Finite Group Databasebeta

← #25146083

Subgroups — #25146083

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×#14583264C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3#19139594C211yesmaximal, characteristic
4#19137691C211yesmaximal, characteristic, complemented
5#19135984C211yesmaximal, characteristic, complemented
6#19135970C211yesmaximal, characteristic, complemented
7#19135832C211yesmaximal, characteristic, complemented
8#19135832C211yesmaximal, characteristic, complemented
9#19135524C211yesmaximal, characteristic, complemented
10#19135524C211yesmaximal, characteristic, complemented
11#19135522C211yesmaximal, characteristic
12#19135318C211yesmaximal, characteristic, complemented
13#19135220C211yesmaximal, characteristic, complemented
14#19135213C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C2×#13063322C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19C2×#13063314C2211yescharacteristic
20#14583264—24no—
21#14583206—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37#14582816—21no—
38#14582816—21no—
39#14582801—21no—
40#14582801—21no—
41#14582800C2211yescharacteristic
42#14582800C2211yescharacteristic
43#14582796—21no—
44#14582795C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582786—21no—
47#14582783—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50C4×Dic43⋊C4—21no—
51C4×C4⋊Dic43C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×D172—21no—
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063322—22no—
68#13063322—22no—
69#13063317—22no—
70#13063317D414yes—
71#13063314—22no—
72#13063314—22no—
73#13063314—41no—
74#13063314—41no—
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43D411yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96#13063256—22no—
97C4⋊(C43⋊C8)—22no—
98Dic43⋊C8—41no—
99Dic43⋊C8—41no—
100#13063249—22no—
101#13063249—22no—
102#13063247—22no—
103#13063247—22no—
104#13063247—22no—
105#13063247—22no—
106#13063245—22no—
107#13063245—22no—
108#13063245—41no—
109#13063245—41no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×Q8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C4×Q8×C43—22no—
120C4×Q8×C43—22no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#103×C43—22no—
129#103×C43—22no—
130#97×C43—22no—
131#95×C43—21no—
132C23×D43—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—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—42no—
166C2×D172—42no—
167C2×D172—42no—
168C2×D172—42no—
169C2×D172—81no—
170C2×D172—81no—
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×C43—21no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43#4112yes—
184C42×C43—42no—
185C42×C43—81no—
186C42×C43C2×D412yes—
187C42×C43#4112yes—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43C2×D412yes—
201C4⋊Dic43C2×D412yes—
202Dic43⋊C4—24no—
203Dic43⋊C4—24no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—42no—
211C4×Dic43—81no—
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×C43C22×D411yescharacteristic
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
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—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
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×C43—41no—
253C2×C4×C43#12112yes—
254C2×C4×C43#12112yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
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—
279D172—41no—
280D172—41no—
281D172—41no—
282D172—41no—
283D172—41no—
284D172—41no—
285D172—41no—
286D172—41no—
287D172—84no—
288D172—84no—
289C8×C43—41no—
290C8×C43—41no—
291C43⋊C8—41no—
292C43⋊C8—41no—
293#25291—431nomaximal, Sylow
294C22×C43C2×#12111yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43#54811yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57611yescharacteristic
300C22×C43#57711yescharacteristic
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43#52911yescharacteristic
322C4×C43#54211yescharacteristic
323C4×C43#54811yescharacteristic
324C4×C43#55011yescharacteristic
325Dic43—42no—
326Dic43—42no—
327Dic43—41no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
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#1925—431no—
345#1763D4311yescharacteristic, complemented
346C2×C43#242611yescharacteristic
347C2×C43#304011yescharacteristic
348C2×C43#304511yescharacteristic
349C2×C43#330911yescharacteristic
350C2×C43#331711yescharacteristic
351C2×C43#337011yescharacteristic
352C2×C43#337111yescharacteristic
353D43—161no—
354D43—161no—
355C2×#127—431no—
356C2×#125—431no—
357C2×#124—431no—
358C2×#124—431no—
359C2×C4×Q8C2×D4311yescharacteristic
360#490—864no—
361#479—864no—
362C2×#107—431no—
363C2×#106—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×C4⋊C8—431no—
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×#102—431no—
378C2×#102—431no—
379C2×#97C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
397#340C2×D4311yescharacteristic
398#336—431no—
399#336—431no—
400C43#2529111yescharacteristic, complemented, Sylow
401C22×Q8C22×D4311yescharacteristic
402C22×D4—431no—
403C22×D4—431no—
404C22×D4—861no—
405C22×D4—861no—
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—22no—
419C4×Q8—22no—
420C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
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—21no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42C22×D4311yescharacteristic
447#107—862no—
448#106—862no—
449C4⋊C8—862no—
450C4⋊C8—1721no—
451C4⋊C8—1721no—
452#103—22no—
453#103—22no—
454#103—862no—
455#103—862no—
456#102—862no—
457#102—862no—
458#102—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—1721no—
463#102—1721no—
464#97—22no—
465#95—21no—
466#95—431no—
467#95—431no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—861no—
473C24—861no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8#1062189812yes—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
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—21no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
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—21no—
528C4⋊C4—42no—
529C4⋊C4—432no—
530C4⋊C4—432no—
531C4⋊C4—864no—
532C4⋊C4—864no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—3441no—
536C4⋊C4—1721no—
537C4⋊C4—1721no—
538C4⋊C4—1722no—
539C4⋊C4#1062189812yes—
540C22⋊C4—3441no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C42—42no—
549C42—81no—
550C42—861no—
551C42—861no—
552C42—861no—
553C42—861no—
554C42—3441no—
555C42—1722no—
556C42#1062189812yes—
557C42D4×D4312yes—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
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—3444no—
578D4—3444no—
579D4—1721no—
580D4—1721no—
581D4—1721no—
582D4—1721no—
583D4—1721no—
584D4—1721no—
585D4—1721no—
586D4—1721no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4#1306329812yes—
622C2×C4#1306329812yes—
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4C2×#1062189811yescharacteristic
626C2×C4C2×#1062189811yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—41no—
630C8—41no—
631C8—1721no—
632C8—1721no—
633C22—3441no—
634C22—3441no—
635C22—3441no—
636C22—3441no—
637C22—3441no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—3441no—
647C22C2×#1306329811yescharacteristic
648C22#1458354511yescharacteristic
649C22#1458355811yescharacteristic
650C22#1458369811yescharacteristic
651C22#1458369811yescharacteristic
652C22#1458370311yescharacteristic
653C22#1458370811yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—81no—
659C4—81no—
660C4—1721no—
661C4—1721no—
662C4—1722no—
663C4—1722no—
664C4—1721no—
665C4—1721no—
666C4#1458343311yescharacteristic
667C4#1458352011yescharacteristic
668C4#1458355811yescharacteristic
669C4#1458357011yescharacteristic
670C2—6881no—
671C2—6881no—
672C2#1913816111yescharacteristic
673C2#1914409211yescharacteristic
674C2#1914413311yescharacteristic
675C2#1914660611yescharacteristic
676C2#1914672611yescharacteristic
677C2#1914734911yescharacteristic
678C2#1914736411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#1763D43
hypocenterC43#25291
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
4. #19137691C2semidirect
5. #19135984C2semidirect
6. #19135970C2semidirect
7. #19135832C2semidirect
8. #19135832C2semidirect
9. #19135524C2semidirect
10. #19135524C2semidirect
12. #19135318C2semidirect
13. #19135220C2semidirect
14. #19135213C2semidirect
15. C43×#1763C2semidirect
345. #1763D43semidirect
400. C43#25291semidirect

Maximal subgroups

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

subgroupindex
C2×#145832642
C2×#145832062
#191395942
#191376912
#191359842
#191359702
#191358322
#191355242
#191355222
#191353182
#191352202
#191352132
C43×#17632
#2529143