Finite Group Databasebeta

← #25155474

Subgroups — #25155474

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583309C211yesmaximal, characteristic, complemented
2C2×#14582939C211yesmaximal, characteristic
3#19138286C211yesmaximal, characteristic
4#19136077C211yesmaximal, characteristic, complemented
5#19136076C211yesmaximal, characteristic, complemented
6#19135930C211yesmaximal, characteristic, complemented
7#19135923C211yesmaximal, characteristic, complemented
8#19135330C211yesmaximal, characteristic, complemented
9#19135325C211yesmaximal, characteristic, complemented
10#19134792C211yesmaximal, characteristic
11#19134783C211yesmaximal, characteristic
12#19134757C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic
14#19134379C211yesmaximal, characteristic
15C43×#2442C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19#14583309—24no—
20#14582939—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582822—21no—
35#14582811—21no—
36#14582803—21no—
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582786—21no—
40#14582765C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#125×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C43×#400—21no—
53C43×#398—21no—
54C43×#389C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#385—21no—
57C43×#382C2211yescharacteristic
58C43×#380—21no—
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C22×Dic86—21no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877Q814yescomplemented
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063325—22no—
70#13063325—41no—
71#13063284—22no—
72#13063284—41no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83#13063258—22no—
84#13063258—22no—
85#13063258—22no—
86#13063258—41no—
87#13063258—41no—
88#13063258D414yes—
89#13063256—22no—
90#13063256—22no—
91#13063256—22no—
92#13063256—22no—
93C22⋊(C43⋊C8)Q814yescomplemented
94#13063236—22no—
95C4×C43⋊C8—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103#125×C43—22no—
104#125×C43—41no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—41no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43D411yescharacteristic
127#95×C43D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—81no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×Q812yes—
146C22×C4×C43C2×Q812yes—
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C2×Dic86—42no—
153C2×Dic86—42no—
154C2×Dic86—81no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—42no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43—81no—
166C4⋊C4×C43—81no—
167C4⋊C4×C43C2×D412yes—
168C22⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C22⋊C4×C43—42no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C22⋊Dic43—42no—
176C22⋊Dic43—81no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—42no—
185C4⋊Dic43C2×D412yes—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188C4×Dic43—42no—
189#10621877—28no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C2×D412yes—
197C2×C43⋊C8C2×Q812yes—
198C2×C43⋊C8C2×Q812yes—
199C2×C43⋊C8C2×Q812yes—
200C2×C43⋊C8C2×Q812yes—
201C2×C43⋊C8#4112yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C4⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—84no—
241C2×C4×C43C4⋊Q812yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×Q811yescharacteristic
244C2×C4×C43C22×Q811yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—22no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260Dic86—84no—
261C43⋊C8—22no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264C43⋊C8C22⋊Q814yes—
265#26079—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43C2×C4⋊Q811yescharacteristic
274C22×C43D4211yescharacteristic
275C22×C43#54711yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57611yescharacteristic
279C22×C43#57811yescharacteristic
280C4×C43—22no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—42no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×C22⋊Q811yescharacteristic
290C4×C43#54411yescharacteristic
291C4×C43D4×Q811yescharacteristic
292C4×C43#55411yescharacteristic
293Dic43—42no—
294Dic43—81no—
295Dic43—81no—
296Dic43—81no—
297C2×#501—431no—
298C2×#428—431no—
299#2442D4311yescharacteristic
300#2439—431no—
301#2085—431no—
302#2085—431no—
303#2059—431no—
304#2057—431no—
305#1943—431no—
306#1942—431no—
307#1854—431no—
308#1852—431no—
309#1846—431no—
310#1809—431no—
311#1753—431no—
312C2×C43—42no—
313C2×C43#244011yescharacteristic
314C2×C43#316411yescharacteristic
315C2×C43#316611yescharacteristic
316C2×C43#327311yescharacteristic
317C2×C43#327711yescharacteristic
318C2×C43#334711yescharacteristic
319C2×C43#334911yescharacteristic
320C22×M16—431no—
321C2×C4⋊Q8—431no—
322C2×#125C2×D4311yescharacteristic
323C2×#117—431no—
324C22×C4⋊C4C2×D4311yescharacteristic
325#501—864no—
326#428—864no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#107—431no—
333C2×#106—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#106—431no—
337C2×C22⋊C8—431no—
338C2×#97—431no—
339C2×C4×C8—431no—
340#400—21no—
341#398—21no—
342#396—861no—
343#393—861no—
344#391—861no—
345#389—431no—
346#389—431no—
347#389C2×D4311yescharacteristic
348#389C2×D4311yescharacteristic
349#387—861no—
350#385—21no—
351#382—431no—
352#382C2×D4311yescharacteristic
353#380—21no—
354#380—431no—
355#380C2×D4311yescharacteristic
356C4×C22⋊C4C2×D4311yescharacteristic
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#336—431no—
364#336—431no—
365C43#2607911yescharacteristic, complemented, Sylow
366C22×Q8—861no—
367C23×C4—21no—
368C23×C4C22×D4311yescharacteristic
369C2×M16—434no—
370C2×M16—862no—
371C2×M16—862no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—431no—
376C4⋊Q8—862no—
377C4⋊Q8—1721no—
378#125—22no—
379#125—41no—
380#117—862no—
381#117—1721no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4C22⋊D4311yescharacteristic
404C2×C22⋊C4C22⋊D4311yescharacteristic
405C2×C42—861no—
406C2×C42C22×D4311yescharacteristic
407C2×C42C22×D4311yescharacteristic
408#107—434no—
409#107—862no—
410#107—862no—
411#107—862no—
412#107—1721no—
413#107—1721no—
414#106—862no—
415#106—862no—
416#106—862no—
417#106—862no—
418C22⋊C8—434no—
419#97—862no—
420C4×C8—862no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95C22⋊D4311yescharacteristic
432#95C22⋊D4311yescharacteristic
433C24C2×C22⋊D4311yescharacteristic
434C2×Q8—3441no—
435C2×Q8—1722no—
436C2×Q8—1722no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—81no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4Q8×D4312yes—
453C22×C4Q8×D4312yes—
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460M16—868no—
461C2×C8—432no—
462C2×C8—432no—
463C2×C8—432no—
464C2×C8—432no—
465C2×C8—432no—
466C2×C8—432no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—432no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—3441no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4D4×D4312yes—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—42no—
500C22⋊C4—3441no—
501C22⋊C4—1722no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—1722no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23#1306332312yes—
514C23C22×C22⋊D4311yescharacteristic
515Q8—3444no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—84no—
547C2×C4—862no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4#1306332312yes—
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4C2×Q8×D4311yescharacteristic
562C2×C4C2×Q8×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#1306337011yescharacteristic
565C2×C4#1306337211yescharacteristic
566C8—434no—
567C8—862no—
568C8—862no—
569C8—862no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×#1306332311yescharacteristic
578C22D4×C22⋊D4311yescharacteristic
579C22#1458354811yescharacteristic
580C22#1458369711yescharacteristic
581C22#1458369711yescharacteristic
582C22#1458370211yescharacteristic
583C22#1458371411yescharacteristic
584C4—22no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—3441no—
594C4—3441no—
595C4—3441no—
596C4—1722no—
597C4C22⋊Q8×D4311yescharacteristic
598C4#1458352811yescharacteristic
599C4#1458356211yescharacteristic
600C4#1458360311yescharacteristic
601C2—42no—
602C2#1913829411yescharacteristic
603C2#1914512911yescharacteristic
604C2#1914514411yescharacteristic
605C2#1914620211yescharacteristic
606C2#1914624811yescharacteristic
607C2#1914708911yescharacteristic
608C2#1914712511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2442C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2442D43
hypocenterC43#26079
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#14583309C2semidirect
4. #19136077C2semidirect
5. #19136076C2semidirect
6. #19135930C2semidirect
7. #19135923C2semidirect
8. #19135330C2semidirect
9. #19135325C2semidirect
12. #19134757C2semidirect
64. C2×#10621877Q8semidirect
93. C22⋊(C43⋊C8)Q8semidirect
365. C43#26079semidirect

Maximal subgroups

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

subgroupindex
C2×#145833092
C2×#145829392
#191382862
#191360772
#191360762
#191359302
#191359232
#191353302
#191353252
#191347922
#191347832
#191347572
#191346262
#191343792
C43×#24422
#2607943