Finite Group Databasebeta

← #25160157

Subgroups — #25160157

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138286C211yesmaximal, characteristic, complemented
2#19136163C211yesmaximal, characteristic, complemented
3#19136096C211yesmaximal, characteristic, complemented
4#19135969C211yesmaximal, characteristic, complemented
5#19135731C211yesmaximal, characteristic, complemented
6#19135547C211yesmaximal, characteristic, complemented
7#19135187C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic
9#19134918C211yesmaximal, characteristic
10#19134842C211yesmaximal, characteristic, complemented
11#19134794C211yesmaximal, characteristic, complemented
12#19134775C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, characteristic, complemented
14#19134311C211yesmaximal, characteristic, complemented
15C43×#2363C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28#14582822—21no—
29#14582811—21no—
30#14582803—21no—
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582786—21no—
34#14582765C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#390—21no—
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#386—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×Dic86—21no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—41no—
62C22×C43⋊C8—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063325—22no—
68#13063325—41no—
69#13063284—22no—
70#13063284—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81#13063258—22no—
82#13063256—41no—
83C4⋊(C43⋊C8)—41no—
84C4⋊(C43⋊C8)—41no—
85#13063246—22no—
86#13063246—41no—
87#13063246—41no—
88#13063246—41no—
89C22⋊(C43⋊C8)—22no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×D4×C43—21no—
96C22×D4×C43C2311yescharacteristic
97C23×C4×C43—21no—
98C23×C4×C43C2311yescharacteristic
99#121×C43—22no—
100#121×C43Q814yescomplemented
101C4×D4×C43—22no—
102C4×D4×C43—41no—
103#117×C43—22no—
104#117×C43—41no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#95×C43—21no—
121#95×C43—21no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124C24×C43—21no—
125C24×C43C2×D411yescharacteristic
126C2×D4×C43—21no—
127C2×D4×C43—24no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—81no—
133C2×D4×C43—81no—
134C2×D4×C43C2×Q812yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×Q812yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C2×Dic86—42no—
158C2×Dic86—42no—
159C2×Dic86—81no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—81no—
165C4⋊C4×C43C2×Q812yes—
166C4⋊C4×C43#4112yes—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—41no—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—81no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—42no—
179C42×C43—81no—
180C22⋊Dic43—42no—
181C22⋊Dic43—81no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—42no—
190C4⋊Dic43#4112yes—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193C4×Dic43—42no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—44no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C22⋊Q812yes—
221C23×C43C22×D411yescharacteristic
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—84no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
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—84no—
254C2×C4×C43C22⋊Q812yes—
255C2×C4×C43#13512yes—
256C2×C4×C43C22×Q811yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274Dic86—84no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#26409—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43C2×C22⋊Q811yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43#54611yescharacteristic
297C22×C43C2×#13511yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57611yescharacteristic
300C22×C43#57711yescharacteristic
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—81no—
309C4×C43#52911yescharacteristic
310C4×C43#53811yescharacteristic
311C4×C43#55411yescharacteristic
312C4×C43#55411yescharacteristic
313Dic43—42no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317#2439—431no—
318#2363D4311yescharacteristic
319#2101—431no—
320#2088—431no—
321#2065—431no—
322#2023—431no—
323#1988—431no—
324#1921—431no—
325#1893—431no—
326#1875—431no—
327#1862—431no—
328#1854—431no—
329#1850—431no—
330#1804—431no—
331#1735—431no—
332C2×C43—42no—
333C2×C43—82no—
334C2×C43#245011yescharacteristic
335C2×C43#307611yescharacteristic
336C2×C43#308111yescharacteristic
337C2×C43#329711yescharacteristic
338C2×C43#330411yescharacteristic
339C2×C43#331911yescharacteristic
340C2×C43#332111yescharacteristic
341C23×C8—431no—
342C2×C4⋊Q8—431no—
343C2×#121C2×D4311yescharacteristic
344C2×C4×D4C2×D4311yescharacteristic
345C2×#117—431no—
346C2×#117C2×D4311yescharacteristic
347C2×#107—431no—
348C2×#106—431no—
349C2×C4⋊C8—431no—
350C2×C4⋊C8—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×C22⋊C8—431no—
356#396—861no—
357#393—861no—
358#391—861no—
359#390—21no—
360#390C2×D4311yescharacteristic
361#389—431no—
362#389—431no—
363#389C2×D4311yescharacteristic
364#388—21no—
365#387—861no—
366#386—21no—
367#382—431no—
368#380—431no—
369C4×C4⋊C4C2×D4311yescharacteristic
370C4×C22⋊C4—21no—
371C4×C22⋊C4C2×D4311yescharacteristic
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#336—431no—
383#336—431no—
384C43#2640911yescharacteristic, complemented, Sylow
385C22×Q8—861no—
386C22×D4—21no—
387C22×D4C22×D4311yescharacteristic
388C23×C4—21no—
389C23×C4C22×D4311yescharacteristic
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—862no—
395C22×C8—1721no—
396C22×C8—1721no—
397C4⋊Q8—862no—
398C4⋊Q8—1721no—
399#121—22no—
400#121Dic8614yescomplemented
401C4×D4—22no—
402C4×D4—41no—
403#117—22no—
404#117—41no—
405#117—862no—
406#117—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4C22⋊D4311yescharacteristic
426C2×C22⋊C4C22⋊D4311yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431C2×C42C22×D4311yescharacteristic
432#107—862no—
433#106—1721no—
434C4⋊C8—1721no—
435C4⋊C8—1721no—
436#102—862no—
437#102—1721no—
438#102—1721no—
439#102—1721no—
440C22⋊C8—862no—
441#95—21no—
442#95—21no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95C22⋊D4311yescharacteristic
449#95C22⋊D4311yescharacteristic
450C24—21no—
451C24C2×C22⋊D4311yescharacteristic
452C2×Q8—3441no—
453C2×Q8—1722no—
454C2×Q8—1722no—
455C2×D4—24no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4C2×Dic8612yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4C2×Dic8612yes—
479C22×C4#1062189812yes—
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—1724no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—81no—
504C4⋊C4—432no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—3441no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4C2×Dic8612yes—
516C4⋊C4#1062190012yes—
517C22⋊C4—24no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—3441no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—81no—
532C42—1722no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23#1306330412yes—
547C23C22×C22⋊D4311yescharacteristic
548Q8—3444no—
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—84no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—862no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4#1306330412yes—
594C2×C4#1306334512yes—
595C2×C4C22×Dic8611yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4C2×#1062190011yescharacteristic
598C2×C4C2×#1062189811yescharacteristic
599C2×C4#1306337011yescharacteristic
600C2×C4#1306337111yescharacteristic
601C8—1721no—
602C8—1721no—
603C8—1721no—
604C8—1721no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C2×#1306330411yescharacteristic
620C22#1458353711yescharacteristic
621C22#1458354311yescharacteristic
622C22C2×#1306334511yescharacteristic
623C22#1458369711yescharacteristic
624C22#1458370211yescharacteristic
625C22#1458371011yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—81no—
634C4—3441no—
635C4—3441no—
636C4—3441no—
637C4—1722no—
638C4#1458342911yescharacteristic
639C4#1458348211yescharacteristic
640C4#1458360611yescharacteristic
641C4#1458360811yescharacteristic
642C2—42no—
643C2—82no—
644C2#1913841311yescharacteristic
645C2#1914438311yescharacteristic
646C2#1914442611yescharacteristic
647C2#1914643911yescharacteristic
648C2#1914653411yescharacteristic
649C2#1914675111yescharacteristic
650C2#1914677511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2363C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2363D43
hypocenterC43#26409
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #19138286C2semidirect
2. #19136163C2semidirect
3. #19136096C2semidirect
4. #19135969C2semidirect
5. #19135731C2semidirect
6. #19135547C2semidirect
7. #19135187C2semidirect
10. #19134842C2semidirect
11. #19134794C2semidirect
12. #19134775C2semidirect
13. #19134605C2semidirect
14. #19134311C2semidirect
100. #121×C43Q8semidirect
384. C43#26409semidirect
400. #121Dic86semidirect

Maximal subgroups

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

subgroupindex
#191382862
#191361632
#191360962
#191359692
#191357312
#191355472
#191351872
#191350242
#191349182
#191348422
#191347942
#191347752
#191346052
#191343112
C43×#23632
#2640943