Finite Group Databasebeta

← #25106591

Subgroups — #25106591

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583507C211yesmaximal, characteristic
2C2×#14582924C211yesmaximal, characteristic
3#19137205C211yesmaximal, characteristic
4#19135551C211yesmaximal, characteristic, complemented
5#19135549C211yesmaximal, characteristic, complemented
6#19135516C211yesmaximal, characteristic, complemented
7#19135516C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic
9#19135025C211yesmaximal, characteristic
10#19135017C211yesmaximal, characteristic
11#19135015C211yesmaximal, characteristic
12#19134607C211yesmaximal, characteristic, complemented
13#19134601C211yesmaximal, characteristic, complemented
14#19134600C211yesmaximal, characteristic, complemented
15C43×#1805C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583507—24no—
19#14583507C418yescomplemented
20C2×#13063323C2211yescharacteristic
21C2×#13063320—21no—
22C2×#13063319—21no—
23C2×#13063317—21no—
24C2×#13063316C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063305C2211yescharacteristic
27C2×#13063301C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063282C2211yescharacteristic
30#14582924—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×Dic43⋊C8C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40#14582791—21no—
41#14582791—21no—
42#14582786—21no—
43#14582786—21no—
44#14582769C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#382C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—41no—
66C2×#10621872—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C2×C8×D43—22no—
70C2×C8×D43—41no—
71C2×C8×D43—41no—
72#13063323—22no—
73#13063323C2×C414yes—
74#13063320—28no—
75#13063319—28no—
76#13063317—28no—
77#13063316—22no—
78#13063316C2×C414yes—
79#13063315—28no—
80#13063305—22no—
81#13063305C2×C414yes—
82#13063301—22no—
83#13063301C2×C414yes—
84C4×Dic86—22no—
85C4×Dic86C2×C414yes—
86#13063282C2×C414yes—
87#13063282D414yes—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4D411yescharacteristic
101C2×Dic43⋊C4D411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4D411yescharacteristic
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112C4⋊(C43⋊C8)—22no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115#13063250—41no—
116#13063250—41no—
117#13063249—41no—
118#13063249—41no—
119#13063248—41no—
120#13063248—41no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C4×Q8×C43—22no—
129C4×Q8×C43C2×C414yes—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—22no—
137#103×C43—41no—
138#103×C43—41no—
139#95×C43—21no—
140#95×C43—21no—
141C23×D43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C2×D412yes—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86C22×C412yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C4⋊C4×C43—24no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43C22×C412yes—
187C42×C43—24no—
188C42×C43C22×C412yes—
189C42×C43C2×D412yes—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4C22⋊C414yes—
195(C2×D43)⋊C4C22⋊C414yes—
196C4⋊Dic43—21no—
197C4⋊Dic43—24no—
198C4⋊Dic43—24no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—81no—
204C4⋊Dic43—81no—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—24no—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4C22⋊C414yes—
212Dic43⋊C4C22⋊C414yes—
213C4×Dic43—24no—
214C4×Dic43—81no—
215C4×Dic43—81no—
216C4×Dic43C22×C412yes—
217C4×Dic43C2×D412yes—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224#10621872—44no—
225C8×D43—44no—
226C23×C43C22×D411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43C2×C22⋊C412yes—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
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×C43C2×C22⋊C412yes—
255C2×C4×C43C2×C22⋊C412yes—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C2×C22⋊C412yes—
281C2×Dic43C2×C22⋊C412yes—
282C2×Dic43C2×C22⋊C412yes—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287Dic86—22no—
288Dic86—22no—
289Dic86—41no—
290Dic86—41no—
291C8×C43—41no—
292C8×C43—41no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295#21898—431nomaximal, Sylow
296C22×C43C22×C22⋊C411yescharacteristic
297C22×C43#53711yescharacteristic
298C22×C43#53711yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57711yescharacteristic
301C22×C43#57811yescharacteristic
302C22×C43#57811yescharacteristic
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43#52011yescharacteristic
317C4×C43#52011yescharacteristic
318C4×C43#53511yescharacteristic
319C4×C43#53611yescharacteristic
320Dic43—22no—
321Dic43—22no—
322Dic43—22no—
323Dic43—42no—
324Dic43—42no—
325Dic43—81no—
326Dic43—81no—
327C2×#541—431no—
328C2×#424—431no—
329#2314—431no—
330#1989—431no—
331#1989—431no—
332#1981—431no—
333#1981—431no—
334#1894—431no—
335#1894—431no—
336#1892—431no—
337#1892—431no—
338#1805—431no—
339#1805D4311yescharacteristic, complemented
340#1803—431no—
341#1803—431no—
342C2×C43#231111yescharacteristic
343C2×C43#289811yescharacteristic
344C2×C43#289811yescharacteristic
345C2×C43#325811yescharacteristic
346C2×C43#325811yescharacteristic
347C2×C43#326011yescharacteristic
348C2×C43#326111yescharacteristic
349D43—42no—
350C22×M16—431no—
351C23×C8—431no—
352#541—438no—
353#541—864no—
354C2×C4⋊Q8—431no—
355C2×#126—861no—
356C2×#126—861no—
357C2×#125—431no—
358C2×#125—861no—
359C2×#125—861no—
360C2×C22⋊Q8—431no—
361C2×C22⋊Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8C2×D4311yescharacteristic
364C2×#117—431no—
365#424—864no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8—431no—
368C2×C4⋊C8—431no—
369C2×C4⋊C8C2×D4311yescharacteristic
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103C2×D4311yescharacteristic
377C2×#103C2×D4311yescharacteristic
378#388—861no—
379#388—861no—
380#387—861no—
381#387—861no—
382#384—431no—
383#382C2×D4311yescharacteristic
384#380—431no—
385#380—431no—
386C4×C4⋊C4—431no—
387C4×C4⋊C4—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#340C2×D4311yescharacteristic
396C43#2189811yescharacteristic, complemented, Sylow
397C22×Q8—431no—
398C22×Q8C22×D4311yescharacteristic
399C23×C4—431no—
400C2×M16—862no—
401C2×M16—1721no—
402C2×M16—1721no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—862no—
406C22×C8—1721no—
407C22×C8—1721no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410C4⋊Q8—434no—
411C4⋊Q8—862no—
412#126—868no—
413#126—868no—
414#125—434no—
415#125—868no—
416#125—862no—
417#125—868no—
418C22⋊Q8—434no—
419C22⋊Q8—434no—
420C22⋊Q8—862no—
421C22⋊Q8—862no—
422C4×Q8—22no—
423C4×Q8—434no—
424C4×Q8—862no—
425C4×Q8C4×D4314yes—
426#117—434no—
427#117—434no—
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⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—431no—
447C2×C22⋊C4—431no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C42—21no—
453C2×C42—431no—
454C2×C42—861no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42C22×D4311yescharacteristic
458C4⋊C8—22no—
459C4⋊C8—862no—
460C4⋊C8—862no—
461C4⋊C8—862no—
462#103—41no—
463#103—41no—
464#103—1721no—
465#103—1721no—
466#103—1721no—
467#103—1721no—
468#103—1721no—
469#103—1721no—
470#95—21no—
471#95—21no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—431no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—432no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8C2×C4×D4312yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—432no—
497C22×C4—432no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4C23×D4311yescharacteristic
509M16—1724no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—1724no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—434no—
530C4⋊C4—434no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—864no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—3441no—
545C4⋊C4—3441no—
546C4⋊C4C2×C4×D4312yes—
547C22⋊C4—434no—
548C22⋊C4—434no—
549C22⋊C4—864no—
550C22⋊C4—864no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C42—24no—
554C42—432no—
555C42—432no—
556C42—864no—
557C42—3441no—
558C42—3441no—
559C42C2×C4×D4312yes—
560C42D4×D4312yes—
561C23—432no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23—861no—
568C23C2×D4×D4311yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—41no—
572Q8—41no—
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4C22⋊C4×D4312yes—
619C2×C4C22⋊C4×D4312yes—
620C2×C4C22×C4×D4311yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4#1306337011yescharacteristic
623C2×C4#1306337111yescharacteristic
624C2×C4#1306337211yescharacteristic
625C2×C4#1306337311yescharacteristic
626C8—41no—
627C8—41no—
628C8—1721no—
629C8—1721no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22C2×C22⋊C4×D4311yescharacteristic
638C22#1458347811yescharacteristic
639C22#1458347911yescharacteristic
640C22#1458370611yescharacteristic
641C22#1458370811yescharacteristic
642C22#1458371311yescharacteristic
643C22#1458371511yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4—862no—
651C4—862no—
652C4—862no—
653C4—3441no—
654C4—3441no—
655C4—1722no—
656C4—1722no—
657C4#1458337911yescharacteristic
658C4#1458338011yescharacteristic
659C4#1458346511yescharacteristic
660C4#1458347211yescharacteristic
661C2—1722no—
662C2#1913718411yescharacteristic
663C2#1914312411yescharacteristic
664C2#1914312711yescharacteristic
665C2#1914601811yescharacteristic
666C2#1914602611yescharacteristic
667C2#1914604011yescharacteristic
668C2#1914604811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1805C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1805D43
hypocenterC43#21898
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
4. #19135551C2semidirect
5. #19135549C2semidirect
6. #19135516C2semidirect
7. #19135516C2semidirect
12. #19134607C2semidirect
13. #19134601C2semidirect
14. #19134600C2semidirect
15. C43×#1805C2semidirect
19. #14583507C4semidirect
339. #1805D43semidirect
396. C43#21898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835072
C2×#145829242
#191372052
#191355512
#191355492
#191355162
#191350272
#191350252
#191350172
#191350152
#191346072
#191346012
#191346002
C43×#18052
#2189843