Finite Group Databasebeta

← #25135405

Subgroups — #25135405

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583053C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic
3#19140395C211yesmaximal, characteristic
4#19137178C211yesmaximal, characteristic
5#19135989C211yesmaximal, characteristic, complemented
6#19135976C211yesmaximal, characteristic, complemented
7#19135917C211yesmaximal, characteristic, complemented
8#19135463C211yesmaximal, characteristic, complemented
9#19135457C211yesmaximal, characteristic, complemented
10#19135287C211yesmaximal, characteristic, complemented
11#19135272C211yesmaximal, characteristic, complemented
12#19134904C211yesmaximal, characteristic
13#19134797C211yesmaximal, characteristic
14#19134528C211yesmaximal, characteristic
15C43×#2056C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21#14583053—24no—
22#14582959—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582840—21no—
37#14582833—21no—
38#14582828—21no—
39#14582826—21no—
40#14582806C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582805C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582803—21no—
45#14582803—21no—
46#14582798C2211yescharacteristic
47#14582797C2211yescharacteristic
48#14582761—21no—
49#14582761—21no—
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C22×Q16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—41no—
68C2×Q8×D43—41no—
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C2×#10621885—22no—
72C2×#10621885—22no—
73C2×#10621885—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063301—22no—
77#13063301—22no—
78#13063283—41no—
79#13063283—41no—
80#13063282—22no—
81#13063282—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4D411yescharacteristic
89C2×Dic43⋊C4D411yescharacteristic
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—
96C2×C4×Dic43C2311yescharacteristic
97#13063259—41no—
98#13063256—41no—
99C4⋊(C43⋊C8)—22no—
100#13063250—22no—
101#13063250—41no—
102#13063249—22no—
103#13063249—41no—
104#13063249—41no—
105#13063248—22no—
106(C2×D43)⋊C8—22no—
107(C2×D43)⋊C8D414yes—
108#13063235—22no—
109C8×Dic43—22no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123C2×Q16×C43—22no—
124C2×Q16×C43—22no—
125C2×Q16×C43—41no—
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—22no—
132#103×C43—22no—
133#103×C43—41no—
134#95×C43—21no—
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—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43#4112yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165Q8×D43—44no—
166Q8×D43—44no—
167Q8×D43—44no—
168Q8×D43—44no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—24no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43C2×D412yes—
177C2×C4×D43#4112yes—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—24no—
183C2×Dic86—21no—
184C2×Dic86—42no—
185C2×Dic86—42no—
186C2×Dic86#4112yes—
187Q16×C43—44no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×D412yes—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200#10621885—44no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—42no—
205(C2×D43)⋊C4—81no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—81no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—42no—
216Dic43⋊C4—81no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—42no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C2×D412yes—
226C23×C43C22×D411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43#12112yes—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43—41no—
239Q8×C43—41no—
240Q8×C43—41no—
241Q8×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—21no—
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—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
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—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—48no—
292Dic86—22no—
293Dic86—22no—
294Dic86—48no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—22no—
298C8×C43—41no—
299C43⋊C8—22no—
300C43⋊C8—41no—
301#24514—431nomaximal, Sylow
302C22×C43C2×#12111yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43#53511yescharacteristic
305C22×C43#57711yescharacteristic
306C22×C43#57811yescharacteristic
307C22×C43#57811yescharacteristic
308C22×C43#57811yescharacteristic
309C2×D43—22no—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#54611yescharacteristic
323C4×C43#54611yescharacteristic
324C4×C43#55111yescharacteristic
325C4×C43#55111yescharacteristic
326Dic43—22no—
327Dic43—42no—
328Dic43—41no—
329Dic43—41no—
330Dic43—81no—
331Dic43—81no—
332Dic43—81no—
333C2×#451—431no—
334C2×#433—431no—
335#2625—431no—
336#2310—431no—
337#2068—431no—
338#2066—431no—
339#2056—431no—
340#2056D4311yescharacteristic, complemented
341#1971—431no—
342#1969—431no—
343#1935—431no—
344#1933—431no—
345#1873—431no—
346#1854—431no—
347#1787—431no—
348C2×C43#241111yescharacteristic
349C2×C43#305911yescharacteristic
350C2×C43#306311yescharacteristic
351C2×C43#312111yescharacteristic
352C2×C43#312711yescharacteristic
353C2×C43#322311yescharacteristic
354C2×C43#322511yescharacteristic
355D43—42no—
356C23×Q8—431no—
357C22×Q16—431no—
358C22×Q16C2×D4311yescharacteristic
359C2×C22⋊Q8—431no—
360C2×#117—431no—
361C2×#117—431no—
362#451—864no—
363#433—864no—
364C2×#107—431no—
365C2×#106—431no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8C2×D4311yescharacteristic
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103C2×D4311yescharacteristic
375C2×#103C2×D4311yescharacteristic
376C2×C22⋊C8—431no—
377C2×C22⋊C8—431no—
378C2×#97—431no—
379C2×C4×C8—431no—
380#400—861no—
381#398—861no—
382#397—861no—
383#397—861no—
384#391—431no—
385#391—431no—
386#391—431no—
387#391—431no—
388#391—861no—
389#391—861no—
390#391C2×D4311yescharacteristic
391#391C2×D4311yescharacteristic
392#389—431no—
393#389—431no—
394#381—861no—
395#381—861no—
396#380—431no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340C2×D4311yescharacteristic
401C43#2451411yescharacteristic, complemented, Sylow
402C22×Q8—431no—
403C22×Q8—861no—
404C22×Q8—862no—
405C22×Q8—862no—
406C22×Q8—862no—
407C22×Q8—862no—
408C22×Q8—1721no—
409C22×Q8—1721no—
410C22×Q8C22×D4311yescharacteristic
411C22×Q8C22×D4311yescharacteristic
412C23×C4—431no—
413C23×C4—861no—
414C2×Q16—22no—
415C2×Q16—22no—
416C2×Q16—41no—
417C2×Q16—862no—
418C2×Q16—862no—
419C2×Q16—1721no—
420C22×C8—431no—
421C22×C8—431no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C22⋊Q8—862no—
425C22⋊Q8—862no—
426#117—862no—
427#117—862no—
428#117—1721no—
429#117—1721no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—431no—
441C2×C22⋊C4—431no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C42—431no—
446C2×C42—861no—
447C2×C42C22×D4311yescharacteristic
448#107—1721no—
449#106—1721no—
450C4⋊C8—22no—
451C4⋊C8—862no—
452#103—22no—
453#103—41no—
454#103—862no—
455#103—862no—
456#103—862no—
457#103—1721no—
458#103—1721no—
459#103—1721no—
460C22⋊C8—434no—
461C22⋊C8—862no—
462#97—862no—
463C4×C8—862no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—431no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—432no—
492C2×Q8—864no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—1722no—
499C2×Q8—1722no—
500C2×Q8—1724no—
501C2×Q8—1724no—
502C2×Q8—1724no—
503C2×Q8—1724no—
504C2×Q8#1062190012yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—431no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—864no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4D4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527C22×C4C23×D4311yescharacteristic
528Q16—44no—
529Q16—1724no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—432no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8D4×D4312yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—3441no—
555C4⋊C4—3441no—
556C4⋊C4—1722no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—3441no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C42—21no—
563C42—21no—
564C42—861no—
565C42—861no—
566C42—1722no—
567C23—432no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23—861no—
572C23—861no—
573C23—861no—
574C23C2×D4×D4311yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—862no—
584Q8—862no—
585Q8—1728no—
586Q8—1721no—
587Q8—1721no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—432no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—1728no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4C2×D4×D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4#41×D4311yescharacteristic
635C2×C4C2×#1062190011yescharacteristic
636C2×C4#1306337011yescharacteristic
637C2×C4#1306337111yescharacteristic
638C8—22no—
639C8—41no—
640C8—862no—
641C8—1721no—
642C22—862no—
643C22—862no—
644C22—862no—
645C22—1721no—
646C22—1721no—
647C22—1721no—
648C22—1721no—
649C22#121×D4311yescharacteristic
650C22#1458340911yescharacteristic
651C22#1458346511yescharacteristic
652C22#1458370811yescharacteristic
653C22#1458371211yescharacteristic
654C22#1458371311yescharacteristic
655C22#1458371511yescharacteristic
656C4—41no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—862no—
663C4—3441no—
664C4—3441no—
665C4—3441no—
666C4—1721no—
667C4—1721no—
668C4—1722no—
669C4#1458353611yescharacteristic
670C4#1458354211yescharacteristic
671C4#1458357211yescharacteristic
672C4#1458357711yescharacteristic
673C2—1722no—
674C2#1913797311yescharacteristic
675C2#1914424511yescharacteristic
676C2#1914428311yescharacteristic
677C2#1914482311yescharacteristic
678C2#1914489311yescharacteristic
679C2#1914567511yescharacteristic
680C2#1914571111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2056C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2056D43
hypocenterC43#24514
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2056

Complements

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

NH ≅ G/Ntype
5. #19135989C2semidirect
6. #19135976C2semidirect
7. #19135917C2semidirect
8. #19135463C2semidirect
9. #19135457C2semidirect
10. #19135287C2semidirect
11. #19135272C2semidirect
15. C43×#2056C2semidirect
340. #2056D43semidirect
401. C43#24514semidirect

Maximal subgroups

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

subgroupindex
C2×#145830532
C2×#145829592
#191403952
#191371782
#191359892
#191359762
#191359172
#191354632
#191354572
#191352872
#191352722
#191349042
#191347972
#191345282
C43×#20562
#2451443