Finite Group Databasebeta

← #25146088

Subgroups — #25146088

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×#14583204C211yesmaximal, characteristic, complemented
3#19139595C211yesmaximal, characteristic
4#19137687C211yesmaximal, characteristic, complemented
5#19135979C211yesmaximal, characteristic, complemented
6#19135968C211yesmaximal, characteristic, complemented
7#19135833C211yesmaximal, characteristic, complemented
8#19135831C211yesmaximal, characteristic, complemented
9#19135524C211yesmaximal, characteristic, complemented
10#19135520C211yesmaximal, characteristic
11#19135315C211yesmaximal, characteristic, complemented
12#19135224C211yesmaximal, characteristic, complemented
13#19135215C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1983C211yesmaximal, characteristic, complemented
16C2×#13063321C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20#14583262—24no—
21#14583204—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35#14582815—21no—
36#14582815—21no—
37#14582802C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582799—21no—
40#14582799—21no—
41#14582798C2211yescharacteristic
42#14582797—21no—
43#14582797C2211yescharacteristic
44#14582786—21no—
45#14582782—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4×Dic43⋊C4—21no—
49C4×Dic43⋊C4C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#124×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063321—22no—
67#13063321—22no—
68#13063316—22no—
69#13063316D414yes—
70#13063314—22no—
71#13063314—41no—
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96#13063257—22no—
97Dic43⋊C8—22no—
98Dic43⋊C8—41no—
99#13063249—22no—
100#13063249—22no—
101#13063247—22no—
102#13063247—41no—
103#13063246—22no—
104#13063246—41no—
105#13063245—22no—
106#13063245—22no—
107#13063235—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118#124×C43—22no—
119#124×C43—41no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—41no—
127#103×C43—22no—
128#103×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#95×C43—21no—
132C24×C43—21no—
133C23×D43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43#4112yes—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—42no—
153C2×C22⋊D43—42no—
154C2×C22⋊D43—42no—
155C2×C22⋊D43—42no—
156C2×C22⋊D43—81no—
157C2×C22⋊D43—81no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
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×C43C2×D412yes—
180C4⋊C4×C43#4112yes—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—81no—
186C22⋊Dic43—81no—
187C22⋊Dic43—81no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—81no—
191(C2×D43)⋊C4—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—24no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43—81no—
200C4⋊Dic43C2×D412yes—
201Dic43⋊C4—24no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
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—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C22⋊D43—84no—
263C22⋊D43—84no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43#12112yes—
284C2×Dic43#12112yes—
285D172—41no—
286D172—41no—
287D172—41no—
288D172—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—42no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43#52911yescharacteristic
321C4×C43#54211yescharacteristic
322C4×C43#54811yescharacteristic
323C4×C43#55011yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—41no—
328Dic43—41no—
329Dic43—81no—
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#1983D4311yescharacteristic, complemented
341#1982—431no—
342#1940—431no—
343#1926—431no—
344#1925—431no—
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×#124C2×D4311yescharacteristic
359C2×C4×Q8—431no—
360#490—864no—
361#479—864no—
362C2×#107—431no—
363C2×#106—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×C4⋊C8C2×D4311yescharacteristic
367C2×#103—431no—
368C2×#103—431no—
369C2×#103C2×D4311yescharacteristic
370C2×#103C2×D4311yescharacteristic
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—431no—
384#390—861no—
385#390—861no—
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#340—431no—
398#336—431no—
399#336—431no—
400C43#2529111yescharacteristic, complemented, Sylow
401C22×Q8C22×D4311yescharacteristic
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—22no—
415#124—41no—
416#124—862no—
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—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
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—862no—
448#106—862no—
449C4⋊C8—41no—
450C4⋊C8—862no—
451C4⋊C8—1721no—
452#103—22no—
453#103—22no—
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—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8#1062189812yes—
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—432no—
526C4⋊C4—864no—
527C4⋊C4—864no—
528C4⋊C4—861no—
529C4⋊C4—861no—
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⋊C4D4×D4312yes—
539C4⋊C4#1062190012yes—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—3441no—
545C22⋊C4—3441no—
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—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
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—22no—
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—1721no—
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×C4C2×#1062190011yescharacteristic
626C2×C4C2×#1062189811yescharacteristic
627C2×C4#1306337011yescharacteristic
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#1458353911yescharacteristic
649C22#1458355511yescharacteristic
650C22#1458369611yescharacteristic
651C22#1458369811yescharacteristic
652C22#1458370311yescharacteristic
653C22#1458370611yescharacteristic
654C4—42no—
655C4—41no—
656C4—42no—
657C4—42no—
658C4—41no—
659C4—862no—
660C4—862no—
661C4—3441no—
662C4—3441no—
663C4—1721no—
664C4—1722no—
665C4—1721no—
666C4#1458342911yescharacteristic
667C4#1458351311yescharacteristic
668C4#1458355811yescharacteristic
669C4#1458356911yescharacteristic
670C2—161no—
671C2—6881no—
672C2#1913815811yescharacteristic
673C2#1914408611yescharacteristic
674C2#1914413511yescharacteristic
675C2#1914660211yescharacteristic
676C2#1914671711yescharacteristic
677C2#1914735211yescharacteristic
678C2#1914736011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1983C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#1983D43
hypocenterC43#25291
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#14583204C2semidirect
4. #19137687C2semidirect
5. #19135979C2semidirect
6. #19135968C2semidirect
7. #19135833C2semidirect
8. #19135831C2semidirect
9. #19135524C2semidirect
11. #19135315C2semidirect
12. #19135224C2semidirect
13. #19135215C2semidirect
14. #19134427C2semidirect
15. C43×#1983C2semidirect
340. #1983D43semidirect
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×#145832042
#191395952
#191376872
#191359792
#191359682
#191358332
#191358312
#191355242
#191355202
#191353152
#191352242
#191352152
#191344272
C43×#19832
#2529143