Finite Group Databasebeta

← #25063559

Subgroups — #25063559

Order 11008.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148188C211yesmaximal, characteristic
2#19143261C211yesmaximal, characteristic, complemented
3#19133065C211yesmaximal, characteristic, complemented
4#19133061C211yesmaximal, characteristic, complemented
5#19133056C211yesmaximal, characteristic, complemented
6#19133043C211yesmaximal, characteristic, complemented
7#19133035C211yesmaximal, characteristic, complemented
8#19133030C211yesmaximal, characteristic, complemented
9#19133013C211yesmaximal, characteristic, complemented
10#19133009C211yesmaximal, characteristic, complemented
11#19133004C211yesmaximal, characteristic, complemented
12#19132991C211yesmaximal, characteristic, complemented
13#19132983C211yesmaximal, characteristic, complemented
14#19132978C211yesmaximal, characteristic, complemented
15C43×#2965C211yesmaximal, characteristic, complemented
16#14583634C411yescharacteristic
17#14583632—21no—
18#14583627C411yescharacteristic
19#14583621—21no—
20#14583619C411yescharacteristic
21#14583598—21no—
22#14583598—21no—
23#14583595C411yescharacteristic
24#14583595C411yescharacteristic
25#14583570C411yescharacteristic
26#14583558C411yescharacteristic
27#14583558C411yescharacteristic
28#14583449C2211yescharacteristic
29#14583445—21no—
30#14583433C2211yescharacteristic
31#14583433C2211yescharacteristic
32#14583427—21no—
33#14583427—21no—
34C4×#10621898C2211yescharacteristic
35C4×#10621898C2211yescharacteristic
36#14583367—21no—
37C2×C4×Dic86C2211yescharacteristic
38#14582960—21no—
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582956C2211yescharacteristic
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582923C2211yescharacteristic
45C2×C4⋊(C43⋊C8)C2211yescharacteristic
46#14582866—21no—
47#14582855—21no—
48#14582631C2211yescharacteristic
49#14582631C2211yescharacteristic
50#14582631C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582628C2211yescharacteristic
57#14582628C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60#14582628C2211yescharacteristic
61#14582628C2211yescharacteristic
62#14582628C2211yescharacteristic
63#14582628C2211yescharacteristic
64C4×#41×C43C2211yescharacteristic
65C43×#446—21no—
66C43×#436—21no—
67C43×#435—21no—
68C43×#435—21no—
69C43×#431C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#431C2211yescharacteristic
72C4×M16×C43C2211yescharacteristic
73C4×M16×C43C2211yescharacteristic
74C2×C4×C8×C43C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898C2×C411yescharacteristic
78C22×Dic86C2×C411yescharacteristic
79C2×#10621877—21no—
80C22×C43⋊C8—21no—
81#13063325C2×C411yescharacteristic
82#13063323—21no—
83#13063322C2×C411yescharacteristic
84#13063321—21no—
85#13063320—21no—
86#13063320—21no—
87#13063319—21no—
88#13063319—21no—
89#13063318—21no—
90#13063318—21no—
91#13063317C2×C411yescharacteristic
92#13063317C2×C411yescharacteristic
93#13063315—21no—
94#13063315—21no—
95#13063314—21no—
96#13063313—21no—
97#13063313C2×C411yescharacteristic
98#13063313C2×C411yescharacteristic
99#13063312—21no—
100#13063311—21no—
101#13063311—21no—
102#13063310—21no—
103#13063310—21no—
104#13063308—21no—
105#13063308—21no—
106#13063307—21no—
107#13063307—21no—
108#13063304C2×C411yescharacteristic
109#13063304C2×C411yescharacteristic
110#13063303—21no—
111#13063303—21no—
112#13063299—21no—
113#13063299C2×C411yescharacteristic
114#13063299C2×C411yescharacteristic
115#13063299C2×C411yescharacteristic
116#13063299C2×C411yescharacteristic
117#13063298—21no—
118#13063298—21no—
119#13063297—21no—
120#13063297—21no—
121#13063297—21no—
122#13063297—21no—
123C4×Dic86—21no—
124C4×Dic86—21no—
125C4×Dic86C2×C411yescharacteristic
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86C2×C411yescharacteristic
128C4×Dic86C2×C411yescharacteristic
129C4×Dic86C2311yescharacteristic
130C4×Dic86C2311yescharacteristic
131#13063290—21no—
132#13063290—21no—
133C4×D172—21no—
134C4×D172C2×C411yescharacteristic
135C4×D172C2×C411yescharacteristic
136C4×D172C2311yescharacteristic
137C4×D172C2311yescharacteristic
138#13063287—21no—
139#13063287—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146(C22⋊D43)⋊C4—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063284C2×C411yescharacteristic
151#13063284C2×C411yescharacteristic
152#13063282—21no—
153#13063282—21no—
154#13063282—21no—
155#13063282—21no—
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×Dic43⋊C4—21no—
158C2×C4×Dic43—21no—
159C42×D43—21no—
160C42×D43—21no—
161C4⋊(C43⋊C8)—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)C2311yescharacteristic
164C4⋊(C43⋊C8)C2311yescharacteristic
165C4⋊(C43⋊C8)C2311yescharacteristic
166C4⋊(C43⋊C8)C2311yescharacteristic
167C22⋊(C43⋊C8)—21no—
168C22⋊(C43⋊C8)—21no—
169C22⋊(C43⋊C8)—21no—
170C22⋊(C43⋊C8)—21no—
171#13063236—21no—
172#13063236—21no—
173C4×C43⋊C8—21no—
174C4×C43⋊C8—21no—
175C2×#41×C43D411yescharacteristic
176C2×M16×C43—21no—
177C2×M16×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—
201C4×C8×C43—21no—
202C4×C8×C43C2311yescharacteristic
203C4×C8×C43C2311yescharacteristic
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206#41×C43—41no—
207#41×C43—41no—
208C2×Q8×C43C22⋊C411yescharacteristic
209C2×D4×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C2×D4×C43C22⋊C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C2×C22⋊D43—21no—
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—
229#10621898—22no—
230#10621898—22no—
231#10621898—41no—
232#10621898—41no—
233#10621898—42no—
234#10621898—42no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172C22×C411yescharacteristic
238C2×D172C22×C411yescharacteristic
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×Dic86—22no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—41no—
249C2×Dic86C22×C411yescharacteristic
250C2×Dic86C22×C411yescharacteristic
251M16×C43—42no—
252M16×C43—42no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—42no—
258C4⋊C4×C43C22⋊C411yescharacteristic
259C4⋊C4×C43C22⋊C411yescharacteristic
260C4⋊C4×C43C22⋊C411yescharacteristic
261C4⋊C4×C43C22⋊C411yescharacteristic
262C4⋊C4×C43C22⋊C411yescharacteristic
263C4⋊C4×C43C22⋊C411yescharacteristic
264C22⋊C4×C43C22⋊C411yescharacteristic
265C22⋊C4×C43C22⋊C411yescharacteristic
266C22⋊C4×C43C22⋊C411yescharacteristic
267C22⋊C4×C43C22⋊C411yescharacteristic
268C22⋊C4×C43C22⋊C411yescharacteristic
269C22⋊C4×C43C22⋊C411yescharacteristic
270C42×C43C22×C411yescharacteristic
271C42×C43C22×C411yescharacteristic
272C42×C43C22×C411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2×D411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2×D411yescharacteristic
279C42×C43C2411yescharacteristic
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284(C2×D43)⋊C4—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—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43C22×C411yescharacteristic
299C4⋊Dic43C22×C411yescharacteristic
300C4⋊Dic43C22×C411yescharacteristic
301C4⋊Dic43C22×C411yescharacteristic
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322#10621877—42no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—42no—
328C23×C43C2×C22⋊C411yescharacteristic
329C23×C43C2×C22⋊C411yescharacteristic
330C23×C43C2×C22⋊C411yescharacteristic
331C22×D43—21no—
332C22×D43—21no—
333Q8×C43—41no—
334D4×C43—41no—
335D4×C43—41no—
336D4×C43—41no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
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×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C23×C411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C22⋊D43—42no—
365C22⋊D43—42no—
366C22⋊D43—42no—
367C22⋊D43—42no—
368C22⋊D43—81no—
369C22⋊D43—81no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—42no—
377C2×Dic43—81no—
378D172—21no—
379D172—21no—
380D172—21no—
381D172—21no—
382D172—42no—
383D172—81no—
384C4×D43—42no—
385C4×D43—42no—
386C4×D43—41no—
387C4×D43—41no—
388C4×D43—41no—
389C4×D43—41no—
390C4×D43—81no—
391C4×D43—81no—
392Dic86—21no—
393Dic86—21no—
394Dic86—21no—
395Dic86—42no—
396Dic86—42no—
397Dic86#13112yes—
398C8×C43—22no—
399C8×C43—41no—
400C8×C43—41no—
401C8×C43—41no—
402C43⋊C8—41no—
403C43⋊C8—41no—
404C43⋊C8—41no—
405C43⋊C8—41no—
406#17516—431nomaximal, Sylow
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—21no—
412C22×C43—21no—
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—21no—
416C22×C43C22×C22⋊C411yescharacteristic
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
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×C43C2×#13111yescharacteristic
434C4×C43#56811yescharacteristic
435C4×C43#57511yescharacteristic
436C4×C43#57511yescharacteristic
437Dic43—22no—
438Dic43—41no—
439Dic43—41no—
440Dic43—41no—
441Dic43—41no—
442Dic43—41no—
443#3480—431no—
444#2965D4311yescharacteristic, complemented
445#2925—431no—
446#1496—431no—
447#1495—431no—
448#1494—431no—
449#1491—431no—
450#1489—431no—
451#1488—431no—
452#1484—431no—
453#1483—431no—
454#1482—431no—
455#1479—431no—
456#1477—431no—
457#1476—431no—
458C2×C43—41no—
459C2×C43—41no—
460C2×C43—41no—
461C2×C43#288011yescharacteristic
462C2×C43#289611yescharacteristic
463C2×C43#290111yescharacteristic
464D43—81no—
465D43—81no—
466#559—431no—
467#559—861no—
468#557—431no—
469#556—431no—
470#556—861no—
471#553—431no—
472#553—431no—
473#553—861no—
474#553—861no—
475#550—431no—
476#548—431no—
477#548—431no—
478#532—431no—
479#532—861no—
480#529—431no—
481#529—431no—
482#529—861no—
483#529—861no—
484C4×#41—431no—
485C4×#41—431no—
486C4×#41—861no—
487C4×#41C2×D4311yescharacteristic
488C2×C4×Q8—431no—
489#446—21no—
490#436—21no—
491#435—21no—
492#435—21no—
493#433—861no—
494#433—861no—
495#432—431no—
496#432—431no—
497#431—431no—
498#431—431no—
499#431C2×D4311yescharacteristic
500#431C2×D4311yescharacteristic
501#431C2×D4311yescharacteristic
502#423—431no—
503C2×C4⋊C8—431no—
504#408—861no—
505#405—861no—
506C4×M16C2×D4311yescharacteristic
507C4×M16C2×D4311yescharacteristic
508C2×C4×C8C2×D4311yescharacteristic
509Q8⋊C8—431no—
510Q8⋊C8—431no—
511Q8⋊C8—431no—
512Q8⋊C8—431no—
513Q8⋊C8—431no—
514Q8⋊C8—431no—
515Q8⋊C8—431no—
516Q8⋊C8—431no—
517D4⋊C8—431no—
518D4⋊C8—431no—
519D4⋊C8—431no—
520D4⋊C8—431no—
521D4⋊C8—431no—
522D4⋊C8—431no—
523D4⋊C8—431no—
524D4⋊C8—431no—
525C43#1751611yescharacteristic, complemented, Sylow
526C2×#41—431no—
527C2×#41—431no—
528C2×#41—861no—
529C2×#41D17211yescharacteristic
530C22×Q8—431no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—861no—
534C22×C8—21no—
535C22×C8—861no—
536C4⋊Q8—431no—
537C4⋊Q8—861no—
538#127—431no—
539#127—861no—
540#126—861no—
541#126—861no—
542#126—861no—
543#126—861no—
544#126—861no—
545#126—861no—
546#125—431no—
547#125—431no—
548#125—861no—
549#125—861no—
550#124—431no—
551#124—431no—
552#124—861no—
553#124—861no—
554#124—861no—
555#124—861no—
556#124—861no—
557#123—861no—
558#123—861no—
559#123—861no—
560#123—861no—
561#123—861no—
562#123—861no—
563C22⋊Q8—431no—
564C22⋊Q8—431no—
565C22⋊Q8—861no—
566C22⋊Q8—861no—
567#121—431no—
568#121—431no—
569#121—431no—
570#121—431no—
571#121—861no—
572#121—861no—
573#121—861no—
574#121—861no—
575#121—861no—
576#121—861no—
577#121—861no—
578C4×Q8—431no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—431no—
584C4×Q8—861no—
585C4×Q8—861no—
586C4×Q8—861no—
587C4×Q8—861no—
588C4×Q8C4×D4311yescharacteristic
589C4×Q8C22⋊D4311yescharacteristic
590C4×D4—431no—
591C4×D4—431no—
592C4×D4—431no—
593C4×D4—431no—
594C4×D4—861no—
595C4×D4—861no—
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×D4—861no—
606C4×D4—861no—
607C4×D4C4×D4311yescharacteristic
608C4×D4C4×D4311yescharacteristic
609C4×D4C4×D4311yescharacteristic
610C4×D4C22⋊D4311yescharacteristic
611C4×D4C22⋊D4311yescharacteristic
612C4×D4C22⋊D4311yescharacteristic
613#117—431no—
614#117—431no—
615#117—861no—
616#117—861no—
617#117—861no—
618#117—861no—
619#117D17211yescharacteristic
620#117D17211yescharacteristic
621#117D17211yescharacteristic
622C2×C4⋊C4—431no—
623C2×C4⋊C4—861no—
624C2×C42—861no—
625C2×C42—861no—
626C2×C42—861no—
627C2×C42C22×D4311yescharacteristic
628C2×C42C22×D4311yescharacteristic
629C2×C42C22×D4311yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—431no—
634C4⋊C8—431no—
635C4⋊C8—431no—
636C4⋊C8—431no—
637C4⋊C8—861no—
638C4⋊C8—861no—
639C22⋊C8—21no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—861no—
643C22⋊C8—861no—
644C22⋊C8—861no—
645C22⋊C8—861no—
646#97—21no—
647#97—21no—
648#97—861no—
649#97—861no—
650C4×C8—21no—
651C4×C8—861no—
652C4×C8—861no—
653C4×C8C22×D4311yescharacteristic
654C4×C8C22×D4311yescharacteristic
655C4×C8C22×D4311yescharacteristic
656C4×C8C22×D4311yescharacteristic
657#41—41no—
658#41—41no—
659#41—862no—
660#41—862no—
661#41—1721no—
662#41—1721no—
663#41—1722no—
664#41—1722no—
665C2×Q8—431no—
666C2×Q8—431no—
667C2×Q8—862no—
668C2×Q8—861no—
669C2×Q8—861no—
670C2×Q8—1721no—
671C2×Q8(C2×D43)⋊C411yescharacteristic
672C2×D4—431no—
673C2×D4—431no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—861no—
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×C4—861no—
693C22×C4C2×C4×D4311yescharacteristic
694C22×C4C2×C4×D4311yescharacteristic
695C22×C4C2×C4×D4311yescharacteristic
696C22×C4C2×D17211yescharacteristic
697C22×C4C2×D17211yescharacteristic
698C22×C4C2×D17211yescharacteristic
699C22×C4C2×C22⋊D4311yescharacteristic
700C22×C4C2×C22⋊D4311yescharacteristic
701C22×C4C2×C22⋊D4311yescharacteristic
702M16—42no—
703M16—42no—
704M16—1722no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—42no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—861no—
714C2×C8—1722no—
715C4⋊C4—431no—
716C4⋊C4—431no—
717C4⋊C4—431no—
718C4⋊C4—431no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4(C2×D43)⋊C411yescharacteristic
734C4⋊C4(C2×D43)⋊C411yescharacteristic
735C4⋊C4(C2×D43)⋊C411yescharacteristic
736C4⋊C4(C2×D43)⋊C411yescharacteristic
737C4⋊C4(C2×D43)⋊C411yescharacteristic
738C4⋊C4(C2×D43)⋊C411yescharacteristic
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—
764C42—861no—
765C42—861no—
766C42—861no—
767C42—861no—
768C42—861no—
769C42C2×C4×D4311yescharacteristic
770C42C2×C4×D4311yescharacteristic
771C42C2×C4×D4311yescharacteristic
772C42C2×D17211yescharacteristic
773C42C2×D17211yescharacteristic
774C42C2×D17211yescharacteristic
775C42C2×C22⋊D4311yescharacteristic
776C42C2×C22⋊D4311yescharacteristic
777C42C2×C22⋊D4311yescharacteristic
778C42C23×D4311yescharacteristic
779C23—861no—
780C23—861no—
781C23C2×(C2×D43)⋊C411yescharacteristic
782C23C2×(C2×D43)⋊C411yescharacteristic
783C23C2×(C2×D43)⋊C411yescharacteristic
784Q8—41no—
785Q8—432no—
786Q8—861no—
787Q8—861no—
788Q8—861no—
789Q8—1722no—
790Q8—1722no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—861no—
795D4—861no—
796D4—861no—
797D4—861no—
798D4—3441no—
799D4—3441no—
800D4—3441no—
801D4—1722no—
802D4—1722no—
803D4—1722no—
804D4—1722no—
805D4—1722no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—3441no—
828C2×C4—3441no—
829C2×C4—3441no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4—1722no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4C2×(C2×D43)⋊C411yescharacteristic
838C2×C4C2×(C2×D43)⋊C411yescharacteristic
839C2×C4C2×(C2×D43)⋊C411yescharacteristic
840C2×C4C2×(C2×D43)⋊C411yescharacteristic
841C2×C4C2×(C2×D43)⋊C411yescharacteristic
842C2×C4C2×(C2×D43)⋊C411yescharacteristic
843C2×C4C2×(C2×D43)⋊C411yescharacteristic
844C2×C4C2×(C2×D43)⋊C411yescharacteristic
845C2×C4C2×(C2×D43)⋊C411yescharacteristic
846C2×C4C22×C4×D4311yescharacteristic
847C2×C4C22×C22⋊D4311yescharacteristic
848C2×C4C22×D17211yescharacteristic
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—1721no—
854C8—1721no—
855C8—1721no—
856C8—1721no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22—1721no—
870C22—1721no—
871C22—1721no—
872C22C22×(C2×D43)⋊C411yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—862no—
884C4—1721no—
885C4—1721no—
886C4—1721no—
887C4—1721no—
888C4—1721no—
889C4#131×D4311yescharacteristic
890C4#1458366411yescharacteristic
891C4#1458369911yescharacteristic
892C4#1458369911yescharacteristic
893C2—41no—
894C2—41no—
895C2—41no—
896C2—3441no—
897C2—3441no—
898C2#1914304211yescharacteristic
899C2#1914311511yescharacteristic
900C2#1914314311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2965C2
socleC22×C43C22×C22⋊C4
prime radical#19148188C2
cosocleC42×C43C24
hypercenter#2965D43
hypocenterC43#17516
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #19143261C2semidirect
3. #19133065C2semidirect
4. #19133061C2semidirect
5. #19133056C2semidirect
6. #19133043C2semidirect
7. #19133035C2semidirect
8. #19133030C2semidirect
9. #19133013C2semidirect
10. #19133009C2semidirect
11. #19133004C2semidirect
12. #19132991C2semidirect
13. #19132983C2semidirect
14. #19132978C2semidirect
15. C43×#2965C2semidirect
444. #2965D43semidirect
525. C43#17516semidirect

Maximal subgroups

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

subgroupindex
#191481882
#191432612
#191330652
#191330612
#191330562
#191330432
#191330352
#191330302
#191330132
#191330092
#191330042
#191329912
#191329832
#191329782
C43×#29652
#1751643