Finite Group Databasebeta

← #25151027

Subgroups — #25151027

Order 11008.

968 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583509C211yesmaximal, characteristic
2C2×#14583307C211yesmaximal, characteristic, complemented
3C2×#14583248C211yesmaximal, characteristic, complemented
4#19140420C211yesmaximal, characteristic
5#19135795C211yesmaximal, characteristic
6#19135792C211yesmaximal, characteristic
7#19135791C211yesmaximal, characteristic
8#19135558C211yesmaximal, characteristic, complemented
9#19135413C211yesmaximal, characteristic, complemented
10#19134865C211yesmaximal, characteristic, complemented
11#19134861C211yesmaximal, characteristic, complemented
12#19134850C211yesmaximal, characteristic, complemented
13#19134846C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic
15C43×#2036C211yesmaximal, characteristic
16#14583509—24no—
17#14583509—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063318—21no—
21C2×#13063318—21no—
22C2×#13063316—21no—
23C2×#13063316C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063304C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#14583307—24no—
30#14583248—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063257C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063235C2211yescharacteristic
42C2×C8×Dic43C2211yescharacteristic
43#14582841—21no—
44#14582835—21no—
45#14582820—21no—
46#14582811—21no—
47#14582798C2211yescharacteristic
48#14582795C2211yescharacteristic
49#14582764C2211yescharacteristic
50#14582759C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—22no—
68#13063324—22no—
69#13063323—22no—
70#13063323D414yes—
71#13063318—28no—
72#13063318—28no—
73#13063316—28no—
74#13063316—22no—
75#13063316D414yes—
76#13063315—28no—
77#13063304—22no—
78#13063304—22no—
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81#13063290—22no—
82#13063290—22no—
83#13063284—22no—
84#13063284—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43D411yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43D411yescharacteristic
103C2×C22⋊Dic43D411yescharacteristic
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108#13063258—22no—
109#13063257—22no—
110#13063256—22no—
111#13063250—22no—
112#13063250—22no—
113#13063249—22no—
114#13063249—22no—
115#13063248—22no—
116#13063248—22no—
117C22⋊(C43⋊C8)—22no—
118#13063235—22no—
119C8×Dic43—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22⋊Q8×C43—22no—
130C22⋊Q8×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137#107×C43—22no—
138#103×C43—22no—
139#103×C43—22no—
140C22⋊C8×C43—22no—
141#95×C43—21no—
142C24×C43C2×D411yescharacteristic
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D412yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—42no—
175C2×Dic86—81no—
176C2×Dic86—81no—
177C2×Dic86C2×D412yes—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43#4112yes—
184C4⋊C4×C43—24no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43C2×D412yes—
191C22⋊C4×C43—24no—
192C22⋊C4×C43—81no—
193C22⋊Dic43—24no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—81no—
197C4⋊Dic43—24no—
198C4⋊Dic43—21no—
199C4⋊Dic43—24no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—81no—
207C4⋊Dic43C2×D412yes—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—42no—
214Dic43⋊C4—81no—
215C4×Dic43—24no—
216C4×Dic43—24no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43C2×D412yes—
220C4×Dic43C2×D412yes—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8#4112yes—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43C22×D411yescharacteristic
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—41no—
238Q8×C43—41no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
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—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
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#12012yes—
287C2×Dic43#12012yes—
288Dic86—22no—
289Dic86—22no—
290Dic86—41no—
291Dic86—41no—
292Dic86—84no—
293C8×C43—22no—
294C8×C43—41no—
295C43⋊C8—22no—
296C43⋊C8—41no—
297#25686—431nomaximal, Sylow
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43C2×#12011yescharacteristic
306C22×C43#53211yescharacteristic
307C22×C43#53611yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57811yescharacteristic
311C22×C43#57811yescharacteristic
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43#54711yescharacteristic
318C4×C43#54711yescharacteristic
319C4×C43#54811yescharacteristic
320C4×C43#54811yescharacteristic
321Dic43—22no—
322Dic43—22no—
323Dic43—42no—
324Dic43—41no—
325Dic43—41no—
326Dic43—42no—
327Dic43—81no—
328Dic43—81no—
329C2×#541—431no—
330C2×#501—431no—
331C2×#487—431no—
332#2628—431no—
333#2036—431no—
334#2036D4311yescharacteristic
335#2035—431no—
336#2035—431no—
337#1991—431no—
338#1960—431no—
339#1865—431no—
340#1865—431no—
341#1863—431no—
342#1863—431no—
343#1750—431no—
344C2×C43—81no—
345C2×C43#243211yescharacteristic
346C2×C43#301011yescharacteristic
347C2×C43#301111yescharacteristic
348C2×C43#317811yescharacteristic
349C2×C43#317811yescharacteristic
350C2×C43#324211yescharacteristic
351C2×C43#324211yescharacteristic
352#541—864no—
353#541—864no—
354C2×C4⋊Q8—431no—
355C2×C4⋊Q8—431no—
356C2×#126—861no—
357C2×#126—861no—
358C2×#125—431no—
359C2×#125—861no—
360C2×#125—861no—
361C2×C22⋊Q8—431no—
362C2×C22⋊Q8C2×D4311yescharacteristic
363C2×C4×Q8—431no—
364C2×C4×Q8—431no—
365C2×#117—431no—
366#501—864no—
367#487—864no—
368C2×#107—431no—
369C2×#107C2×D4311yescharacteristic
370C2×#106—431no—
371C2×#106—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103C2×D4311yescharacteristic
379C2×#103C2×D4311yescharacteristic
380C2×C22⋊C8—431no—
381C2×C22⋊C8C2×D4311yescharacteristic
382C2×#97—431no—
383C2×C4×C8—431no—
384#400—861no—
385#399—861no—
386#395—861no—
387#393—861no—
388#389—431no—
389#389—431no—
390#382—431no—
391#380—431no—
392#380C2×D4311yescharacteristic
393#340—431no—
394#340—431no—
395#340—431no—
396#340C2×D4311yescharacteristic
397#336—431no—
398#336—431no—
399C43#2568611yescharacteristic, complemented, Sylow
400C22×Q8—431no—
401C22×Q8—861no—
402C22×Q8C22×D4311yescharacteristic
403C23×C4C22×D4311yescharacteristic
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408C4⋊Q8—434no—
409C4⋊Q8—862no—
410C4⋊Q8—862no—
411C4⋊Q8—862no—
412#126—868no—
413#126—868no—
414#125—434no—
415#125—862no—
416#125—868no—
417#125—868no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—862no—
421C22⋊Q8—862no—
422C4×Q8—862no—
423C4×Q8—862no—
424C4×Q8—862no—
425C4×Q8—862no—
426#117—862no—
427#117—862no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—431no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—861no—
456C2×C42—861no—
457#107—22no—
458#107—862no—
459#106—862no—
460#106—862no—
461#103—22no—
462#103—22no—
463#103—862no—
464#103—862no—
465#103—862no—
466#103—862no—
467#103—862no—
468#103—862no—
469C22⋊C8—22no—
470C22⋊C8—862no—
471#97—862no—
472C4×C8—862no—
473#95—21no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24D4×D4311yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—432no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—3441no—
492C2×Q8—3441no—
493C2×Q8—1722no—
494C2×Q8D4×D4312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4D4×D4311yescharacteristic
514C22×C4C23×D4311yescharacteristic
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—432no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8#1062190012yes—
527C4⋊C4—24no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—432no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—864no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—3441no—
549C4⋊C4—3441no—
550C4⋊C4—1722no—
551C4⋊C4D4×D4312yes—
552C22⋊C4—24no—
553C22⋊C4—81no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—864no—
557C22⋊C4—3441no—
558C42—432no—
559C42—432no—
560C42—864no—
561C42—864no—
562C42—861no—
563C42—861no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23C2×D4×D4311yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—862no—
577Q8—862no—
578Q8—3444no—
579Q8—1721no—
580Q8—1721no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4C2×D4×D4311yescharacteristic
625C2×C4C2×D4×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4C2×#1062190011yescharacteristic
628C2×C4#1306337211yescharacteristic
629C2×C4#1306337211yescharacteristic
630C8—22no—
631C8—41no—
632C8—862no—
633C8—1721no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22#120×D4311yescharacteristic
642C22#1458344411yescharacteristic
643C22#1458347111yescharacteristic
644C22#1458370611yescharacteristic
645C22#1458370911yescharacteristic
646C22#1458371211yescharacteristic
647C22#1458371511yescharacteristic
648C4—41no—
649C4—42no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—862no—
654C4—862no—
655C4—3441no—
656C4—3441no—
657C4—1722no—
658C4—1721no—
659C4—1721no—
660C4—1722no—
661C4#1458354711yescharacteristic
662C4#1458354911yescharacteristic
663C4#1458355511yescharacteristic
664C4#1458355711yescharacteristic
665C2—81no—
666C2#1913821811yescharacteristic
667C2#1914387811yescharacteristic
668C2#1914388511yescharacteristic
669C2#1914525611yescharacteristic
670C2#1914526611yescharacteristic
671C2#1914586711yescharacteristic
672C2#1914586911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2036C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2036D43
hypocenterC43#25686
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#14583307C2semidirect
3. C2×#14583248C2semidirect
8. #19135558C2semidirect
9. #19135413C2semidirect
10. #19134865C2semidirect
11. #19134861C2semidirect
12. #19134850C2semidirect
13. #19134846C2semidirect
399. C43#25686semidirect

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145833072
C2×#145832482
#191404202
#191357952
#191357922
#191357912
#191355582
#191354132
#191348652
#191348612
#191348502
#191348462
#191343632
C43×#20362
#2568643