Finite Group Databasebeta

← #25134999

Subgroups — #25134999

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583236C211yesmaximal, characteristic
2C2×#103×D43C211yesmaximal, characteristic
3#19138238C211yesmaximal, characteristic
4#19137471C211yesmaximal, characteristic
5#19135985C211yesmaximal, characteristic, complemented
6#19135841C211yesmaximal, characteristic, complemented
7#19135840C211yesmaximal, characteristic, complemented
8#19135517C211yesmaximal, characteristic, complemented
9#19135516C211yesmaximal, characteristic, complemented
10#19135234C211yesmaximal, characteristic, complemented
11#19135233C211yesmaximal, characteristic, complemented
12#19135017C211yesmaximal, characteristic
13#19134771C211yesmaximal, characteristic
14#19134528C211yesmaximal, characteristic
15C43×#2068C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063305C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14583236—24no—
23C2×#13063258C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35#103×D43—24no—
36C2×(C2×D43)⋊C8C2211yescharacteristic
37#14582820—21no—
38#14582820—21no—
39#14582804C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582786—21no—
42#14582780—21no—
43#14582773—21no—
44#14582773—21no—
45#14582756—21no—
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582746—21no—
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—41no—
69C2×Q8×D43—41no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C2×C8×D43—22no—
76C2×C8×D43—41no—
77C2×C8×D43—41no—
78#13063325—22no—
79#13063325—41no—
80#13063323—22no—
81#13063323—41no—
82#13063305—22no—
83#13063305—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43D414yes—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063258—22no—
103Dic43⋊C8—41no—
104#13063250—22no—
105#13063250—22no—
106#13063250—41no—
107#13063250—41no—
108#13063249—22no—
109#13063249—22no—
110#13063248—22no—
111#13063248—22no—
112#13063248—22no—
113#13063248—41no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95D411yescharacteristic
122C43⋊#95D411yescharacteristic
123C22×Q8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132C4⋊C8×C43—41no—
133#103×C43—22no—
134#103×C43—41no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C23×D43C2×D411yescharacteristic
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43#4112yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159Q8×D43—28no—
160Q8×D43—44no—
161Q8×D43—44no—
162Q8×D43—44no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—24no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×C4×D43C2×D412yes—
174C2×C4×D43#4112yes—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—42no—
187C2×Dic86—42no—
188C2×Dic86—42no—
189C2×Dic86#4112yes—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—81no—
202C4⋊C4×C43C2×D412yes—
203C42×C43—21no—
204C42×C43—21no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4Q1614yes—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—42no—
213C4⋊Dic43—42no—
214C4⋊Dic43—42no—
215C4⋊Dic43—81no—
216C4⋊Dic43C2×D412yes—
217Dic43⋊C4—24no—
218Dic43⋊C4—42no—
219Dic43⋊C4—42no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—81no—
223C4×Dic43—81no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C8×D43—44no—
231C23×C43C22×D411yescharacteristic
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—21no—
236C22×D43#12112yes—
237C22×D43C2×Q1612yes—
238C22×D43#13712yes—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43—41no—
242Q8×C43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
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—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43C2×Q1612yes—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
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×Dic43—41no—
286C2×Dic43#12112yes—
287C2×Dic43C2×Q1612yes—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—48no—
293C4×D43—84no—
294Dic86—22no—
295Dic86—22no—
296Dic86—48no—
297Dic86—41no—
298Dic86—41no—
299Dic86—41no—
300Dic86—41no—
301Dic86—41no—
302Dic86—41no—
303C8×C43—41no—
304C8×C43—41no—
305C43⋊C8—41no—
306C43⋊C8—41no—
307#24482—431nomaximal, Sylow
308C22×C43C2×#12111yescharacteristic
309C22×C43#54611yescharacteristic
310C22×C43#54611yescharacteristic
311C22×C43C22×Q1611yescharacteristic
312C22×C43C2×#13711yescharacteristic
313C22×C43#57711yescharacteristic
314C22×C43#57711yescharacteristic
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—22no—
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—22no—
321C2×D43#46214yes—
322C4×C43—22no—
323C4×C43—42no—
324C4×C43—42no—
325C4×C43—41no—
326C4×C43—81no—
327C4×C43—81no—
328C4×C43#52511yescharacteristic
329C4×C43#53511yescharacteristic
330C4×C43#55111yescharacteristic
331C4×C43#55111yescharacteristic
332Dic43—22no—
333Dic43—22no—
334Dic43—42no—
335Dic43—42no—
336Dic43—41no—
337Dic43—81no—
338Dic43—81no—
339C2×#484—431no—
340C22×#103—431no—
341#2434—431no—
342#2345—431no—
343#2068—431no—
344#2068D4311yescharacteristic, complemented
345#2043—431no—
346#2043—431no—
347#1981—431no—
348#1981—431no—
349#1928—431no—
350#1928—431no—
351#1892—431no—
352#1850—431no—
353#1787—431no—
354C2×C43#241111yescharacteristic
355C2×C43C2×#46211yescharacteristic
356C2×C43#304211yescharacteristic
357C2×C43#329911yescharacteristic
358C2×C43#329911yescharacteristic
359C2×C43#332011yescharacteristic
360C2×C43#332011yescharacteristic
361D43—24no—
362C23×Q8—431no—
363C23×C8—431no—
364C2×C4⋊Q8—431no—
365C2×C4⋊Q8—431no—
366C2×C22⋊Q8—431no—
367C22×C4⋊C4—431no—
368#484—864no—
369C2×#107—431no—
370C2×#107C2×D4311yescharacteristic
371C2×C4⋊C8—431no—
372C2×C4⋊C8C2×D4311yescharacteristic
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—864no—
384C2×#103C2×D4311yescharacteristic
385C2×#103C2×D4311yescharacteristic
386C2×C22⋊C8—431no—
387#395—861no—
388#395—861no—
389#391—431no—
390#391C2×D4311yescharacteristic
391#389—431no—
392#389C2×D4311yescharacteristic
393#387—861no—
394#387—861no—
395#385—861no—
396#385—861no—
397#380—431no—
398#380—861no—
399C4×C4⋊C4—431no—
400C4×C4⋊C4—431no—
401C4×C22⋊C4—431no—
402C4×C22⋊C4—861no—
403#340—431no—
404#340C2×D4311yescharacteristic
405#336—431no—
406#336—431no—
407C43#2448211yescharacteristic, complemented, Sylow
408C22×Q8—431no—
409C22×Q8—431no—
410C22×Q8—861no—
411C22×Q8—862no—
412C22×Q8—862no—
413C22×Q8—862no—
414C22×Q8—862no—
415C22×Q8—1721no—
416C22×Q8—1721no—
417C22×Q8C22×D4311yescharacteristic
418C23×C4—431no—
419C23×C4—861no—
420C23×C4—861no—
421C22×C8—431no—
422C22×C8—431no—
423C22×C8—862no—
424C22×C8—1721no—
425C22×C8—1721no—
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428C4⋊Q8—862no—
429C4⋊Q8—862no—
430C4⋊Q8—1721no—
431C4⋊Q8—1721no—
432C22⋊Q8—862no—
433C22⋊Q8—862no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—434no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C22⋊C4—431no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C42—431no—
454C2×C42—861no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457#107—22no—
458#107—862no—
459C4⋊C8—41no—
460C4⋊C8—1721no—
461#103—22no—
462#103—41no—
463#103—862no—
464#103—862no—
465#103—862no—
466#103—862no—
467#103—862no—
468#103—862no—
469#103—862no—
470#103—1721no—
471#103—1721no—
472#103—1721no—
473C22⋊C8—862no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—431no—
478#95—431no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95—861no—
485C24—431no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—432no—
492C2×Q8—861no—
493C2×Q8—868no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—1722no—
505C2×Q8—1722no—
506C2×Q8—1722no—
507C2×Q8—1724no—
508C2×Q8—1724no—
509C2×Q8—1724no—
510C2×Q8#1062190212yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—432no—
518C22×C4—432no—
519C22×C4—431no—
520C22×C4—864no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—3441no—
530C22×C4—3441no—
531C22×C4—1722no—
532C22×C4—1722no—
533C22×C4—1722no—
534C22×C4D4×D4311yescharacteristic
535C22×C4D4×D4311yescharacteristic
536C22×C4C23×D4311yescharacteristic
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—1724no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—81no—
556C4⋊C4—432no—
557C4⋊C4—864no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—3441no—
562C4⋊C4—1722no—
563C4⋊C4—1722no—
564C4⋊C4—1722no—
565C4⋊C4—1722no—
566C4⋊C4—1722no—
567C4⋊C4D4×D4312yes—
568C22⋊C4—434no—
569C22⋊C4—862no—
570C22⋊C4—1722no—
571C22⋊C4—1722no—
572C42—21no—
573C42—21no—
574C42—861no—
575C42—861no—
576C42—3441no—
577C42—3441no—
578C23—432no—
579C23—432no—
580C23—432no—
581C23—861no—
582C23—861no—
583C23—861no—
584C23—861no—
585C23C2×D4×D4311yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590Q8—862no—
591Q8—862no—
592Q8—1728no—
593Q8—1721no—
594Q8—1721no—
595Q8—1721no—
596Q8—1721no—
597Q8—1721no—
598Q8—1721no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—432no—
617C2×C4—432no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—862no—
630C2×C4—861no—
631C2×C4—3444no—
632C2×C4—1728no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4Q16×D4312yes—
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4C2×#1062190211yescharacteristic
648C2×C4#1306337011yescharacteristic
649C2×C4#1306337111yescharacteristic
650C8—41no—
651C8—41no—
652C8—1721no—
653C8—1721no—
654C22—434no—
655C22—862no—
656C22—862no—
657C22—862no—
658C22—862no—
659C22—862no—
660C22—862no—
661C22#121×D4311yescharacteristic
662C22#1458353811yescharacteristic
663C22#1458354011yescharacteristic
664C22C2×Q16×D4311yescharacteristic
665C22#137×D4311yescharacteristic
666C22#1458370611yescharacteristic
667C22#1458370911yescharacteristic
668C4—22no—
669C4—41no—
670C4—42no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—862no—
675C4—862no—
676C4—3441no—
677C4—3441no—
678C4—1721no—
679C4—1722no—
680C4—1722no—
681C4#1458341211yescharacteristic
682C4#1458346511yescharacteristic
683C4#1458357411yescharacteristic
684C4#1458357611yescharacteristic
685C2—864no—
686C2#1913797511yescharacteristic
687C2#462×D4311yescharacteristic
688C2#1914410511yescharacteristic
689C2#1914646611yescharacteristic
690C2#1914646811yescharacteristic
691C2#1914676111yescharacteristic
692C2#1914676311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2068C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2068D43
hypocenterC43#24482
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2068

Complements

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

NH ≅ G/Ntype
5. #19135985C2semidirect
6. #19135841C2semidirect
7. #19135840C2semidirect
8. #19135517C2semidirect
9. #19135516C2semidirect
10. #19135234C2semidirect
11. #19135233C2semidirect
15. C43×#2068C2semidirect
344. #2068D43semidirect
407. C43#24482semidirect

Maximal subgroups

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

subgroupindex
C2×#145832362
C2×#103×D432
#191382382
#191374712
#191359852
#191358412
#191358402
#191355172
#191355162
#191352342
#191352332
#191350172
#191347712
#191345282
C43×#20682
#2448243