Finite Group Databasebeta

← #25063231

Subgroups — #25063231

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133066C212yesmaximal, complemented
5#19133062C212yesmaximal, complemented
6#19133061C211yesmaximal, characteristic, complemented
7#19133060C211yesmaximal, characteristic, complemented
8#19133058C211yesmaximal, characteristic, complemented
9#19132976C212yesmaximal, complemented
10#19132974C212yesmaximal, complemented
11C43×#1495C211yesmaximal, characteristic, complemented
12#14583455C411yescharacteristic
13#14583453C2211yescharacteristic
14#14583451C411yescharacteristic
15#14583448C411yescharacteristic
16#14583446C2211yescharacteristic
17#14583444C411yescharacteristic
18#14583434C411yescharacteristic
19#14583433C2211yescharacteristic
20#14583432—21no—
21#14583432—21no—
22#14583428C411yescharacteristic
23#14583427—21no—
24#14583426—21no—
25#14583412C411yescharacteristic
26#14583409C411yescharacteristic
27#14583408—21no—
28#14583407—21no—
29C4×#10621902C2211yescharacteristic
30#14583367—21no—
31C4×#10621900—21no—
32C4×#10621900C2211yescharacteristic
33C2×C42×D43C2211yescharacteristic
34#14582955—21no—
35#14582955C2212yes—
36#14582952C2211yescharacteristic
37#14582951—21no—
38#14582951—21no—
39#14582951C2212yes—
40#14582950C2212yes—
41#14582949—21no—
42#14582923C2211yescharacteristic
43C4⋊C8×D43—21no—
44#14582862—21no—
45C22⋊C8×D43—21no—
46M16×Dic43—21no—
47C4×C8×D43C2212yes—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic
56C43×#423C2211yescharacteristic
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621900—21no—
62C2×#10621900C2×C411yescharacteristic
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C2×#10621877—21no—
67C2×C8×D43—22no—
68#13063324C2×C411yescharacteristic
69#13063324C2×C411yescharacteristic
70#13063323C2×C411yescharacteristic
71#13063321C2×C411yescharacteristic
72#13063320—21no—
73#13063319—21no—
74#13063318—21no—
75#13063317C2×C411yescharacteristic
76#13063315—21no—
77#13063315—21no—
78#13063313C2×C411yescharacteristic
79#13063311—21no—
80#13063311—21no—
81#13063310—21no—
82#13063310—21no—
83#13063308—21no—
84#13063307—21no—
85#13063307—21no—
86#13063305C2×C411yescharacteristic
87#13063304C2×C411yescharacteristic
88#13063303—21no—
89#13063303—21no—
90#13063303—21no—
91#13063302—21no—
92#13063301C2×C411yescharacteristic
93#13063300C2×C411yescharacteristic
94#13063299C2×C411yescharacteristic
95#13063298—21no—
96#13063298—21no—
97#13063298—21no—
98#13063297—21no—
99#13063296C2×C411yescharacteristic
100#13063295—21no—
101#13063293—21no—
102Q8×Dic43C2×C411yescharacteristic
103C4×Dic86—21no—
104C4×Dic86C2311yescharacteristic
105#13063290—21no—
106#13063290—21no—
107#13063290—21no—
108#13063290C2×C411yescharacteristic
109C4×D172—21no—
110C4×D172C2311yescharacteristic
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic
113#13063287—21no—
114#13063287—21no—
115#13063287—21no—
116#13063287C2×C411yescharacteristic
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(C22⋊D43)⋊C4—21no—
127#13063283—21no—
128#13063283—21no—
129#13063283C2×C411yescharacteristic
130#13063283C2×C411yescharacteristic
131#13063282—21no—
132#13063282—21no—
133#13063281—21no—
134#13063281—21no—
135#13063281—21no—
136C2×C4×Dic43—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)—21no—
150C4⋊(C43⋊C8)—21no—
151C4⋊(C43⋊C8)C2312yes—
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⋊C8C2312yes—
159C8×Dic43—22no—
160C8×Dic43—22no—
161C2×M16×C43—21no—
162#126×C43—21no—
163#125×C43C2×C411yescharacteristic
164#124×C43C2×C411yescharacteristic
165#123×C43—21no—
166C22⋊Q8×C43C2×C411yescharacteristic
167#121×C43C2×C411yescharacteristic
168C4×Q8×C43C2311yescharacteristic
169C4×D4×C43—21no—
170C4×D4×C43C2311yescharacteristic
171#117×C43—21no—
172C2×C42×C43C2311yescharacteristic
173C4⋊C8×C43—21no—
174C4⋊C8×C43—21no—
175C4⋊C8×C43C2312yes—
176C22⋊C8×C43—21no—
177C4×C8×C43C2312yes—
178C23×D43C22⋊C411yescharacteristic
179C2×Q8×C43C22×C411yescharacteristic
180C2×D4×C43—21no—
181C2×D4×C43C22×C411yescharacteristic
182C22×C4×C43—21no—
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43C22⋊C411yescharacteristic
194C22×Dic43C22⋊C411yescharacteristic
195C22×Dic43C22⋊C411yescharacteristic
196#10621902—24no—
197#10621900—24no—
198#10621900—44no—
199#10621898—42no—
200#10621898—42no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172C22×C411yescharacteristic
204C2×C4×D43—24no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—42no—
209C2×C4×D43—41no—
210C2×C4×D43—41no—
211C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86C22×C411yescharacteristic
226M16×C43—42no—
227C2×C8×C43—22no—
228C2×C8×C43—22no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C22×C411yescharacteristic
234C4⋊C4×C43C22×C411yescharacteristic
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C42×C43—21no—
241C42×C43C22×C411yescharacteristic
242C42×C43C2×D411yescharacteristic
243C42×C43C2×D411yescharacteristic
244C42×C43C2411yescharacteristic
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248(C2×D43)⋊C4—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—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43C22×C411yescharacteristic
261C4⋊Dic43C22×C411yescharacteristic
262Dic43⋊C4—21no—
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22×C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289#10621877—42no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—22no—
292C8×D43—44no—
293C23×C43—21no—
294C23×C43C2×C22⋊C411yescharacteristic
295C22×D43—22no—
296C22×D43—21no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43C2×C22⋊C411yescharacteristic
300C22×D43C2×C22⋊C411yescharacteristic
301Q8×C43—22no—
302D4×C43—22no—
303D4×C43—42no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43C2×C22⋊C411yescharacteristic
314C2×C4×C43C2×C22⋊C411yescharacteristic
315C2×C4×C43C2×C22⋊C411yescharacteristic
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C22⋊D43—42no—
320C22⋊D43—42no—
321C22⋊D43—42no—
322C22⋊D43—42no—
323C22⋊D43—42no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—41no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43C2×C22⋊C411yescharacteristic
333C2×Dic43C2×C22⋊C411yescharacteristic
334C2×Dic43C2×C22⋊C411yescharacteristic
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338D172—22no—
339D172—42no—
340D172—42no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—21no—
344C4×D43—21no—
345C4×D43—21no—
346C4×D43—21no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—42no—
357C4×D43—42no—
358C4×D43#13114yes—
359Dic86—22no—
360Dic86—42no—
361Dic86—42no—
362C8×C43—42no—
363C8×C43—42no—
364C43⋊C8—42no—
365C43⋊C8—42no—
366#17477—431nomaximal, Sylow
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43C22×C22⋊C411yescharacteristic
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—44no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43#40812yes—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43C2×#13112yes—
392C4×C43#57511yescharacteristic
393C4×C43#57511yescharacteristic
394Dic43—21no—
395Dic43—21no—
396Dic43—21no—
397Dic43—21no—
398Dic43—41no—
399Dic43—41no—
400Dic43—41no—
401Dic43#40812yes—
402Dic43#42112yes—
403#3444—431no—
404#2920—431no—
405C2×#431—431no—
406#1497—432no—
407#1496—432no—
408#1495—431no—
409#1495—431no—
410#1495—431no—
411#1495D4311yescharacteristic, complemented
412#1476—432no—
413#1476—432no—
414C2×C43—41no—
415C2×C43—81no—
416C2×C43C2×#40811yescharacteristic
417C2×C43#289611yescharacteristic
418C2×C43C2×#42111yescharacteristic
419D43—22no—
420D43—41no—
421D43—81no—
422#533—431no—
423#533—431no—
424#533—431no—
425#532—431no—
426#532—431no—
427#532—431no—
428#529—431no—
429#529—431no—
430#529—431no—
431#529—861no—
432#529—861no—
433#529—861no—
434#529—861no—
435#529C2×D4311yescharacteristic
436#525—431no—
437#525—431no—
438#525—861no—
439#525—861no—
440C4×#41—431no—
441C4×#41—431no—
442C4×#41—861no—
443C4×#41—861no—
444C22×C42—431no—
445#432—432no—
446#432—861no—
447#431—431no—
448#431—432no—
449#431—432no—
450#431—861no—
451#431—861no—
452#431—861no—
453#431C2×D4311yescharacteristic
454#423—431no—
455#423C2×D4311yescharacteristic
456C2×C4⋊C8—861no—
457#407—861no—
458C2×C22⋊C8—861no—
459C4×M16—861no—
460C2×C4×C8—432no—
461Q8⋊C8—432no—
462Q8⋊C8—432no—
463Q8⋊C8—432no—
464Q8⋊C8C2×D4312yescomplemented
465D4⋊C8—432no—
466D4⋊C8—432no—
467D4⋊C8—432no—
468D4⋊C8C2×D4312yescomplemented
469C43#1747711yescharacteristic, complemented, Sylow
470C2×#41—431no—
471C2×#41—431no—
472C2×#41—861no—
473C2×#41—861no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C2×M16—21no—
478C2×M16—861no—
479C22×C8—862no—
480C4⋊Q8—431no—
481C4⋊Q8—431no—
482C4⋊Q8—431no—
483#127—431no—
484#126—21no—
485#126—861no—
486#126—861no—
487#126—861no—
488#125—431no—
489#125—861no—
490#125—861no—
491#125C4×D4311yescharacteristic
492#124—431no—
493#124—861no—
494#124—861no—
495#124C4×D4311yescharacteristic
496#123—21no—
497#123—861no—
498#123—861no—
499#123—861no—
500#123—861no—
501#123—861no—
502C22⋊Q8—431no—
503C22⋊Q8—431no—
504C22⋊Q8—431no—
505C22⋊Q8—861no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508C22⋊Q8—861no—
509C22⋊Q8C4×D4311yescharacteristic
510#121—431no—
511#121—431no—
512#121—431no—
513#121—861no—
514#121—861no—
515#121—861no—
516#121—861no—
517#121C4×D4311yescharacteristic
518#120—861no—
519#120—861no—
520C4×Q8—431no—
521C4×Q8—431no—
522C4×Q8—431no—
523C4×Q8—861no—
524C4×Q8—861no—
525C4×Q8—861no—
526C4×Q8—861no—
527C4×Q8C22×D4311yescharacteristic
528C4×D4—21no—
529C4×D4—431no—
530C4×D4—431no—
531C4×D4—431no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4—861no—
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×D4C22×D4311yescharacteristic
548#117—21no—
549#117—431no—
550#117—431no—
551#117—861no—
552#117—861no—
553#117—861no—
554#117—861no—
555#117—861no—
556#117—861no—
557#117—861no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—861no—
570C2×C42—861no—
571C2×C42C22×D4311yescharacteristic
572C4⋊C8—21no—
573C4⋊C8—21no—
574C4⋊C8—432no—
575C4⋊C8—862no—
576C4⋊C8—861no—
577C4⋊C8—861no—
578C4⋊C8C22×D4312yes—
579C22⋊C8—21no—
580C22⋊C8—862no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—861no—
584#97—862no—
585C4×C8—432no—
586C4×C8—862no—
587C4×C8—862no—
588C4×C8C22×D4312yes—
589C24—431no—
590#41—864no—
591#41—864no—
592#41—1722no—
593#41—1722no—
594#41—1724no—
595C2×Q8—431no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8C2×C4×D4311yescharacteristic
599C2×D4—21no—
600C2×D4—431no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4C2×C4×D4311yescharacteristic
609C22×C4—21no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
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—864no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—1721no—
632C22×C4—1721no—
633C22×C4—1722no—
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637M16—42no—
638M16—1722no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—862no—
642C2×C8—862no—
643C2×C8—1724no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—431no—
649C4⋊C4—431no—
650C4⋊C4—861no—
651C4⋊C4—861no—
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⋊C4C2×C4×D4311yescharacteristic
663C4⋊C4C2×C4×D4311yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—861no—
670C22⋊C4—861no—
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—
682C42—21no—
683C42—431no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—861no—
696C42—861no—
697C42—861no—
698C42—861no—
699C42—861no—
700C42C2×C4×D4311yescharacteristic
701C42D4×D4311yescharacteristic
702C42D4×D4311yescharacteristic
703C42C23×D4311yescharacteristic
704C23—21no—
705C23—431no—
706C23—431no—
707C23—862no—
708C23—861no—
709C23—1721no—
710C23—1721no—
711C23C22⋊C4×D4311yescharacteristic
712Q8—22no—
713Q8—862no—
714Q8—1722no—
715Q8—1722no—
716D4—22no—
717D4—42no—
718D4—862no—
719D4—1722no—
720D4—1722no—
721D4—1722no—
722D4—1722no—
723D4—1722no—
724D4—1722no—
725D4—1722no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—431no—
736C2×C4—431no—
737C2×C4—434no—
738C2×C4—431no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—431no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4C22⋊C4×D4311yescharacteristic
768C2×C4C22⋊C4×D4311yescharacteristic
769C2×C4C22⋊C4×D4311yescharacteristic
770C2×C4C22×C4×D4311yescharacteristic
771C2×C4C2×D4×D4311yescharacteristic
772C2×C4C2×D4×D4311yescharacteristic
773C8—42no—
774C8—42no—
775C8—1722no—
776C8—1722no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—432no—
784C22—861no—
785C22—861no—
786C22—861no—
787C22—861no—
788C22—861no—
789C22—1724no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22C2×C22⋊C4×D4311yescharacteristic
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—432no—
802C4—432no—
803C4—861no—
804C4—861no—
805C4—861no—
806C4—861no—
807C4—1721no—
808C4—1721no—
809C4—1721no—
810C4#131×D4312yes—
811C4#1458369511yescharacteristic
812C4#1458369811yescharacteristic
813C2—41no—
814C2—81no—
815C2—862no—
816C2—3441no—
817C2—1721no—
818C2#408×D4311yescharacteristic
819C2#1914311111yescharacteristic
820C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1495C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC42×C43C24
hypercenter#1495D43
hypocenterC43#17477
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. #431×D43C2semidirect
4. #19133066C2semidirect
5. #19133062C2semidirect
6. #19133061C2semidirect
7. #19133060C2semidirect
8. #19133058C2semidirect
9. #19132976C2semidirect
10. #19132974C2semidirect
11. C43×#1495C2semidirect
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
411. #1495D43semidirect
464. Q8⋊C8C2×D43semidirect
468. D4⋊C8C2×D43semidirect
469. C43#17477semidirect

Maximal subgroups

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

subgroupindex
#191478892
#191432272
#431×D432
#191330662
#191330622
#191330612
#191330602
#191330582
#191329762
#191329742
C43×#14952
#1747743