Finite Group Databasebeta

← #25113840

Subgroups — #25113840

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582897C211yesmaximal, characteristic
2#19137471C211yesmaximal, characteristic, complemented
3#19137434C211yesmaximal, characteristic
4#19135294C211yesmaximal, characteristic, complemented
5#19135219C211yesmaximal, characteristic, complemented
6#19135218C211yesmaximal, characteristic, complemented
7#19134864C211yesmaximal, characteristic, complemented
8#19134848C211yesmaximal, characteristic, complemented
9#19134680C211yesmaximal, characteristic, complemented
10#19134627C211yesmaximal, characteristic, complemented
11#19134532C211yesmaximal, characteristic
12#19134424C211yesmaximal, characteristic, complemented
13C4×#13063250C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23#14582897C418yescomplemented
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582799—21no—
34#14582799—21no—
35#14582798C2211yescharacteristic
36#14582786—21no—
37#14582780—21no—
38#14582757—21no—
39#14582756—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582746—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C2×#10621900—22no—
61C2×#10621900—22no—
62C2×#10621900—22no—
63C2×#10621900—41no—
64C2×#10621900—41no—
65C2×#10621900C2×C414yes—
66C22×Dic86C2311yescharacteristic
67C22×C22⋊D43—21no—
68C23×Dic43—21no—
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C2×#10621872—41no—
72C2×#10621872—41no—
73C2×#10621872C2×C414yes—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C4×Dic86—22no—
77C4×Dic86—41no—
78#13063290—22no—
79#13063290—41no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43C2×C414yes—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
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×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100#13063258—41no—
101#13063256—41no—
102#13063250—22no—
103#13063250C2×C414yes—
104#13063248—22no—
105#13063248C2×C414yes—
106#13063246—41no—
107#13063246C2×C414yes—
108(C2×D43)⋊C8—22no—
109#13063235—41no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#102×C43—41no—
128#102×C43C2×C414yes—
129C4×C8×C43—41no—
130#95×C43—21no—
131C24×C43—21no—
132C23×D43C2×D411yescharacteristic
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43C22×C412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C22×Dic43—24no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158#10621900—28no—
159#10621900—44no—
160#10621900—44no—
161#10621900—44no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—24no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43C22×C412yes—
170C2×C4×D43#4112yes—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86C22×C412yes—
175C2×Dic86#4112yes—
176C2×Dic86#4112yes—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C22×C412yes—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—81no—
189C4⋊C4×C43C22×C412yes—
190C22⋊C4×C43—42no—
191C22⋊C4×C43—81no—
192C42×C43—21no—
193C42×C43—21no—
194C22⋊Dic43—42no—
195C22⋊Dic43—81no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—81no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—81no—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—24no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—42no—
213C4×Dic43—42no—
214C4×Dic43—81no—
215C4×Dic43—81no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C22×C412yes—
222#10621872—44no—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—21no—
237C22×D43C4×D412yes—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—41no—
241D4×C43—41no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43#13712yes—
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C22⋊D43—48no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—48no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43C4×D412yes—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—84no—
291Dic86—22no—
292Dic86—22no—
293Dic86—22no—
294Dic86#11714yes—
295C8×C43—22no—
296C8×C43—41no—
297C43⋊C8—22no—
298C43⋊C8—41no—
299#22579—431nomaximal, Sylow
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43C2×C4×D411yescharacteristic
308C22×C43#54611yescharacteristic
309C22×C43#54611yescharacteristic
310C22×C43C2×#13711yescharacteristic
311C22×C43#57511yescharacteristic
312C22×C43#57611yescharacteristic
313C22×C43#57711yescharacteristic
314C2×D43—22no—
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—41no—
318C2×D43—41no—
319C2×D43—41no—
320C2×D43—41no—
321C4×C43—22no—
322C4×C43—42no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43—81no—
326C4×C43C2×#11711yescharacteristic
327C4×C43#51811yescharacteristic
328C4×C43#55111yescharacteristic
329C4×C43#55111yescharacteristic
330Dic43—24no—
331Dic43—22no—
332Dic43—41no—
333Dic43—42no—
334Dic43—41no—
335Dic43—81no—
336Dic43—81no—
337C2×#417—431no—
338#2345—431no—
339#2341—431no—
340#1936—431no—
341#1934D4311yescharacteristic, complemented
342#1926—431no—
343#1925—431no—
344#1865—431no—
345#1863—431no—
346#1823—431no—
347#1809—431no—
348#1788—431no—
349#1763—431no—
350C4×#103—431no—
351#1753—431no—
352C2×C43—82no—
353C2×C43#234211yescharacteristic
354C2×C43C4×#13711yescharacteristic
355C2×C43#294611yescharacteristic
356C2×C43#330911yescharacteristic
357C2×C43#331611yescharacteristic
358C2×C43#332611yescharacteristic
359C2×C43#333311yescharacteristic
360D43—42no—
361C22×#41—431no—
362C22×M16—431no—
363C2×C4×Q8—431no—
364C2×C4×Q8—431no—
365C22×C4⋊C4—431no—
366C2×#107—431no—
367C2×#106—431no—
368#417—438no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102C2×D4311yescharacteristic
376C2×#102C2×D4311yescharacteristic
377C2×C22⋊C8—431no—
378C2×#97—431no—
379C2×C4×C8C2×D4311yescharacteristic
380#390—431no—
381#390—861no—
382#390—861no—
383#390C2×D4311yescharacteristic
384#389—431no—
385#389C2×D4311yescharacteristic
386#387—861no—
387#387—861no—
388#380—431no—
389#380—431no—
390#380—861no—
391#380—861no—
392C4×C4⋊C4—431no—
393C4×C4⋊C4—431no—
394C4×C22⋊C4—431no—
395C4×C22⋊C4—861no—
396C4×C22⋊C4—861no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#340C2×D4311yescharacteristic
402#340C2×D4311yescharacteristic
403#336—431no—
404#336—431no—
405C43#2257911yescharacteristic, complemented, Sylow
406C2×#41—434no—
407C2×#41—862no—
408C2×#41—862no—
409C2×#41—862no—
410C2×#41—1721no—
411C2×#41—1721no—
412C22×Q8—431no—
413C22×D4—861no—
414C22×D4C22×D4311yescharacteristic
415C23×C4—431no—
416C23×C4—861no—
417C23×C4—861no—
418C2×M16—434no—
419C2×M16—1721no—
420C2×M16—1721no—
421C22×C8—431no—
422C22×C8—431no—
423C22×C8C22×D4311yescharacteristic
424C22×C8C22×D4311yescharacteristic
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—1721no—
428C4×Q8—1721no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—434no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—431no—
445C2×C22⋊C4—431no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—431no—
451C2×C42—861no—
452C2×C42—861no—
453C2×C42—861no—
454C2×C42—861no—
455C2×C42C22×D4311yescharacteristic
456#107—1721no—
457#106—1721no—
458#103—434no—
459#103—434no—
460#103—862no—
461#103—862no—
462#102—41no—
463#102—434no—
464#102—1721no—
465#102C4×D4314yes—
466C22⋊C8—862no—
467#97—1721no—
468C4×C8—41no—
469#95—21no—
470#95—431no—
471#95—431no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477C24—21no—
478C24—431no—
479#41—868no—
480#41—1724no—
481#41—1724no—
482#41—1724no—
483C2×Q8—432no—
484C2×Q8—432no—
485C2×Q8—432no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—864no—
495C2×D4—1722no—
496C2×D4—1722no—
497C2×D4C2×C4×D4312yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—431no—
502C22×C4—432no—
503C22×C4—432no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—864no—
507C22×C4—864no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—3441no—
517C22×C4—3441no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4D4×D4311yescharacteristic
521C22×C4D4×D4311yescharacteristic
522C22×C4C23×D4311yescharacteristic
523M16—1724no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—432no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8C2×C4×D4312yes—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—81no—
542C4⋊C4—432no—
543C4⋊C4—864no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—3441no—
550C4⋊C4—1722no—
551C4⋊C4—1722no—
552C4⋊C4C2×C4×D4312yes—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—862no—
556C22⋊C4—3441no—
557C22⋊C4—3441no—
558C22⋊C4—1721no—
559C22⋊C4—1722no—
560C22⋊C4—1722no—
561C42—21no—
562C42—21no—
563C42—861no—
564C42—861no—
565C42—3441no—
566C42—3441no—
567C42—1722no—
568C42—1722no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—432no—
577C23—861no—
578C23—861no—
579C23—861no—
580C23—861no—
581C23—861no—
582C23—861no—
583C23C2×D4×D4311yescharacteristic
584Q8—434no—
585Q8—862no—
586Q8—862no—
587Q8—862no—
588D4—22no—
589D4—22no—
590D4—41no—
591D4—41no—
592D4—1728no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—432no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—862no—
612C2×C4—861no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—3444no—
625C2×C4—1728no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4#1306335412yes—
635C2×C4C22×C4×D4311yescharacteristic
636C2×C4#41×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4#41×D4311yescharacteristic
639C2×C4#1306337011yescharacteristic
640C2×C4#1306337111yescharacteristic
641C8—22no—
642C8—41no—
643C8—862no—
644C8—1721no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—862no—
653C22—862no—
654C22—862no—
655C22—1721no—
656C22—1721no—
657C22—1721no—
658C22—1721no—
659C22C4×D4×D4311yescharacteristic
660C22#1458353811yescharacteristic
661C22#1458354211yescharacteristic
662C22C2×#1306335411yescharacteristic
663C22#1458369611yescharacteristic
664C22#1458370011yescharacteristic
665C22#1458370611yescharacteristic
666C4—22no—
667C4—41no—
668C4—42no—
669C4—81no—
670C4—81no—
671C4—862no—
672C4—864no—
673C4—3441no—
674C4—3441no—
675C4—1721no—
676C4—1721no—
677C4—1722no—
678C4#117×D4311yescharacteristic
679C4#1458337111yescharacteristic
680C4#1458357411yescharacteristic
681C4#1458357711yescharacteristic
682C2—82no—
683C2—1722no—
684C2#1913744311yescharacteristic
685C2C4×#1306335411yescharacteristic
686C2#1914342011yescharacteristic
687C2#1914660711yescharacteristic
688C2#1914671211yescharacteristic
689C2#1914684711yescharacteristic
690C2#1914693211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1934D43
hypocenterC43#22579
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #19137471C2semidirect
4. #19135294C2semidirect
5. #19135219C2semidirect
6. #19135218C2semidirect
7. #19134864C2semidirect
8. #19134848C2semidirect
9. #19134680C2semidirect
10. #19134627C2semidirect
12. #19134424C2semidirect
13. C4×#13063250C2semidirect
14. #19134378C2semidirect
15. C43×#1934C2semidirect
23. #14582897C4semidirect
341. #1934D43semidirect
405. C43#22579semidirect

Maximal subgroups

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

subgroupindex
C2×#145828972
#191374712
#191374342
#191352942
#191352192
#191352182
#191348642
#191348482
#191346802
#191346272
#191345322
#191344242
C4×#130632502
#191343782
C43×#19342
#2257943