52C2×(C2×D43)⋊C4—42no—
53C2×(C2×D43)⋊C4—42no—
54C2×(C2×D43)⋊C4—42no—
55C2×(C2×D43)⋊C4—42no—
56C2×(C2×D43)⋊C4—42no—
57C2×(C2×D43)⋊C4—42no—
58C2×(C2×D43)⋊C4—42no—
59C2×(C2×D43)⋊C4—42no—
60C2×(C2×D43)⋊C4—42no—
61C2×(C2×D43)⋊C4—42no—
62C2×(C2×D43)⋊C4—42no—
63C2×(C2×D43)⋊C4C2×C418yes—
64C2×(C2×D43)⋊C4C2×C418yes—
65C43⋊#95—24no—
66C43⋊#95—24no—
67C43⋊#95—42no—
68C43⋊#95—42no—
69C43⋊#95—41no—
70C43⋊#95—42no—
71C43⋊#95C2×C414yes—
72C23×C4×C43C2312yes—
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2312yes—
76C23×C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43—22no—
78C2×C4⋊C4×C43—41no—
79C2×C4⋊C4×C43—41no—
80C2×C4⋊C4×C43—41no—
81C2×C4⋊C4×C43—41no—
82C2×C4⋊C4×C43C2×C414yes—
83C2×C42×C43—41no—
84C2×C42×C43—41no—
85C2×C42×C43D414yescomplemented
86#95×C43—42no—
87#95×C43—42no—
88C24×C43C2411yescharacteristic
89C23×D43—22no—
90C23×D43—22no—
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—22no—
94C23×D43—22no—
95C23×D43—22no—
96C23×D43—22no—
97C23×D43—22no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—22no—
103C23×D43C22×C414yes—
104C22×C4×C43—22no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
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—22no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C2×D414yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43#4112yes—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
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×Dic43C22×C414yes—
156C2×D172—48no—
157C2×D172—44no—
158C2×D172—44no—
159C2×D172—48no—
160C2×D172—44no—
161C4⋊C4×C43—44no—
162C4⋊C4×C43—44no—
163C42×C43—44no—
164(C2×D43)⋊C4—216no—
165(C2×D43)⋊C4—48no—
166(C2×D43)⋊C4—48no—
167(C2×D43)⋊C4—48no—
168(C2×D43)⋊C4—48no—
169(C2×D43)⋊C4—48no—
170C4⋊Dic43—44no—
171Dic43⋊C4—48no—
172C23×C43C23×C411yescharacteristic
173C23×C43C22×D411yescharacteristic
174C23×C43C2×#4111yescharacteristic
175C23×C43H(5,𝔽2)11yescharacteristic
176C23×C43H(5,𝔽2)11yescharacteristic
177C23×C43H(5,𝔽2)12yes—
178C23×C43H(5,𝔽2)11yescharacteristic
179C23×C43H(5,𝔽2)12yes—
180C23×C43H(5,𝔽2)12yes—
181C23×C432−1+411yescharacteristic
182C23×C432−1+412yes—
183C22×D43—24no—
184C22×D43—24no—
185C22×D43—24no—
186C22×D43—24no—
187C22×D43—24no—
188C22×D43—24no—
189C22×D43—24no—
190C22×D43—42no—
191C22×D43—42no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
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×C43—42no—
248C2×C4×C43C4×D414yes—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—42no—
253C2×Dic43—42no—
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—
270D172—416no—
271#14632—431nomaximal, Sylow
272C22×C43C2×C4×D411yescharacteristic
273C22×C43#51812yes—
274C22×C43#51811yescharacteristic
275C22×C43#52011yescharacteristic
276C22×C43#52012yes—
277C22×C43#53411yescharacteristic
278C22×C43#53512yes—
279C22×C43#53711yescharacteristic
280C22×C43#53712yes—
281C22×C43#53811yescharacteristic
282C22×C43#53911yescharacteristic
283C22×C43#54012yes—
284C22×C43#54212yes—
285C22×C43#56011yescharacteristic
286C22×C43#56012yes—
287C22×C43#56012yes—
288C22×C43H(3,𝔽4)11yescharacteristic
289C22×C43H(3,𝔽4)11yescharacteristic
290C22×C43#56212yes—
291C22×C43#56212yes—
292C22×C43#56212yes—
293C22×C43#56311yescharacteristic
294C22×C43#56312yes—
295C2×D43—44no—
296C2×D43—44no—
297C2×D43—44no—
298C2×D43—44no—
299C2×D43—44no—
300C2×D43—44no—
301C2×D43—44no—
302C2×D43—82no—
303C2×D43—82no—
304C2×D43—82no—
305C2×D43—82no—
306C2×D43—82no—
307C2×D43—82no—
308C2×D43—82no—
309C2×D43—82no—
310C4×C43—24no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—44no—
314C4×C43—82no—
315Dic43—44no—
316Dic43—82no—
317Dic43—82no—
318C2×#394—431no—
319C2×#388—432no—
320#1442—432no—
321#1441—431no—
322#1439—432no—
323#1439—432no—
324#1439—432no—
325#1438—432no—
326C4⋊#95D4311yescharacteristic, complemented
327C2×C43#232412yes—
328C2×C43#232511yescharacteristic
329C2×C43#237511yescharacteristic
330C2×C43#237612yes—
331C2×C43#237911yescharacteristic
332C2×C43#281312yes—
333C2×C43#281911yescharacteristic
334C2×C43#282311yescharacteristic
335C2×C43#282811yescharacteristic
336C2×C43#283211yescharacteristic
337C2×C43#283712yes—
338D43—84no—
339C23×D4—431no—
340C22×C4⋊C4—432no—
341C22×C4⋊C4—431no—
342C22×C4⋊C4C2×D4311yescharacteristic
343C22×C4⋊C4C2×D4311yescharacteristic
344C22×C22⋊C4—432no—
345C22×C22⋊C4—432no—
346C22×C22⋊C4—432no—
347C22×C22⋊C4—432no—
348C22×C22⋊C4—432no—
349C22×C22⋊C4—432no—
350C22×C42C2×D4311yescharacteristic
351#394—438no—
352#388—868no—
353C2×#95—431no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—431no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95C2×D4312yes—
361C2×#95C2×D4312yes—
362C43#1463211yescharacteristic, complemented, Sylow
363C25—432no—
364C22×D4—434no—
365C22×D4—1722no—
366C22×D4—1721no—
367C22×D4—1721no—
368C22×D4—1722no—
369C23×C4—432no—
370C23×C4—432no—
371C23×C4—432no—
372C23×C4C22×D4312yes—
373C23×C4C22×D4311yescharacteristic
374C23×C4C22×D4311yescharacteristic
375C23×C4C22×D4312yes—
376C23×C4C22×D4311yescharacteristic
377C2×C4⋊C4—22no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—864no—
383C2×C4⋊C4—1722no—
384C2×C4⋊C4—1722no—
385C2×C4⋊C4—1721no—
386C2×C4⋊C4—1722no—
387C2×C4⋊C4C4×D4314yes—
388C2×C22⋊C4—438no—
389C2×C22⋊C4—438no—
390C2×C22⋊C4—864no—
391C2×C22⋊C4—864no—
392C2×C22⋊C4—864no—
393C2×C22⋊C4—864no—
394C2×C22⋊C4—1722no—
395C2×C22⋊C4—1722no—
396C2×C22⋊C4—1722no—
397C2×C22⋊C4—1722no—
398C2×C22⋊C4—1722no—
399C2×C22⋊C4—1722no—
400C2×C22⋊C4—1722no—
401C2×C22⋊C4—1722no—
402C2×C22⋊C4—1722no—
403C2×C22⋊C4—1722no—
404C2×C22⋊C4—1722no—
405C2×C22⋊C4—1722no—
406C2×C42—41no—
407C2×C42—41no—
408C2×C42D17214yescomplemented
409#95—42no—
410#95—42no—
411#95—434no—
412#95—864no—
413#95—864no—
414#95—1721no—
415#95—1722no—
416#95—1722no—
417#95—1722no—
418C24—434no—
419C24—862no—
420C24—862no—
421C24—862no—
422C24—862no—
423C24—862no—
424C24—862no—
425C24—862no—
426C24—862no—
427C24—862no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24—862no—
432C24—862no—
433C24C23×D4311yescharacteristic
434C2×D4—1728no—
435C2×D4—1724no—
436C2×D4—1724no—
437C2×D4—1728no—
438C2×D4—1724no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
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—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—434no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
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×C4C2×C4×D4312yes—
486C22×C4C2×C4×D4312yes—
487C22×C4C2×C4×D4312yes—
488C22×C4C2×D17214yes—
489C22×C4C2×D17212yes—
490C22×C4#1062189812yes—
491C4⋊C4—44no—
492C4⋊C4—44no—
493C4⋊C4—1728no—
494C4⋊C4—1724no—
495C22⋊C4—8616no—
496C22⋊C4—1728no—
497C22⋊C4—1728no—
498C22⋊C4—1728no—
499C22⋊C4—1728no—
500C22⋊C4—1728no—
501C42—44no—
502C23—864no—
503C23—864no—
504C23—864no—
505C23—864no—
506C23—864no—
507C23—864no—
508C23—864no—
509C23—1722no—
510C23—1722no—
511C23—1722no—
512C23—1722no—
513C23—1722no—
514C23—1722no—
515C23—1722no—
516C23—1722no—
517C23—1722no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1722no—
523C23—1722no—
524C23—1722no—
525C23—1722no—
526C23—1722no—
527C23—1722no—
528C23—1722no—
529C23—1722no—
530C23—1722no—
531C23—1722no—
532C23—1722no—
533C23—1722no—
534C23—1722no—
535C23—1722no—
536C23—1722no—
537C23C22×C4×D4311yescharacteristic
538C23C22×D17211yescharacteristic
539C23C2×#1062189811yescharacteristic
540C23#1306337012yes—
541C23#1306337011yescharacteristic
542C23#1306337011yescharacteristic
543C23#1306337011yescharacteristic
544C23#1306337112yes—
545C23#1306337112yes—
546C23#1306337311yescharacteristic
547C23#1306337312yes—
548D4—17216no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
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—864no—
580C2×C4—864no—
581C2×C4—864no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
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×C4C4×D17214yes—
601C22—3442no—
602C22—3442no—
603C22—3442no—
604C22—3442no—
605C22—3442no—
606C22—3442no—
607C22—3442no—
608C22—3442no—
609C22—1724no—
610C22—1724no—
611C22—1724no—
612C22—1724no—
613C22—1724no—
614C22—1724no—
615C22—1724no—
616C22C2×C4×D17211yescharacteristic
617C22#1458337112yes—
618C22#1458337211yescharacteristic
619C22#1458338011yescharacteristic
620C22#1458338112yes—
621C22#1458346111yescharacteristic
622C22#1458346812yes—
623C22#1458348012yes—
624C22#1458348011yescharacteristic
625C22#1458348711yescharacteristic
626C22#1458349611yescharacteristic
627C22#1458350012yes—
628C22#1458352112yes—
629C22#1458363611yescharacteristic
630C22#1458363712yes—
631C22#1458363712yes—
632C22#1458364111yescharacteristic
633C22#1458364111yescharacteristic
634C22#1458364512yes—
635C22#1458364512yes—
636C22#1458364712yes—
637C22#1458364811yescharacteristic
638C22#1458364812yes—
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—82no—
644C4—3442no—
645C4—3442no—
646C4—1724no—
647C2—3444no—
648C2#1913728912yes—
649C2#1913729811yescharacteristic
650C2#1913773211yescharacteristic
651C2#1913774012yes—
652C2#1913776711yescharacteristic
653C2#1914259912yes—
654C2#1914264111yescharacteristic
655C2#1914266911yescharacteristic
656C2#1914271411yescharacteristic
657C2#1914276211yescharacteristic
658C2#1914280512yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenterC4⋊#95D43
hypocenterC43#14632
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582790C2semidirect
3. #19132850C2semidirect
4. #19132848C2semidirect
5. #19132841C2semidirect
6. #19132839C2semidirect
7. #19132837C2semidirect
9. C43×C4⋊#95C2semidirect
19. #14582816C4semidirect
85. C2×C42×C43D4semidirect
326. C4⋊#95D43semidirect
362. C43#14632semidirect
408. C2×C42D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828162
C2×#145827902
#191328502
#191328482
#191328412
#191328392
#191328372
#191328352
C43×C4⋊#952
#1463243