Finite Group Databasebeta

← #25965052

Subgroups — #25965052

Order 11008.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583430C211yesmaximal, characteristic, complemented
2C2×#14583367C211yesmaximal, characteristic, complemented
3#19144763C212yesmaximal, complemented
4#19144730C212yesmaximal, complemented
5#19144699C214yesmaximal, complemented
6#19144672C212yesmaximal, complemented
7#19144639C212yesmaximal, complemented
8#19144608C214yesmaximal, complemented
9#19144543C211yesmaximal, characteristic, complemented
10#19144416C212yesmaximal, complemented
11#19144088C212yesmaximal, complemented
12#19143857C211yesmaximal, characteristic, complemented
13#19143845C211yesmaximal, characteristic
14#19143413C212yesmaximal, complemented
15#19143399C212yesmaximal, complemented
16#19143224C211yesmaximal, characteristic, complemented
17C43×#3094C211yesmaximal, characteristic, complemented
18C22×#10621898C2211yescharacteristic
19C2×#13063358C2212yes—
20C2×#13063351C2212yes—
21#14583430—21no—
22#14583430—21no—
23#14583430—21no—
24#14583430—21no—
25#14583430C2212yes—
26#14583430C2212yes—
27#14583430C2212yescomplemented
28#14583430C2212yescomplemented
29C2×#13063318—21no—
30C2×#13063316C2211yescharacteristic, complemented
31C2×#13063312C2211yescharacteristic, complemented
32C2×#13063306—21no—
33C2×#13063304C2211yescharacteristic
34#14583367—21no—
35#14583367—21no—
36#14583367—21no—
37#14583367—21no—
38#14583367C2212yes—
39#14583367C2212yes—
40#14583367C2212yescomplemented
41#14583367C2212yescomplemented
42C2×#13063290C2211yescharacteristic, complemented
43C2×#13063290C2211yescharacteristic, complemented
44C2×#13063290C2211yescharacteristic, complemented
45C2×D4×Dic43—21no—
46C2×D4×Dic43C2211yescharacteristic, complemented
47C2×#13063287C2211yescharacteristic, complemented
48C2×#13063287C2211yescharacteristic, complemented
49C2×(C22⋊D43)⋊C4—21no—
50C2×(C22⋊D43)⋊C4—21no—
51C2×#13063282—21no—
52C2×#13063281—21no—
53C22×C4×Dic43C2211yescharacteristic
54C2×C42×D43—21no—
55#14583240C2214yescomplemented
56#14583234C2212yescomplemented
57#14583229C2212yescomplemented
58#14583209C2214yescomplemented
59#14583205C2214yescomplemented
60#14583202C2214yescomplemented
61#14583198C2214yescomplemented
62#14583120C2214yescomplemented
63#14583120C2214yescomplemented
64#14583113C2214yescomplemented
65#14583113C2214yescomplemented
66#14583063C2214yescomplemented
67#14583057C2212yescomplemented
68#14583052C2212yescomplemented
69#14583042C2214yes—
70#14583037C2212yes—
71#14583032C2212yes—
72#14583008C2214yescomplemented
73#14583005C2214yescomplemented
74#14582998C2214yescomplemented
75#14582996C2214yescomplemented
76#14582993C2214yescomplemented
77#14582990C2214yescomplemented
78#14582986C2214yescomplemented
79#14582979C2214yescomplemented
80#14582953C2212yescomplemented
81#14582953C2212yescomplemented
82#14582949C2212yescomplemented
83#14582949C2212yescomplemented
84#14582942C2212yescomplemented
85#14582922C2212yescomplemented
86#14582907C2212yescomplemented
87#14582901C2212yes—
88#14582898C2212yes—
89#14582863C2211yescharacteristic
90M16×Dic43C2212yescomplemented
91C2×#121×C43C2211yescharacteristic
92C2×#117×C43C2211yescharacteristic
93C43×#482C2214yescomplemented
94C43×#481C2212yes—
95C43×#480C2212yes—
96C43×#428C2212yescomplemented
97C43×#418C2212yescomplemented
98C43×#407C2211yescharacteristic
99C2×#10621898—21no—
100C2×#10621898—21no—
101C2×#10621898—28no—
102C2×#10621898C2312yes—
103C2×#10621898C2312yes—
104C22×Dic86C2311yescharacteristic
105C22×Dic86C2311yescharacteristic
106C22×D172C2311yescharacteristic
107C22×C22⋊D43—21no—
108C23×Dic43—21no—
109C23×Dic43D411yescharacteristic
110C23×Dic43D411yescharacteristic
111C22×C4×D43—21no—
112C22×C4×D43—21no—
113C22×C4×D43—21no—
114#13063358—28no—
115#13063351—28no—
116C2×Dic172C2314yes—
117C2×#10621873C2314yes—
118C2×#10621883C2314yes—
119C2×#10621882C2314yes—
120C2×#10621877C2312yes—
121#13063318—22no—
122#13063318—22no—
123#13063318—22no—
124#13063318—22no—
125#13063316—21no—
126#13063316—21no—
127#13063316C2312yes—
128#13063316C2312yes—
129#13063312—21no—
130#13063312—21no—
131#13063312C2312yes—
132#13063312C2312yes—
133#13063306—22no—
134#13063306—22no—
135#13063306—22no—
136#13063306—22no—
137#13063304—21no—
138#13063304—21no—
139#13063304C2312yes—
140#13063304C2312yes—
141#13063290—21no—
142#13063290—21no—
143#13063290—21no—
144#13063290—21no—
145#13063290—21no—
146#13063290—21no—
147#13063290C2312yes—
148#13063290C2312yes—
149#13063290C2312yes—
150#13063290C2312yes—
151#13063290C2312yes—
152#13063290C2312yes—
153D4×Dic43—22no—
154D4×Dic43—22no—
155D4×Dic43—22no—
156D4×Dic43—22no—
157D4×Dic43—21no—
158D4×Dic43—21no—
159D4×Dic43C2312yes—
160D4×Dic43C2312yes—
161#13063287—21no—
162#13063287—21no—
163#13063287—21no—
164#13063287—21no—
165#13063287C2312yes—
166#13063287C2312yes—
167#13063287C2312yes—
168#13063287C2312yes—
169(C22⋊D43)⋊C4—22no—
170(C22⋊D43)⋊C4—22no—
171(C22⋊D43)⋊C4—22no—
172(C22⋊D43)⋊C4—22no—
173(C22⋊D43)⋊C4—22no—
174(C22⋊D43)⋊C4—22no—
175(C22⋊D43)⋊C4—22no—
176(C22⋊D43)⋊C4—22no—
177#13063282—22no—
178#13063282—22no—
179#13063282—22no—
180#13063282—22no—
181#13063281—22no—
182#13063281—22no—
183#13063281—22no—
184#13063281—22no—
185C2×C4⋊Dic43—21no—
186C2×C4⋊Dic43C2311yescharacteristic
187C2×Dic43⋊C4—21no—
188C2×Dic43⋊C4—21no—
189C2×Dic43⋊C4—21no—
190C2×Dic43⋊C4—21no—
191C2×Dic43⋊C4—21no—
192C2×C22⋊Dic43—21no—
193C2×C22⋊Dic43—21no—
194C2×C22⋊Dic43—21no—
195C2×C22⋊Dic43—21no—
196C2×(C2×D43)⋊C4—21no—
197C2×(C2×D43)⋊C4—21no—
198C2×C4×Dic43—21no—
199C2×C4×Dic43—21no—
200C2×C4×Dic43—21no—
201C2×C4×Dic43D411yescharacteristic
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43D411yescharacteristic
204C2×C4×Dic43D411yescharacteristic
205C2×C4×Dic43D411yescharacteristic
206C2×C4×Dic43D411yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213C42×D43—22no—
214C42×D43—22no—
215C42×D43—22no—
216C42×D43—22no—
217#13063258C2314yes—
218#13063256C2314yes—
219Dic43⋊C8C2314yes—
220Dic43⋊C8C2314yes—
221#13063250C2314yes—
222#13063248C2314yes—
223#13063248C2314yes—
224#13063248C2314yes—
225#13063247C2314yes—
226#13063245C2314yes—
227C22⋊(C43⋊C8)C2312yes—
228C22⋊(C43⋊C8)C2312yes—
229#13063235C2314yes—
230C8×Dic43C2314yes—
231C22×D4×C43—21no—
232C22×D4×C43C2311yescharacteristic
233C23×C4×C43C2311yescharacteristic
234C2×M16×C43C2312yes—
235#121×C43—21no—
236#121×C43—21no—
237#121×C43C2312yes—
238#121×C43C2312yes—
239#117×C43—21no—
240#117×C43—21no—
241#117×C43C2312yes—
242#117×C43C2312yes—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2311yescharacteristic
246C2×C22⋊C4×C43—21no—
247C2×C22⋊C4×C43—21no—
248C2×C42×C43—21no—
249#107×C43C2314yes—
250#106×C43C2314yes—
251#102×C43C2314yes—
252#102×C43C2314yes—
253C22⋊C8×C43C2312yes—
254C22⋊C8×C43C2312yes—
255C24×C43—21no—
256C24×C43C2×D411yescharacteristic
257C23×D43—21no—
258C2×D4×C43—21no—
259C2×D4×C43—22no—
260C2×D4×C43—22no—
261C2×D4×C43—24no—
262C2×D4×C43—44no—
263C2×D4×C43C2412yes—
264C22×C4×C43—24no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2×D411yescharacteristic
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2411yescharacteristic
272C22×C4×C43C2411yescharacteristic
273C22×C4×C43C2411yescharacteristic
274C2×C22⋊D43—28no—
275C2×C22⋊D43—22no—
276C2×C22⋊D43—22no—
277C22×Dic43—22no—
278C22×Dic43—22no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—42no—
283C22×Dic43—42no—
284C22×Dic43—44no—
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287C22×Dic43C2×D411yescharacteristic
288C22×Dic43C2×D411yescharacteristic
289C22×Dic43C2×D411yescharacteristic
290C22×Dic43C2×D411yescharacteristic
291C22×Dic43C2×D411yescharacteristic
292C22×Dic43C2×D411yescharacteristic
293C22×Dic43C2×D411yescharacteristic
294C22×Dic43C2×D411yescharacteristic
295C22×Dic43C2×D411yescharacteristic
296C22×Dic43C2×D411yescharacteristic
297#10621898—28no—
298#10621898—28no—
299#10621898—24no—
300#10621898—24no—
301#10621898—24no—
302#10621898#4118yes—
303C2×D172—21no—
304C2×D172—24no—
305C2×D172C2412yes—
306C2×C4×D43—28no—
307C2×C4×D43—22no—
308C2×C4×D43—22no—
309C2×C4×D43—22no—
310C2×C4×D43—22no—
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—44no—
314C2×C4×D43—44no—
315C2×Dic86—21no—
316C2×Dic86—24no—
317C2×Dic86—24no—
318C2×Dic86—21no—
319C2×Dic86C2412yes—
320C2×Dic86C2412yes—
321M16×C43—24no—
322C2×C8×C43C2414yes—
323C4⋊C4×C43—21no—
324C4⋊C4×C43—21no—
325C4⋊C4×C43—21no—
326C4⋊C4×C43C2412yes—
327C4⋊C4×C43C2412yes—
328C4⋊C4×C43C2412yes—
329C22⋊C4×C43—22no—
330C22⋊C4×C43—22no—
331C22⋊C4×C43—22no—
332C22⋊C4×C43—22no—
333C42×C43—22no—
334C42×C43—22no—
335C22⋊Dic43—22no—
336C22⋊Dic43—22no—
337C22⋊Dic43—22no—
338C22⋊Dic43—22no—
339C22⋊Dic43—22no—
340C22⋊Dic43—22no—
341C22⋊Dic43—22no—
342C22⋊Dic43—22no—
343#10621883—28no—
344#10621882—28no—
345(C2×D43)⋊C4—22no—
346(C2×D43)⋊C4—22no—
347(C2×D43)⋊C4—22no—
348(C2×D43)⋊C4—22no—
349C4⋊Dic43—21no—
350C4⋊Dic43—22no—
351C4⋊Dic43—22no—
352C4⋊Dic43C2412yes—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
355Dic43⋊C4—22no—
356Dic43⋊C4—22no—
357Dic43⋊C4—22no—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363C4×Dic43—22no—
364C4×Dic43—22no—
365C4×Dic43—22no—
366C4×Dic43—22no—
367C4×Dic43—22no—
368C4×Dic43—22no—
369C4×Dic43C2×D411yescharacteristic
370C4×Dic43C2×D411yescharacteristic
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2411yescharacteristic
382C4×Dic43C2411yescharacteristic
383C4×Dic43C2411yescharacteristic
384C4×Dic43C2411yescharacteristic
385#10621877—24no—
386C2×C43⋊C8C2414yes—
387Dic172—28no—
388#10621873—28no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—41no—
393C23×C43—42no—
394C23×C43—42no—
395C23×C43—42no—
396C23×C43C22×D411yescharacteristic
397C23×C43C22×D411yescharacteristic
398C23×C43C22×D411yescharacteristic
399C22×D43—24no—
400C22×D43—22no—
401C22×D43—42no—
402C22×D43—42no—
403D4×C43—24no—
404D4×C43—44no—
405D4×C43—44no—
406D4×C43—42no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—42no—
416C2×C4×C43—42no—
417C2×C4×C43—42no—
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C22×D411yescharacteristic
420C2×C4×C43C22×D411yescharacteristic
421C2×C4×C43C2×#4114yes—
422C2×C4×C43C2511yescharacteristic
423C22⋊D43—28no—
424C22⋊D43—28no—
425C2×Dic43—24no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—44no—
442C2×Dic43—42no—
443C2×Dic43—42no—
444C2×Dic43—44no—
445C2×Dic43C22×D411yescharacteristic
446C2×Dic43C22×D411yescharacteristic
447C2×Dic43C22×D411yescharacteristic
448C2×Dic43C22×D411yescharacteristic
449C2×Dic43C22×D411yescharacteristic
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452C2×Dic43C22×D411yescharacteristic
453D172—24no—
454D172—22no—
455D172C2×#4114yes—
456C4×D43—28no—
457C4×D43—28no—
458C4×D43—44no—
459C4×D43—44no—
460C4×D43—44no—
461C4×D43—44no—
462Dic86—24no—
463Dic86—22no—
464Dic86—24no—
465Dic86—42no—
466Dic86C2×#4114yes—
467C8×C43—24no—
468C43⋊C8—24no—
469#60563—431nomaximal, Sylow
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—21no—
477C22×C43—44no—
478C22×C43—42no—
479C22×C43—42no—
480C22×C43—42no—
481C22×C43—84no—
482C22×C43#52512yes—
483C22×C43#57512yes—
484C22×C43C23×D411yescharacteristic
485C2×D43—24no—
486C2×D43—48no—
487C2×D43—42no—
488C2×D43—42no—
489C4×C43—21no—
490C4×C43—21no—
491C4×C43—42no—
492C4×C43—42no—
493C4×C43—42no—
494C4×C43#52512yes—
495C4×C43C22×#4112yes—
496Dic43—24no—
497Dic43—21no—
498Dic43—21no—
499Dic43—21no—
500Dic43—21no—
501Dic43—21no—
502Dic43—21no—
503Dic43—21no—
504Dic43—42no—
505Dic43—42no—
506Dic43#57512yes—
507C2×#529—431no—
508C2×C4×#41—431no—
509#3117—432no—
510#3114—432no—
511#3111—434no—
512#3108—432no—
513#3105—432no—
514#3102—434no—
515#3095—431no—
516#3094D4311yescharacteristic, complemented
517#3080—432no—
518#3040—432no—
519#3007—431no—
520#3006—431no—
521C4×#137—432no—
522C4×AGL(1,ℤ/8)—432no—
523#2920—431no—
524C2×C43—22no—
525C2×C43—22no—
526C2×C43—41no—
527C2×C43—82no—
528C2×C43C2×#52511yescharacteristic
529C2×C43C2×#57511yescharacteristic
530C2×C43C2×#57511yescharacteristic
531D43—44no—
532C22×#41—431no—
533C2×#137—432no—
534C2×AGL(1,ℤ/8)—432no—
535#529—432no—
536#529—432no—
537#529—432no—
538#529—432no—
539#529—861no—
540#529—861no—
541#529—861no—
542#529—861no—
543C2×#126—861no—
544C2×#125—431no—
545C2×#124—431no—
546C2×#123—861no—
547C2×C22⋊Q8—431no—
548C2×#121C2×D4311yescharacteristic
549C4×#41—432no—
550C4×#41—432no—
551C4×#41—432no—
552C4×#41—432no—
553C4×#41—861no—
554C4×#41—861no—
555C4×#41—861no—
556C4×#41—861no—
557C2×C4×Q8—431no—
558C2×C4×Q8—431no—
559C2×C4×Q8—431no—
560C2×C4×D4—431no—
561C2×C4×D4—431no—
562C2×C4×D4—431no—
563C2×C4×D4—861no—
564C2×C4×D4—861no—
565C2×C4×D4—861no—
566C2×#117—861no—
567C2×#117—861no—
568C2×#117C2×D4311yescharacteristic
569C22×C42—431no—
570C22×C42—861no—
571#485—434no—
572#484—432no—
573#483—432no—
574#482C2×D4314yescomplemented
575#481C2×D4312yes—
576#480C2×D4312yes—
577#479—434no—
578#479—434no—
579#478—434no—
580#478—434no—
581#464—434no—
582#464—434no—
583#463—434no—
584#463—434no—
585#452—434no—
586#451—432no—
587#450—432no—
588#449—434no—
589#448—432no—
590#447—432no—
591#442—434no—
592#441—434no—
593#440—434no—
594#440—434no—
595C4×Q16—434no—
596C4×SD16—434no—
597C4×SD16—434no—
598C4×D8—434no—
599#432—432no—
600#432—432no—
601#431—432no—
602#431—432no—
603#428—432no—
604#428C2×D4312yescomplemented
605#423—432no—
606#419—432no—
607#418C2×D4312yescomplemented
608#417—432no—
609#417—432no—
610#407—431no—
611#407C2×D4311yescharacteristic
612C4×M16—432no—
613C43#6056311yescharacteristic, complemented, Sylow
614C2×#41—432no—
615C2×#41—432no—
616C2×#41—868no—
617C2×#41—861no—
618C2×#41—861no—
619C22×Q8—431no—
620C22×Q8—431no—
621C22×D4—21no—
622C22×D4—431no—
623C22×D4—861no—
624C22×D4C22×D4311yescharacteristic
625C23×C4—431no—
626C23×C4—431no—
627C23×C4—861no—
628C23×C4—861no—
629C23×C4—861no—
630C23×C4—861no—
631C23×C4C22×D4311yescharacteristic
632#137—868no—
633AGL(1,ℤ/8)—868no—
634C2×Q16—434no—
635C2×SD16—434no—
636C2×SD16—434no—
637C2×D8—434no—
638C2×M16—432no—
639C2×M16C22×D4312yes—
640#126—862no—
641#126—862no—
642#126—862no—
643#126—862no—
644#125—432no—
645#125—432no—
646#125—861no—
647#125—861no—
648#124—432no—
649#124—432no—
650#124—861no—
651#124—861no—
652#123—862no—
653#123—862no—
654#123—862no—
655#123—862no—
656C22⋊Q8—432no—
657C22⋊Q8—432no—
658C22⋊Q8—861no—
659C22⋊Q8—861no—
660#121—21no—
661#121—21no—
662#121C22×D4312yes—
663#121C22×D4312yes—
664C4×Q8—432no—
665C4×Q8—432no—
666C4×Q8—432no—
667C4×Q8—432no—
668C4×Q8—432no—
669C4×Q8—432no—
670C4×Q8—861no—
671C4×Q8—861no—
672C4×Q8—861no—
673C4×Q8—861no—
674C4×Q8—861no—
675C4×Q8—861no—
676C4×D4—432no—
677C4×D4—432no—
678C4×D4—432no—
679C4×D4—432no—
680C4×D4—432no—
681C4×D4—432no—
682C4×D4—861no—
683C4×D4—861no—
684C4×D4—861no—
685C4×D4—861no—
686C4×D4—861no—
687C4×D4—861no—
688C4×D4—862no—
689C4×D4—862no—
690C4×D4—862no—
691C4×D4—862no—
692C4×D4—862no—
693C4×D4—862no—
694C4×D4—862no—
695C4×D4—862no—
696C4×D4—862no—
697C4×D4—862no—
698C4×D4—862no—
699C4×D4—862no—
700#117—21no—
701#117—21no—
702#117—862no—
703#117—862no—
704#117—862no—
705#117—862no—
706#117—862no—
707#117—862no—
708#117—862no—
709#117—862no—
710#117C22×D4312yes—
711#117C22×D4312yes—
712C2×C4⋊C4—431no—
713C2×C4⋊C4—861no—
714C2×C4⋊C4—861no—
715C2×C4⋊C4—861no—
716C2×C4⋊C4—861no—
717C2×C4⋊C4—861no—
718C2×C4⋊C4—861no—
719C2×C4⋊C4C22×D4311yescharacteristic
720C2×C4⋊C4C22×D4311yescharacteristic
721C2×C4⋊C4C22×D4311yescharacteristic
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—861no—
725C2×C22⋊C4—861no—
726C2×C22⋊C4—861no—
727C2×C22⋊C4—861no—
728C2×C22⋊C4—861no—
729C2×C22⋊C4—861no—
730C2×C42—21no—
731C2×C42—431no—
732C2×C42—431no—
733C2×C42—431no—
734C2×C42—431no—
735C2×C42—431no—
736C2×C42—431no—
737C2×C42—431no—
738C2×C42—431no—
739C2×C42—431no—
740C2×C42—431no—
741C2×C42—431no—
742C2×C42—431no—
743C2×C42—862no—
744C2×C42—862no—
745C2×C42—862no—
746C2×C42—862no—
747C2×C42—861no—
748C2×C42—861no—
749C2×C42—861no—
750#107—434no—
751#107C22×D4314yes—
752#106—434no—
753#106C22×D4314yes—
754C4⋊C8—434no—
755C4⋊C8—434no—
756#103—434no—
757#103—434no—
758#103—434no—
759#103—434no—
760#102—434no—
761#102—434no—
762#102C22×D4314yes—
763#102C22×D4314yes—
764C22⋊C8—432no—
765C22⋊C8—432no—
766C22⋊C8C22×D4312yes—
767C22⋊C8C22×D4312yes—
768#97—434no—
769C4×C8—434no—
770C24—21no—
771C24—861no—
772C24D4×D4311yescharacteristic
773#41—438no—
774#41—864no—
775#41—864no—
776#41—868no—
777#41—868no—
778#41—864no—
779C2×Q8—432no—
780C2×Q8—432no—
781C2×Q8—864no—
782C2×Q8—861no—
783C2×Q8—861no—
784C2×Q8—864no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—24no—
789C2×D4—44no—
790C2×D4—432no—
791C2×D4—864no—
792C2×D4—868no—
793C2×D4—862no—
794C2×D4—862no—
795C2×D4—861no—
796C2×D4C23×D4312yes—
797C22×C4—24no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—431no—
805C22×C4—431no—
806C22×C4—431no—
807C22×C4—431no—
808C22×C4—431no—
809C22×C4—431no—
810C22×C4—431no—
811C22×C4—431no—
812C22×C4—431no—
813C22×C4—862no—
814C22×C4—862no—
815C22×C4—862no—
816C22×C4—862no—
817C22×C4—868no—
818C22×C4—862no—
819C22×C4—862no—
820C22×C4—861no—
821C22×C4—862no—
822C22×C4—862no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—1724no—
826C22×C4—1724no—
827C22×C4—1722no—
828C22×C4—1722no—
829C22×C4—1724no—
830C22×C4D4×D4311yescharacteristic
831C22×C4D4×D4311yescharacteristic
832C22×C4D4×D4311yescharacteristic
833C22×C4C23×D4311yescharacteristic
834C22×C4C23×D4311yescharacteristic
835C22×C4C23×D4311yescharacteristic
836Q16—868no—
837SD16—868no—
838SD16—868no—
839D8—868no—
840M16—24no—
841M16—864no—
842C2×C8—434no—
843C2×C8C23×D4314yes—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—432no—
848C4⋊C4—862no—
849C4⋊C4—862no—
850C4⋊C4—862no—
851C4⋊C4—862no—
852C4⋊C4—862no—
853C4⋊C4—862no—
854C4⋊C4—862no—
855C4⋊C4—862no—
856C4⋊C4—862no—
857C4⋊C4—862no—
858C4⋊C4—861no—
859C4⋊C4—862no—
860C4⋊C4—862no—
861C4⋊C4C23×D4312yes—
862C4⋊C4C23×D4312yes—
863C4⋊C4C23×D4312yes—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—862no—
869C22⋊C4—862no—
870C22⋊C4—862no—
871C22⋊C4—862no—
872C22⋊C4—862no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—862no—
876C22⋊C4—862no—
877C22⋊C4—862no—
878C22⋊C4—862no—
879C22⋊C4—862no—
880C42—22no—
881C42—22no—
882C42—431no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42—431no—
894C42—431no—
895C42—431no—
896C42—431no—
897C42—431no—
898C42—862no—
899C42—862no—
900C42—862no—
901C42—862no—
902C42—862no—
903C42—862no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—864no—
912C23—862no—
913C23—1722no—
914C23—1722no—
915C23C2×D4×D4311yescharacteristic
916C23C2×D4×D4311yescharacteristic
917C23C2×D4×D4311yescharacteristic
918Q8—434no—
919Q8—864no—
920Q8—862no—
921Q8—864no—
922Q8—1722no—
923D4—24no—
924D4—44no—
925D4—44no—
926D4—42no—
927D4—434no—
928D4—864no—
929D4—868no—
930D4—868no—
931D4—862no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—431no—
944C2×C4—431no—
945C2×C4—431no—
946C2×C4—431no—
947C2×C4—431no—
948C2×C4—431no—
949C2×C4—431no—
950C2×C4—431no—
951C2×C4—868no—
952C2×C4—862no—
953C2×C4—862no—
954C2×C4—862no—
955C2×C4—864no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—868no—
960C2×C4—862no—
961C2×C4—862no—
962C2×C4—1724no—
963C2×C4—1724no—
964C2×C4—1724no—
965C2×C4—1724no—
966C2×C4—1724no—
967C2×C4—1721no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1721no—
973C2×C4—1721no—
974C2×C4—1724no—
975C2×C4—1722no—
976C2×C4—1722no—
977C2×C4C2×D4×D4311yescharacteristic
978C2×C4C2×D4×D4311yescharacteristic
979C2×C4C2×D4×D4311yescharacteristic
980C2×C4#41×D4314yes—
981C2×C4C24×D4311yescharacteristic
982C8—24no—
983C8—864no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—44no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—84no—
996C22—864no—
997C22—1728no—
998C22—1722no—
999C22—1722no—
1000C22#1458340712yes—
1001C22#1458369512yes—
1002C22C22×D4×D4311yescharacteristic
1003C4—21no—
1004C4—21no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—432no—
1009C4—861no—
1010C4—861no—
1011C4—861no—
1012C4—861no—
1013C4—861no—
1014C4—861no—
1015C4—861no—
1016C4—864no—
1017C4—1722no—
1018C4—1722no—
1019C4#1458340712yes—
1020C4C2×#41×D4312yes—
1021C2—22no—
1022C2—22no—
1023C2—41no—
1024C2—82no—
1025C2—1724no—
1026C2C2×#1458340711yescharacteristic
1027C2#575×D4311yescharacteristic
1028C2C2×#1458369511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
prime radical#19143845C2
hypercenter#3094D43
hypocenterC43#60563
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. C2×#14583430C2semidirect
2. C2×#14583367C2semidirect
3. #19144763C2semidirect
4. #19144730C2semidirect
5. #19144699C2semidirect
6. #19144672C2semidirect
7. #19144639C2semidirect
8. #19144608C2semidirect
9. #19144543C2semidirect
10. #19144416C2semidirect
11. #19144088C2semidirect
12. #19143857C2semidirect
14. #19143413C2semidirect
15. #19143399C2semidirect
16. #19143224C2semidirect
17. C43×#3094C2semidirect
27. #14583430C22semidirect
28. #14583430C22semidirect
30. C2×#13063316C22semidirect
31. C2×#13063312C22semidirect
40. #14583367C22semidirect
41. #14583367C22semidirect
42. C2×#13063290C22semidirect
43. C2×#13063290C22semidirect
44. C2×#13063290C22semidirect
46. C2×D4×Dic43C22semidirect
47. C2×#13063287C22semidirect
48. C2×#13063287C22semidirect
55. #14583240C22semidirect
56. #14583234C22semidirect
57. #14583229C22semidirect
58. #14583209C22semidirect
59. #14583205C22semidirect
60. #14583202C22semidirect
61. #14583198C22semidirect
62. #14583120C22semidirect
63. #14583120C22semidirect
64. #14583113C22semidirect
65. #14583113C22semidirect
66. #14583063C22semidirect
67. #14583057C22semidirect
68. #14583052C22semidirect
72. #14583008C22semidirect
73. #14583005C22semidirect
74. #14582998C22semidirect
75. #14582996C22semidirect
76. #14582993C22semidirect
77. #14582990C22semidirect
78. #14582986C22semidirect
79. #14582979C22semidirect
80. #14582953C22semidirect
81. #14582953C22semidirect
82. #14582949C22semidirect
83. #14582949C22semidirect
84. #14582942C22semidirect
85. #14582922C22semidirect
86. #14582907C22semidirect
90. M16×Dic43C22semidirect
93. C43×#482C22semidirect
96. C43×#428C22semidirect
97. C43×#418C22semidirect
516. #3094D43semidirect
574. #482C2×D43semidirect
604. #428C2×D43semidirect
607. #418C2×D43semidirect
613. C43#60563semidirect

Maximal subgroups

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

subgroupindex
C2×#145834302
C2×#145833672
#191447632
#191447302
#191446992
#191446722
#191446392
#191446082
#191445432
#191444162
#191440882
#191438572
#191438452
#191434132
#191433992
#191432242
C43×#30942
#6056343