Finite Group Databasebeta

← #25164792

Subgroups — #25164792

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138971C211yesmaximal, characteristic, complemented
2#19137633C211yesmaximal, characteristic
3#19135909C211yesmaximal, characteristic, complemented
4#19135778C211yesmaximal, characteristic
5#19135730C211yesmaximal, characteristic, complemented
6#19135596C211yesmaximal, characteristic
7#19135545C211yesmaximal, characteristic, complemented
8#19135268C211yesmaximal, characteristic, complemented
9#19135238C211yesmaximal, characteristic, complemented
10#19135204C211yesmaximal, characteristic, complemented
11#19135186C211yesmaximal, characteristic, complemented
12#19134926C211yesmaximal, characteristic, complemented
13#19134690C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1873C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582837—21no—
29#14582811—21no—
30#14582806C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582804—21no—
33#14582800C2211yescharacteristic
34#14582799—21no—
35#14582795C2211yescharacteristic
36#14582793—21no—
37#14582790—21no—
38#14582775—21no—
39#14582759C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4—21no—
43C4×C22⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621884—22no—
64C2×#10621884—41no—
65C2×#10621884—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—22no—
69#13063324—41no—
70#13063299—22no—
71#13063299—22no—
72#13063287—22no—
73#13063287—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43D411yescharacteristic
81C2×C22⋊Dic43D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91Dic43⋊C8—41no—
92#13063249—22no—
93#13063247—22no—
94#13063247—41no—
95#13063245—22no—
96C22⋊(C43⋊C8)—41no—
97C8×Dic43—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C23×C4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43—41no—
114#117×C43—22no—
115#117×C43—41no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123#103×C43—22no—
124#103×C43—41no—
125C22⋊C8×C43—41no—
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C22×C4×C43—21no—
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—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—24no—
147C2×C22⋊D43—81no—
148C2×C22⋊D43—81no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172#4112yes—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—81no—
165C2×Dic86—42no—
166C2×Dic86—42no—
167C2×Dic86—81no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43#4112yes—
180C4⋊C4×C43#4112yes—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C42×C43—42no—
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—81no—
187#10621884—44no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43#4112yes—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—81no—
205C4×Dic43—81no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
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×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C22⋊D43—84no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43#13512yes—
277C2×Dic43#13712yes—
278D172—22no—
279D172—22no—
280D172—41no—
281D172—41no—
282C4×D43—84no—
283Dic86—84no—
284C8×C43—41no—
285C8×C43—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#26731—431nomaximal, Sylow
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43#52511yescharacteristic
297C22×C43#54611yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43C2×#13511yescharacteristic
300C22×C43C2×#13711yescharacteristic
301C22×C43#57611yescharacteristic
302C22×C43#57711yescharacteristic
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C4×C43—41no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43#52911yescharacteristic
316C4×C43#53811yescharacteristic
317C4×C43#55511yescharacteristic
318C4×C43#55911yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—41no—
322Dic43—42no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
326#2492—431no—
327#2363—431no—
328#2055—431no—
329#2033—431no—
330#2023—431no—
331#2000—431no—
332#1988—431no—
333#1933—431no—
334#1928—431no—
335#1923—431no—
336#1921—431no—
337#1877—431no—
338#1873D4311yescharacteristic, complemented
339#1825—431no—
340C4×#102—431no—
341C2×C43—81no—
342C2×C43#245911yescharacteristic
343C2×C43#310711yescharacteristic
344C2×C43#311811yescharacteristic
345C2×C43#329711yescharacteristic
346C2×C43#330411yescharacteristic
347C2×C43#331411yescharacteristic
348C2×C43#332911yescharacteristic
349D43—82no—
350C22×SD16—431no—
351C2×C4⋊Q8—431no—
352C2×C22⋊Q8C2×D4311yescharacteristic
353C2×#121—431no—
354C2×C4×D4—431no—
355C2×#117C2×D4311yescharacteristic
356C2×#107—431no—
357C2×C4⋊C8—431no—
358C2×#103—431no—
359C2×#103C2×D4311yescharacteristic
360C2×#103C2×D4311yescharacteristic
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×C22⋊C8—431no—
365C2×C22⋊C8C2×D4311yescharacteristic
366C2×C4×C8—431no—
367#400—861no—
368#393—861no—
369#391—431no—
370#391—431no—
371#391—861no—
372#390—431no—
373#390—861no—
374#389—431no—
375#388—861no—
376#388—861no—
377#386—861no—
378#380—431no—
379C4×C4⋊C4—431no—
380C4×C4⋊C4—431no—
381C4×C22⋊C4—431no—
382C4×C22⋊C4—861no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340C2×D4311yescharacteristic
390#340C2×D4311yescharacteristic
391#336—431no—
392#336—431no—
393C43#2673111yescharacteristic, complemented, Sylow
394C22×Q8—861no—
395C22×Q8C22×D4311yescharacteristic
396C22×D4—431no—
397C22×D4—861no—
398C23×C4—861no—
399C23×C4C22×D4311yescharacteristic
400C2×SD16—862no—
401C2×SD16—1721no—
402C2×SD16—1721no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C4⋊Q8—862no—
408C4⋊Q8—1721no—
409C22⋊Q8—22no—
410C22⋊Q8—41no—
411#121—862no—
412#121—862no—
413C4×D4—862no—
414C4×D4—1721no—
415#117—22no—
416#117—41no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—431no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440#107—862no—
441C4⋊C8—1721no—
442#103—22no—
443#103—41no—
444#103—862no—
445#102—862no—
446#102—862no—
447#102—1721no—
448C22⋊C8—41no—
449C22⋊C8—1721no—
450C4×C8—1721no—
451#95—431no—
452#95—431no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—861no—
462C24D4×D4311yescharacteristic
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—3441no—
470C2×Q8—1722no—
471C2×Q8—1722no—
472C2×D4—432no—
473C2×D4—864no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—3441no—
480C2×D4—3441no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—3441no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4D4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503SD16—1724no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—432no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—3441no—
528C4⋊C4—1722no—
529C4⋊C4#1062189812yes—
530C4⋊C4#1062190012yes—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—864no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—3441no—
537C22⋊C4—3441no—
538C22⋊C4—1722no—
539C22⋊C4—1722no—
540C42—42no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42—861no—
545C42—3441no—
546C42—3441no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—862no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23C2×D4×D4311yescharacteristic
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—3444no—
567D4—862no—
568D4—862no—
569D4—3444no—
570D4—1721no—
571D4—1721no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—3444no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4#41×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4C2×#1062190011yescharacteristic
616C2×C4C2×#1062189811yescharacteristic
617C2×C4#1306337011yescharacteristic
618C2×C4#1306337011yescharacteristic
619C8—41no—
620C8—41no—
621C8—1721no—
622C8—1721no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—3441no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22#1458340711yescharacteristic
638C22#1458353611yescharacteristic
639C22#1458353911yescharacteristic
640C22#135×D4311yescharacteristic
641C22#137×D4311yescharacteristic
642C22#1458370111yescharacteristic
643C22#1458370811yescharacteristic
644C4—42no—
645C4—42no—
646C4—41no—
647C4—81no—
648C4—81no—
649C4—862no—
650C4—862no—
651C4—3441no—
652C4—3441no—
653C4—1721no—
654C4—1722no—
655C4—1721no—
656C4#1458343111yescharacteristic
657C4#1458348111yescharacteristic
658C4#1458361311yescharacteristic
659C4#1458363211yescharacteristic
660C2—81no—
661C2—3442no—
662C2#1913853111yescharacteristic
663C2#1914466111yescharacteristic
664C2#1914478211yescharacteristic
665C2#1914644611yescharacteristic
666C2#1914652711yescharacteristic
667C2#1914666911yescharacteristic
668C2#1914688511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1873C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1873D43
hypocenterC43#26731
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
1. #19138971C2semidirect
3. #19135909C2semidirect
5. #19135730C2semidirect
7. #19135545C2semidirect
8. #19135268C2semidirect
9. #19135238C2semidirect
10. #19135204C2semidirect
11. #19135186C2semidirect
12. #19134926C2semidirect
13. #19134690C2semidirect
14. #19134409C2semidirect
15. C43×#1873C2semidirect
338. #1873D43semidirect
393. C43#26731semidirect

Maximal subgroups

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

subgroupindex
#191389712
#191376332
#191359092
#191357782
#191357302
#191355962
#191355452
#191352682
#191352382
#191352042
#191351862
#191349262
#191346902
#191344092
C43×#18732
#2673143