Finite Group Databasebeta

← #25113744

Subgroups — #25113744

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#103×D43C211yesmaximal, characteristic
2#19137460C211yesmaximal, characteristic
3#19137429C211yesmaximal, characteristic
4#19135274C211yesmaximal, characteristic, complemented
5#19135268C211yesmaximal, characteristic, complemented
6#19135231C211yesmaximal, characteristic, complemented
7#19134866C211yesmaximal, characteristic, complemented
8#19134860C211yesmaximal, characteristic, complemented
9#19134680C211yesmaximal, characteristic
10#19134617C211yesmaximal, characteristic
11#19134528C211yesmaximal, characteristic
12C4×#13063248C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#19134365C211yesmaximal, characteristic
15C43×#1927C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063282—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29#103×D43C418yescomplemented
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582803—21no—
35#14582803—21no—
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582783—21no—
39#14582781—21no—
40#14582761—21no—
41#14582758—21no—
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582746—21no—
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86C2311yescharacteristic
62C2×Q8×D43—22no—
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—41no—
66C2×Q8×D43—41no—
67C2×Q8×D43C2×C414yes—
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—41no—
74C2×C8×D43—41no—
75C2×C8×D43C2×C414yes—
76C4×Dic86—22no—
77C4×Dic86—41no—
78#13063290—22no—
79#13063290—41no—
80#13063282—44no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43C2×C414yes—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063257—41no—
100#13063250—22no—
101#13063250C2×C414yes—
102#13063249—41no—
103#13063249C2×C414yes—
104#13063248—22no—
105#13063248C2×C414yes—
106(C2×D43)⋊C8—22no—
107C4×C43⋊C8—41no—
108C8×Dic43—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C22×Q8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#106×C43—41no—
127#103×C43—41no—
128#103×C43C2×C414yes—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132C23×D43C2×D411yescharacteristic
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C22×C412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153Q8×D43—28no—
154Q8×D43—44no—
155Q8×D43—44no—
156Q8×D43—44no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—24no—
162C2×C4×D43—24no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43C22×C412yes—
168C2×C4×D43#4112yes—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—24no—
173C2×Dic86—42no—
174C2×Dic86—42no—
175C2×Dic86C22×C412yes—
176C2×Dic86#4112yes—
177C2×Dic86#4112yes—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43C22×C412yes—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C22×C412yes—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—42no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4SD1614yes—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—24no—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—42no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C22×C412yes—
219C8×D43—44no—
220C23×C43C22×D411yescharacteristic
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43C4×D412yes—
226C22×D43C2×SD1612yes—
227C22×D43#13512yes—
228Q8×C43—22no—
229Q8×C43—22no—
230Q8×C43—41no—
231Q8×C43—41no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
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×C43C2×SD1612yes—
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
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×Dic43C4×D412yes—
276C2×Dic43C2×SD1612yes—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—48no—
282C4×D43—48no—
283Dic86—22no—
284Dic86—22no—
285Dic86—22no—
286Dic86—48no—
287Dic86#11714yescomplemented
288C8×C43—22no—
289C8×C43—41no—
290C43⋊C8—22no—
291C43⋊C8—41no—
292#22571—431nomaximal, Sylow
293C22×C43C2×C4×D411yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43C22×SD1611yescharacteristic
297C22×C43C2×#13511yescharacteristic
298C22×C43#57811yescharacteristic
299C22×C43#57811yescharacteristic
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43C4×SD1614yes—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43C2×#11711yescharacteristic
314C4×C43#51811yescharacteristic
315C4×C43#55111yescharacteristic
316C4×C43#55111yescharacteristic
317Dic43—24no—
318Dic43—22no—
319Dic43—22no—
320Dic43—42no—
321Dic43—41no—
322Dic43—81no—
323Dic43—81no—
324C22×#103—431no—
325#2344—431no—
326Q8×C22⋊C4—431no—
327#1933—431no—
328#1933—431no—
329#1927—431no—
330#1927D4311yescharacteristic, complemented
331#1865—431no—
332#1865—431no—
333#1823—431no—
334#1807—431no—
335#1787—431no—
336C4×#103—431no—
337C4×#103—431no—
338C8×C22⋊C4—431no—
339C2×C43#234211yescharacteristic
340C2×C43C2×C4×SD1611yescharacteristic
341C2×C43#295011yescharacteristic
342C2×C43#329811yescharacteristic
343C2×C43#329811yescharacteristic
344C2×C43#330011yescharacteristic
345C2×C43#330011yescharacteristic
346D43—24no—
347C23×Q8—431no—
348C23×C8—431no—
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×#117—861no—
352C22×C4⋊C4—431no—
353C2×#106—431no—
354C2×#106C2×D4311yescharacteristic
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—438no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#103C2×D4311yescharacteristic
364C2×C22⋊C8—431no—
365C2×C4×C8—431no—
366C2×C4×C8—431no—
367#391—431no—
368#391—861no—
369#391—861no—
370#391C2×D4311yescharacteristic
371#389—431no—
372#389—431no—
373#387—861no—
374#387—861no—
375#381—861no—
376#380—431no—
377#380—431no—
378#380—861no—
379C4×C4⋊C4—431no—
380C4×C4⋊C4C2×D4311yescharacteristic
381C4×C22⋊C4—431no—
382C4×C22⋊C4—861no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#336—431no—
390#336C2×D4311yescharacteristic
391C43#2257111yescharacteristic, complemented, Sylow
392C22×Q8—434no—
393C22×Q8—431no—
394C22×Q8—861no—
395C22×Q8—862no—
396C22×Q8—862no—
397C22×Q8—862no—
398C22×Q8—1721no—
399C22×Q8—1721no—
400C22×Q8C22×D4311yescharacteristic
401C23×C4—431no—
402C23×C4—861no—
403C23×C4—861no—
404C22×C8—431no—
405C22×C8—434no—
406C22×C8—431no—
407C22×C8—1721no—
408C22×C8—1721no—
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—1721no—
414C4×Q8—1721no—
415#117—1724no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—434no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—862no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—21no—
434C2×C42—431no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439#106—41no—
440#106—1721no—
441#103—41no—
442#103—434no—
443#103—434no—
444#103—434no—
445#103—862no—
446#103—862no—
447#103—1721no—
448#103C4×D4314yes—
449C22⋊C8—862no—
450C4×C8—1721no—
451C4×C8—1721no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—431no—
456#95—431no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464C24—431no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—432no—
471C2×Q8—432no—
472C2×Q8—432no—
473C2×Q8—864no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—868no—
478C2×Q8—1722no—
479C2×Q8—1722no—
480C2×Q8—1724no—
481C2×Q8—1724no—
482C2×Q8—1724no—
483C2×Q8C2×C4×D4312yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—431no—
493C22×C4—864no—
494C22×C4—864no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4C23×D4311yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—432no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—1724no—
522C2×C8C2×C4×D4312yes—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—432no—
529C4⋊C4—864no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4C2×C4×D4312yes—
540C22⋊C4—434no—
541C22⋊C4—862no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C42—21no—
545C42—21no—
546C42—42no—
547C42—861no—
548C42—861no—
549C42—1722no—
550C42—1722no—
551C42—1722no—
552C23—432no—
553C23—432no—
554C23—432no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23C2×D4×D4311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—434no—
565Q8—862no—
566Q8—862no—
567Q8—862no—
568Q8—1728no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
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—432no—
587C2×C4—432no—
588C2×C4—862no—
589C2×C4—861no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—1728no—
604C2×C4—1728no—
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×C4SD16×D4312yes—
614C2×C4C22×C4×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4#41×D4311yescharacteristic
617C2×C4#41×D4311yescharacteristic
618C2×C4#1306337011yescharacteristic
619C2×C4#1306337111yescharacteristic
620C8—22no—
621C8—41no—
622C8—862no—
623C8—1721no—
624C22—434no—
625C22—862no—
626C22—862no—
627C22—862no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22C4×D4×D4311yescharacteristic
632C22#1458354111yescharacteristic
633C22#1458354611yescharacteristic
634C22C2×SD16×D4311yescharacteristic
635C22#135×D4311yescharacteristic
636C22#1458371511yescharacteristic
637C22#1458371511yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—41no—
642C4—81no—
643C4—81no—
644C4—862no—
645C4—864no—
646C4—862no—
647C4—3441no—
648C4—3441no—
649C4—1722no—
650C4—1721no—
651C4#117×D4311yescharacteristic
652C4#1458337111yescharacteristic
653C4#1458357411yescharacteristic
654C4#1458357911yescharacteristic
655C2—864no—
656C2#1913743911yescharacteristic
657C2C4×SD16×D4311yescharacteristic
658C2#1914346011yescharacteristic
659C2#1914645811yescharacteristic
660C2#1914646311yescharacteristic
661C2#1914648511yescharacteristic
662C2#1914648911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1927C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1927D43
hypocenterC43#22571
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
4. #19135274C2semidirect
5. #19135268C2semidirect
6. #19135231C2semidirect
7. #19134866C2semidirect
8. #19134860C2semidirect
12. C4×#13063248C2semidirect
13. #19134414C2semidirect
15. C43×#1927C2semidirect
29. #103×D43C4semidirect
287. Dic86#117semidirect
330. #1927D43semidirect
391. C43#22571semidirect

Maximal subgroups

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

subgroupindex
C2×#103×D432
#191374602
#191374292
#191352742
#191352682
#191352312
#191348662
#191348602
#191346802
#191346172
#191345282
C4×#130632482
#191344142
#191343652
C43×#19272
#2257143