Finite Group Databasebeta

← #25200769

Subgroups — #25200769

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140555C211yesmaximal, characteristic, complemented
2#19137306C211yesmaximal, characteristic, complemented
3#19136068C211yesmaximal, characteristic, complemented
4#19136000C211yesmaximal, characteristic, complemented
5#19135837C211yesmaximal, characteristic, complemented
6#19135675C211yesmaximal, characteristic
7#19135476C211yesmaximal, characteristic, complemented
8#19135461C211yesmaximal, characteristic
9#19135292C211yesmaximal, characteristic, complemented
10#19135271C211yesmaximal, characteristic, complemented
11#19134949C211yesmaximal, characteristic, complemented
12#19134942C211yesmaximal, characteristic
13#19134852C211yesmaximal, characteristic, complemented
14#19134845C211yesmaximal, characteristic, complemented
15C43×#1746C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31#14582828—21no—
32#14582828—21no—
33#14582828—21no—
34#14582823—21no—
35#14582805C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582791—21no—
44#14582791—21no—
45#14582773—21no—
46#14582773—21no—
47#14582769C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×#97×C43C2211yescharacteristic
53C2×C4×C8×C43C2211yescharacteristic
54C43×#376C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873—41no—
66C2×D344—22no—
67C2×D344—22no—
68C2×D344—41no—
69#13063313—22no—
70#13063313—22no—
71C4×Dic86—41no—
72C4×Dic86—41no—
73C4×D172—41no—
74C4×D172—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98#13063259—41no—
99#13063259—41no—
100#13063250—22no—
101#13063250—22no—
102#13063250—41no—
103#13063247—22no—
104#13063247—22no—
105#13063247—41no—
106#13063247—41no—
107#13063247—41no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#97×C43—22no—
121C4×C8×C43—22no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C23×D43—21no—
127C23×D43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172#4112yes—
153C2×C4×D43—42no—
154C2×C4×D43—81no—
155C2×C4×D43—81no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
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#4112yes—
173C2×C8×C43#4112yes—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189(C2×D43)⋊C4—81no—
190(C2×D43)⋊C4—81no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—81no—
202C4⋊Dic43—81no—
203Dic43⋊C4—42no—
204Dic43⋊C4—81no—
205Dic43⋊C4—81no—
206Dic43⋊C4—81no—
207C4×Dic43—42no—
208D344—44no—
209#10621873—44no—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
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—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×Dic43—22no—
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—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267D172—22no—
268D172—22no—
269D172—41no—
270D172—41no—
271D172—41no—
272D172—41no—
273D172—41no—
274D172—41no—
275C4×D43—84no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280C8×C43—22no—
281C8×C43—22no—
282C8×C43—41no—
283C8×C43—41no—
284#29507—431nomaximal, Sylow
285C22×C43#52511yescharacteristic
286C22×C43#53211yescharacteristic
287C22×C43#53511yescharacteristic
288C22×C43#57611yescharacteristic
289C22×C43#57611yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57811yescharacteristic
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43#55111yescharacteristic
313C4×C43#55111yescharacteristic
314C4×C43#55311yescharacteristic
315C4×C43#55311yescharacteristic
316Dic43—42no—
317Dic43—81no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322#2644—431no—
323#2326—431no—
324#2083—431no—
325#2071—431no—
326#2042—431no—
327#2012—431no—
328#1973—431no—
329#1970—431no—
330#1936—431no—
331#1933—431no—
332#1880—431no—
333#1879—431no—
334#1863—431no—
335#1862—431no—
336#1746D4311yescharacteristic, complemented
337C2×C43#260311yescharacteristic
338C2×C43#311911yescharacteristic
339C2×C43#312411yescharacteristic
340C2×C43#317511yescharacteristic
341C2×C43#317911yescharacteristic
342C2×C43#322011yescharacteristic
343C2×C43#322511yescharacteristic
344D43—82no—
345D43—161no—
346C22×SD16—431no—
347C22×D8—431no—
348C2×#124—431no—
349C2×C4×Q8—431no—
350C2×C4×D4—431no—
351C2×#107—431no—
352C2×#107—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#97C2×D4311yescharacteristic
362C2×C4×C8C2×D4311yescharacteristic
363#397—861no—
364#397—861no—
365#397—861no—
366#396—861no—
367#391—431no—
368#390—431no—
369#390—431no—
370#390—431no—
371#390—431no—
372#389—431no—
373#389—431no—
374#389—431no—
375#388—861no—
376#388—861no—
377#385—861no—
378#385—861no—
379#384—431no—
380#376C2×D4311yescharacteristic
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336C2×D4311yescharacteristic
386#336C2×D4311yescharacteristic
387#336C2×D4311yescharacteristic
388#336C2×D4311yescharacteristic
389C43#2950711yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×D4—431no—
392C22×D4—431no—
393C23×C4—861no—
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—1721no—
397C2×D8—862no—
398C2×D8—862no—
399C2×D8—1721no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404#124—862no—
405#124—862no—
406C4×Q8—1721no—
407C4×Q8—1721no—
408C4×D4—1721no—
409C4×D4—1721no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434C2×C42C22×D4311yescharacteristic
435C2×C42C22×D4311yescharacteristic
436#107—1721no—
437#107—1721no—
438#103—862no—
439#103—862no—
440#103—1721no—
441#102—862no—
442#102—862no—
443#102—1721no—
444#102—1721no—
445#102—1721no—
446#97—22no—
447C4×C8—22no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95D17211yescharacteristic
454#95D17211yescharacteristic
455#95D17211yescharacteristic
456#95D17211yescharacteristic
457C24—861no—
458C24—861no—
459C2×Q8—432no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×D4—432no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—1722no—
486C22×C4C2×D17211yescharacteristic
487C22×C4C2×D17211yescharacteristic
488C22×C4C2×D17211yescharacteristic
489C22×C4C2×D17211yescharacteristic
490C22×C4C2×D17211yescharacteristic
491C22×C4C2×D17211yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—1724no—
494D8—1724no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8#1062189812yes—
506C2×C8#1062189812yes—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1722no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—1722no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—1722no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23C22×D17211yescharacteristic
556Q8—862no—
557Q8—862no—
558Q8—1721no—
559Q8—1721no—
560D4—862no—
561D4—862no—
562D4—1721no—
563D4—1721no—
564D4—1721no—
565D4—1721no—
566D4—1721no—
567D4—1721no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—862no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4#41×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4C2×#1062189811yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337111yescharacteristic
610C2×C4#1306337111yescharacteristic
611C8—22no—
612C8—22no—
613C8—41no—
614C8—41no—
615C22—3441no—
616C22—3441no—
617C22—3441no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22#1458341111yescharacteristic
630C22#1458344911yescharacteristic
631C22#1458346811yescharacteristic
632C22#1458370411yescharacteristic
633C22#1458370411yescharacteristic
634C22#1458371111yescharacteristic
635C22#1458371611yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—3441no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1722no—
648C4#1458357311yescharacteristic
649C4#1458357311yescharacteristic
650C4#1458359311yescharacteristic
651C4#1458359311yescharacteristic
652C2—3442no—
653C2—6881no—
654C2#1914022211yescharacteristic
655C2#1914479611yescharacteristic
656C2#1914485911yescharacteristic
657C2#1914523411yescharacteristic
658C2#1914527811yescharacteristic
659C2#1914564711yescharacteristic
660C2#1914570611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1746C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenter#1746D43
hypocenterC43#29507
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
1. #19140555C2semidirect
2. #19137306C2semidirect
3. #19136068C2semidirect
4. #19136000C2semidirect
5. #19135837C2semidirect
7. #19135476C2semidirect
9. #19135292C2semidirect
10. #19135271C2semidirect
11. #19134949C2semidirect
13. #19134852C2semidirect
14. #19134845C2semidirect
15. C43×#1746C2semidirect
336. #1746D43semidirect
389. C43#29507semidirect

Maximal subgroups

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

subgroupindex
#191405552
#191373062
#191360682
#191360002
#191358372
#191356752
#191354762
#191354612
#191352922
#191352712
#191349492
#191349422
#191348522
#191348452
C43×#17462
#2950743