Finite Group Databasebeta

← #25146090

Subgroups — #25146090

Order 11008.

828 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×#14583262C211yesmaximal, characteristic
2C2×#14583205C211yesmaximal, characteristic, complemented
3#19139599C211yesmaximal, characteristic
4#19137687C211yesmaximal, characteristic, complemented
5#19135978C211yesmaximal, characteristic, complemented
6#19135969C211yesmaximal, characteristic, complemented
7#19135837C211yesmaximal, characteristic, complemented
8#19135835C211yesmaximal, characteristic, complemented
9#19135527C211yesmaximal, characteristic, complemented
10#19135526C211yesmaximal, characteristic, complemented
11#19135520C211yesmaximal, characteristic
12#19135317C211yesmaximal, characteristic, complemented
13#19135220C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C2×#13063321C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063312C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21#14583262—24no—
22#14583205—24no—
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38#14582814—21no—
39#14582814—21no—
40#14582800C2211yescharacteristic
41#14582799—21no—
42#14582799—21no—
43#14582798C2211yescharacteristic
44#14582797—21no—
45#14582797C2211yescharacteristic
46#14582786—21no—
47#14582782—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50C4×Dic43⋊C4—21no—
51C4×Dic43⋊C4C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063321—22no—
68#13063321—22no—
69#13063316—22no—
70#13063316D414yes—
71#13063313—22no—
72#13063313—41no—
73#13063312—22no—
74#13063312—41no—
75#13063290—22no—
76#13063290—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C2×Dic43⋊C4D411yescharacteristic
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063256—22no—
98C4⋊(C43⋊C8)—41no—
99Dic43⋊C8—22no—
100Dic43⋊C8—41no—
101#13063250—22no—
102#13063250—22no—
103#13063248—22no—
104#13063248—22no—
105#13063247—22no—
106#13063247—41no—
107#13063246—22no—
108#13063246—41no—
109#13063245—22no—
110#13063245—22no—
111#13063235—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C22×D4×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#107×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#95×C43—21no—
132C24×C43—21no—
133C23×D43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43—42no—
149C2×C22⋊D43—42no—
150C2×C22⋊D43—81no—
151C2×C22⋊D43—81no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86#4112yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D412yes—
182C4⋊C4×C43#4112yes—
183C22⋊C4×C43—81no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—81no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194C4⋊Dic43—21no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—81no—
199C4⋊Dic43C2×D412yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C4×Dic43—81no—
210C4×Dic43C2×D412yes—
211C4×Dic43#4112yes—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43C22×D411yescharacteristic
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C22⋊D43—84no—
259C22⋊D43—84no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43#12112yes—
280C2×Dic43#12112yes—
281D172—41no—
282D172—41no—
283D172—41no—
284D172—41no—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—41no—
290C8×C43—41no—
291C43⋊C8—41no—
292C43⋊C8—41no—
293#25291—431nomaximal, Sylow
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43C2×#12111yescharacteristic
302C22×C43#54611yescharacteristic
303C22×C43#54811yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57511yescharacteristic
306C22×C43#57611yescharacteristic
307C22×C43#57711yescharacteristic
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C4×C43—42no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—81no—
320C4×C43#52911yescharacteristic
321C4×C43#54211yescharacteristic
322C4×C43#54811yescharacteristic
323C4×C43#55011yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—42no—
328Dic43—41no—
329Dic43—41no—
330Dic43—81no—
331C2×#490—431no—
332C2×#479—431no—
333#2548—431no—
334#2370—431no—
335#2067—431no—
336#2065—431no—
337#2042—431no—
338#2042—431no—
339#1983—431no—
340#1983—431no—
341#1982—431no—
342#1940—431no—
343#1926—431no—
344#1925D4311yescharacteristic, complemented
345#1763—431no—
346C2×C43—161no—
347C2×C43#242611yescharacteristic
348C2×C43#304011yescharacteristic
349C2×C43#304511yescharacteristic
350C2×C43#330911yescharacteristic
351C2×C43#331711yescharacteristic
352C2×C43#337011yescharacteristic
353C2×C43#337111yescharacteristic
354D43—161no—
355C2×#127—431no—
356C2×#125—431no—
357C2×#124—431no—
358C2×#124—431no—
359C2×C4×Q8—431no—
360#490—864no—
361#479—864no—
362C2×#107C2×D4311yescharacteristic
363C2×#106—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×C4⋊C8—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102C2×D4311yescharacteristic
378C2×#102C2×D4311yescharacteristic
379C2×#97—431no—
380#394—861no—
381#394—861no—
382#390—431no—
383#390—861no—
384#390—861no—
385#390C2×D4311yescharacteristic
386#389—431no—
387#389—431no—
388#389—861no—
389#387—861no—
390#387—861no—
391C4×C4⋊C4—431no—
392C4×C4⋊C4—431no—
393C4×C4⋊C4—431no—
394C4×C4⋊C4—861no—
395C4×C4⋊C4C2×D4311yescharacteristic
396#340—431no—
397#340C2×D4311yescharacteristic
398#336—431no—
399#336C2×D4311yescharacteristic
400C43#2529111yescharacteristic, complemented, Sylow
401C22×Q8—431no—
402C22×D4—431no—
403C22×D4—861no—
404C22×D4—861no—
405C22×D4C22×D4311yescharacteristic
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#127—862no—
411#127—862no—
412#125—434no—
413#125—862no—
414#124—862no—
415#124—862no—
416#124—1721no—
417#124—1721no—
418C4×Q8—862no—
419C4×Q8—862no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C42—21no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42C22×D4311yescharacteristic
447#107—22no—
448#106—862no—
449C4⋊C8—862no—
450C4⋊C8—1721no—
451C4⋊C8—1721no—
452#103—862no—
453#103—862no—
454#103—862no—
455#103—862no—
456#102—22no—
457#102—22no—
458#102—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—1721no—
463#102—1721no—
464#97—862no—
465#95—21no—
466#95—431no—
467#95—431no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—21no—
473C24—861no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—3441no—
493C2×D4—3441no—
494C2×D4—1722no—
495C2×D4—1722no—
496C2×D4—1722no—
497C2×D4—1722no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—432no—
528C4⋊C4—864no—
529C4⋊C4—864no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—3441no—
534C4⋊C4—1721no—
535C4⋊C4—1721no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4#1062189812yes—
539C4⋊C4D4×D4312yes—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C42—21no—
549C42—21no—
550C42—81no—
551C42—432no—
552C42—432no—
553C42—861no—
554C42—861no—
555C42—3441no—
556C42—1722no—
557C42—1722no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C2×D4×D4311yescharacteristic
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—3444no—
582D4—3444no—
583D4—1721no—
584D4—1721no—
585D4—1721no—
586D4—1721no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—862no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4C2×#1062189811yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—41no—
630C8—41no—
631C8—1721no—
632C8—1721no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—3441no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—3441no—
647C22#121×D4311yescharacteristic
648C22#1458354111yescharacteristic
649C22#1458355811yescharacteristic
650C22#1458369611yescharacteristic
651C22#1458369811yescharacteristic
652C22#1458370011yescharacteristic
653C22#1458370911yescharacteristic
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—81no—
659C4—862no—
660C4—862no—
661C4—3441no—
662C4—1721no—
663C4—1722no—
664C4—1722no—
665C4—1721no—
666C4#1458342711yescharacteristic
667C4#1458351511yescharacteristic
668C4#1458355711yescharacteristic
669C4#1458357011yescharacteristic
670C2—161no—
671C2—6881no—
672C2#1913816011yescharacteristic
673C2#1914408611yescharacteristic
674C2#1914412911yescharacteristic
675C2#1914660411yescharacteristic
676C2#1914671911yescharacteristic
677C2#1914734411yescharacteristic
678C2#1914736811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#1925D43
hypocenterC43#25291
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. C2×#14583205C2semidirect
4. #19137687C2semidirect
5. #19135978C2semidirect
6. #19135969C2semidirect
7. #19135837C2semidirect
8. #19135835C2semidirect
9. #19135527C2semidirect
10. #19135526C2semidirect
12. #19135317C2semidirect
13. #19135220C2semidirect
14. #19134424C2semidirect
15. C43×#1925C2semidirect
344. #1925D43semidirect
400. C43#25291semidirect

Maximal subgroups

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

subgroupindex
C2×#145832622
C2×#145832052
#191395992
#191376872
#191359782
#191359692
#191358372
#191358352
#191355272
#191355262
#191355202
#191353172
#191352202
#191344242
C43×#19252
#2529143