Finite Group Databasebeta

← #25064173

Subgroups — #25064173

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148689C211yesmaximal, characteristic
2#19143682C211yesmaximal, characteristic, complemented
3#19137245C211yesmaximal, characteristic, complemented
4#19133169C211yesmaximal, characteristic
5#19133160C211yesmaximal, characteristic, complemented
6#19133157C211yesmaximal, characteristic, complemented
7#19133145C211yesmaximal, characteristic, complemented
8#19133144C211yesmaximal, characteristic, complemented
9#19133133C211yesmaximal, characteristic
10#19133130C211yesmaximal, characteristic
11#19133117C211yesmaximal, characteristic
12#19133105C211yesmaximal, characteristic, complemented
13#19133092C211yesmaximal, characteristic, complemented
14#19133078C211yesmaximal, characteristic
15C43×#1521C211yesmaximal, characteristic
16#14583628C411yescharacteristic, complemented
17#14583627C411yescharacteristic, complemented
18#14583626C411yescharacteristic, complemented
19#14583626C411yescharacteristic, complemented
20#14583619C411yescharacteristic, complemented
21#14583618C411yescharacteristic, complemented
22#14583618C411yescharacteristic, complemented
23#14583589—21no—
24#14583586—21no—
25#14583586—21no—
26D4×Dic86—21no—
27D4×Dic86C411yescharacteristic, complemented
28#14583511—21no—
29#14583506—21no—
30#14583506—21no—
31#14583456C2211yescharacteristic
32#14583451C2211yescharacteristic
33#14583451C2211yescharacteristic
34#14583430C2211yescharacteristic
35#14583430C2211yescharacteristic
36#14583376—21no—
37C2×C4×Dic86C2211yescharacteristic
38#14583029—21no—
39#14583028—21no—
40#14583028—21no—
41C8×Dic86—21no—
42#14582956C2211yescharacteristic
43#14582953C2211yescharacteristic
44#14582953C2211yescharacteristic
45#14582949C2211yescharacteristic
46#14582949C2211yescharacteristic
47#14582803—21no—
48#14582796—21no—
49#14582786—21no—
50#14582784—21no—
51#14582766C2211yescharacteristic
52#14582765C2211yescharacteristic
53#14582763C2211yescharacteristic
54#14582750C2211yescharacteristic
55#14582744C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582637C2211yescharacteristic
59#14582637C2211yescharacteristic
60#14582636C2211yescharacteristic
61#14582636C2211yescharacteristic
62#14582635C2211yescharacteristic
63#14582635C2211yescharacteristic
64#14582635C2211yescharacteristic
65#14582635C2211yescharacteristic
66#14582633C2211yescharacteristic
67#14582633C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#431C2211yescharacteristic
70C43×#383C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C22×Dic86—21no—
76C22×Dic86D411yescharacteristic
77#13063325—21no—
78#13063325C2×C411yescharacteristic
79#13063325C2×C411yescharacteristic
80#13063324—21no—
81#13063324—21no—
82#13063324C2×C411yescharacteristic
83#13063324C2×C411yescharacteristic
84#13063323C2×C411yescharacteristic
85#13063323C2×C411yescharacteristic
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063318—21no—
94#13063317—21no—
95#13063317—21no—
96#13063316—21no—
97#13063316—21no—
98#13063316C2×C411yescharacteristic
99#13063316C2×C411yescharacteristic
100#13063315—21no—
101#13063315—21no—
102#13063315—21no—
103#13063315—21no—
104#13063315—21no—
105#13063315—21no—
106#13063315—21no—
107#13063315—21no—
108#13063312C2×C411yescharacteristic
109#13063312C2×C411yescharacteristic
110#13063306—21no—
111#13063306—21no—
112#13063304—21no—
113#13063304—21no—
114#13063304—21no—
115#13063304C2311yescharacteristic
116#13063304C2311yescharacteristic
117#13063302—21no—
118#13063302—21no—
119#13063302—21no—
120#13063302—21no—
121#13063302—21no—
122#13063302—21no—
123Q8×Dic43C2×C411yescharacteristic
124Q8×Dic43C2×C411yescharacteristic
125C4×Dic86—21no—
126C4×Dic86—21no—
127C4×Dic86—21no—
128C4×Dic86C2×C411yescharacteristic
129C4×Dic86C2×C411yescharacteristic
130C4×Dic86C2×C411yescharacteristic
131C4×Dic86C2×C411yescharacteristic
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86D411yescharacteristic
135C4×Dic86D411yescharacteristic
136C4×Dic86D411yescharacteristic
137C4×Dic86D411yescharacteristic
138#13063290—21no—
139#13063290—21no—
140#13063290—21no—
141#13063290—21no—
142#13063290C2×C411yescharacteristic
143#13063290C2×C411yescharacteristic
144#13063290C2×C411yescharacteristic
145#13063290C2×C411yescharacteristic
146D4×Dic43—21no—
147D4×Dic43—21no—
148D4×Dic43C2×C411yescharacteristic
149D4×Dic43C2×C411yescharacteristic
150#13063284—21no—
151#13063284—21no—
152#13063281—21no—
153#13063281—21no—
154#13063281—21no—
155#13063281—21no—
156#13063281—21no—
157#13063281—21no—
158C2×C4⋊Dic43—21no—
159C2×C4⋊Dic43D411yescharacteristic
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4D411yescharacteristic
163C2×Dic43⋊C4D411yescharacteristic
164C2×C4×Dic43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167C2×C4×Dic43C2311yescharacteristic
168C4⋊(C43⋊C8)—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)C2311yescharacteristic
174C22⋊(C43⋊C8)C2311yescharacteristic
175#13063236—21no—
176#13063235—21no—
177#13063235—21no—
178C8×Dic43—21no—
179C8×Dic43—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic
189#124×C43C2×C411yescharacteristic
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic
196#117×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201C4×C8×C43—21no—
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43C22×C411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2411yescharacteristic
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—42no—
227C2×Dic86—44no—
228C2×Dic86C22⋊C411yescharacteristic
229C2×Dic86C22⋊C411yescharacteristic
230C2×Dic86C22⋊C411yescharacteristic
231C2×Dic86C22⋊C411yescharacteristic
232C2×Dic86C22×C411yescharacteristic
233C2×Dic86C22×C411yescharacteristic
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43C22×C411yescharacteristic
241C4⋊C4×C43C22×C411yescharacteristic
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C42×C43—21no—
248C42×C43C22×C411yescharacteristic
249C42×C43C22×C411yescharacteristic
250C42×C43C2×D411yescharacteristic
251C42×C43C2×D411yescharacteristic
252C22⋊Dic43—21no—
253C22⋊Dic43—21no—
254C22⋊Dic43—21no—
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—81no—
268C4⋊Dic43C22⋊C411yescharacteristic
269C4⋊Dic43C22⋊C411yescharacteristic
270C4⋊Dic43C22⋊C411yescharacteristic
271C4⋊Dic43C22⋊C411yescharacteristic
272C4⋊Dic43C22×C411yescharacteristic
273C4⋊Dic43C22×C411yescharacteristic
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—42no—
291Dic43⋊C4—81no—
292Dic43⋊C4C22⋊C411yescharacteristic
293Dic43⋊C4C22⋊C411yescharacteristic
294Dic43⋊C4C22⋊C411yescharacteristic
295Dic43⋊C4C22⋊C411yescharacteristic
296Dic43⋊C4C22⋊C411yescharacteristic
297Dic43⋊C4C22⋊C411yescharacteristic
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300C4×Dic43—21no—
301C4×Dic43—21no—
302C4×Dic43—21no—
303C4×Dic43—21no—
304C4×Dic43—21no—
305C4×Dic43—21no—
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43—42no—
309C4×Dic43—81no—
310C4×Dic43C22×C411yescharacteristic
311C4×Dic43C22×C411yescharacteristic
312C4×Dic43C22×C411yescharacteristic
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C2×D411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C23×C43—21no—
321C23×C43C22×D411yescharacteristic
322Q8×C43—41no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—41no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—42no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C23×C411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—22no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—41no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366C2×Dic43C2×C22⋊C411yescharacteristic
367C2×Dic43C2×C22⋊C411yescharacteristic
368C2×Dic43C2×C22⋊C411yescharacteristic
369C2×Dic43C2×C22⋊C411yescharacteristic
370C2×Dic43C2×C22⋊C411yescharacteristic
371C2×Dic43C2×C22⋊C411yescharacteristic
372Dic86—22no—
373Dic86—22no—
374Dic86—41no—
375Dic86—41no—
376Dic86—42no—
377Dic86—42no—
378Dic86—42no—
379Dic86—41no—
380Dic86—41no—
381C8×C43—41no—
382C8×C43—41no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385#17601—431nomaximal, Sylow
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43C22×C22⋊C411yescharacteristic
392C22×C43#57711yescharacteristic
393C22×C43#57811yescharacteristic
394C4×C43—21no—
395C4×C43—21no—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—41no—
403C4×C43—81no—
404C4×C43—81no—
405Dic43—21no—
406Dic43—21no—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—41no—
413Dic43—41no—
414Dic43—41no—
415Dic43—41no—
416Dic43—81no—
417Dic43—81no—
418Dic43#42112yes—
419#3523—431no—
420#2984—431no—
421#2320—431no—
422#1521—431no—
423#1521D4311yescharacteristic
424#1518—431no—
425#1518—431no—
426#1515—431no—
427#1515—431no—
428#1512—431no—
429#1512—431no—
430#1509—431no—
431#1506—431no—
432#1503—431no—
433#1500—431no—
434C2×C43—21no—
435C2×C43—21no—
436C2×C43—81no—
437C2×C43#288411yescharacteristic
438C2×C43#289811yescharacteristic
439C2×C43C2×#42111yescharacteristic
440#557—431no—
441#557—431no—
442#557—431no—
443#557—431no—
444#556—431no—
445#556—431no—
446#556—431no—
447#552—861no—
448#552—861no—
449#552—861no—
450D4×Q8—431no—
451D4×Q8—861no—
452#541—861no—
453#541—861no—
454#541—861no—
455#533—431no—
456#533—431no—
457#533—431no—
458#529—431no—
459#529—431no—
460#529C2×D4311yescharacteristic
461#519—861no—
462C2×C4×Q8—431no—
463#446—861no—
464#446—861no—
465#446—861no—
466C8×Q8—861no—
467#432—431no—
468#432—431no—
469#432—431no—
470#431—431no—
471#431—431no—
472#431C2×D4311yescharacteristic
473#391—861no—
474#389—861no—
475#387—861no—
476#387—861no—
477#383—431no—
478#383C2×D4311yescharacteristic
479#382—431no—
480#382—431no—
481C4×C4⋊C4—431no—
482#376—431no—
483#328—431no—
484#328—431no—
485#328—431no—
486#328—431no—
487#328—431no—
488#328—431no—
489#328—431no—
490#328—431no—
491#328—431no—
492#328—431no—
493#328C2×D4311yescharacteristic
494#328C2×D4311yescharacteristic
495#327—431no—
496#327—431no—
497#327C2×D4311yescharacteristic
498#327C2×D4311yescharacteristic
499C43#1760111yescharacteristic, complemented, Sylow
500C22×Q8—431no—
501C22×Q8—861no—
502C4⋊Q8—431no—
503C4⋊Q8—431no—
504C4⋊Q8—431no—
505C4⋊Q8—431no—
506C4⋊Q8—431no—
507C4⋊Q8—431no—
508C4⋊Q8—861no—
509C4⋊Q8—861no—
510C4⋊Q8—861no—
511#126—21no—
512#126—861no—
513#126—861no—
514#126—861no—
515#126—861no—
516#126—861no—
517#126—861no—
518#126—861no—
519#126—861no—
520#125—431no—
521#125—431no—
522#125—861no—
523#125—861no—
524#125—861no—
525#125—861no—
526#125—861no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125—861no—
533#125—861no—
534#125C4×D4311yescharacteristic
535#124—431no—
536#124—431no—
537#124C4×D4311yescharacteristic
538#123—21no—
539#123—861no—
540#123—861no—
541C22⋊Q8—431no—
542C22⋊Q8—431no—
543C22⋊Q8—861no—
544C22⋊Q8—861no—
545C22⋊Q8—861no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549C22⋊Q8—861no—
550C22⋊Q8—861no—
551C22⋊Q8—861no—
552C22⋊Q8C22×D4311yescharacteristic
553#121C22×D4311yescharacteristic
554C4×Q8—431no—
555C4×Q8—431no—
556C4×Q8—431no—
557C4×Q8—431no—
558C4×Q8—431no—
559C4×Q8—431no—
560C4×Q8—431no—
561C4×Q8—431no—
562C4×Q8—431no—
563C4×Q8—431no—
564C4×Q8—431no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—861no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8—861no—
577C4×Q8C4×D4311yescharacteristic
578C4×D4—21no—
579C4×D4—431no—
580C4×D4—431no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4C4×D4311yescharacteristic
584#117—21no—
585#117—861no—
586#117—861no—
587#117—861no—
588#117—861no—
589#117—861no—
590#117—861no—
591#117—861no—
592#117—861no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—431no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4—861no—
599C2×C42—431no—
600C2×C42—431no—
601C2×C42—861no—
602C2×C42—861no—
603C2×C42C22×D4311yescharacteristic
604C4⋊C8—21no—
605C4⋊C8—861no—
606C4⋊C8—861no—
607C4⋊C8—861no—
608C4⋊C8—861no—
609C4⋊C8—861no—
610C22⋊C8—431no—
611C22⋊C8—431no—
612C22⋊C8C22×D4311yescharacteristic
613C22⋊C8C22×D4311yescharacteristic
614#97—861no—
615#97—861no—
616#97—861no—
617C4×C8—21no—
618C4×C8—861no—
619C4×C8—861no—
620#95—21no—
621#95—21no—
622#95—431no—
623#95—431no—
624#95—861no—
625#95—861no—
626#95—861no—
627#95—861no—
628#95—861no—
629#95C22×D4311yescharacteristic
630#95C22×D4311yescharacteristic
631C2×Q8—431no—
632C2×Q8—431no—
633C2×Q8—431no—
634C2×Q8—431no—
635C2×Q8—431no—
636C2×Q8—431no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—861no—
640C2×Q8—1722no—
641C2×Q8—1724no—
642C2×Q8C2×C4×D4311yescharacteristic
643C2×D4—21no—
644C2×D4C2×C4×D4311yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—431no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4D4×D4311yescharacteristic
657C22×C4D4×D4311yescharacteristic
658C22×C4C23×D4311yescharacteristic
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—861no—
662C2×C8—861no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—431no—
668C4⋊C4—431no—
669C4⋊C4—431no—
670C4⋊C4—431no—
671C4⋊C4—431no—
672C4⋊C4—431no—
673C4⋊C4—431no—
674C4⋊C4—431no—
675C4⋊C4—431no—
676C4⋊C4—431no—
677C4⋊C4—431no—
678C4⋊C4—431no—
679C4⋊C4—431no—
680C4⋊C4—431no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—3441no—
705C4⋊C4—3441no—
706C4⋊C4—1722no—
707C4⋊C4C2×C4×D4311yescharacteristic
708C4⋊C4C2×C4×D4311yescharacteristic
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—861no—
715C22⋊C4—861no—
716C22⋊C4—861no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C42—21no—
723C42—431no—
724C42—431no—
725C42—431no—
726C42—431no—
727C42—431no—
728C42—431no—
729C42—431no—
730C42—431no—
731C42—861no—
732C42—861no—
733C42—861no—
734C42—861no—
735C42—861no—
736C42—861no—
737C42—861no—
738C42—861no—
739C42—3441no—
740C42—1722no—
741C42C2×C4×D4311yescharacteristic
742C42C2×C4×D4311yescharacteristic
743C42D4×D4311yescharacteristic
744C42D4×D4311yescharacteristic
745C23—21no—
746C23C2×D4×D4311yescharacteristic
747Q8—41no—
748Q8—862no—
749Q8—862no—
750Q8—1721no—
751Q8—1721no—
752Q8—1721no—
753Q8—1721no—
754Q8—1722no—
755Q8—1722no—
756Q8—1722no—
757D4—41no—
758D4—41no—
759D4—41no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—431no—
775C2×C4—431no—
776C2×C4—431no—
777C2×C4—431no—
778C2×C4—431no—
779C2×C4—431no—
780C2×C4—431no—
781C2×C4—431no—
782C2×C4—862no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—1722no—
792C2×C4—1721no—
793C2×C4—1722no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4C22⋊C4×D4311yescharacteristic
801C2×C4C22⋊C4×D4311yescharacteristic
802C2×C4C22⋊C4×D4311yescharacteristic
803C2×C4C22⋊C4×D4311yescharacteristic
804C2×C4C22×C4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C8—41no—
807C8—41no—
808C8—1721no—
809C8—1721no—
810C22—21no—
811C22—21no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22C2×C22⋊C4×D4311yescharacteristic
816C22#1458370611yescharacteristic
817C22#1458371311yescharacteristic
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—432no—
830C4—861no—
831C4—861no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—861no—
837C4—3441no—
838C4—3441no—
839C4—1721no—
840C4—1721no—
841C4—1721no—
842C4—1721no—
843C2—21no—
844C2—21no—
845C2—81no—
846C2#1914305711yescharacteristic
847C2#1914312411yescharacteristic
848C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1521C2
socleC22×C43C22×C22⋊C4
prime radical#121×C43C23
cosocleC22×C4×C43C24
hypercenter#1521D43
hypocenterC43#17601
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #19143682C2semidirect
3. #19137245C2semidirect
5. #19133160C2semidirect
6. #19133157C2semidirect
7. #19133145C2semidirect
8. #19133144C2semidirect
12. #19133105C2semidirect
13. #19133092C2semidirect
16. #14583628C4semidirect
17. #14583627C4semidirect
18. #14583626C4semidirect
19. #14583626C4semidirect
20. #14583619C4semidirect
21. #14583618C4semidirect
22. #14583618C4semidirect
27. D4×Dic86C4semidirect
499. C43#17601semidirect

Maximal subgroups

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

subgroupindex
#191486892
#191436822
#191372452
#191331692
#191331602
#191331572
#191331452
#191331442
#191331332
#191331302
#191331172
#191331052
#191330922
#191330782
C43×#15212
#1760143