Finite Group Databasebeta

← #25063749

Subgroups — #25063749

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3C2×#14582744C211yesmaximal, characteristic, complemented
4#19133105C212yesmaximal, complemented
5#19133101C212yesmaximal, complemented
6#19133100C211yesmaximal, characteristic, complemented
7#19133099C211yesmaximal, characteristic, complemented
8#19133097C211yesmaximal, characteristic, complemented
9#19133080C212yesmaximal, complemented
10#19133078C212yesmaximal, complemented
11C43×#1504C211yesmaximal, characteristic, complemented
12#14583452C411yescharacteristic, complemented
13#14583451C411yescharacteristic, complemented
14#14583451C2211yescharacteristic
15#14583445C411yescharacteristic, complemented
16#14583444C411yescharacteristic, complemented
17#14583444C2211yescharacteristic
18#14583435C411yescharacteristic, complemented
19#14583435C2211yescharacteristic
20#14583430C411yescharacteristic, complemented
21#14583430C2211yescharacteristic
22#14583429—21no—
23#14583429—21no—
24#14583426—21no—
25#14583426—21no—
26#14583410C2211yescharacteristic
27#14583405—21no—
28#14583405—21no—
29#41×Dic43C411yescharacteristic, complemented
30#14583367C411yescharacteristic, complemented
31C4×#10621900—21no—
32C4×#10621900—21no—
33C22×C4×Dic43—21no—
34C22×C4×Dic43C2211yescharacteristic
35#14582953—21no—
36#14582953C2212yes—
37#14582949—21no—
38#14582949C2212yes—
39#14582922—21no—
40#14582863C2211yescharacteristic
41M16×Dic43—21no—
42#14582744—21no—
43#14582744—21no—
44#14582744C2212yes—
45#14582744C2212yes—
46C2×C43⋊#95—21no—
47C2×C43⋊#95C2211yescharacteristic
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#525C2211yescharacteristic
55C43×#407C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621898C2×C411yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43—21no—
63C23×Dic43D411yescharacteristic
64C23×Dic43D411yescharacteristic
65C2×#10621877—21no—
66#13063324C2×C411yescharacteristic, complemented
67#13063324C2×C411yescharacteristic, complemented
68#13063323C2×C411yescharacteristic, complemented
69#13063321C2×C411yescharacteristic, complemented
70#13063320—21no—
71#13063320—21no—
72#13063318—21no—
73#13063318—21no—
74#13063316C2×C411yescharacteristic, complemented
75#13063316C2×C411yescharacteristic, complemented
76#13063315—21no—
77#13063315—21no—
78#13063314C2×C411yescharacteristic, complemented
79#13063312C2×C411yescharacteristic, complemented
80#13063311—21no—
81#13063311—21no—
82#13063309—21no—
83#13063309—21no—
84#13063308—21no—
85#13063306—21no—
86#13063306—21no—
87#13063304C2×C411yescharacteristic
88#13063304C2311yescharacteristic
89#13063302—21no—
90#13063302—21no—
91#13063302—21no—
92#13063302—21no—
93#13063299C2×C411yescharacteristic
94#13063299C2311yescharacteristic
95#13063297—21no—
96#13063297—21no—
97#13063297—21no—
98#13063297—21no—
99#13063294—21no—
100Q8×Dic43C2×C411yescharacteristic, complemented
101Q8×Dic43C2×C411yescharacteristic, complemented
102C4×Dic86—21no—
103C4×Dic86—21no—
104#13063290—21no—
105#13063290—21no—
106#13063290C2×C411yescharacteristic, complemented
107#13063290C2×C411yescharacteristic, complemented
108D4×Dic43—21no—
109D4×Dic43—21no—
110D4×Dic43—21no—
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic, complemented
113D4×Dic43C2×C411yescharacteristic, complemented
114#13063287C2×C411yescharacteristic, complemented
115#13063287C2×C411yescharacteristic, complemented
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126#13063284—21no—
127#13063284C2×C411yescharacteristic
128#13063283—21no—
129#13063283—21no—
130#13063282—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134#13063281—21no—
135C2×C4×Dic43—28no—
136C2×C4×Dic43—22no—
137C2×C4×Dic43—22no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43C2×C411yescharacteristic
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43C2×C411yescharacteristic
142C2×C4×Dic43C2×C411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43C2311yescharacteristic
150C2×C4×Dic43C2311yescharacteristic
151C42×D43—21no—
152Dic43⋊C8—22no—
153Dic43⋊C8—22no—
154C22⋊(C43⋊C8)—21no—
155C22⋊(C43⋊C8)C2312yes—
156#13063235—22no—
157C8×Dic43—22no—
158C43⋊#95—21no—
159C43⋊#95—22no—
160C43⋊#95—22no—
161C43⋊#95C2312yes—
162C2×#41×C43C2×C411yescharacteristic
163C23×C4×C43—21no—
164C23×C4×C43C2311yescharacteristic
165C2×M16×C43—21no—
166#123×C43—21no—
167C22⋊Q8×C43C2×C411yescharacteristic
168C22⋊Q8×C43C2311yescharacteristic
169#121×C43C2×C411yescharacteristic
170#121×C43C2311yescharacteristic
171#120×C43—21no—
172C4×D4×C43—21no—
173C4×D4×C43—21no—
174#117×C43C2×C411yescharacteristic
175C22⋊C8×C43—21no—
176C22⋊C8×C43C2312yes—
177#95×C43—21no—
178#95×C43C2312yes—
179C24×C43C2×D411yescharacteristic
180#41×C43—42no—
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43C22×C411yescharacteristic
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—22no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—21no—
203C22×Dic43—24no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—22no—
208C22×Dic43—41no—
209C22×Dic43—41no—
210C22×Dic43—42no—
211C22×Dic43—42no—
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C22⋊C411yescharacteristic
214C22×Dic43C22⋊C411yescharacteristic
215C22×Dic43C22⋊C411yescharacteristic
216C22×Dic43C22⋊C411yescharacteristic
217C22×Dic43C22⋊C411yescharacteristic
218C22×Dic43C22⋊C411yescharacteristic
219C22×Dic43C22⋊C411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224#10621900—42no—
225#10621900—42no—
226#10621900—44no—
227#10621898—42no—
228C2×D172C22×C411yescharacteristic
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C22×C411yescharacteristic
235M16×C43—42no—
236C2×C8×C43—22no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C22×C411yescharacteristic
240C4⋊C4×C43C22×C411yescharacteristic
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C42×C43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—21no—
251C22⋊Dic43—21no—
252C22⋊Dic43—21no—
253C22⋊Dic43—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43C22×C411yescharacteristic
265C4⋊Dic43C22×C411yescharacteristic
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276C4×Dic43—28no—
277C4×Dic43—28no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282C4×Dic43—21no—
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22⋊C411yescharacteristic
288C4×Dic43C22⋊C411yescharacteristic
289C4×Dic43C22⋊C411yescharacteristic
290C4×Dic43C22⋊C411yescharacteristic
291C4×Dic43C22×C411yescharacteristic
292C4×Dic43C22×C411yescharacteristic
293C4×Dic43C22×C411yescharacteristic
294C4×Dic43C22×C411yescharacteristic
295C4×Dic43C2×D411yescharacteristic
296C4×Dic43C2×D411yescharacteristic
297C4×Dic43C2×D411yescharacteristic
298C4×Dic43C2×D411yescharacteristic
299#10621877—42no—
300C2×C43⋊C8—22no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—21no—
306C23×C43C2×C22⋊C411yescharacteristic
307C23×C43C2×C22⋊C411yescharacteristic
308C23×C43C22×D411yescharacteristic
309C22×D43—21no—
310Q8×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—42no—
315D4×C43—42no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—24no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—42no—
327C2×C4×C43—48no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43C2×C22⋊C411yescharacteristic
331C2×C4×C43C2×C22⋊C411yescharacteristic
332C2×C4×C43C23×C411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C22⋊D43—42no—
335C22⋊D43—41no—
336C22⋊D43—41no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—42no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—24no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—42no—
358C2×Dic43—48no—
359C2×Dic43—42no—
360C2×Dic43—42no—
361C2×Dic43—42no—
362C2×Dic43#10414yes—
363C2×Dic43C2×C22⋊C411yescharacteristic
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
371D172—41no—
372C4×D43—42no—
373C4×D43—42no—
374C4×D43—42no—
375Dic86—42no—
376Dic86—42no—
377Dic86—41no—
378C8×C43—42no—
379C43⋊C8—42no—
380#17541—431nomaximal, Sylow
381C22×C43—24no—
382C22×C43—24no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43#41012yes—
393C22×C43C2×#10412yes—
394C22×C43C22×C22⋊C411yescharacteristic
395C22×C43#57511yescharacteristic
396C22×C43#57511yescharacteristic
397C2×D43—41no—
398C2×D43—41no—
399C2×D43—41no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—44no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—41no—
408Dic43—21no—
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—21no—
414Dic43—44no—
415Dic43—41no—
416Dic43—41no—
417Dic43—41no—
418Dic43C2×#10412yes—
419Dic43C2×#10412yes—
420#3444—431no—
421#2920—431no—
422C2×#376—431no—
423#1506—432no—
424#1505—432no—
425#1504—431no—
426#1504—431no—
427#1504—431no—
428#1504D4311yescharacteristic, complemented
429#1500—432no—
430#1500—432no—
431C2×C43—21no—
432C2×C43—21no—
433C2×C43—22no—
434C2×C43—22no—
435C2×C43—81no—
436C2×C43C2×#41011yescharacteristic
437C2×C43#289611yescharacteristic
438C2×C43C22×#10411yescharacteristic
439D43—81no—
440#533—431no—
441#533—431no—
442#533—431no—
443#532—431no—
444#532—431no—
445#532—431no—
446#529—431no—
447#529—431no—
448#529—431no—
449#529—431no—
450#529—861no—
451#529—861no—
452#529—861no—
453#529—861no—
454#525—431no—
455#525—861no—
456#525—861no—
457#525C2×D4311yescharacteristic
458C4×#41—431no—
459C4×#41—431no—
460C4×#41—861no—
461C4×#41—861no—
462C22×C42—431no—
463C22×C42—861no—
464#432—432no—
465#432—861no—
466#431—432no—
467#431—861no—
468#423—861no—
469#407—431no—
470#407C2×D4311yescharacteristic
471C4×M16—861no—
472#376—432no—
473#376—432no—
474#376—861no—
475#376—861no—
476C2×#95—431no—
477C2×#95—861no—
478C2×#95C2×D4311yescharacteristic
479#328—432no—
480#328—432no—
481#328—432no—
482#328C2×D4312yes—
483#327—432no—
484#327—432no—
485#327—432no—
486#327C2×D4312yes—
487C43#1754111yescharacteristic, complemented, Sylow
488C2×#41—431no—
489C2×#41—861no—
490C2×#41—861no—
491C2×#41C4×D4311yescharacteristic
492C23×C4—21no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C2×M16—21no—
498C2×M16—861no—
499C4⋊Q8—431no—
500C4⋊Q8—431no—
501C4⋊Q8—431no—
502#127—431no—
503#126—861no—
504#126—861no—
505#126—861no—
506#126—861no—
507#125—431no—
508#125—431no—
509#125—861no—
510#125—861no—
511#124—431no—
512#124—431no—
513#124—861no—
514#124—861no—
515#123—21no—
516#123—861no—
517#123—861no—
518#123—861no—
519#123—861no—
520#123—861no—
521C22⋊Q8—431no—
522C22⋊Q8—431no—
523C22⋊Q8—861no—
524C22⋊Q8—861no—
525C22⋊Q8—861no—
526C22⋊Q8—861no—
527C22⋊Q8C4×D4311yescharacteristic
528C22⋊Q8C22×D4311yescharacteristic
529#121—431no—
530#121—431no—
531#121—861no—
532#121—861no—
533#121—861no—
534#121—861no—
535#121C4×D4311yescharacteristic
536#121C22×D4311yescharacteristic
537#120—21no—
538#120—861no—
539C4×Q8—431no—
540C4×Q8—431no—
541C4×Q8—431no—
542C4×Q8—431no—
543C4×Q8—861no—
544C4×Q8—861no—
545C4×Q8—861no—
546C4×Q8—861no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—431no—
550C4×D4—431no—
551C4×D4—431no—
552C4×D4—431no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567#117—431no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117—861no—
574#117—861no—
575#117—861no—
576#117C4×D4311yescharacteristic
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—431no—
588C2×C42—431no—
589C2×C42—861no—
590C2×C42—861no—
591C2×C42—862no—
592C2×C42—862no—
593C2×C42—868no—
594C4⋊C8—862no—
595C4⋊C8—862no—
596C22⋊C8—21no—
597C22⋊C8—432no—
598C22⋊C8—861no—
599C22⋊C8C22×D4312yes—
600#97—862no—
601C4×C8—862no—
602#95—21no—
603#95—432no—
604#95—862no—
605#95—862no—
606#95—861no—
607#95C22×D4312yes—
608C24D4×D4311yescharacteristic
609#41—42no—
610#41—1722no—
611#41—1724no—
612#41—1722no—
613#41—1722no—
614C2×Q8—431no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8C2×C4×D4311yescharacteristic
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—431no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4C2×C4×D4311yescharacteristic
628C22×C4—24no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—864no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—864no—
652C22×C4—862no—
653C22×C4—861no—
654C22×C4—1721no—
655C22×C4—1721no—
656C22×C4—1722no—
657C22×C4—1722no—
658C22×C4C2×C4×D4311yescharacteristic
659C22×C4C2×C4×D4311yescharacteristic
660C22×C4D4×D4311yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664M16—42no—
665M16—1722no—
666C2×C8—22no—
667C2×C8—862no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—431no—
671C4⋊C4—431no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4C2×C4×D4311yescharacteristic
687C4⋊C4C2×C4×D4311yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C22⋊C4—861no—
699C22⋊C4—861no—
700C22⋊C4—861no—
701C22⋊C4—861no—
702C22⋊C4—861no—
703C22⋊C4—861no—
704C22⋊C4—861no—
705C22⋊C4—861no—
706C42—21no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—431no—
718C42—431no—
719C42—431no—
720C42—431no—
721C42—431no—
722C42—431no—
723C42—861no—
724C42—861no—
725C42—861no—
726C42—861no—
727C42—868no—
728C42—868no—
729C42—861no—
730C23—22no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—861no—
736C23C22⋊C4×D4311yescharacteristic
737C23C22⋊C4×D4311yescharacteristic
738C23C2×D4×D4311yescharacteristic
739Q8—41no—
740Q8—1721no—
741Q8—1722no—
742Q8—1722no—
743D4—41no—
744D4—42no—
745D4—42no—
746D4—41no—
747D4—41no—
748D4—1721no—
749D4—1722no—
750D4—1722no—
751D4—1722no—
752D4—1722no—
753D4—1721no—
754D4—1721no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—48no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—431no—
770C2×C4—431no—
771C2×C4—434no—
772C2×C4—431no—
773C2×C4—431no—
774C2×C4—431no—
775C2×C4—431no—
776C2×C4—431no—
777C2×C4—431no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—864no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1722no—
800C2×C4—1728no—
801C2×C4—1722no—
802C2×C4—1722no—
803C2×C4C22⋊C4×D4311yescharacteristic
804C2×C4C22⋊C4×D4311yescharacteristic
805C2×C4C22×C4×D4311yescharacteristic
806C2×C4C2×D4×D4311yescharacteristic
807C8—42no—
808C8—1722no—
809C22—24no—
810C22—24no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—1721no—
821C22—1721no—
822C22—1721no—
823C22#1458287112yes—
824C22#104×D4312yes—
825C22C2×C22⋊C4×D4311yescharacteristic
826C22#1458369511yescharacteristic
827C22#1458369811yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—44no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—432no—
837C4—432no—
838C4—861no—
839C4—861no—
840C4—861no—
841C4—861no—
842C4—861no—
843C4—861no—
844C4—1724no—
845C4—1721no—
846C4—1721no—
847C4—1721no—
848C2—21no—
849C2—21no—
850C2—22no—
851C2—22no—
852C2—81no—
853C2—3441no—
854C2C2×#1458287111yescharacteristic
855C2#1914311111yescharacteristic
856C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1504C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1504D43
hypocenterC43#17541
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. C2×#14582744C2semidirect
4. #19133105C2semidirect
5. #19133101C2semidirect
6. #19133100C2semidirect
7. #19133099C2semidirect
8. #19133097C2semidirect
9. #19133080C2semidirect
10. #19133078C2semidirect
11. C43×#1504C2semidirect
12. #14583452C4semidirect
13. #14583451C4semidirect
15. #14583445C4semidirect
16. #14583444C4semidirect
18. #14583435C4semidirect
20. #14583430C4semidirect
29. #41×Dic43C4semidirect
30. #14583367C4semidirect
66. #13063324C2×C4semidirect
67. #13063324C2×C4semidirect
68. #13063323C2×C4semidirect
69. #13063321C2×C4semidirect
74. #13063316C2×C4semidirect
75. #13063316C2×C4semidirect
78. #13063314C2×C4semidirect
79. #13063312C2×C4semidirect
100. Q8×Dic43C2×C4semidirect
101. Q8×Dic43C2×C4semidirect
106. #13063290C2×C4semidirect
107. #13063290C2×C4semidirect
112. D4×Dic43C2×C4semidirect
113. D4×Dic43C2×C4semidirect
114. #13063287C2×C4semidirect
115. #13063287C2×C4semidirect
428. #1504D43semidirect
487. C43#17541semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191432242
C2×#145827442
#191331052
#191331012
#191331002
#191330992
#191330972
#191330802
#191330782
C43×#15042
#1754143