Finite Group Databasebeta

← #25063230

Subgroups — #25063230

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3C2×#14582950C211yesmaximal, characteristic, complemented
4#19133066C212yesmaximal, complemented
5#19133062C212yesmaximal, complemented
6#19133059C212yesmaximal, complemented
7#19133057C212yesmaximal, complemented
8#19132978C211yesmaximal, characteristic, complemented
9#19132977C211yesmaximal, characteristic, complemented
10#19132975C211yesmaximal, characteristic, complemented
11C43×#1476C211yesmaximal, characteristic, complemented
12#14583453C411yescharacteristic
13#14583453C2211yescharacteristic
14#14583452C411yescharacteristic
15#14583446C411yescharacteristic
16#14583446C2211yescharacteristic
17#14583445C411yescharacteristic
18#14583436C411yescharacteristic
19#14583436C2211yescharacteristic
20#14583431C411yescharacteristic
21#14583431C2211yescharacteristic
22#14583429—21no—
23#14583429—21no—
24#14583427—21no—
25#14583427—21no—
26#14583411C411yescharacteristic
27#14583408—21no—
28#14583408—21no—
29#14583406C411yescharacteristic
30C4×#10621898—21no—
31C4×#10621898—21no—
32C4×#10621898C2211yescharacteristic
33C2×C42×D43C2211yescharacteristic
34#14582955C2212yes—
35#14582953—21no—
36#14582952C2211yescharacteristic
37#14582950—21no—
38#14582950—21no—
39#14582950—21no—
40#14582950C2212yes—
41#14582950C2212yes—
42#14582921C2212yes—
43C2×Dic43⋊C8—21no—
44#14582861—21no—
45C2×(C2×D43)⋊C8—21no—
46C4×#10621872—21no—
47C2×C4×C43⋊C8C2211yescharacteristic
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#431C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2×C411yescharacteristic
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C2×#10621872—22no—
66C22×C43⋊C8—21no—
67#13063324C2×C411yescharacteristic
68#13063324C2×C411yescharacteristic
69#13063323C2×C411yescharacteristic
70#13063321C2×C411yescharacteristic
71#13063320—21no—
72#13063320—21no—
73#13063318—21no—
74#13063318—21no—
75#13063316C2×C411yescharacteristic
76#13063316C2×C411yescharacteristic
77#13063315—21no—
78#13063315—21no—
79#13063314C2×C411yescharacteristic
80#13063312C2×C411yescharacteristic
81#13063311—21no—
82#13063311—21no—
83#13063310—21no—
84#13063310—21no—
85#13063309—21no—
86#13063307—21no—
87#13063307—21no—
88#13063306—21no—
89#13063305C2×C411yescharacteristic
90#13063305C2×C411yescharacteristic
91#13063303—21no—
92#13063303—21no—
93#13063302—21no—
94#13063302—21no—
95#13063301C2×C411yescharacteristic
96#13063301C2×C411yescharacteristic
97#13063300C2×C411yescharacteristic
98#13063300C2×C411yescharacteristic
99#13063298—21no—
100#13063298—21no—
101#13063297—21no—
102#13063297—21no—
103#13063296C2×C411yescharacteristic
104#13063296C2×C411yescharacteristic
105#13063295—21no—
106#13063293—21no—
107C4×Dic86—21no—
108C4×Dic86—21no—
109C4×Dic86—21no—
110C4×Dic86—21no—
111C4×Dic86C2×C411yescharacteristic
112C4×Dic86C2311yescharacteristic
113C4×D172—21no—
114C4×D172—21no—
115C4×D172—21no—
116C4×D172—21no—
117C4×D172C2×C411yescharacteristic
118C4×D172C2311yescharacteristic
119C4×C22⋊D43—21no—
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129#13063284—21no—
130#13063284—21no—
131#13063284C2×C411yescharacteristic
132#13063282—21no—
133#13063282—21no—
134#13063282—21no—
135#13063282—21no—
136#13063282—21no—
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C2×C4×Dic43D411yescharacteristic
140C42×D43—21no—
141C42×D43C2×C411yescharacteristic
142C42×D43C2×C411yescharacteristic
143C42×D43D411yescharacteristic
144C42×D43D411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43C2311yescharacteristic
148C42×D43C2311yescharacteristic
149C4⋊(C43⋊C8)C2312yes—
150Dic43⋊C8—22no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154(C2×D43)⋊C8—22no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063235—22no—
158C4×C43⋊C8—21no—
159C4×C43⋊C8—21no—
160C4×C43⋊C8C2312yes—
161C2×#41×C43C2×C411yescharacteristic
162C22×C8×C43—21no—
163C4×Q8×C43C2×C411yescharacteristic
164C4×Q8×C43C2311yescharacteristic
165C4×D4×C43—21no—
166C4×D4×C43—21no—
167C4×D4×C43C2×C411yescharacteristic
168C4×D4×C43C2311yescharacteristic
169#117×C43—21no—
170#117×C43C2×C411yescharacteristic
171C2×C42×C43—21no—
172C2×C42×C43C2311yescharacteristic
173C4⋊C8×C43C2312yes—
174C22⋊C8×C43—21no—
175C4×C8×C43—21no—
176C4×C8×C43—21no—
177C4×C8×C43C2312yes—
178C23×D43C22⋊C411yescharacteristic
179#41×C43—22no—
180#41×C43—22no—
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C2×C22⋊D43—21no—
195C22×Dic43C22⋊C411yescharacteristic
196C22×Dic43C22⋊C411yescharacteristic
197C22×Dic43C22⋊C411yescharacteristic
198#10621898—22no—
199#10621898—22no—
200#10621898—44no—
201#10621898—44no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172C22×C411yescharacteristic
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C22×C411yescharacteristic
219C2×C4×D43C22×C411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86C22×C411yescharacteristic
227C2×C8×C43—22no—
228C2×C8×C43—22no—
229C2×C8×C43—42no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43C22×C411yescharacteristic
233C4⋊C4×C43C22×C411yescharacteristic
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C42×C43—21no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43C22×C411yescharacteristic
241C42×C43C2×D411yescharacteristic
242C42×C43C2×D411yescharacteristic
243C42×C43C2411yescharacteristic
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—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—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43C22×C411yescharacteristic
264C4⋊Dic43C22×C411yescharacteristic
265Dic43⋊C4—21no—
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—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C22×C411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C2×C43⋊C8—22no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—42no—
293#10621872—44no—
294C23×C43—21no—
295C23×C43C2×C22⋊C411yescharacteristic
296C22×D43—22no—
297C22×D43—21no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43C2×C22⋊C411yescharacteristic
301C22×D43C2×C22⋊C411yescharacteristic
302Q8×C43—21no—
303Q8×C43—21no—
304D4×C43—21no—
305D4×C43—21no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43C2×C22⋊C411yescharacteristic
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43#13112yes—
319C2×C4×C43#13112yes—
320C2×C4×C43C23×C411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C22⋊D43—42no—
328C2×Dic43—22no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43C2×C22⋊C411yescharacteristic
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340D172—21no—
341D172—21no—
342D172—42no—
343D172—42no—
344C4×D43—21no—
345C4×D43—21no—
346C4×D43—21no—
347C4×D43—21no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—41no—
357C4×D43—41no—
358C4×D43—42no—
359C4×D43—42no—
360C4×D43—42no—
361Dic86—21no—
362Dic86—21no—
363Dic86—42no—
364Dic86—42no—
365C8×C43—42no—
366C8×C43—42no—
367C43⋊C8—42no—
368C43⋊C8—42no—
369#17477—431nomaximal, Sylow
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43#40812yes—
376C22×C43C22×C22⋊C411yescharacteristic
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—21no—
380C2×D43—21no—
381C2×D43—21no—
382C2×D43—21no—
383C2×D43—44no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43#40812yes—
393C4×C43#42112yes—
394C4×C43C2×#13111yescharacteristic
395C4×C43C2×#13111yescharacteristic
396C4×C43#57512yes—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—21no—
403Dic43—41no—
404Dic43—41no—
405Dic43—41no—
406#3444—431no—
407#2920—431no—
408C2×#431—431no—
409#1497—432no—
410#1496—432no—
411#1495—432no—
412#1495—432no—
413#1476—431no—
414#1476—431no—
415#1476—431no—
416#1476D4311yescharacteristic, complemented
417C2×C43—22no—
418C2×C43—81no—
419C2×C43C2×#40811yescharacteristic
420C2×C43#289611yescharacteristic
421C2×C43C2×#42111yescharacteristic
422D43—41no—
423D43—41no—
424D43—81no—
425#533—431no—
426#533—431no—
427#533—431no—
428#532—431no—
429#532—431no—
430#532—431no—
431#529—431no—
432#529—431no—
433#529—431no—
434#529—431no—
435#529—861no—
436#529—861no—
437#529—861no—
438#529—861no—
439#525—431no—
440#525—431no—
441#525—861no—
442#525—861no—
443C4×#41—431no—
444C4×#41—861no—
445C4×#41—861no—
446C4×#41C2×D4311yescharacteristic
447C22×C42—431no—
448#432—432no—
449#432—861no—
450#431—432no—
451#431—432no—
452#431—431no—
453#431—861no—
454#431—861no—
455#431—861no—
456#431C2×D4311yescharacteristic
457#423—432no—
458C2×C4⋊C8—861no—
459#407—861no—
460C2×C22⋊C8—861no—
461C4×M16—861no—
462C2×C4×C8—431no—
463C2×C4×C8C2×D4311yescharacteristic
464Q8⋊C8—432no—
465Q8⋊C8—432no—
466Q8⋊C8—432no—
467Q8⋊C8C2×D4312yescomplemented
468D4⋊C8—432no—
469D4⋊C8—432no—
470D4⋊C8—432no—
471D4⋊C8C2×D4312yescomplemented
472C43#1747711yescharacteristic, complemented, Sylow
473C2×#41—431no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41C4×D4311yescharacteristic
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C2×M16—862no—
481C22×C8—21no—
482C22×C8—861no—
483C4⋊Q8—431no—
484C4⋊Q8—431no—
485C4⋊Q8—431no—
486#127—431no—
487#126—861no—
488#126—861no—
489#126—861no—
490#126—861no—
491#125—431no—
492#125—431no—
493#125—861no—
494#125—861no—
495#124—431no—
496#124—431no—
497#124—861no—
498#124—861no—
499#123—861no—
500#123—861no—
501#123—861no—
502#123—861no—
503#123—861no—
504#123—861no—
505C22⋊Q8—431no—
506C22⋊Q8—431no—
507C22⋊Q8—431no—
508C22⋊Q8—431no—
509C22⋊Q8—861no—
510C22⋊Q8—861no—
511C22⋊Q8—861no—
512C22⋊Q8—861no—
513#121—431no—
514#121—431no—
515#121—431no—
516#121—431no—
517#121—861no—
518#121—861no—
519#121—861no—
520#121—861no—
521#120—861no—
522#120—861no—
523C4×Q8—431no—
524C4×Q8—431no—
525C4×Q8—861no—
526C4×Q8—861no—
527C4×Q8—861no—
528C4×Q8—861no—
529C4×Q8C4×D4311yescharacteristic
530C4×Q8C22×D4311yescharacteristic
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—431no—
534C4×D4—431no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4C4×D4311yescharacteristic
550C4×D4C22×D4311yescharacteristic
551#117—21no—
552#117—431no—
553#117—861no—
554#117—861no—
555#117—861no—
556#117—861no—
557#117—861no—
558#117—861no—
559#117—861no—
560#117C4×D4311yescharacteristic
561C2×C42—21no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—861no—
574C2×C42C22×D4311yescharacteristic
575C4⋊C8—432no—
576C4⋊C8—862no—
577C4⋊C8—862no—
578C4⋊C8—862no—
579C4⋊C8C22×D4312yes—
580C22⋊C8—21no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—862no—
584C22⋊C8—861no—
585#97—862no—
586C4×C8—21no—
587C4×C8—21no—
588C4×C8—432no—
589C4×C8—861no—
590C4×C8—861no—
591C4×C8C22×D4312yes—
592C24—431no—
593#41—22no—
594#41—22no—
595#41—862no—
596#41—862no—
597#41—1724no—
598#41—1724no—
599C2×Q8—431no—
600C2×Q8—861no—
601C2×Q8—861no—
602C2×Q8C2×C4×D4311yescharacteristic
603C2×D4—21no—
604C2×D4—431no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4C2×C4×D4311yescharacteristic
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—1722no—
637C22×C4—1722no—
638C22×C4C2×C4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641M16—1724no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—42no—
645C2×C8—862no—
646C2×C8—862no—
647C2×C8—1722no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—431no—
651C4⋊C4—431no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4C2×C4×D4311yescharacteristic
667C4⋊C4C2×C4×D4311yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—861no—
702C42—861no—
703C42—861no—
704C42C2×C4×D4311yescharacteristic
705C42D4×D4311yescharacteristic
706C42D4×D4311yescharacteristic
707C42C23×D4311yescharacteristic
708C23—21no—
709C23—431no—
710C23—431no—
711C23—862no—
712C23—861no—
713C23—1721no—
714C23—1721no—
715C23C22⋊C4×D4311yescharacteristic
716Q8—21no—
717Q8—21no—
718Q8—861no—
719Q8—861no—
720Q8—1722no—
721Q8—1722no—
722D4—21no—
723D4—21no—
724D4—42no—
725D4—861no—
726D4—861no—
727D4—1722no—
728D4—1722no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732D4—1722no—
733D4—1722no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—431no—
743C2×C4—431no—
744C2×C4—431no—
745C2×C4—431no—
746C2×C4—431no—
747C2×C4—431no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—861no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4C22⋊C4×D4311yescharacteristic
772C2×C4C22⋊C4×D4311yescharacteristic
773C2×C4C22⋊C4×D4311yescharacteristic
774C2×C4#1306333112yes—
775C2×C4#1306333312yes—
776C2×C4C22×C4×D4311yescharacteristic
777C2×C4C2×D4×D4311yescharacteristic
778C2×C4C2×D4×D4311yescharacteristic
779C8—42no—
780C8—42no—
781C8—1722no—
782C8—1722no—
783C22—21no—
784C22—21no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—861no—
789C22—861no—
790C22—861no—
791C22—861no—
792C22—861no—
793C22—861no—
794C22—1724no—
795C22—1721no—
796C22—1721no—
797C22—1721no—
798C22#1458286412yes—
799C22C2×C22⋊C4×D4311yescharacteristic
800C4—21no—
801C4—21no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—861no—
806C4—861no—
807C4—861no—
808C4—861no—
809C4—861no—
810C4—861no—
811C4—1721no—
812C4—1721no—
813C4—1721no—
814C4#1458286412yes—
815C4#1458291412yes—
816C4C2×#1306333111yescharacteristic
817C4C2×#1306333311yescharacteristic
818C4#1458369612yes—
819C2—22no—
820C2—81no—
821C2—3441no—
822C2—1721no—
823C2—1721no—
824C2C2×#1458286411yescharacteristic
825C2#1914311011yescharacteristic
826C2C2×#1458291411yescharacteristic
subgroupG/H
centerC42D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1476C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC42×C43C24
hypercenter#1476D43
hypocenterC43#17477
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. C2×#14582950C2semidirect
4. #19133066C2semidirect
5. #19133062C2semidirect
6. #19133059C2semidirect
7. #19133057C2semidirect
8. #19132978C2semidirect
9. #19132977C2semidirect
10. #19132975C2semidirect
11. C43×#1476C2semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
416. #1476D43semidirect
467. Q8⋊C8C2×D43semidirect
471. D4⋊C8C2×D43semidirect
472. C43#17477semidirect

Maximal subgroups

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

subgroupindex
#191478882
#191432232
C2×#145829502
#191330662
#191330622
#191330592
#191330572
#191329782
#191329772
#191329752
C43×#14762
#1747743