Finite Group Databasebeta

← #25064746

Subgroups — #25064746

Order 11008.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148556C211yesmaximal, characteristic
2#19143246C211yesmaximal, characteristic, complemented
3#19133229C211yesmaximal, characteristic, complemented
4#19133227C211yesmaximal, characteristic, complemented
5#19133224C211yesmaximal, characteristic, complemented
6#19133218C211yesmaximal, characteristic, complemented
7#19133216C211yesmaximal, characteristic, complemented
8#19133213C211yesmaximal, characteristic, complemented
9#19133205C211yesmaximal, characteristic, complemented
10#19133200C211yesmaximal, characteristic, complemented
11#19133194C211yesmaximal, characteristic, complemented
12#19133192C211yesmaximal, characteristic, complemented
13#19133181C211yesmaximal, characteristic, complemented
14C2×#14582638C211yesmaximal, characteristic, complemented
15C43×#2970C211yesmaximal, characteristic, complemented
16#14583634C411yescharacteristic
17#14583622C411yescharacteristic
18#14583612—21no—
19#14583573—21no—
20#14583573—21no—
21D4×Dic86C411yescharacteristic
22#14583558C411yescharacteristic
23#14583558C411yescharacteristic
24#14583545C411yescharacteristic
25#14583545C411yescharacteristic
26#14583537—21no—
27D4×D172C411yescharacteristic
28#14583521—21no—
29#14583482—21no—
30#14583482—21no—
31#14583449C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583433C2211yescharacteristic
34#14583433C2211yescharacteristic
35C2×#13063313C2211yescharacteristic
36C2×#13063313C2211yescharacteristic
37#14583371—21no—
38#14582960—21no—
39#14582960—21no—
40#14582956C2211yescharacteristic, complemented
41#14582956C2211yescharacteristic, complemented
42#14582956C2211yescharacteristic, complemented
43#14582956C2211yescharacteristic, complemented
44#14582926—21no—
45#14582866—21no—
46C4×#10621877C2211yescharacteristic, complemented
47C2×#13063236C2211yescharacteristic, complemented
48#14582640C2211yescharacteristic, complemented
49#14582640C2211yescharacteristic, complemented
50#14582640C2211yescharacteristic, complemented
51#14582640C2211yescharacteristic, complemented
52#14582638C2211yescharacteristic
53#14582638C2211yescharacteristic
54#14582638C2211yescharacteristic
55#14582638C2211yescharacteristic
56#14582638C2211yescharacteristic, complemented
57#14582638C2211yescharacteristic, complemented
58#14582638C2211yescharacteristic, complemented
59#14582638C2211yescharacteristic, complemented
60#14582638C2211yescharacteristic, complemented
61#14582638C2211yescharacteristic, complemented
62#14582638C2211yescharacteristic, complemented
63#14582638C2211yescharacteristic, complemented
64C4×#41×C43C2211yescharacteristic
65C43×#446—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#432C2211yescharacteristic, complemented
70C43×#432C2211yescharacteristic, complemented
71C43×#432C2211yescharacteristic, complemented
72C4×M16×C43C2211yescharacteristic, complemented
73C2×#97×C43C2211yescharacteristic, complemented
74C2×#97×C43C2211yescharacteristic, complemented
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C22×Dic86C2×C411yescharacteristic
78C22×Dic86C2×C411yescharacteristic
79C22×D172C2×C411yescharacteristic
80C22×D172C2×C411yescharacteristic
81C2×D4×D43—21no—
82C2×#10621877—21no—
83C22×C43⋊C8—21no—
84#13063325C2×C411yescharacteristic
85#13063324—21no—
86#13063322C2×C411yescharacteristic
87#13063320—21no—
88#13063320—21no—
89#13063319—21no—
90#13063319—21no—
91#13063319—21no—
92#13063317C2311yescharacteristic
93#13063314—21no—
94#13063313—21no—
95#13063313—21no—
96#13063313—21no—
97#13063313—21no—
98#13063313C2×C411yescharacteristic
99#13063313C2×C411yescharacteristic
100#13063313C2×C411yescharacteristic
101#13063313C2×C411yescharacteristic
102#13063313C2311yescharacteristic
103#13063313C2311yescharacteristic
104#13063313C2311yescharacteristic
105#13063311—21no—
106#13063311—21no—
107#13063310—21no—
108#13063310—21no—
109#13063310—21no—
110#13063310—21no—
111#13063308—21no—
112#13063308—21no—
113#13063308—21no—
114#13063304C2×C411yescharacteristic
115#13063304C2×C411yescharacteristic
116#13063304C2×C411yescharacteristic
117#13063303—21no—
118#13063303—21no—
119#13063302—21no—
120#13063302—21no—
121#13063301—21no—
122#13063300—21no—
123#13063299—21no—
124#13063299—21no—
125#13063299C2×C411yescharacteristic
126#13063299C2×C411yescharacteristic
127#13063299C2×C411yescharacteristic
128#13063298—21no—
129#13063298—21no—
130#13063297—21no—
131#13063297—21no—
132#13063295—21no—
133#13063295—21no—
134#13063293—21no—
135#13063293—21no—
136C4×Dic86C2×C411yescharacteristic
137C4×Dic86C2×C411yescharacteristic
138C4×Dic86C2×C411yescharacteristic
139C4×D172—21no—
140C4×D172—21no—
141C4×D172C2×C411yescharacteristic
142C4×D172C2×C411yescharacteristic
143C4×D172C2×C411yescharacteristic
144D4×Dic43—21no—
145#13063287—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151#13063283—21no—
152#13063282—21no—
153#13063282—21no—
154#13063282—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4—21no—
159C22⋊C4×D43—21no—
160C22⋊C4×D43—21no—
161C4⋊(C43⋊C8)—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)—21no—
168C22⋊(C43⋊C8)—21no—
169#13063236—21no—
170#13063236C2311yescharacteristic
171#13063236C2311yescharacteristic
172#13063236C2311yescharacteristic
173#13063236C2311yescharacteristic
174C4×C43⋊C8—21no—
175C2×#41×C43D411yescharacteristic
176C2×M16×C43—21no—
177C22×C8×C43—21no—
178C22×C8×C43—21no—
179C4×Q8×C43C2×C411yescharacteristic
180C4×Q8×C43D411yescharacteristic
181C4×D4×C43C2×C411yescharacteristic
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43C2×C411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187#117×C43D411yescharacteristic
188#117×C43D411yescharacteristic
189#117×C43D411yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199#97×C43—21no—
200#97×C43—21no—
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205C4×C8×C43—21no—
206C23×D43—21no—
207C23×D43—21no—
208#41×C43—42no—
209C2×Q8×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C2×D4×C43C22⋊C411yescharacteristic
212C2×D4×C43C22⋊C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229D4×D43—44no—
230#10621898—81no—
231#10621898—81no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—81no—
237C2×D172—81no—
238C2×D172C22×C411yescharacteristic
239C2×D172C22×C411yescharacteristic
240C2×D172C22×C411yescharacteristic
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—81no—
249C2×Dic86—81no—
250C2×Dic86C22×C411yescharacteristic
251C2×Dic86C22×C411yescharacteristic
252C2×Dic86C22×C411yescharacteristic
253M16×C43—42no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—42no—
259C2×C8×C43—42no—
260C4⋊C4×C43C22⋊C411yescharacteristic
261C4⋊C4×C43C22⋊C411yescharacteristic
262C4⋊C4×C43C22⋊C411yescharacteristic
263C4⋊C4×C43C22⋊C411yescharacteristic
264C4⋊C4×C43C22⋊C411yescharacteristic
265C4⋊C4×C43C22⋊C411yescharacteristic
266C22⋊C4×C43C22⋊C411yescharacteristic
267C22⋊C4×C43C22⋊C411yescharacteristic
268C22⋊C4×C43C22⋊C411yescharacteristic
269C22⋊C4×C43C22⋊C411yescharacteristic
270C22⋊C4×C43C22⋊C411yescharacteristic
271C22⋊C4×C43C22⋊C411yescharacteristic
272C42×C43C22×C411yescharacteristic
273C42×C43C22×C411yescharacteristic
274C42×C43C22×C411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2411yescharacteristic
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43—21no—
307C4⋊Dic43C22×C411yescharacteristic
308C4⋊Dic43C22×C411yescharacteristic
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320#10621877—42no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—42no—
326C23×C43C2×C22⋊C411yescharacteristic
327C23×C43C2×C22⋊C411yescharacteristic
328C23×C43C2×C22⋊C411yescharacteristic
329C22×D43—21no—
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—42no—
333C22×D43—42no—
334C22×D43—81no—
335C22×D43—81no—
336C22×D43—81no—
337C22×D43—81no—
338Q8×C43—41no—
339D4×C43—22no—
340D4×C43—22no—
341D4×C43—41no—
342C2×C4×C43—22no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C2×C22⋊C411yescharacteristic
357C2×C4×C43C2×C22⋊C411yescharacteristic
358C2×C4×C43C2×C22⋊C411yescharacteristic
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C23×C411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C22⋊D43—42no—
364C22⋊D43—42no—
365C22⋊D43—81no—
366C22⋊D43—81no—
367C22⋊D43—81no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—81no—
374C2×Dic43—81no—
375D172—41no—
376D172—41no—
377D172—41no—
378D172—42no—
379D172—81no—
380D172—81no—
381D172—81no—
382C4×D43—42no—
383C4×D43—81no—
384C4×D43—81no—
385C4×D43—81no—
386C4×D43—81no—
387Dic86—41no—
388Dic86—41no—
389Dic86—41no—
390Dic86—81no—
391Dic86—81no—
392C8×C43—22no—
393C8×C43—41no—
394C8×C43—41no—
395C8×C43—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398C43⋊C8—41no—
399C43⋊C8—41no—
400#17679—431nomaximal, Sylow
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43#42112yes—
410C22×C43C22×C22⋊C411yescharacteristic
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—41no—
414C2×D43—41no—
415C2×D43—41no—
416C2×D43—41no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—162no—
421C2×D43—162no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—21no—
433C4×C43—21no—
434Dic43—41no—
435Dic43—41no—
436Dic43—41no—
437Dic43—41no—
438Dic43—41no—
439#3514—431no—
440#2970D4311yescharacteristic, complemented
441#2923—431no—
442#1536—431no—
443#1535—431no—
444#1535—431no—
445#1533—431no—
446#1532—431no—
447#1532—431no—
448#1530—431no—
449#1529—431no—
450#1527—431no—
451#1527—431no—
452#1524—431no—
453C2×#329—431no—
454C2×C43—22no—
455C2×C43—41no—
456C2×C43—41no—
457C2×C43#288811yescharacteristic
458C2×C43C2×#42111yescharacteristic
459C2×C43#290111yescharacteristic
460D43—81no—
461D43—81no—
462D43—81no—
463#559—431no—
464#556—431no—
465#555—861no—
466#551—861no—
467#551—861no—
468D4×Q8—431no—
469#548—431no—
470#548—431no—
471#546—431no—
472#546—431no—
473#546—861no—
474D42—431no—
475#542—861no—
476#538—861no—
477#538—861no—
478#532—431no—
479#529—431no—
480#529—431no—
481#529—431no—
482C2×#124—431no—
483C2×#124—431no—
484#518—861no—
485C4×#41C2×D4311yescharacteristic
486#446—21no—
487#435—21no—
488#435—21no—
489C8×D4—21no—
490#433—861no—
491#433—861no—
492#432—431no—
493#432—431no—
494#432—431no—
495#432—431no—
496#432C2×D4311yescharacteristic, complemented
497#432C2×D4311yescharacteristic, complemented
498#432C2×D4311yescharacteristic, complemented
499#424—861no—
500#408—861no—
501C4×M16—431no—
502C4×M16C2×D4311yescharacteristic, complemented
503C2×#97—431no—
504C2×#97C2×D4311yescharacteristic, complemented
505C2×#97C2×D4311yescharacteristic, complemented
506#330—431no—
507#330—431no—
508#330—431no—
509#330—431no—
510#329—431no—
511#329—431no—
512#329—431no—
513#329—431no—
514#329—431no—
515#329—431no—
516#329—431no—
517#329—431no—
518#329—431no—
519#329—431no—
520#329—431no—
521#329—431no—
522C43#1767911yescharacteristic, complemented, Sylow
523C2×#41—431no—
524C2×#41—431no—
525C2×#41D17211yescharacteristic
526C22×Q8—431no—
527C22×Q8—431no—
528C22×D4—431no—
529C22×D4—431no—
530C22×D4—861no—
531C2×M16—21no—
532C2×M16—861no—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—861no—
536C4⋊Q8—431no—
537C4⋊Q8—861no—
538#127—431no—
539#126—861no—
540#126—861no—
541#126—861no—
542#126—861no—
543#126—861no—
544#125—431no—
545#124—431no—
546#124—431no—
547#124—431no—
548#124—431no—
549#124—431no—
550#124—431no—
551#124—431no—
552#124—861no—
553#124—861no—
554#124—861no—
555#124—861no—
556#124—861no—
557#124—861no—
558#124—861no—
559#123—861no—
560#123—861no—
561#123—861no—
562#123—861no—
563#123—861no—
564#123—861no—
565#123—861no—
566C22⋊Q8—431no—
567C22⋊Q8—431no—
568C22⋊Q8—431no—
569C22⋊Q8—861no—
570C22⋊Q8—861no—
571C22⋊Q8—861no—
572C22⋊Q8—861no—
573C22⋊Q8—861no—
574#121—431no—
575#121—431no—
576#121—431no—
577#121—861no—
578#121—861no—
579#121—861no—
580#121—861no—
581#121—861no—
582#121—861no—
583#121—861no—
584#120—861no—
585#120—861no—
586#120—861no—
587#120—861no—
588C4×Q8—431no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8C4×D4311yescharacteristic
592C4×Q8C22⋊D4311yescharacteristic
593C4×D4—431no—
594C4×D4—431no—
595C4×D4—431no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4—861no—
601C4×D4—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4C4×D4311yescharacteristic
606C4×D4C4×D4311yescharacteristic
607C4×D4C4×D4311yescharacteristic
608C4×D4C22⋊D4311yescharacteristic
609C4×D4C22⋊D4311yescharacteristic
610C4×D4C22⋊D4311yescharacteristic
611#117—861no—
612#117—861no—
613#117—861no—
614#117—861no—
615#117D17211yescharacteristic
616#117D17211yescharacteristic
617#117D17211yescharacteristic
618C2×C22⋊C4—861no—
619C2×C22⋊C4—861no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C42C22×D4311yescharacteristic
625C2×C42C22×D4311yescharacteristic
626C2×C42C22×D4311yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—861no—
631C4⋊C8—861no—
632C4⋊C8—861no—
633C4⋊C8—861no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—861no—
638C22⋊C8—861no—
639C22⋊C8—861no—
640C22⋊C8—861no—
641#97—21no—
642#97—21no—
643#97—431no—
644#97—431no—
645#97—431no—
646#97—431no—
647#97—861no—
648#97C22×D4311yescharacteristic
649#97C22×D4311yescharacteristic
650#97C22×D4311yescharacteristic
651#97C22×D4311yescharacteristic
652C4×C8—21no—
653C4×C8—861no—
654C24—861no—
655C24—861no—
656#41—42no—
657#41—3441no—
658#41—3441no—
659C2×Q8—431no—
660C2×Q8—431no—
661C2×Q8—431no—
662C2×Q8—861no—
663C2×Q8—861no—
664C2×Q8—3441no—
665C2×Q8—3441no—
666C2×Q8(C2×D43)⋊C411yescharacteristic
667C2×D4—431no—
668C2×D4—431no—
669C2×D4—431no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—3441no—
680C2×D4—3441no—
681C2×D4—1724no—
682C2×D4(C2×D43)⋊C411yescharacteristic
683C2×D4(C2×D43)⋊C411yescharacteristic
684C2×D4(C2×D43)⋊C411yescharacteristic
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4C2×C4×D4311yescharacteristic
693C22×C4C2×C4×D4311yescharacteristic
694C22×C4C2×C4×D4311yescharacteristic
695C22×C4C2×D17211yescharacteristic
696C22×C4C2×D17211yescharacteristic
697C22×C4C2×D17211yescharacteristic
698C22×C4C2×C22⋊D4311yescharacteristic
699C22×C4C2×C22⋊D4311yescharacteristic
700C22×C4C2×C22⋊D4311yescharacteristic
701M16—42no—
702M16—1722no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—1722no—
714C4⋊C4—431no—
715C4⋊C4—431no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4(C2×D43)⋊C411yescharacteristic
727C4⋊C4(C2×D43)⋊C411yescharacteristic
728C4⋊C4(C2×D43)⋊C411yescharacteristic
729C4⋊C4(C2×D43)⋊C411yescharacteristic
730C4⋊C4(C2×D43)⋊C411yescharacteristic
731C4⋊C4(C2×D43)⋊C411yescharacteristic
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C22⋊C4—861no—
742C22⋊C4—861no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—861no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4(C2×D43)⋊C411yescharacteristic
756C22⋊C4(C2×D43)⋊C411yescharacteristic
757C22⋊C4(C2×D43)⋊C411yescharacteristic
758C22⋊C4(C2×D43)⋊C411yescharacteristic
759C22⋊C4(C2×D43)⋊C411yescharacteristic
760C22⋊C4(C2×D43)⋊C411yescharacteristic
761C42—861no—
762C42—861no—
763C42—861no—
764C42C2×C4×D4311yescharacteristic
765C42C2×C4×D4311yescharacteristic
766C42C2×C4×D4311yescharacteristic
767C42C2×D17211yescharacteristic
768C42C2×D17211yescharacteristic
769C42C2×D17211yescharacteristic
770C42C2×C22⋊D4311yescharacteristic
771C42C2×C22⋊D4311yescharacteristic
772C42C2×C22⋊D4311yescharacteristic
773C42C23×D4311yescharacteristic
774C23—861no—
775C23—861no—
776C23—861no—
777C23—3441no—
778C23—3441no—
779C23—3441no—
780C23—3441no—
781C23—1722no—
782C23—1722no—
783C23C2×(C2×D43)⋊C411yescharacteristic
784C23C2×(C2×D43)⋊C411yescharacteristic
785C23C2×(C2×D43)⋊C411yescharacteristic
786Q8—41no—
787Q8—3441no—
788Q8—3441no—
789Q8—1721no—
790Q8—1721no—
791Q8—1721no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—3441no—
796D4—3441no—
797D4—3441no—
798D4—3441no—
799D4—3441no—
800D4—3441no—
801D4—1721no—
802D4—1721no—
803D4—1721no—
804D4—1722no—
805D4—1722no—
806D4—1722no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—3441no—
822C2×C4—3441no—
823C2×C4—3441no—
824C2×C4—3441no—
825C2×C4—3441no—
826C2×C4—3441no—
827C2×C4—1722no—
828C2×C4C2×(C2×D43)⋊C411yescharacteristic
829C2×C4C2×(C2×D43)⋊C411yescharacteristic
830C2×C4C2×(C2×D43)⋊C411yescharacteristic
831C2×C4C2×(C2×D43)⋊C411yescharacteristic
832C2×C4C2×(C2×D43)⋊C411yescharacteristic
833C2×C4C2×(C2×D43)⋊C411yescharacteristic
834C2×C4C2×(C2×D43)⋊C411yescharacteristic
835C2×C4C2×(C2×D43)⋊C411yescharacteristic
836C2×C4C2×(C2×D43)⋊C411yescharacteristic
837C2×C4C22×C4×D4311yescharacteristic
838C2×C4C22×C22⋊D4311yescharacteristic
839C2×C4C22×D17211yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—1721no—
845C8—1721no—
846C8—1721no—
847C8—1721no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—1721no—
857C22—1721no—
858C22—1721no—
859C22—1721no—
860C22—1721no—
861C22—1721no—
862C22—1721no—
863C22—1721no—
864C22—1721no—
865C22—6882no—
866C22—6882no—
867C22#1458291512yes—
868C22C22×(C2×D43)⋊C411yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—1721no—
882C4—1721no—
883C4—1721no—
884C4—1721no—
885C4—1721no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—3441no—
890C2—3441no—
891C2—3441no—
892C2#1914307311yescharacteristic
893C2C2×#1458291511yescharacteristic
894C2#1914314311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2970C2
socleC22×C43C22×C22⋊C4
prime radical#19148556C2
cosocleC42×C43C24
hypercenter#2970D43
hypocenterC43#17679
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #19143246C2semidirect
3. #19133229C2semidirect
4. #19133227C2semidirect
5. #19133224C2semidirect
6. #19133218C2semidirect
7. #19133216C2semidirect
8. #19133213C2semidirect
9. #19133205C2semidirect
10. #19133200C2semidirect
11. #19133194C2semidirect
12. #19133192C2semidirect
13. #19133181C2semidirect
14. C2×#14582638C2semidirect
15. C43×#2970C2semidirect
40. #14582956C22semidirect
41. #14582956C22semidirect
42. #14582956C22semidirect
43. #14582956C22semidirect
46. C4×#10621877C22semidirect
47. C2×#13063236C22semidirect
48. #14582640C22semidirect
49. #14582640C22semidirect
50. #14582640C22semidirect
51. #14582640C22semidirect
56. #14582638C22semidirect
57. #14582638C22semidirect
58. #14582638C22semidirect
59. #14582638C22semidirect
60. #14582638C22semidirect
61. #14582638C22semidirect
62. #14582638C22semidirect
63. #14582638C22semidirect
69. C43×#432C22semidirect
70. C43×#432C22semidirect
71. C43×#432C22semidirect
72. C4×M16×C43C22semidirect
73. C2×#97×C43C22semidirect
74. C2×#97×C43C22semidirect
440. #2970D43semidirect
496. #432C2×D43semidirect
497. #432C2×D43semidirect
498. #432C2×D43semidirect
502. C4×M16C2×D43semidirect
504. C2×#97C2×D43semidirect
505. C2×#97C2×D43semidirect
522. C43#17679semidirect

Maximal subgroups

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

subgroupindex
#191485562
#191432462
#191332292
#191332272
#191332242
#191332182
#191332162
#191332132
#191332052
#191332002
#191331942
#191331922
#191331812
C2×#145826382
C43×#29702
#1767943