Finite Group Databasebeta

← #25146723

Subgroups — #25146723

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583192C211yesmaximal, characteristic, complemented
2C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic
3#19139765C211yesmaximal, characteristic
4#19139514C211yesmaximal, characteristic
5#19136027C211yesmaximal, characteristic, complemented
6#19136023C211yesmaximal, characteristic, complemented
7#19135796C211yesmaximal, characteristic, complemented
8#19135554C211yesmaximal, characteristic, complemented
9#19135350C211yesmaximal, characteristic, complemented
10#19135019C211yesmaximal, characteristic, complemented
11#19135015C211yesmaximal, characteristic, complemented
12#19134622C211yesmaximal, characteristic, complemented
13#19134621C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#2036C211yesmaximal, characteristic, complemented
16C23×C43⋊C8C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22#14583192—24no—
23(C22⋊D43)⋊C8—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582822—21no—
33#14582821—21no—
34#14582812—21no—
35#14582811—21no—
36#14582799—21no—
37#14582799—21no—
38#14582794—21no—
39#14582768C2211yescharacteristic
40#14582763—21no—
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×C22⋊D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8—22no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C2×C8×D43—22no—
70C2×C8×D43—22no—
71C2×C8×D43—41no—
72#13063324—22no—
73#13063324—22no—
74#13063301—22no—
75#13063301—41no—
76Q8×Dic43—22no—
77Q8×Dic43—22no—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101#13063259—22no—
102#13063258—22no—
103#13063258—41no—
104Dic43⋊C8D414yes—
105#13063249—22no—
106#13063249—22no—
107(C2×D43)⋊C8—22no—
108C8×Dic43—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×Q8×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22⋊Q8×C43—22no—
120C22⋊Q8×C43—41no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127#107×C43—41no—
128#103×C43—22no—
129#103×C43—22no—
130C22⋊C8×C43—22no—
131#95×C43—21no—
132C24×C43C2×D411yescharacteristic
133C23×D43C2×D411yescharacteristic
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43#4112yes—
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×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43Q1614yes—
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×D43—21no—
167C2×C4×D43—21no—
168C2×Dic86—42no—
169C2×Dic86—81no—
170C2×Dic86—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D412yes—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—81no—
186C22⋊Dic43—22no—
187C22⋊Dic43—81no—
188C22⋊Dic43—81no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—81no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—42no—
203Dic43⋊C4—22no—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—81no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43C2×D412yes—
211C4×Dic43#4112yes—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—44no—
217C2×C43⋊C8C2×D412yes—
218C2×C43⋊C8#4112yes—
219C8×D43—44no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43C2×Q1612yes—
227C23×C43C22×D411yescharacteristic
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43C2×Q1612yes—
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—41no—
238Q8×C43—41no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
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—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×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C22⋊D43—28no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
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×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43#12112yes—
283C2×Dic43#12112yes—
284C2×Dic43C2×Q1612yes—
285C2×Dic43#13512yes—
286C4×D43—41no—
287C4×D43—41no—
288C4×D43—41no—
289C4×D43—41no—
290Dic86—84no—
291C8×C43—22no—
292C8×C43—41no—
293C43⋊C8—22no—
294C43⋊C8—22no—
295#25340—431nomaximal, Sylow
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43C2×#12111yescharacteristic
304C22×C43#54611yescharacteristic
305C22×C43#54711yescharacteristic
306C22×C43C22×Q1611yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57611yescharacteristic
309C22×C43#57711yescharacteristic
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C4×C43—41no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#52911yescharacteristic
323C4×C43#54211yescharacteristic
324C4×C43#54611yescharacteristic
325C4×C43#54811yescharacteristic
326Dic43—22no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330Dic43—81no—
331Dic43—81no—
332Dic43#46714yes—
333C2×#477—431no—
334C2×C8×D4—431no—
335#2563—431no—
336#2538—431no—
337#2076—431no—
338#2076—431no—
339#2036—431no—
340#2036D4311yescharacteristic, complemented
341#1990—431no—
342#1947—431no—
343#1892—431no—
344#1892—431no—
345#1808—431no—
346#1808—431no—
347C4×#103—431no—
348C2×C43—42no—
349C2×C43#242711yescharacteristic
350C2×C43C2×#46711yescharacteristic
351C2×C43#306211yescharacteristic
352C2×C43#329911yescharacteristic
353C2×C43#330511yescharacteristic
354C2×C43#333811yescharacteristic
355C2×C43#334011yescharacteristic
356D43—42no—
357C23×C8—431no—
358C23×C8—431no—
359C2×C4⋊Q8—431no—
360C2×C22⋊Q8—431no—
361C2×C22⋊Q8C2×D4311yescharacteristic
362C2×C4×Q8—431no—
363C2×C4×D4—431no—
364#477—864no—
365C8×D4—864no—
366C2×#107—431no—
367C2×#107—431no—
368C2×#107—431no—
369C2×#107C2×D4311yescharacteristic
370C2×C4⋊C8—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103C2×D4311yescharacteristic
374C2×#103C2×D4311yescharacteristic
375C2×C22⋊C8—431no—
376C2×C22⋊C8C2×D4311yescharacteristic
377C2×C4×C8—431no—
378#396—861no—
379#396—861no—
380#393—861no—
381#393—861no—
382#390—861no—
383#390—861no—
384#389—861no—
385#384—431no—
386#382—861no—
387#380—431no—
388#380—431no—
389#380—431no—
390#380—431no—
391#380—431no—
392#380C2×D4311yescharacteristic
393C4×C4⋊C4—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#340C2×D4311yescharacteristic
402C43#2534011yescharacteristic, complemented, Sylow
403C22×Q8—861no—
404C22×Q8C22×D4311yescharacteristic
405C22×D4—431no—
406C23×C4—431no—
407C23×C4C22×D4311yescharacteristic
408C22×C8—431no—
409C22×C8—431no—
410C22×C8—862no—
411C22×C8—862no—
412C22×C8—862no—
413C22×C8—862no—
414C22×C8—1721no—
415C22×C8—1721no—
416C22×C8C22×D4311yescharacteristic
417C22×C8C22×D4311yescharacteristic
418C4⋊Q8—862no—
419C4⋊Q8—862no—
420C22⋊Q8—22no—
421C22⋊Q8—41no—
422C22⋊Q8—862no—
423C22⋊Q8—1721no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×D4—862no—
427C4×D4—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⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—431no—
445C2×C22⋊C4—431no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C42—431no—
453C2×C42—861no—
454C2×C42—861no—
455#107—41no—
456#107—862no—
457#107—862no—
458#107—1721no—
459C4⋊C8—434no—
460#103—22no—
461#103—22no—
462#103—862no—
463#103—862no—
464C22⋊C8—22no—
465C22⋊C8—862no—
466C4×C8—862no—
467#95—21no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474C24—431no—
475C24D4×D4311yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—3441no—
482C2×Q8—3441no—
483C2×Q8—1722no—
484C2×Q8#1062190012yes—
485C2×D4—434no—
486C2×D4—862no—
487C2×D4—862no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4D4×D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—432no—
519C2×C8—432no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—1724no—
525C2×C8—1724no—
526C2×C8D4×D4312yes—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—862no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—3441no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C4⋊C4—1722no—
547C4⋊C4—1722no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—3441no—
553C22⋊C4—3441no—
554C22⋊C4—3441no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—1722no—
558C42—432no—
559C42—432no—
560C42—1722no—
561C42—1722no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—432no—
569C23—861no—
570C23—861no—
571C23—861no—
572C23—861no—
573C23—861no—
574C23—861no—
575C23Q16×D4312yes—
576C23C2×D4×D4311yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581Q8—3444no—
582D4—868no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
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—41no—
601C2×C4—41no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—432no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
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×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4C2×D4×D4311yescharacteristic
628C2×C4#41×D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4C2×#1062190011yescharacteristic
631C2×C4#1306337011yescharacteristic
632C2×C4#1306337211yescharacteristic
633C8—22no—
634C8—41no—
635C8—862no—
636C8—862no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—862no—
645C22—862no—
646C22—862no—
647C22—1721no—
648C22—1721no—
649C22—1721no—
650C22—1721no—
651C22#121×D4311yescharacteristic
652C22#1458353611yescharacteristic
653C22#1458354711yescharacteristic
654C22C2×Q16×D4311yescharacteristic
655C22#135×D4311yescharacteristic
656C22#1458370311yescharacteristic
657C22#1458370811yescharacteristic
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—434no—
664C4—862no—
665C4—3441no—
666C4—3441no—
667C4—3441no—
668C4—3441no—
669C4—1721no—
670C4#1458342611yescharacteristic
671C4#1458351311yescharacteristic
672C4#1458353811yescharacteristic
673C4#1458355511yescharacteristic
674C2—42no—
675C2—1722no—
676C2#1913816511yescharacteristic
677C2#467×D4311yescharacteristic
678C2#1914427011yescharacteristic
679C2#1914646411yescharacteristic
680C2#1914653811yescharacteristic
681C2#1914698211yescharacteristic
682C2#1914700111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2036C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2036D43
hypocenterC43#25340
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
1. C2×#14583192C2semidirect
5. #19136027C2semidirect
6. #19136023C2semidirect
7. #19135796C2semidirect
8. #19135554C2semidirect
9. #19135350C2semidirect
10. #19135019C2semidirect
11. #19135015C2semidirect
12. #19134622C2semidirect
13. #19134621C2semidirect
14. #103×Dic43C2semidirect
15. C43×#2036C2semidirect
340. #2036D43semidirect
402. C43#25340semidirect

Maximal subgroups

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

subgroupindex
C2×#145831922
C2×(C22⋊D43)⋊C82
#191397652
#191395142
#191360272
#191360232
#191357962
#191355542
#191353502
#191350192
#191350152
#191346222
#191346212
#103×Dic432
C43×#20362
#2534043