Finite Group Databasebeta

← #25164730

Subgroups — #25164730

Order 11008.

790 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138943C211yesmaximal, characteristic
2#19137600C211yesmaximal, characteristic, complemented
3#19135914C211yesmaximal, characteristic, complemented
4#19135798C211yesmaximal, characteristic, complemented
5#19135745C211yesmaximal, characteristic, complemented
6#19135600C211yesmaximal, characteristic
7#19135549C211yesmaximal, characteristic, complemented
8#19135276C211yesmaximal, characteristic, complemented
9#19135213C211yesmaximal, characteristic, complemented
10#19135198C211yesmaximal, characteristic, complemented
11#19135185C211yesmaximal, characteristic, complemented
12#19134951C211yesmaximal, characteristic, complemented
13#19134912C211yesmaximal, characteristic
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1823C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582828—21no—
32#14582815—21no—
33#14582804C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582799—21no—
37#14582795C2211yescharacteristic
38#14582794—21no—
39#14582791—21no—
40#14582780—21no—
41#14582772—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C22⋊Dic43—21no—
45C4×C22⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C2×#10621873—22no—
63C2×#10621873—41no—
64C2×#10621873—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063316—22no—
68#13063316—41no—
69#13063304—22no—
70#13063304—22no—
71#13063299—22no—
72#13063299—41no—
73#13063290—22no—
74#13063290—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43D411yescharacteristic
84C2×C22⋊Dic43D411yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96Dic43⋊C8—41no—
97#13063250—22no—
98#13063248—22no—
99#13063248—41no—
100#13063247—22no—
101#13063245—22no—
102#13063245—41no—
103C22⋊(C43⋊C8)—41no—
104C8×Dic43—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C23×C4×C43—21no—
113C23×C4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—41no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C22⋊C8×C43—41no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C23×D43—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×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—81no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C2×C22⋊D43—42no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—81no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86#4112yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×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—
180C22⋊C4×C43—81no—
181C22⋊Dic43—24no—
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—42no—
192C4⋊Dic43#4112yes—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—24no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—42no—
203C4×Dic43—81no—
204C4×Dic43—81no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211#10621873—44no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43#13512yes—
219C23×C43C22×D411yescharacteristic
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
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×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—84no—
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C22⋊D43—84no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—22no—
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#13712yes—
275D172—41no—
276D172—41no—
277D172—41no—
278D172—41no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283C8×C43—41no—
284C8×C43—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#26727—431nomaximal, Sylow
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43#52511yescharacteristic
296C22×C43#54611yescharacteristic
297C22×C43#54611yescharacteristic
298C22×C43C2×#13511yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57611yescharacteristic
301C22×C43#57711yescharacteristic
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C4×C43—41no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43#52911yescharacteristic
315C4×C43#53811yescharacteristic
316C4×C43#55511yescharacteristic
317C4×C43#55911yescharacteristic
318Dic43—22no—
319Dic43—41no—
320Dic43—42no—
321Dic43—42no—
322Dic43—41no—
323Dic43—42no—
324Dic43—41no—
325#2490—431no—
326#2360—431no—
327#2055—431no—
328#2036—431no—
329#2026—431no—
330#2000—431no—
331#1989—431no—
332#1934—431no—
333#1925—431no—
334#1923—431no—
335#1921—431no—
336#1880—431no—
337#1874—431no—
338#1823D4311yescharacteristic, complemented
339C4×#103—431no—
340C2×C43—42no—
341C2×C43#245911yescharacteristic
342C2×C43#310811yescharacteristic
343C2×C43#311911yescharacteristic
344C2×C43#329611yescharacteristic
345C2×C43#329711yescharacteristic
346C2×C43#332011yescharacteristic
347C2×C43#333311yescharacteristic
348D43—161no—
349C22×SD16—431no—
350C2×#125—431no—
351C2×C22⋊Q8—431no—
352C2×#121—431no—
353C2×C4×Q8—431no—
354C22×C4⋊C4C2×D4311yescharacteristic
355C2×#107—431no—
356C2×C4⋊C8—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×C22⋊C8—431no—
364C2×C22⋊C8C2×D4311yescharacteristic
365C2×C4×C8—431no—
366#397—861no—
367#394—861no—
368#391—431no—
369#390—431no—
370#390—431no—
371#390—861no—
372#389—431no—
373#389—861no—
374#388—861no—
375#387—861no—
376#385—861no—
377#380C2×D4311yescharacteristic
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C22⋊C4—431no—
381C4×C22⋊C4—861no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388#340C2×D4311yescharacteristic
389#340C2×D4311yescharacteristic
390#336—431no—
391#336—431no—
392C43#2672711yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×D4—431no—
395C22×D4—861no—
396C23×C4—21no—
397C23×C4C22×D4311yescharacteristic
398C2×SD16—862no—
399C2×SD16—1721no—
400C2×SD16—1721no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405#125—862no—
406#125—1721no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409#121—862no—
410#121—1721no—
411C4×Q8—862no—
412C4×Q8—1721no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
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×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42—861no—
441#107—862no—
442C4⋊C8—1721no—
443#103—862no—
444#103—862no—
445#103—1721no—
446#102—862no—
447#102—862no—
448#102—1721no—
449C22⋊C8—41no—
450C22⋊C8—1721no—
451C4×C8—1721no—
452#95—21no—
453#95—431no—
454#95—431no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24—861no—
461C24D4×D4311yescharacteristic
462C2×Q8—432no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—3441no—
475C2×D4—1722no—
476C2×D4—1722no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—81no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4D4×D4311yescharacteristic
498C22×C4C23×D4311yescharacteristic
499SD16—1724no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—432no—
521C4⋊C4—432no—
522C4⋊C4—864no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—3441no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4#1062189812yes—
530C22⋊C4—81no—
531C22⋊C4—862no—
532C22⋊C4—864no—
533C22⋊C4—862no—
534C22⋊C4—3441no—
535C22⋊C4—3441no—
536C22⋊C4—3441no—
537C22⋊C4—1722no—
538C22⋊C4—1722no—
539C42—861no—
540C42—861no—
541C42—861no—
542C42—861no—
543C42—3441no—
544C42—3441no—
545C42—1722no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23#1306334612yes—
560C23C2×D4×D4311yescharacteristic
561Q8—862no—
562Q8—862no—
563Q8—1721no—
564Q8—1721no—
565D4—3444no—
566D4—1721no—
567D4—1721no—
568D4—1721no—
569D4—1721no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
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—84no—
590C2×C4—432no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—862no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4#41×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4C2×#1062189811yescharacteristic
615C2×C4#1306337011yescharacteristic
616C2×C4#1306337111yescharacteristic
617C8—41no—
618C8—41no—
619C8—1721no—
620C8—1721no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22#1458340711yescharacteristic
636C22#1458353911yescharacteristic
637C22#1458354111yescharacteristic
638C22C2×#1306334611yescharacteristic
639C22#137×D4311yescharacteristic
640C22#1458370011yescharacteristic
641C22#1458370811yescharacteristic
642C4—42no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4—81no—
647C4—862no—
648C4—1722no—
649C4—1721no—
650C4—1721no—
651C4—1722no—
652C4—1721no—
653C4—1722no—
654C4#1458342711yescharacteristic
655C4#1458348511yescharacteristic
656C4#1458361211yescharacteristic
657C4#1458363311yescharacteristic
658C2—42no—
659C2—6881no—
660C2#1913852911yescharacteristic
661C2#1914467811yescharacteristic
662C2#1914479711yescharacteristic
663C2#1914642811yescharacteristic
664C2#1914644111yescharacteristic
665C2#1914676711yescharacteristic
666C2#1914693111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1823C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1823D43
hypocenterC43#26727
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. #19137600C2semidirect
3. #19135914C2semidirect
4. #19135798C2semidirect
5. #19135745C2semidirect
7. #19135549C2semidirect
8. #19135276C2semidirect
9. #19135213C2semidirect
10. #19135198C2semidirect
11. #19135185C2semidirect
12. #19134951C2semidirect
14. #19134414C2semidirect
15. C43×#1823C2semidirect
338. #1823D43semidirect
392. C43#26727semidirect

Maximal subgroups

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

subgroupindex
#191389432
#191376002
#191359142
#191357982
#191357452
#191356002
#191355492
#191352762
#191352132
#191351982
#191351852
#191349512
#191349122
#191344142
C43×#18232
#2672743