Finite Group Databasebeta

← #25146077

Subgroups — #25146077

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×#14583265C211yesmaximal, characteristic
2C2×#14583203C211yesmaximal, characteristic, complemented
3#19139597C211yesmaximal, characteristic
4#19135980C211yesmaximal, characteristic, complemented
5#19135966C211yesmaximal, characteristic, complemented
6#19135836C211yesmaximal, characteristic, complemented
7#19135836C211yesmaximal, characteristic, complemented
8#19135527C211yesmaximal, characteristic, complemented
9#19135527C211yesmaximal, characteristic, complemented
10#19135522C211yesmaximal, characteristic
11#19135319C211yesmaximal, characteristic, complemented
12#19135222C211yesmaximal, characteristic, complemented
13#19135215C211yesmaximal, characteristic, complemented
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2370C211yesmaximal, characteristic, complemented
16C2×#13063322C2211yescharacteristic
17C2×#13063313C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583265—24no—
21#14583203—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063236C2211yescharacteristic
40#14582817—21no—
41#14582817—21no—
42#14582801C2211yescharacteristic
43#14582801C2211yescharacteristic
44#14582800—21no—
45#14582800—21no—
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#125×C43C2211yescharacteristic
51C43×#389—21no—
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#387—21no—
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172—21no—
63C22×D172—21no—
64C22×D172C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063322—22no—
71#13063322—22no—
72#13063313—22no—
73#13063313—22no—
74#13063313—41no—
75#13063313—41no—
76C4×Dic86—22no—
77C4×Dic86—22no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊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×C4×Dic43—21no—
89#13063258—22no—
90#13063256—22no—
91C4⋊(C43⋊C8)—22no—
92C4⋊(C43⋊C8)—41no—
93C4⋊(C43⋊C8)—41no—
94#13063248—22no—
95#13063248—22no—
96#13063248—22no—
97#13063248—22no—
98#13063245—22no—
99#13063245—22no—
100#13063245—22no—
101#13063245—22no—
102#13063245—22no—
103#13063245—22no—
104#13063245—41no—
105#13063245—41no—
106#13063236—22no—
107#125×C43—22no—
108#125×C43D414yes—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C23×D43—21no—
133C23×D43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—42no—
160C2×D172—42no—
161C2×D172—42no—
162C2×D172—42no—
163C2×D172—81no—
164C2×D172—81no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86#4112yes—
171C4⋊C4×C43—24no—
172C4⋊C4×C43—24no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43C2×D412yes—
183C4⋊C4×C43C2×D412yes—
184C4⋊C4×C43#4112yes—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—42no—
190C42×C43—81no—
191C42×C43—81no—
192C42×C43C2×D412yes—
193C42×C43#4112yes—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—81no—
199(C2×D43)⋊C4—81no—
200(C2×D43)⋊C4—81no—
201(C2×D43)⋊C4—81no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204Dic43⋊C4—42no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
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—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43#12112yes—
262C2×C4×C43#12112yes—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275D172—41no—
276D172—41no—
277D172—41no—
278D172—41no—
279D172—41no—
280D172—41no—
281D172—41no—
282D172—41no—
283D172—84no—
284D172—84no—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289C43⋊C8—41no—
290C43⋊C8—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—42no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43#52911yescharacteristic
326C4×C43#54211yescharacteristic
327C4×C43#54811yescharacteristic
328C4×C43#55011yescharacteristic
329Dic43—42no—
330Dic43—81no—
331C2×#490—431no—
332C2×#479—431no—
333#2548—431no—
334#2370D4311yescharacteristic, complemented
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#1763—431no—
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×#125C2×D4311yescharacteristic
357C2×#124—431no—
358C2×#124—431no—
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⋊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×#102—431no—
378C2×#102—431no—
379C2×#97—431no—
380#394—861no—
381#394—861no—
382#390—431no—
383#390—431no—
384#390—861no—
385#390—861no—
386#389—21no—
387#389C2×D4311yescharacteristic
388#389C2×D4311yescharacteristic
389#387—21no—
390#387—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4C2×D4311yescharacteristic
393C4×C4⋊C4C2×D4311yescharacteristic
394C4×C4⋊C4C2×D4311yescharacteristic
395C4×C4⋊C4C2×D4311yescharacteristic
396#340—431no—
397#340—431no—
398#336—431no—
399#336—431no—
400C43#2529111yescharacteristic, complemented, Sylow
401C22×Q8—431no—
402C22×D4—431no—
403C22×D4—431no—
404C22×D4—861no—
405C22×D4—861no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8—431no—
410#127—862no—
411#127—862no—
412#125—22no—
413#125D17214yes—
414#124—862no—
415#124—862no—
416#124—1721no—
417#124—1721no—
418C4×Q8—862no—
419C4×Q8—862no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22⋊D4311yescharacteristic
427C2×C4⋊C4C22⋊D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445C2×C42C22×D4311yescharacteristic
446C2×C42C22×D4311yescharacteristic
447#107—862no—
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—862no—
457#102—862no—
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—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95C22⋊D4311yescharacteristic
471#95C22⋊D4311yescharacteristic
472C24—861no—
473C24—861no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
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—861no—
503C22×C4—861no—
504C22×C4C2×C22⋊D4311yescharacteristic
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C2×C22⋊D4311yescharacteristic
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—1722no—
537C4⋊C4C2×D17212yes—
538C4⋊C4C2×D17212yes—
539C4⋊C4#1062190212yes—
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—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42—81no—
554C42—81no—
555C42—1722no—
556C42C2×D17212yes—
557C42#1062189812yes—
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—
572C23C22×C22⋊D4311yescharacteristic
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
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—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—862no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4#1306329912yes—
622C2×C4#1306329912yes—
623C2×C4C22×D17211yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4C2×#1062189811yescharacteristic
626C2×C4C2×#1062190211yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337311yescharacteristic
629C8—1721no—
630C8—1721no—
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×#1306329911yescharacteristic
648C22#1458353711yescharacteristic
649C22#1458356011yescharacteristic
650C22#1458369711yescharacteristic
651C22#1458369711yescharacteristic
652C22#1458370211yescharacteristic
653C22#1458370711yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—81no—
664C4—3441no—
665C4—1722no—
666C4#1458343611yescharacteristic
667C4#1458352111yescharacteristic
668C4#1458356111yescharacteristic
669C4#1458357111yescharacteristic
670C2—6881no—
671C2—6881no—
672C2#1913815511yescharacteristic
673C2#1914408911yescharacteristic
674C2#1914413411yescharacteristic
675C2#1914659511yescharacteristic
676C2#1914671511yescharacteristic
677C2#1914734811yescharacteristic
678C2#1914736311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2370C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#2370D43
hypocenterC43#25291
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
2. C2×#14583203C2semidirect
4. #19135980C2semidirect
5. #19135966C2semidirect
6. #19135836C2semidirect
7. #19135836C2semidirect
8. #19135527C2semidirect
9. #19135527C2semidirect
11. #19135319C2semidirect
12. #19135222C2semidirect
13. #19135215C2semidirect
14. #19134428C2semidirect
15. C43×#2370C2semidirect
334. #2370D43semidirect
400. C43#25291semidirect

Maximal subgroups

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

subgroupindex
C2×#145832652
C2×#145832032
#191395972
#191359802
#191359662
#191358362
#191355272
#191355222
#191353192
#191352222
#191352152
#191344282
C43×#23702
#2529143