Finite Group Databasebeta

← #25146763

Subgroups — #25146763

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582964C211yesmaximal, characteristic
2#19139762C211yesmaximal, characteristic
3#19139500C211yesmaximal, characteristic
4#19136029C211yesmaximal, characteristic, complemented
5#19136019C211yesmaximal, characteristic, complemented
6#19135797C211yesmaximal, characteristic, complemented
7#19135790C211yesmaximal, characteristic, complemented
8#19135561C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135015C211yesmaximal, characteristic, complemented
11#19135015C211yesmaximal, characteristic, complemented
12#19134621C211yesmaximal, characteristic, complemented
13#19134617C211yesmaximal, characteristic, complemented
14C4×#13063249C211yesmaximal, characteristic, complemented
15C2×C43×#479C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14582964—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582838—21no—
30#14582829—21no—
31#14582816—21no—
32#14582816—21no—
33#14582790—21no—
34#14582790—21no—
35#14582789—21no—
36#14582789—21no—
37#14582765C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#125×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C43×#479—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C22×D172D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43—22no—
69C2×C8×D43—22no—
70C2×C8×D43—41no—
71C2×C8×D43—41no—
72#13063301—22no—
73#13063301—22no—
74#13063301—41no—
75#13063301—41no—
76C4×D172—22no—
77C4×D172—22no—
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊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)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96#13063259—41no—
97#13063257—41no—
98#13063249—22no—
99#13063249—22no—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8—22no—
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#125×C43—22no—
116#125×C43—22no—
117C4×Q8×C43—22no—
118C4×Q8×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#107×C43—22no—
128#106×C43—22no—
129C4⋊C8×C43D414yes—
130#103×C43—22no—
131#103×C43—22no—
132C23×D43C2×D411yescharacteristic
133C23×D43C2×D411yescharacteristic
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43#4112yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—22no—
154C2×D172—22no—
155C2×D172—22no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D412yes—
173C2×C8×C43C2×D412yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C42×C43—42no—
184C42×C43C2×D412yes—
185C42×C43#4112yes—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
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—42no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196C4⋊Dic43—22no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207C4×Dic43—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8#4112yes—
214C8×D43—44no—
215C8×D43—44no—
216C23×C43C22×D411yescharacteristic
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43#13512yes—
230C22×D43#13512yes—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
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×C43—41no—
251C2×C4×C43#12112yes—
252C2×C4×C43#12112yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
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—41no—
277D172—28no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—41no—
285C4×D43—41no—
286C8×C43—22no—
287C8×C43—22no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290#25343—431nomaximal, Sylow
291C22×C43C2×#12111yescharacteristic
292C22×C43#54611yescharacteristic
293C22×C43#54711yescharacteristic
294C22×C43C2×#13511yescharacteristic
295C22×C43C2×#13511yescharacteristic
296C22×C43#57711yescharacteristic
297C22×C43#57811yescharacteristic
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43#52911yescharacteristic
319C4×C43#54211yescharacteristic
320C4×C43#54611yescharacteristic
321C4×C43#54811yescharacteristic
322Dic43—41no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328C2×#479D4311yescharacteristic, complemented
329C2×C8×D4—431no—
330#2562—431no—
331#2536—431no—
332#2077—431no—
333#2075—431no—
334#2036—431no—
335#2035—431no—
336#1991—431no—
337#1949—431no—
338#1892—431no—
339#1892—431no—
340#1808—431no—
341#1807—431no—
342C4×#103—431no—
343C2×C43#242711yescharacteristic
344C2×C43#305011yescharacteristic
345C2×C43#306311yescharacteristic
346C2×C43#330011yescharacteristic
347C2×C43#330111yescharacteristic
348C2×C43#333611yescharacteristic
349C2×C43#333711yescharacteristic
350D43—42no—
351D43—42no—
352C23×C8—431no—
353C23×C8—431no—
354C2×#125C2×D4311yescharacteristic
355C2×C22⋊Q8—431no—
356C2×C22⋊Q8—431no—
357C2×C4×Q8C2×D4311yescharacteristic
358C2×C4×D4—431no—
359#479—24no—
360C8×D4—864no—
361C2×#107—431no—
362C2×#107C2×D4311yescharacteristic
363C2×#106—431no—
364C2×#106C2×D4311yescharacteristic
365C2×C4⋊C8C2×D4311yescharacteristic
366C2×#103—431no—
367C2×#103—431no—
368C2×#103C2×D4311yescharacteristic
369C2×#103C2×D4311yescharacteristic
370C2×C22⋊C8—431no—
371C2×C22⋊C8—431no—
372C2×C4×C8—431no—
373#400—861no—
374#398—861no—
375#394—861no—
376#394—861no—
377#388—861no—
378#388—861no—
379#388—861no—
380#388—861no—
381#382—431no—
382#380—431no—
383#380—431no—
384#380—431no—
385#380—431no—
386#380—431no—
387#380—431no—
388C4×C4⋊C4—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397C43#2534311yescharacteristic, complemented, Sylow
398C22×Q8C22×D4311yescharacteristic
399C22×D4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—862no—
405C22×C8—862no—
406C22×C8—862no—
407C22×C8—862no—
408C22×C8—1721no—
409C22×C8—1721no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412#125—22no—
413#125—22no—
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416C22⋊Q8—1721no—
417C22⋊Q8—1721no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×D4—862no—
421C4×D4—862no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C22⋊C4—431no—
436C2×C22⋊C4—431no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C42—21no—
446C2×C42—861no—
447C2×C42C22×D4311yescharacteristic
448#107—22no—
449#107—1721no—
450#106—22no—
451#106—1721no—
452C4⋊C8C22⋊D4314yes—
453#103—22no—
454#103—22no—
455#103—862no—
456#103—862no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459C4×C8—862no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469C24—431no—
470C24—431no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8#1062190212yes—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—862no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
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×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—432no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—1724no—
516C2×C8—1724no—
517C2×C8C2×C22⋊D4312yes—
518C2×C8C2×C22⋊D4312yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—862no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—42no—
550C42—3441no—
551C42#1062190012yes—
552C42C2×C22⋊D4312yes—
553C23—432no—
554C23—432no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23C2×D4×D4311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—868no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
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—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
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—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4#1306329612yes—
616C2×C4#1306329612yes—
617C2×C4C22×C22⋊D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4C2×#1062190011yescharacteristic
620C2×C4C2×#1062190211yescharacteristic
621C2×C4#1306337111yescharacteristic
622C2×C4#1306337311yescharacteristic
623C8—22no—
624C8—22no—
625C8—862no—
626C8—1721no—
627C22—862no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22—1721no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22C2×#1306329611yescharacteristic
642C22#1458354011yescharacteristic
643C22#1458355111yescharacteristic
644C22#135×D4311yescharacteristic
645C22#135×D4311yescharacteristic
646C22#1458370811yescharacteristic
647C22#1458371511yescharacteristic
648C4—22no—
649C4—22no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—3441no—
655C4—3441no—
656C4—3441no—
657C4—3441no—
658C4—1721no—
659C4—1721no—
660C4#1458343511yescharacteristic
661C4#1458352211yescharacteristic
662C4#1458353711yescharacteristic
663C4#1458356011yescharacteristic
664C2—1722no—
665C2—1722no—
666C2#1913816811yescharacteristic
667C2#1914417211yescharacteristic
668C2#1914428011yescharacteristic
669C2#1914647911yescharacteristic
670C2#1914649411yescharacteristic
671C2#1914696011yescharacteristic
672C2#1914697111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenterC2×#479D43
hypocenterC43#25343
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
4. #19136029C2semidirect
5. #19136019C2semidirect
6. #19135797C2semidirect
7. #19135790C2semidirect
8. #19135561C2semidirect
9. #19135365C2semidirect
10. #19135015C2semidirect
11. #19135015C2semidirect
12. #19134621C2semidirect
13. #19134617C2semidirect
14. C4×#13063249C2semidirect
15. C2×C43×#479C2semidirect
328. C2×#479D43semidirect
397. C43#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#145829642
#191397622
#191395002
#191360292
#191360192
#191357972
#191357902
#191355612
#191353652
#191350152
#191346212
#191346172
C4×#130632492
C2×C43×#4792
#2534343