Finite Group Databasebeta

← #25064736

Subgroups — #25064736

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#19148550C211yesmaximal, characteristic
2#19143606C211yesmaximal, characteristic, complemented
3#19143244C211yesmaximal, characteristic, complemented
4#19133228C211yesmaximal, characteristic, complemented
5#19133223C211yesmaximal, characteristic, complemented
6#19133223C211yesmaximal, characteristic, complemented
7#19133217C211yesmaximal, characteristic, complemented
8#19133213C211yesmaximal, characteristic, complemented
9#19133212C211yesmaximal, characteristic, complemented
10#19133204C211yesmaximal, characteristic, complemented
11#19133199C211yesmaximal, characteristic, complemented
12#19133193C211yesmaximal, characteristic, complemented
13#19133191C211yesmaximal, characteristic, complemented
14#19133181C211yesmaximal, characteristic, complemented
15C2×C43×#329C211yesmaximal, characteristic, complemented
16#14583631C411yescharacteristic
17#14583618C411yescharacteristic
18#14583611—21no—
19#14583579—21no—
20#14583575—21no—
21Q8×C22⋊D43C411yescharacteristic
22#14583560C411yescharacteristic
23#14583557C411yescharacteristic
24#14583543C411yescharacteristic
25#14583542C411yescharacteristic
26#14583539—21no—
27D4×C22⋊D43C411yescharacteristic
28#14583513—21no—
29#14583487—21no—
30#14583483—21no—
31#14583448C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583428C2211yescharacteristic
34#14583428C2211yescharacteristic
35#124×D43C2211yescharacteristic
36#14583372—21no—
37C4×#10621898C2211yescharacteristic
38#14583027—21no—
39#14582972—21no—
40#14582970—21no—
41C8×C22⋊D43—21no—
42#14582961—21no—
43#14582961—21no—
44#14582956C2211yescharacteristic, complemented
45#14582954C2211yescharacteristic, complemented
46#14582954C2211yescharacteristic, complemented
47#14582954C2211yescharacteristic, complemented
48#14582954C2211yescharacteristic, complemented
49#14582954C2211yescharacteristic, complemented
50#14582954C2211yescharacteristic, complemented
51#14582925—21no—
52#14582865—21no—
53C4×#10621877C2211yescharacteristic, complemented
54#14582851C2211yescharacteristic, complemented
55#97×D43C2211yescharacteristic, complemented
56#14582640C2211yescharacteristic, complemented
57#14582640C2211yescharacteristic, complemented
58#14582640C2211yescharacteristic, complemented
59#14582640C2211yescharacteristic, complemented
60#14582639C2211yescharacteristic
61#14582639C2211yescharacteristic
62#14582639C2211yescharacteristic, complemented
63#14582639C2211yescharacteristic, complemented
64#14582638C2211yescharacteristic, complemented
65#14582638C2211yescharacteristic, complemented
66#14582638C2211yescharacteristic, complemented
67#14582638C2211yescharacteristic, complemented
68C2×#124×C43C2211yescharacteristic
69C2×#97×C43C2211yescharacteristic, complemented
70C2×#97×C43C2211yescharacteristic, complemented
71C43×#329C2211yescharacteristic
72C43×#329C2211yescharacteristic
73C43×#329C2211yescharacteristic, complemented
74C43×#329C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898D411yescharacteristic
77C2×#10621900C2×C411yescharacteristic
78C2×Q8×D43C2×C411yescharacteristic
79C22×C22⋊D43—21no—
80C2×D4×D43C2×C411yescharacteristic
81C2×#10621877—21no—
82C2×#10621872—21no—
83C2×C8×D43—21no—
84#13063323—21no—
85#13063323C2×C411yescharacteristic
86#13063321C2×C411yescharacteristic
87#13063319—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063317C2311yescharacteristic
93#13063314—21no—
94#13063314C2×C411yescharacteristic
95#13063313C2311yescharacteristic
96#13063312C2×C411yescharacteristic
97#13063311—21no—
98#13063311—21no—
99#13063311—21no—
100#13063311—21no—
101#13063309—21no—
102#13063308—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063307—21no—
107#13063306—21no—
108#13063304—21no—
109#13063304C2×C411yescharacteristic
110#13063302—21no—
111#13063302—21no—
112#13063301—21no—
113#13063301—21no—
114#13063301C2×C411yescharacteristic
115#13063301C2×C411yescharacteristic
116#13063299—21no—
117#13063299C2×C411yescharacteristic
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063296C2×C411yescharacteristic
125#13063296C2×C411yescharacteristic
126#13063295—21no—
127#13063294—21no—
128#13063294—21no—
129#13063293—21no—
130Q8×Dic43C2×C411yescharacteristic
131Q8×Dic43C2×C411yescharacteristic
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86D411yescharacteristic
135C4×D172C2×C411yescharacteristic
136C4×D172C2×C411yescharacteristic
137C4×D172D411yescharacteristic
138D4×Dic43C2×C411yescharacteristic
139D4×Dic43C2×C411yescharacteristic
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063284D411yescharacteristic
154#13063282—21no—
155#13063282D411yescharacteristic
156#13063282D411yescharacteristic
157#13063281—21no—
158#13063281—21no—
159#13063281—21no—
160C2×C22⋊Dic43—21no—
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C42×D43C2311yescharacteristic
165C42×D43C2311yescharacteristic
166C4⋊(C43⋊C8)—21no—
167Dic43⋊C8—21no—
168Dic43⋊C8—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174(C2×D43)⋊C8—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063236C2311yescharacteristic
181#13063236C2311yescharacteristic
182#13063236C2311yescharacteristic
183#13063236C2311yescharacteristic
184#13063235—21no—
185C4×C43⋊C8—21no—
186C8×Dic43—21no—
187C22×Q8×C43C2×C411yescharacteristic
188C22×D4×C43C2×C411yescharacteristic
189C22×C8×C43—21no—
190C22×C8×C43—21no—
191#124×C43—21no—
192#124×C43—21no—
193#124×C43C2×C411yescharacteristic
194#124×C43C2×C411yescharacteristic
195#124×C43C2311yescharacteristic
196#124×C43C2311yescharacteristic
197C2×C22⋊C4×C43—21no—
198C2×C22⋊C4×C43—21no—
199C2×C42×C43C2311yescharacteristic
200#97×C43—21no—
201#97×C43—21no—
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205#97×C43C2311yescharacteristic
206C24×C43—21no—
207C23×D43—21no—
208C2×Q8×C43—21no—
209C2×Q8×C43—81no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×Q8×C43C22×C411yescharacteristic
212C2×D4×C43—21no—
213C2×D4×C43—81no—
214C2×D4×C43C22×C411yescharacteristic
215C2×D4×C43C22×C411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43C22⋊C411yescharacteristic
229C2×C22⋊D43C22⋊C411yescharacteristic
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233#10621902—81no—
234Q8×D43—81no—
235#10621900—81no—
236D4×D43—81no—
237#10621898—42no—
238C2×D172—21no—
239C2×D172C22⋊C411yescharacteristic
240C2×D172C22×C411yescharacteristic
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43C22×C411yescharacteristic
245C2×C4×D43C22×C411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×C4×D43C2×D411yescharacteristic
248C2×C4×D43C2×D411yescharacteristic
249C2×C4×D43C2×D411yescharacteristic
250C2×Dic86—21no—
251C2×Dic86C22⋊C411yescharacteristic
252C2×Dic86C22×C411yescharacteristic
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—42no—
258C2×C8×C43—42no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C42×C43C22×C411yescharacteristic
268C42×C43C2×D411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2411yescharacteristic
271C22⋊Dic43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43C22⋊C411yescharacteristic
279C22⋊Dic43C22⋊C411yescharacteristic
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4C22⋊C411yescharacteristic
289(C2×D43)⋊C4C22⋊C411yescharacteristic
290(C2×D43)⋊C4C22⋊C411yescharacteristic
291(C2×D43)⋊C4C22⋊C411yescharacteristic
292C4⋊Dic43—21no—
293C4⋊Dic43—21no—
294C4⋊Dic43C22⋊C411yescharacteristic
295C4⋊Dic43C22⋊C411yescharacteristic
296C4⋊Dic43C22×C411yescharacteristic
297C4⋊Dic43C22×C411yescharacteristic
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C22×C411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319#10621877—42no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324#10621872—42no—
325C8×D43—42no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—42no—
329C23×C43—81no—
330C23×C43—81no—
331C23×C43C2×C22⋊C411yescharacteristic
332C22×D43—21no—
333C22×D43—42no—
334C22×D43—81no—
335C22×D43—81no—
336C22×D43C2×C22⋊C411yescharacteristic
337C22×D43C2×C22⋊C411yescharacteristic
338Q8×C43—41no—
339Q8×C43—41no—
340Q8×C43—81no—
341D4×C43—41no—
342D4×C43—41no—
343D4×C43—81no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—81no—
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C23×C411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C22⋊D43—22no—
357C22⋊D43—22no—
358C22⋊D43—42no—
359C22⋊D43—42no—
360C22⋊D43—42no—
361C22⋊D43—81no—
362C22⋊D43—81no—
363C22⋊D43—81no—
364C22⋊D43—81no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—21no—
368C2×Dic43—42no—
369C2×Dic43—81no—
370C2×Dic43—81no—
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377D172—41no—
378D172—41no—
379D172—81no—
380C4×D43—41no—
381C4×D43—41no—
382C4×D43—41no—
383C4×D43—41no—
384C4×D43—41no—
385C4×D43—41no—
386C4×D43—81no—
387C4×D43—81no—
388C4×D43—81no—
389Dic86—41no—
390Dic86—41no—
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—41no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43—162no—
410C22×C43#42112yes—
411C22×C43C22×C22⋊C411yescharacteristic
412C2×D43—21no—
413C2×D43—21no—
414C2×D43—21no—
415C2×D43—21no—
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—162no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—41no—
429C4×C43—41no—
430Dic43—21no—
431Dic43—21no—
432Dic43—21no—
433Dic43—21no—
434Dic43—21no—
435Dic43—21no—
436Dic43—41no—
437Dic43—41no—
438Dic43—41no—
439#3514—431no—
440#2970—431no—
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×#329D4311yescharacteristic, complemented
454C2×C43—22no—
455C2×C43—81no—
456C2×C43—81no—
457C2×C43#288811yescharacteristic
458C2×C43C2×#42111yescharacteristic
459C2×C43#290111yescharacteristic
460D43—41no—
461D43—41no—
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×#124C2×D4311yescharacteristic
484#518—861no—
485C4×#41—431no—
486#446—861no—
487#435—861no—
488#435—861no—
489C8×D4—861no—
490#433—861no—
491#433—861no—
492#432—431no—
493#432—431no—
494#432—431no—
495#432—431no—
496#432—431no—
497#432—431no—
498#432—431no—
499#424—861no—
500#408—861no—
501C4×M16—431no—
502C4×M16—431no—
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#329C2×D4311yescharacteristic
519#329C2×D4311yescharacteristic
520#329C2×D4311yescharacteristic, complemented
521#329C2×D4311yescharacteristic, complemented
522C43#1767911yescharacteristic, complemented, Sylow
523C2×#41—431no—
524C2×#41—431no—
525C2×#41—431no—
526C22×Q8—431no—
527C22×Q8C4×D4311yescharacteristic
528C22×D4—431no—
529C22×D4—861no—
530C22×D4C4×D4311yescharacteristic
531C2×M16—861no—
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—21no—
546#124—21no—
547#124—431no—
548#124—431no—
549#124—431no—
550#124—861no—
551#124—861no—
552#124—861no—
553#124—861no—
554#124—861no—
555#124C4×D4311yescharacteristic
556#124C4×D4311yescharacteristic
557#124C22×D4311yescharacteristic
558#124C22×D4311yescharacteristic
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×Q8—431no—
592C4×Q8—431no—
593C4×D4—431no—
594C4×D4—431no—
595C4×D4—431no—
596C4×D4—431no—
597C4×D4—431no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611#117—431no—
612#117—431no—
613#117—431no—
614#117—861no—
615#117—861no—
616#117—861no—
617#117—861no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C42—431no—
625C2×C42—431no—
626C2×C42C22×D4311yescharacteristic
627C4⋊C8—861no—
628C4⋊C8—861no—
629C4⋊C8—861no—
630C4⋊C8—861no—
631C4⋊C8—861no—
632C4⋊C8—861no—
633C4⋊C8—861no—
634C22⋊C8—861no—
635C22⋊C8—861no—
636C22⋊C8—861no—
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—861no—
653C4×C8—861no—
654C24—21no—
655C24—861no—
656#41—3441no—
657#41—3441no—
658#41—1722no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8—431no—
662C2×Q8—431no—
663C2×Q8—861no—
664C2×Q8—3441no—
665C2×Q8C2×C4×D4311yescharacteristic
666C2×Q8C2×C4×D4311yescharacteristic
667C2×D4—21no—
668C2×D4—81no—
669C2×D4—431no—
670C2×D4—431no—
671C2×D4—431no—
672C2×D4—431no—
673C2×D4—861no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—3441no—
682C2×D4—1724no—
683C2×D4C2×C4×D4311yescharacteristic
684C2×D4C2×C4×D4311yescharacteristic
685C22×C4—21no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—431no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4C2×C4×D4311yescharacteristic
699C22×C4D4×D4311yescharacteristic
700C22×C4D4×D4311yescharacteristic
701M16—1722no—
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—431no—
717C4⋊C4—431no—
718C4⋊C4—431no—
719C4⋊C4—431no—
720C4⋊C4—431no—
721C4⋊C4—431no—
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—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—431no—
741C22⋊C4—431no—
742C22⋊C4—431no—
743C22⋊C4—431no—
744C22⋊C4—431no—
745C22⋊C4—431no—
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—861no—
756C22⋊C4—861no—
757C22⋊C4—861no—
758C22⋊C4—861no—
759C22⋊C4—861no—
760C22⋊C4—861no—
761C42—431no—
762C42—431no—
763C42—431no—
764C42—431no—
765C42—431no—
766C42—431no—
767C42—861no—
768C42—861no—
769C42—861no—
770C42C2×C4×D4311yescharacteristic
771C42D4×D4311yescharacteristic
772C42D4×D4311yescharacteristic
773C42C23×D4311yescharacteristic
774C23—21no—
775C23—21no—
776C23—42no—
777C23—81no—
778C23—81no—
779C23—431no—
780C23—431no—
781C23—861no—
782C23—3441no—
783C23—3441no—
784C23—1722no—
785C23C22⋊C4×D4311yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—81no—
789Q8—3441no—
790Q8—1721no—
791Q8—1721no—
792D4—41no—
793D4—41no—
794D4—81no—
795D4—862no—
796D4—862no—
797D4—3441no—
798D4—3441no—
799D4—3441no—
800D4—3441no—
801D4—3441no—
802D4—1721no—
803D4—1721no—
804D4—1722no—
805D4—1722no—
806D4—1722no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—81no—
813C2×C4—431no—
814C2×C4—431no—
815C2×C4—431no—
816C2×C4—431no—
817C2×C4—431no—
818C2×C4—431no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—3441no—
823C2×C4—3441no—
824C2×C4—3441no—
825C2×C4—3441no—
826C2×C4—3441no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4—1721no—
832C2×C4—1721no—
833C2×C4—1722no—
834C2×C4C22⋊C4×D4311yescharacteristic
835C2×C4C22⋊C4×D4311yescharacteristic
836C2×C4C22⋊C4×D4311yescharacteristic
837C2×C4C22×C4×D4311yescharacteristic
838C2×C4C2×D4×D4311yescharacteristic
839C2×C4C2×D4×D4311yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—1721no—
845C8—1721no—
846C8—1721no—
847C8—1721no—
848C22—21no—
849C22—21no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—162no—
857C22—861no—
858C22—861no—
859C22—861no—
860C22—861no—
861C22—861no—
862C22—861no—
863C22—1721no—
864C22—1721no—
865C22—1721no—
866C22—6882no—
867C22#1458291412yes—
868C22C2×C22⋊C4×D4311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—41no—
876C4—41no—
877C4—861no—
878C4—861no—
879C4—861no—
880C4—861no—
881C4—861no—
882C4—861no—
883C4—1721no—
884C4—1721no—
885C4—1721no—
886C2—22no—
887C2—81no—
888C2—81no—
889C2—3441no—
890C2—1721no—
891C2—1721no—
892C2#1914307111yescharacteristic
893C2C2×#1458291411yescharacteristic
894C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#329C2
socleC22×C43C22×C22⋊C4
prime radical#19148550C2
cosocleC42×C43C24
hypercenterC2×#329D43
hypocenterC43#17679
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. #19143606C2semidirect
3. #19143244C2semidirect
4. #19133228C2semidirect
5. #19133223C2semidirect
6. #19133223C2semidirect
7. #19133217C2semidirect
8. #19133213C2semidirect
9. #19133212C2semidirect
10. #19133204C2semidirect
11. #19133199C2semidirect
12. #19133193C2semidirect
13. #19133191C2semidirect
14. #19133181C2semidirect
15. C2×C43×#329C2semidirect
44. #14582956C22semidirect
45. #14582954C22semidirect
46. #14582954C22semidirect
47. #14582954C22semidirect
48. #14582954C22semidirect
49. #14582954C22semidirect
50. #14582954C22semidirect
53. C4×#10621877C22semidirect
54. #14582851C22semidirect
55. #97×D43C22semidirect
56. #14582640C22semidirect
57. #14582640C22semidirect
58. #14582640C22semidirect
59. #14582640C22semidirect
62. #14582639C22semidirect
63. #14582639C22semidirect
64. #14582638C22semidirect
65. #14582638C22semidirect
66. #14582638C22semidirect
67. #14582638C22semidirect
69. C2×#97×C43C22semidirect
70. C2×#97×C43C22semidirect
73. C43×#329C22semidirect
74. C43×#329C22semidirect
453. C2×#329D43semidirect
504. C2×#97C2×D43semidirect
505. C2×#97C2×D43semidirect
520. #329C2×D43semidirect
521. #329C2×D43semidirect
522. C43#17679semidirect

Maximal subgroups

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

subgroupindex
#191485502
#191436062
#191432442
#191332282
#191332232
#191332172
#191332132
#191332122
#191332042
#191331992
#191331932
#191331912
#191331812
C2×C43×#3292
#1767943