Finite Group Databasebeta

← #25126586

Subgroups — #25126586

Order 11008.

880 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137101C211yesmaximal, characteristic
2#19136997C211yesmaximal, characteristic, complemented
3#19136155C211yesmaximal, characteristic, complemented
4#19136120C211yesmaximal, characteristic, complemented
5#19136070C211yesmaximal, characteristic, complemented
6#19136021C211yesmaximal, characteristic, complemented
7#19136002C211yesmaximal, characteristic, complemented
8#19135778C211yesmaximal, characteristic
9#19135777C211yesmaximal, characteristic
10#107×Dic43C211yesmaximal, characteristic, complemented
11#19134487C211yesmaximal, characteristic, complemented
12#19134409C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#2075C211yesmaximal, characteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×#13063287C2211yescharacteristic
18C2×(C22⋊D43)⋊C4—21no—
19C2×#13063281—21no—
20C22×C4×Dic43C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582800C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582788—21no—
34#14582776—21no—
35#14582768C2211yescharacteristic
36#14582768C2211yescharacteristic
37#14582763—21no—
38#14582759C2211yescharacteristic
39#14582757—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43#14582750—21no—
44#14582746—21no—
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C23×Dic43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063299—22no—
67#13063299—22no—
68#13063287—22no—
69#13063287—22no—
70(C22⋊D43)⋊C4—44no—
71#13063281—44no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43—22no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063259—22no—
95#13063258—22no—
96#13063258—22no—
97#13063247—22no—
98#13063247—22no—
99#13063245—22no—
100#13063245—22no—
101C22⋊(C43⋊C8)—22no—
102C8×Dic43—22no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C23×C4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118#107×C43—22no—
119C22⋊C8×C43—22no—
120#95×C43—21no—
121#95×C43—21no—
122C24×C43C2×D411yescharacteristic
123C23×D43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—24no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—41no—
147C22×Dic43D814yes—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172#4112yes—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43#4112yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊Dic43—42no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43#4112yes—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—42no—
200C4×Dic43#4112yes—
201C4×Dic43#4112yes—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8#4112yes—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C2×D812yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
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—41no—
241C2×C4×C43—41no—
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C22⋊D43—48no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—28no—
256C2×Dic43—22no—
257C2×Dic43—44no—
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#12312yes—
267C2×Dic43#12312yes—
268C2×Dic43C2×D812yes—
269C2×Dic43C2×D812yes—
270C2×Dic43#13512yes—
271C2×Dic43#13712yes—
272D172—22no—
273D172—22no—
274D172—41no—
275D172—41no—
276C4×D43—84no—
277C8×C43—22no—
278C8×C43—41no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281#23754—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43C2×#12311yescharacteristic
290C22×C43#52511yescharacteristic
291C22×C43#53211yescharacteristic
292C22×C43C22×D811yescharacteristic
293C22×C43C2×#13511yescharacteristic
294C22×C43C2×#13711yescharacteristic
295C22×C43#57511yescharacteristic
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#52911yescharacteristic
309C4×C43#52911yescharacteristic
310C4×C43#52911yescharacteristic
311C4×C43#52911yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—81no—
317Dic43—81no—
318Dic43#48014yes—
319C4×#121—431no—
320#2285—431no—
321#2099—431no—
322#2093—431no—
323#2083—431no—
324#2075—431no—
325#2075D4311yescharacteristic, complemented
326#2071—431no—
327#2033—431no—
328#2033—431no—
329C4×#107—431no—
330C4×#107—431no—
331C4×#102—431no—
332C4×#102—431no—
333C4×C22⋊C8—431no—
334C2×C43—42no—
335C2×C43#239511yescharacteristic
336C2×C43C2×#48011yescharacteristic
337C2×C43#309111yescharacteristic
338C2×C43#310011yescharacteristic
339C2×C43#310711yescharacteristic
340C2×C43#316911yescharacteristic
341C2×C43#317211yescharacteristic
342D43—82no—
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×C4×D4—861no—
346C2×#117—861no—
347C22×C42—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#107—431no—
351C2×#107C2×D4311yescharacteristic
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×C22⋊C8—431no—
357C2×C22⋊C8C2×D4311yescharacteristic
358C2×C4×C8—431no—
359C2×C4×C8—431no—
360#390—431no—
361#389—431no—
362#388—861no—
363#386—861no—
364#384—431no—
365#384—431no—
366#382—861no—
367#380—431no—
368#380—861no—
369#380C2×D4311yescharacteristic
370#380C2×D4311yescharacteristic
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—861no—
375C4×C22⋊C4—861no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340C2×D4311yescharacteristic
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386C43#2375411yescharacteristic, complemented, Sylow
387C22×D4—431no—
388C22×D4—861no—
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#121—862no—
398#121—862no—
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—1724no—
402#117—1724no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—862no—
427C2×C42—862no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431#107—22no—
432#107—862no—
433#107—862no—
434#107—862no—
435#102—862no—
436#102—862no—
437#102—862no—
438#102—862no—
439C22⋊C8—22no—
440C22⋊C8—862no—
441C4×C8—862no—
442C4×C8—862no—
443#95—21no—
444#95—21no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—861no—
451C24D4×D4311yescharacteristic
452C2×D4—432no—
453C2×D4—864no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—1722no—
460C2×D4—1722no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—434no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4—1721no—
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—432no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8#1062190012yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—432no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—864no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—432no—
528C42—432no—
529C42—862no—
530C42—862no—
531C42—861no—
532C42—861no—
533C42—1722no—
534C42—1722no—
535C42—1722no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23D8×D4312yes—
550C23C2×D4×D4311yescharacteristic
551D4—862no—
552D4—862no—
553D4—1728no—
554D4—1721no—
555D4—1721no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—432no—
576C2×C4—432no—
577C2×C4—432no—
578C2×C4—432no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—868no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—862no—
589C2×C4—3444no—
590C2×C4—1724no—
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#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4C2×#1062190011yescharacteristic
605C8—22no—
606C8—41no—
607C8—862no—
608C8—1721no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—3441no—
617C22—3441no—
618C22—3441no—
619C22—3441no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22#123×D4311yescharacteristic
624C22#1458340711yescharacteristic
625C22#1458344411yescharacteristic
626C22C2×D8×D4311yescharacteristic
627C22#135×D4311yescharacteristic
628C22#137×D4311yescharacteristic
629C22#1458369811yescharacteristic
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—434no—
636C4—862no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—3441no—
641C4—1722no—
642C4#1458342611yescharacteristic
643C4#1458342811yescharacteristic
644C4#1458343211yescharacteristic
645C4#1458343211yescharacteristic
646C2—42no—
647C2—3442no—
648C2#1913785311yescharacteristic
649C2#480×D4311yescharacteristic
650C2#1914451311yescharacteristic
651C2#1914459211yescharacteristic
652C2#1914466111yescharacteristic
653C2#1914516911yescharacteristic
654C2#1914519611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2075C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2075D43
hypocenterC43#23754
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2075

Complements

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

NH ≅ G/Ntype
2. #19136997C2semidirect
3. #19136155C2semidirect
4. #19136120C2semidirect
5. #19136070C2semidirect
6. #19136021C2semidirect
7. #19136002C2semidirect
10. #107×Dic43C2semidirect
11. #19134487C2semidirect
12. #19134409C2semidirect
13. #19134409C2semidirect
14. C22⋊C8×Dic43C2semidirect
15. C43×#2075C2semidirect
325. #2075D43semidirect
386. C43#23754semidirect

Maximal subgroups

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

subgroupindex
#191371012
#191369972
#191361552
#191361202
#191360702
#191360212
#191360022
#191357782
#191357772
#107×Dic432
#191344872
#191344092
C22⋊C8×Dic432
C43×#20752
#2375443