Finite Group Databasebeta

← #25160161

Subgroups — #25160161

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#19137631C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136093C211yesmaximal, characteristic, complemented
5#19135968C211yesmaximal, characteristic, complemented
6#19135732C211yesmaximal, characteristic, complemented
7#19135546C211yesmaximal, characteristic, complemented
8#19135188C211yesmaximal, characteristic, complemented
9#19135023C211yesmaximal, characteristic
10#19134915C211yesmaximal, characteristic
11#19134845C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134606C211yesmaximal, characteristic, complemented
14#19134312C211yesmaximal, characteristic, complemented
15C43×#1850C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27#14582822—21no—
28#14582811—21no—
29#14582803—21no—
30#14582801C2211yescharacteristic
31#14582799—21no—
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582788—21no—
36#14582786—21no—
37#14582775—21no—
38#14582765C2211yescharacteristic
39#14582759C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41#14582746—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C23×C8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63#13063325—22no—
64#13063325—41no—
65#13063299—22no—
66#13063299Q814yescomplemented
67C4×D172—22no—
68C4×D172—41no—
69#13063284—22no—
70#13063284—22no—
71#13063284—41no—
72#13063284—41no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—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×Dic43—21no—
94#13063259—22no—
95#13063257—41no—
96#13063247—22no—
97#13063247—41no—
98#13063247—41no—
99#13063247—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43—22no—
109C22×C8×C43—41no—
110C22×C8×C43—41no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C4⋊C8×C43—41no—
120C4⋊C8×C43—41no—
121C22⋊C8×C43—22no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124C24×C43C2×D411yescharacteristic
125C23×D43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×Q812yes—
136C22×C4×C43#4112yes—
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—81no—
140C2×C22⋊D43—81no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C2×Q812yes—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—81no—
157C2×Dic86—42no—
158C2×Dic86—42no—
159C2×Dic86—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—44no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C22⋊Dic43—42no—
180C22⋊Dic43—42no—
181C22⋊Dic43—81no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—42no—
198C4⋊Dic43C2×Q812yes—
199C4⋊Dic43#4112yes—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C4×Dic43—81no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C22⋊Q812yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43C22⋊Q812yes—
240C2×C4×C43#13512yes—
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C22⋊D43—84no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
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—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269D172—22no—
270D172—22no—
271D172—41no—
272D172—41no—
273C4×D43—84no—
274Dic86—84no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—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×C43C2×C22⋊Q811yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54611yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57711yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43#52911yescharacteristic
307C4×C43#53811yescharacteristic
308C4×C43#55411yescharacteristic
309C4×C43#55411yescharacteristic
310Dic43—42no—
311Dic43—42no—
312Dic43—42no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317#2439—431no—
318#2363—431no—
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#1850D4311yescharacteristic, complemented
330#1804—431no—
331#1735—431no—
332C2×C43—42no—
333C2×C43#245011yescharacteristic
334C2×C43#307611yescharacteristic
335C2×C43#308111yescharacteristic
336C2×C43#329711yescharacteristic
337C2×C43#330411yescharacteristic
338C2×C43#331911yescharacteristic
339C2×C43#332111yescharacteristic
340D43—82no—
341C23×C8C2×D4311yescharacteristic
342C2×C4⋊Q8—431no—
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×#117—431no—
346C2×#117—431no—
347C2×#107—431no—
348C2×#106—431no—
349C2×C4⋊C8C2×D4311yescharacteristic
350C2×C4⋊C8C2×D4311yescharacteristic
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×C22⋊C8C2×D4311yescharacteristic
356#396—861no—
357#393—861no—
358#391—861no—
359#390—431no—
360#390—861no—
361#389—431no—
362#389—431no—
363#389—431no—
364#388—861no—
365#387—861no—
366#386—861no—
367#382—431no—
368#380—431no—
369C4×C4⋊C4—431no—
370C4×C22⋊C4—861no—
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#336C2×D4311yescharacteristic
383#336C2×D4311yescharacteristic
384C43#2640911yescharacteristic, complemented, Sylow
385C22×Q8—861no—
386C22×D4—431no—
387C22×D4—861no—
388C23×C4—861no—
389C23×C4C22×D4311yescharacteristic
390C22×C8—22no—
391C22×C8—41no—
392C22×C8—41no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C4⋊Q8—862no—
398C4⋊Q8—1721no—
399#121—434no—
400#121—862no—
401C4×D4—862no—
402C4×D4—1721no—
403#117—862no—
404#117—862no—
405#117—1721no—
406#117—1721no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4D17211yescharacteristic
426C2×C22⋊C4D17211yescharacteristic
427C2×C42—861no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431C2×C42C22×D4311yescharacteristic
432#107—862no—
433#106—1721no—
434C4⋊C8—41no—
435C4⋊C8—41no—
436#102—862no—
437#102—1721no—
438#102—1721no—
439#102—1721no—
440C22⋊C8—22no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95D17211yescharacteristic
449#95D17211yescharacteristic
450C24—861no—
451C24C2×D17211yescharacteristic
452C2×Q8—3441no—
453C2×Q8—1722no—
454C2×Q8—1722no—
455C2×D4—432no—
456C2×D4—864no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—3441no—
463C2×D4—3441no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—3441no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4C2×D17211yescharacteristic
479C22×C4C2×D17211yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4#1062190012yes—
484C22×C4Q8×D4312yes—
485C22×C4C23×D4311yescharacteristic
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—44no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—3441no—
514C4⋊C4—3441no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C22⋊C4—22no—
518C22⋊C4—41no—
519C22⋊C4—864no—
520C22⋊C4—3441no—
521C22⋊C4—3441no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—3441no—
531C42—1722no—
532C42—1722no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—862no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23#1306330512yes—
547C23C22×D17211yescharacteristic
548Q8—3444no—
549D4—862no—
550D4—862no—
551D4—3444no—
552D4—1721no—
553D4—1721no—
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—21no—
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—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—3444no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
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#1306330512yes—
594C2×C4#1306334712yes—
595C2×C4C2×Q8×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4C2×#1062190011yescharacteristic
599C2×C4#1306337011yescharacteristic
600C2×C4#1306337011yescharacteristic
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22C2×#1306330511yescharacteristic
620C22#1458354411yescharacteristic
621C22#1458354411yescharacteristic
622C22C2×#1306334711yescharacteristic
623C22#1458369911yescharacteristic
624C22#1458370411yescharacteristic
625C22#1458371111yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—3441no—
632C4—3441no—
633C4—3441no—
634C4—3441no—
635C4—1722no—
636C4—1722no—
637C4—1722no—
638C4#1458342611yescharacteristic
639C4#1458348411yescharacteristic
640C4#1458360311yescharacteristic
641C4#1458360311yescharacteristic
642C2—42no—
643C2—3442no—
644C2#1913841711yescharacteristic
645C2#1914438511yescharacteristic
646C2#1914442711yescharacteristic
647C2#1914644711yescharacteristic
648C2#1914653511yescharacteristic
649C2#1914675311yescharacteristic
650C2#1914678311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1850C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1850D43
hypocenterC43#26409
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. #19138286C2semidirect
3. #19136164C2semidirect
4. #19136093C2semidirect
5. #19135968C2semidirect
6. #19135732C2semidirect
7. #19135546C2semidirect
8. #19135188C2semidirect
11. #19134845C2semidirect
12. #19134796C2semidirect
13. #19134606C2semidirect
14. #19134312C2semidirect
15. C43×#1850C2semidirect
66. #13063299Q8semidirect
329. #1850D43semidirect
384. C43#26409semidirect

Maximal subgroups

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

subgroupindex
#191382862
#191376312
#191361642
#191360932
#191359682
#191357322
#191355462
#191351882
#191350232
#191349152
#191348452
#191347962
#191346062
#191343122
C43×#18502
#2640943