Finite Group Databasebeta

← #25196742

Subgroups — #25196742

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140416C211yesmaximal, characteristic
2#19136163C211yesmaximal, characteristic, complemented
3#19136143C211yesmaximal, characteristic, complemented
4#19135928C211yesmaximal, characteristic, complemented
5#19135736C211yesmaximal, characteristic, complemented
6#19135187C211yesmaximal, characteristic, complemented
7#19135180C211yesmaximal, characteristic, complemented
8#19135029C211yesmaximal, characteristic
9#19135019C211yesmaximal, characteristic
10#19134863C211yesmaximal, characteristic, complemented
11#19134863C211yesmaximal, characteristic, complemented
12#19134626C211yesmaximal, characteristic
13#19134618C211yesmaximal, characteristic
14#19134292C211yesmaximal, characteristic
15C43×#2323C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27#14582838—21no—
28#14582835—21no—
29#14582819—21no—
30#14582811—21no—
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582765C2211yescharacteristic
34#14582759C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389—21no—
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C43×#387—21no—
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×Dic86—21no—
60C2×#10621877—22no—
61C2×#10621877—22no—
62C2×#10621877—41no—
63C22×C43⋊C8—22no—
64C22×C43⋊C8—22no—
65C22×C43⋊C8—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063325—41no—
71#13063325—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81#13063258—22no—
82#13063256—22no—
83#13063256—41no—
84#13063256—41no—
85#13063249—22no—
86#13063249—22no—
87#13063249—41no—
88#13063249—41no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×Q8×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43Q814yescomplemented
99C4×Q8×C43—41no—
100C4×Q8×C43—41no—
101#117×C43—41no—
102#117×C43—41no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×Q812yes—
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—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×Q812yes—
145C22×C4×C43#4112yes—
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C2×Dic86—42no—
152C2×Dic86—81no—
153C2×Dic86—81no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43—41no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43C2×Q812yes—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—81no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—42no—
174C42×C43—81no—
175C22⋊Dic43—81no—
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—21no—
185C4⋊Dic43—42no—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188#10621877—44no—
189C2×C43⋊C8—21no—
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⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—44no—
200C2×C43⋊C8#4112yes—
201C2×C43⋊C8#4112yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C22⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
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—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43C22⋊Q812yes—
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
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—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263Dic86—84no—
264C43⋊C8—22no—
265C43⋊C8—22no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#29170—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C2×C22⋊Q811yescharacteristic
277C22×C43#53211yescharacteristic
278C22×C43#53411yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57811yescharacteristic
283C4×C43—22no—
284C4×C43—42no—
285C4×C43—42no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43#55111yescharacteristic
293C4×C43#55111yescharacteristic
294C4×C43#55411yescharacteristic
295C4×C43#55411yescharacteristic
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300#2628—431no—
301#2323D4311yescharacteristic
302#2101—431no—
303#2097—431no—
304#2058—431no—
305#2024—431no—
306#1921—431no—
307#1920—431no—
308#1894—431no—
309#1892—431no—
310#1865—431no—
311#1865—431no—
312#1809—431no—
313#1807—431no—
314#1729—431no—
315C2×C43—42no—
316C2×C43#256411yescharacteristic
317C2×C43#308211yescharacteristic
318C2×C43#308411yescharacteristic
319C2×C43#317311yescharacteristic
320C2×C43#317811yescharacteristic
321C2×C43#320011yescharacteristic
322C2×C43#320111yescharacteristic
323C22×M16—431no—
324C23×C8—431no—
325C2×C4⋊Q8—431no—
326C2×C22⋊Q8C2×D4311yescharacteristic
327C2×C4×Q8C2×D4311yescharacteristic
328C2×#117C2×D4311yescharacteristic
329C2×#107—431no—
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#103—431no—
337#400—861no—
338#399—861no—
339#395—861no—
340#393—861no—
341#391C2×D4311yescharacteristic
342#389—21no—
343#389—431no—
344#389—431no—
345#389C2×D4311yescharacteristic
346#388—21no—
347#388—21no—
348#387—21no—
349#382—431no—
350#380—431no—
351#380—431no—
352#380C2×D4311yescharacteristic
353C4×C4⋊C4C2×D4311yescharacteristic
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#336—431no—
363#336—431no—
364#336—431no—
365#336—431no—
366C43#2917011yescharacteristic, complemented, Sylow
367C22×Q8—861no—
368C22×Q8C22×D4311yescharacteristic
369C23×C4C22×D4311yescharacteristic
370C2×M16—862no—
371C2×M16—862no—
372C2×M16—1721no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—862no—
378C22×C8—862no—
379C22×C8—1721no—
380C4⋊Q8—1721no—
381C4⋊Q8—1721no—
382C22⋊Q8—22no—
383C22⋊Q8Dic8614yescomplemented
384C4×Q8—41no—
385C4×Q8—41no—
386#117—41no—
387#117—41no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22⋊D4311yescharacteristic
399C2×C4⋊C4C22⋊D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4C22⋊D4311yescharacteristic
408C2×C22⋊C4C22⋊D4311yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C22×D4311yescharacteristic
412C2×C42C22×D4311yescharacteristic
413#107—862no—
414#106—862no—
415#106—1721no—
416#106—1721no—
417#103—862no—
418#103—862no—
419#103—1721no—
420#103—1721no—
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#95—861no—
432C24C2×C22⋊D4311yescharacteristic
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—3441no—
439C2×Q8—3441no—
440C2×Q8—1722no—
441C2×Q8C2×Dic8612yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4C2×Dic8612yes—
455C22×C4#1062189812yes—
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462M16—1724no—
463C2×C8—432no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—1724no—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—1722no—
497C4⋊C4C2×Dic8612yes—
498C22⋊C4—24no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—81no—
502C22⋊C4—3441no—
503C22⋊C4—3441no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42—81no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23#1306330412yes—
517C23C22×C22⋊D4311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—3444no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4#1306330412yes—
566C2×C4C22×Dic8611yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4C2×#1062189811yescharacteristic
570C2×C4#1306337011yescharacteristic
571C2×C4#1306337011yescharacteristic
572C8—862no—
573C8—862no—
574C8—1721no—
575C8—1721no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#1306330411yescharacteristic
584C22#1458344511yescharacteristic
585C22#1458345811yescharacteristic
586C22#1458370711yescharacteristic
587C22#1458370711yescharacteristic
588C22#1458371011yescharacteristic
589C22#1458371411yescharacteristic
590C4—22no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—3441no—
600C4—3441no—
601C4—3441no—
602C4—3441no—
603C4#1458357811yescharacteristic
604C4#1458357811yescharacteristic
605C4#1458360811yescharacteristic
606C4#1458360811yescharacteristic
607C2—42no—
608C2#1913977111yescharacteristic
609C2#1914443711yescharacteristic
610C2#1914445711yescharacteristic
611C2#1914520611yescharacteristic
612C2#1914526511yescharacteristic
613C2#1914546211yescharacteristic
614C2#1914547111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2323C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2323D43
hypocenterC43#29170
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. #19136163C2semidirect
3. #19136143C2semidirect
4. #19135928C2semidirect
5. #19135736C2semidirect
6. #19135187C2semidirect
7. #19135180C2semidirect
10. #19134863C2semidirect
11. #19134863C2semidirect
98. C22⋊Q8×C43Q8semidirect
366. C43#29170semidirect
383. C22⋊Q8Dic86semidirect

Maximal subgroups

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

subgroupindex
#191404162
#191361632
#191361432
#191359282
#191357362
#191351872
#191351802
#191350292
#191350192
#191348632
#191346262
#191346182
#191342922
C43×#23232
#2917043