Finite Group Databasebeta

← #25135410

Subgroups — #25135410

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×#14583057C211yesmaximal, characteristic
2C2×#14582957C211yesmaximal, characteristic
3#19140394C211yesmaximal, characteristic
4#19137179C211yesmaximal, characteristic
5#19135985C211yesmaximal, characteristic, complemented
6#19135971C211yesmaximal, characteristic, complemented
7#19135919C211yesmaximal, characteristic, complemented
8#19135919C211yesmaximal, characteristic, complemented
9#19135464C211yesmaximal, characteristic, complemented
10#19135454C211yesmaximal, characteristic, complemented
11#19135286C211yesmaximal, characteristic, complemented
12#19135272C211yesmaximal, characteristic, complemented
13#19134907C211yesmaximal, characteristic
14#19134529C211yesmaximal, characteristic
15C43×#1854C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583057—24no—
22#14582957—24no—
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582839—21no—
37#14582831—21no—
38#14582824—21no—
39#14582824—21no—
40#14582805—21no—
41#14582805—21no—
42#14582804C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582804C2211yescharacteristic
45#14582804C2211yescharacteristic
46#14582804C2211yescharacteristic
47#14582804C2211yescharacteristic
48#14582798C2211yescharacteristic
49#14582798C2211yescharacteristic
50#14582760—21no—
51#14582760—21no—
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C22×Dic86C2311yescharacteristic
71C23×Dic43—21no—
72C2×Dic172—22no—
73C2×Dic172—22no—
74C2×Dic172—22no—
75C2×Dic172—22no—
76C2×Dic172—41no—
77C2×Dic172—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063304—22no—
81#13063304—22no—
82#13063284—22no—
83#13063284—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43D411yescharacteristic
92C2×C22⋊Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95Dic43⋊C8—22no—
96Dic43⋊C8—22no—
97#13063250—22no—
98#13063250—22no—
99#13063248—22no—
100#13063248—22no—
101#13063248—41no—
102#13063248—41no—
103#13063248—41no—
104#13063248—41no—
105C22⋊(C43⋊C8)—22no—
106#13063235—22no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
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—
121C43⋊#95—21no—
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125#117×C43—41no—
126#117×C43—41no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43—21no—
134#107×C43—41no—
135#106×C43—41no—
136C22⋊C8×C43D414yes—
137#95×C43—21no—
138C24×C43C2×D411yescharacteristic
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43#4112yes—
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—24no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—24no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—44no—
180C2×Dic86—44no—
181C2×Dic86—44no—
182C2×Dic86—44no—
183C2×Dic86—42no—
184C2×Dic86—42no—
185C2×Dic86#4112yes—
186C2×Dic86#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43C2×D412yes—
192C2×C8×C43C2×D412yes—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C22⋊C4×C43—42no—
202C22⋊C4×C43—81no—
203C42×C43—42no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206C22⋊Dic43—42no—
207C4⋊Dic43—22no—
208C4⋊Dic43—22no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—81no—
212C4⋊Dic43—81no—
213Dic43⋊C4—42no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224Dic172—44no—
225Dic172—44no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43#12112yes—
233C23×C43C22×D411yescharacteristic
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
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—41no—
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×C43H(5,𝔽2)11yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—48no—
274C2×Dic43—41no—
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—
284Dic86—22no—
285Dic86—22no—
286Dic86—22no—
287Dic86—22no—
288Dic86—48no—
289Dic86—41no—
290Dic86—41no—
291Dic86—41no—
292Dic86—41no—
293Dic86—41no—
294Dic86—41no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—22no—
298C8×C43—22no—
299C43⋊C8—41no—
300C43⋊C8—41no—
301#24514—431nomaximal, Sylow
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43C2×#12111yescharacteristic
310C22×C43#52511yescharacteristic
311C22×C43#53511yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57811yescharacteristic
314C22×C43#57811yescharacteristic
315C22×C43#57811yescharacteristic
316C4×C43—22no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43#54611yescharacteristic
322C4×C43#54611yescharacteristic
323C4×C43#55111yescharacteristic
324C4×C43#55111yescharacteristic
325Dic43—42no—
326Dic43—42no—
327Dic43—41no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
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#2056—431no—
341#1971—431no—
342#1969—431no—
343#1935—431no—
344#1933—431no—
345#1873—431no—
346#1854D4311yescharacteristic
347#1787—431no—
348C2×C43—42no—
349C2×C43#241111yescharacteristic
350C2×C43#305911yescharacteristic
351C2×C43#306311yescharacteristic
352C2×C43#312111yescharacteristic
353C2×C43#312711yescharacteristic
354C2×C43#322311yescharacteristic
355C2×C43#322511yescharacteristic
356C23×Q8—431no—
357C22×Q16—431no—
358C22×Q16—431no—
359C2×C22⋊Q8—431no—
360C2×#117—431no—
361C2×#117C2×D4311yescharacteristic
362#451—864no—
363#433—864no—
364C2×#107C2×D4311yescharacteristic
365C2×#106C2×D4311yescharacteristic
366C2×C4⋊C8—431no—
367C2×C4⋊C8—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×C22⋊C8—431no—
377C2×C22⋊C8C2×D4311yescharacteristic
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—431no—
389#391—431no—
390#391—861no—
391#391—861no—
392#389—431no—
393#389—431no—
394#381—861no—
395#381—861no—
396#380C2×D4311yescharacteristic
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400#340C2×D4311yescharacteristic
401C43#2451411yescharacteristic, complemented, Sylow
402C22×Q8—431no—
403C22×Q8—431no—
404C22×Q8—431no—
405C22×Q8—862no—
406C22×Q8—862no—
407C22×Q8—861no—
408C22×Q8—862no—
409C22×Q8—862no—
410C22×Q8—1721no—
411C22×Q8—1721no—
412C23×C4—861no—
413C23×C4C22×D4311yescharacteristic
414C2×Q16—862no—
415C2×Q16—862no—
416C2×Q16—862no—
417C2×Q16—862no—
418C2×Q16—1721no—
419C2×Q16—1721no—
420C22×C8—431no—
421C22×C8—431no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C22⋊Q8—862no—
425C22⋊Q8—862no—
426#117—41no—
427#117—41no—
428#117—862no—
429#117—862no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—431no—
443C2×C22⋊C4—431no—
444C2×C22⋊C4—861no—
445C2×C42—21no—
446C2×C42—431no—
447C2×C42—431no—
448#107—41no—
449#106—41no—
450C4⋊C8—862no—
451C4⋊C8—862no—
452#103—862no—
453#103—862no—
454#103—862no—
455#103—862no—
456#103—1721no—
457#103—1721no—
458#103—1721no—
459#103—1721no—
460C22⋊C8—862no—
461C22⋊C8D17214yes—
462#97—862no—
463C4×C8—862no—
464#95—21no—
465#95—861no—
466#95—861no—
467#95—861no—
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—
479C24D4×D4311yescharacteristic
480C2×Q8—432no—
481C2×Q8—432no—
482C2×Q8—864no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—1724no—
500C2×Q8—1724no—
501C2×Q8—1724no—
502C2×Q8—1724no—
503C2×Q8—1722no—
504C2×Q8—1722no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—864no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4C2×D17212yes—
525C22×C4D4×D4311yescharacteristic
526C22×C4#1062190212yes—
527C22×C4C23×D4311yescharacteristic
528Q16—1724no—
529Q16—1724no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8C2×D17212yes—
541C2×C8C2×D17212yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—862no—
551C4⋊C4—862no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—3441no—
555C4⋊C4—3441no—
556C4⋊C4—1722no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—1722no—
562C42—42no—
563C42—861no—
564C42—861no—
565C42—861no—
566C42—861no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#1306330012yes—
574C23C2×D4×D4311yescharacteristic
575Q8—862no—
576Q8—862no—
577Q8—862no—
578Q8—862no—
579Q8—1728no—
580Q8—1721no—
581Q8—1721no—
582Q8—1721no—
583Q8—1721no—
584Q8—1721no—
585Q8—1721no—
586Q8—1721no—
587Q8—1721no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
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—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1728no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4#1306330012yes—
632C2×C4C22×D17211yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4#41×D4311yescharacteristic
635C2×C4C2×#1062190211yescharacteristic
636C2×C4#1306337011yescharacteristic
637C2×C4#1306337011yescharacteristic
638C8—22no—
639C8—22no—
640C8—1721no—
641C8—1721no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#1306330011yescharacteristic
650C22#1458340711yescharacteristic
651C22#1458346411yescharacteristic
652C22#1458370911yescharacteristic
653C22#1458371311yescharacteristic
654C22#1458371311yescharacteristic
655C22#1458371511yescharacteristic
656C4—22no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—3441no—
662C4—3441no—
663C4—1721no—
664C4—1721no—
665C4—1721no—
666C4—1721no—
667C4—1722no—
668C4—1722no—
669C4#1458354411yescharacteristic
670C4#1458354411yescharacteristic
671C4#1458357611yescharacteristic
672C4#1458357611yescharacteristic
673C2—42no—
674C2#1913797811yescharacteristic
675C2#1914425111yescharacteristic
676C2#1914428711yescharacteristic
677C2#1914481911yescharacteristic
678C2#1914489111yescharacteristic
679C2#1914567611yescharacteristic
680C2#1914570011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1854D43
hypocenterC43#24514
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
5. #19135985C2semidirect
6. #19135971C2semidirect
7. #19135919C2semidirect
8. #19135919C2semidirect
9. #19135464C2semidirect
10. #19135454C2semidirect
11. #19135286C2semidirect
12. #19135272C2semidirect
401. C43#24514semidirect

Maximal subgroups

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

subgroupindex
C2×#145830572
C2×#145829572
#191403942
#191371792
#191359852
#191359712
#191359192
#191354642
#191354542
#191352862
#191352722
#191349072
#191345292
C43×#18542
#2451443