Finite Group Databasebeta

← #25165055

Subgroups — #25165055

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#19138961C211yesmaximal, characteristic
2#19137624C211yesmaximal, characteristic, complemented
3#19135913C211yesmaximal, characteristic, complemented
4#19135801C211yesmaximal, characteristic, complemented
5#19135733C211yesmaximal, characteristic, complemented
6#19135601C211yesmaximal, characteristic
7#19135293C211yesmaximal, characteristic, complemented
8#19135215C211yesmaximal, characteristic, complemented
9#19135207C211yesmaximal, characteristic, complemented
10#19135190C211yesmaximal, characteristic, complemented
11#19134951C211yesmaximal, characteristic, complemented
12#19134916C211yesmaximal, characteristic
13#19134689C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1988C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063314—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582816—21no—
33#14582810—21no—
34#14582805C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582791—21no—
39#14582790—21no—
40#14582789—21no—
41#14582784—21no—
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43—21no—
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C2×#10621873—22no—
64C2×#10621873—41no—
65C2×#10621873—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063314—44no—
69#13063305—22no—
70#13063305—22no—
71#13063300—22no—
72#13063300—41no—
73#13063290—22no—
74#13063290—41no—
75#13063283—22no—
76#13063283—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
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×(C2×D43)⋊C4D411yescharacteristic
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96#13063258—22no—
97#13063250—22no—
98#13063248—22no—
99#13063248—41no—
100#13063247—41no—
101#13063245—22no—
102#13063245—22no—
103(C2×D43)⋊C8—41no—
104(C2×D43)⋊C8—41no—
105#13063235—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×Q8×C43—21no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4⋊Q8×C43—22no—
117C4⋊Q8×C43—41no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C42×C43—21no—
124C2×C42×C43C2311yescharacteristic
125C4⋊C8×C43—41no—
126#95×C43—21no—
127C23×D43—21no—
128C23×D43C2×D411yescharacteristic
129C2×Q8×C43—42no—
130C2×Q8×C43—42no—
131C2×Q8×C43—81no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—42no—
152C2×D172—42no—
153C2×D172—81no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86#4112yes—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×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—42no—
178C4⋊C4×C43#4112yes—
179C4⋊C4×C43#4112yes—
180C4⋊C4×C43#4112yes—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—42no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—81no—
194C4⋊Dic43—24no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200Dic43⋊C4—42no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—42no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212#10621873—44no—
213C23×C43C22×D411yescharacteristic
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228Q8×C43—84no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
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×C43AGL(1,ℤ/8)12yes—
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
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271D172—41no—
272D172—41no—
273D172—41no—
274D172—41no—
275D172—84no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280Dic86—22no—
281Dic86—22no—
282Dic86—41no—
283Dic86—41no—
284C8×C43—41no—
285C8×C43—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#26748—431nomaximal, Sylow
289C22×C43#52511yescharacteristic
290C22×C43#54611yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C43#57511yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43#52911yescharacteristic
317C4×C43#53811yescharacteristic
318C4×C43#55511yescharacteristic
319C4×C43#55911yescharacteristic
320Dic43—41no—
321Dic43—42no—
322Dic43—41no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
326#2491—431no—
327#2362—431no—
328#2055—431no—
329#2036—431no—
330#2024—431no—
331#2000—431no—
332#1988D4311yescharacteristic, complemented
333#1936—431no—
334#1925—431no—
335#1924—431no—
336#1921—431no—
337#1880—431no—
338#1875—431no—
339#1825—431no—
340#1763—431no—
341C2×C43#245911yescharacteristic
342C2×C43#311511yescharacteristic
343C2×C43#312111yescharacteristic
344C2×C43#331011yescharacteristic
345C2×C43#331311yescharacteristic
346C2×C43#332111yescharacteristic
347C2×C43#333011yescharacteristic
348D43—81no—
349D43—161no—
350C22×SD16—431no—
351C2×C4⋊Q8C2×D4311yescharacteristic
352C2×#124—861no—
353C2×C22⋊Q8—431no—
354C2×#121—431no—
355C2×C4×Q8—431no—
356C2×#117—431no—
357C2×#107—431no—
358C2×C4⋊C8C2×D4311yescharacteristic
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×C22⋊C8—431no—
366C2×C22⋊C8—431no—
367C2×#97—431no—
368#394—861no—
369#393—861no—
370#391—431no—
371#390—431no—
372#390—431no—
373#389—431no—
374#388—861no—
375#388—861no—
376#388—861no—
377#387—861no—
378#380—431no—
379C4×C4⋊C4—431no—
380C4×C4⋊C4—861no—
381C4×C4⋊C4C2×D4311yescharacteristic
382C4×C22⋊C4—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340C2×D4311yescharacteristic
388#340C2×D4311yescharacteristic
389#340C2×D4311yescharacteristic
390#340C2×D4311yescharacteristic
391#336—431no—
392#336—431no—
393C43#2674811yescharacteristic, complemented, Sylow
394C22×Q8—21no—
395C22×Q8—431no—
396C22×D4—431no—
397C22×D4—861no—
398C23×C4—431no—
399C2×SD16—862no—
400C2×SD16—1721no—
401C2×SD16—1721no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4⋊Q8—22no—
407C4⋊Q8—41no—
408#124—1724no—
409C22⋊Q8—862no—
410C22⋊Q8—862no—
411#121—862no—
412#121—1721no—
413C4×Q8—862no—
414C4×Q8—1721no—
415#117—862no—
416#117—1721no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
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—431no—
428C2×C22⋊C4—431no—
429C2×C22⋊C4—861no—
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×C22⋊C4—861no—
437C2×C42—21no—
438C2×C42—431no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443#107—862no—
444C4⋊C8—41no—
445#103—862no—
446#103—862no—
447#103—1721no—
448#102—862no—
449#102—862no—
450#102—1721no—
451C22⋊C8—1721no—
452C22⋊C8—1721no—
453#97—1721no—
454#95—21no—
455#95—431no—
456#95—431no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—431no—
463C24—861no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—81no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—3441no—
480C2×D4—1722no—
481C2×D4—1722no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4D4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500C22×C4C23×D4311yescharacteristic
501SD16—1724no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—864no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4#1062189812yes—
528C4⋊C4#1062190212yes—
529C4⋊C4#1062190212yes—
530C22⋊C4—864no—
531C22⋊C4—862no—
532C22⋊C4—3441no—
533C22⋊C4—1721no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C22⋊C4—1722no—
539C22⋊C4—1722no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—861no—
544C42—861no—
545C42—1722no—
546C42—1722no—
547C42—1722no—
548C23—861no—
549C23—861no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23C2×D4×D4311yescharacteristic
563Q8—84no—
564Q8—862no—
565Q8—862no—
566Q8—1721no—
567Q8—1721no—
568D4—3444no—
569D4—1721no—
570D4—1721no—
571D4—1721no—
572D4—1721no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
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—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4#1306334912yes—
613C2×C4#41×D4311yescharacteristic
614C2×C4C2×#1062189811yescharacteristic
615C2×C4C2×#1062190211yescharacteristic
616C2×C4C2×#1062190211yescharacteristic
617C2×C4#1306337011yescharacteristic
618C2×C4#1306337111yescharacteristic
619C8—41no—
620C8—41no—
621C8—1721no—
622C8—1721no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—3441no—
630C22—1721no—
631C22—1721no—
632C22—1721no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22#1458341211yescharacteristic
638C22#1458353911yescharacteristic
639C22#1458354011yescharacteristic
640C22C2×#1306334911yescharacteristic
641C22#1458369811yescharacteristic
642C22#1458370511yescharacteristic
643C22#1458371511yescharacteristic
644C4—22no—
645C4—42no—
646C4—42no—
647C4—42no—
648C4—41no—
649C4—81no—
650C4—3441no—
651C4—3441no—
652C4—1721no—
653C4—1721no—
654C4—1721no—
655C4—1722no—
656C4#1458343611yescharacteristic
657C4#1458348311yescharacteristic
658C4#1458361511yescharacteristic
659C4#1458363411yescharacteristic
660C2—3441no—
661C2—6881no—
662C2#1913853911yescharacteristic
663C2#1914474811yescharacteristic
664C2#1914483111yescharacteristic
665C2#1914661211yescharacteristic
666C2#1914666211yescharacteristic
667C2#1914677811yescharacteristic
668C2#1914689711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1988C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1988D43
hypocenterC43#26748
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
2. #19137624C2semidirect
3. #19135913C2semidirect
4. #19135801C2semidirect
5. #19135733C2semidirect
7. #19135293C2semidirect
8. #19135215C2semidirect
9. #19135207C2semidirect
10. #19135190C2semidirect
11. #19134951C2semidirect
13. #19134689C2semidirect
14. #19134424C2semidirect
15. C43×#1988C2semidirect
332. #1988D43semidirect
393. C43#26748semidirect

Maximal subgroups

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

subgroupindex
#191389612
#191376242
#191359132
#191358012
#191357332
#191356012
#191352932
#191352152
#191352072
#191351902
#191349512
#191349162
#191346892
#191344242
C43×#19882
#2674843