Finite Group Databasebeta

← #25146342

Subgroups — #25146342

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583096C211yesmaximal, characteristic
2C2×#14583030C211yesmaximal, characteristic, complemented
3#19139961C211yesmaximal, characteristic, complemented
4#19135983C211yesmaximal, characteristic, complemented
5#19135969C211yesmaximal, characteristic, complemented
6#19135912C211yesmaximal, characteristic, complemented
7#19135912C211yesmaximal, characteristic, complemented
8#19135475C211yesmaximal, characteristic, complemented
9#19135448C211yesmaximal, characteristic, complemented
10#19135420C211yesmaximal, characteristic
11#19135363C211yesmaximal, characteristic, complemented
12#19135295C211yesmaximal, characteristic, complemented
13#19135281C211yesmaximal, characteristic, complemented
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2548C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583096—24no—
20#14583030—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582837—21no—
38#14582818—21no—
39#14582805C2211yescharacteristic
40#14582805C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582780—21no—
44#14582780—21no—
45#14582765C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C2×#127×C43C2211yescharacteristic
51C2×#124×C43—21no—
52C2×C4×Q8×C43C2211yescharacteristic
53C43×#394—21no—
54C43×#394—21no—
55C43×#390—21no—
56C43×#390C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—41no—
67C2×#10621883—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C4×Dic86—22no—
73C4×Dic86—22no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C4×Dic43—21no—
81#13063258—41no—
82#13063256—41no—
83C4⋊(C43⋊C8)—22no—
84C4⋊(C43⋊C8)—22no—
85C4⋊(C43⋊C8)D414yes—
86#13063248—22no—
87#13063248—22no—
88#13063246—22no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92#13063246—41no—
93#13063246—41no—
94#13063236—22no—
95#13063236—22no—
96C4×C43⋊C8—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×Q8×C43D411yescharacteristic
106C22×D4×C43—21no—
107C22×D4×C43—21no—
108C22×D4×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110#127×C43—22no—
111#127×C43—22no—
112#124×C43—44no—
113C4×Q8×C43—22no—
114C4×Q8×C43—22no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133C24×C43—21no—
134C24×C43—21no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43—41no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—42no—
151C2×D4×C43—42no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—81no—
155C2×D4×C43—81no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86#4112yes—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—81no—
187C22⋊C4×C43—81no—
188C22⋊C4×C43—81no—
189C22⋊C4×C43—81no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—42no—
195C42×C43C2×D412yes—
196C42×C43#4112yes—
197#10621883—44no—
198#10621883—44no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208C4×Dic43—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C2×D412yes—
219C2×C43⋊C8C2×D412yes—
220C2×C43⋊C8#4112yes—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236Q8×C43—44no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—84no—
246D4×C43—84no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43#12112yes—
269C2×C4×C43#12112yes—
270C2×C4×C43AGL(1,ℤ/8)12yes—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C2×Dic43—22no—
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—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289Dic86—22no—
290Dic86—22no—
291Dic86—41no—
292Dic86—41no—
293C43⋊C8—22no—
294C43⋊C8—22no—
295C43⋊C8—22no—
296C43⋊C8—41no—
297#25310—431nomaximal, Sylow
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43C2×#12111yescharacteristic
313C22×C43#54811yescharacteristic
314C22×C43#55011yescharacteristic
315C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C43#57511yescharacteristic
317C22×C43#57711yescharacteristic
318C22×C43#57711yescharacteristic
319C4×C43—22no—
320C4×C43—22no—
321C4×C43—22no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43#52911yescharacteristic
328C4×C43#54211yescharacteristic
329C4×C43#54611yescharacteristic
330C4×C43#54811yescharacteristic
331Dic43—42no—
332Dic43—81no—
333Dic43—81no—
334Dic43—81no—
335C2×#460—431no—
336C2×#446—431no—
337#2581—431no—
338#2548D4311yescharacteristic
339#2067—431no—
340#2065—431no—
341#2055—431no—
342#2055—431no—
343#1973—431no—
344#1968—431no—
345#1961—431no—
346#1949—431no—
347#1936—431no—
348#1934—431no—
349#1763—431no—
350C2×C43—161no—
351C2×C43—161no—
352C2×C43#242611yescharacteristic
353C2×C43#305511yescharacteristic
354C2×C43#305711yescharacteristic
355C2×C43#336811yescharacteristic
356C2×C43#337111yescharacteristic
357C2×C43#339711yescharacteristic
358C2×C43#340111yescharacteristic
359C22×SD16—431no—
360C22×SD16—431no—
361C2×#127C2×D4311yescharacteristic
362C2×#124—21no—
363C2×C4×Q8—431no—
364C2×C4×Q8C2×D4311yescharacteristic
365#460—864no—
366#446—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8—431no—
370C2×C4⋊C8—431no—
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#97—431no—
381C2×#97—431no—
382C2×C4×C8—431no—
383#400—861no—
384#395—861no—
385#394—21no—
386#394—21no—
387#391—431no—
388#391—431no—
389#390—21no—
390#390C2×D4311yescharacteristic
391#390C2×D4311yescharacteristic
392#390C2×D4311yescharacteristic
393#390C2×D4311yescharacteristic
394#389—431no—
395#389—431no—
396#387—861no—
397#387—861no—
398#382—431no—
399C4×C4⋊C4C2×D4311yescharacteristic
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404C43#2531011yescharacteristic, complemented, Sylow
405C22×Q8—431no—
406C22×Q8C22⋊D4311yescharacteristic
407C22×D4—21no—
408C22×D4—21no—
409C22×D4C22×D4311yescharacteristic
410C22×D4C22×D4311yescharacteristic
411C2×SD16—862no—
412C2×SD16—862no—
413C2×SD16—862no—
414C2×SD16—862no—
415C2×SD16—1721no—
416C2×SD16—1721no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8—431no—
420C22×C8—431no—
421#127—22no—
422#127—22no—
423#124—44no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—862no—
427C4×Q8—862no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22⋊D4311yescharacteristic
435C2×C4⋊C4C22⋊D4311yescharacteristic
436C2×C4⋊C4C22⋊D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C42—21no—
448C2×C42—861no—
449C2×C42C22×D4311yescharacteristic
450C2×C42C22×D4311yescharacteristic
451C2×C42C22×D4311yescharacteristic
452#107—1721no—
453#106—1721no—
454C4⋊C8—434no—
455C4⋊C8—862no—
456C4⋊C8—862no—
457#103—862no—
458#103—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—862no—
463#102—1721no—
464#102—1721no—
465#97—862no—
466#97—862no—
467C4×C8—862no—
468#95—21no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477C24—21no—
478C24—21no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—41no—
482C2×Q8—432no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C22×C4C2×C22⋊D4311yescharacteristic
518C22×C4C23×D4311yescharacteristic
519SD16—1724no—
520SD16—1724no—
521C2×C8—432no—
522C2×C8—432no—
523C2×C8—432no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—1722no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C42—1722no—
563C42D4×D4312yes—
564C42#1062190012yes—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C22×C22⋊D4311yescharacteristic
580Q8—44no—
581Q8—862no—
582Q8—862no—
583Q8—1721no—
584Q8—1721no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—84no—
594D4—84no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—862no—
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×C4—1721no—
628C2×C4#1306329712yes—
629C2×C4#1306329712yes—
630C2×C4#1306335112yes—
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4C2×#1062190011yescharacteristic
635C2×C4#1306337111yescharacteristic
636C2×C4#1306337211yescharacteristic
637C8—862no—
638C8—862no—
639C8—862no—
640C8—1721no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×#1306329711yescharacteristic
656C22#1458355611yescharacteristic
657C22#1458356811yescharacteristic
658C22C2×#1306335111yescharacteristic
659C22#1458369711yescharacteristic
660C22#1458371011yescharacteristic
661C22#1458371011yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—3441no—
671C4—3441no—
672C4—3441no—
673C4—1722no—
674C4#1458342811yescharacteristic
675C4#1458351811yescharacteristic
676C4#1458354211yescharacteristic
677C4#1458355711yescharacteristic
678C2—161no—
679C2—161no—
680C2#1913816411yescharacteristic
681C2#1914421011yescharacteristic
682C2#1914423111yescharacteristic
683C2#1914732011yescharacteristic
684C2#1914735711yescharacteristic
685C2#1914761111yescharacteristic
686C2#1914765511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2548C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenter#2548D43
hypocenterC43#25310
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
2. C2×#14583030C2semidirect
3. #19139961C2semidirect
4. #19135983C2semidirect
5. #19135969C2semidirect
6. #19135912C2semidirect
7. #19135912C2semidirect
8. #19135475C2semidirect
9. #19135448C2semidirect
11. #19135363C2semidirect
12. #19135295C2semidirect
13. #19135281C2semidirect
14. #19134428C2semidirect
404. C43#25310semidirect

Maximal subgroups

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

subgroupindex
C2×#145830962
C2×#145830302
#191399612
#191359832
#191359692
#191359122
#191354752
#191354482
#191354202
#191353632
#191352952
#191352812
#191344282
C43×#25482
#2531043