Finite Group Databasebeta

← #25961792

Subgroups — #25961792

Order 11008.

1864 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#19143761C214yesmaximal, complemented
3#19143730C214yesmaximal, complemented
4#19143715C214yesmaximal, complemented
5#19143707C214yesmaximal, complemented
6#19143535C211yesmaximal, characteristic, complemented
7#19143532C211yesmaximal, characteristic, complemented
8#19143325C212yesmaximal, complemented
9#19143317C212yesmaximal, complemented
10#19143313C211yesmaximal, characteristic, complemented
11#19143257C212yesmaximal, complemented
12C2×#14582954C211yesmaximal, characteristic, complemented
13#19143161C212yesmaximal, complemented
14#423×D43C211yesmaximal, characteristic, complemented
15C43×#2932C211yesmaximal, characteristic, complemented
16C2×#13063332C2212yes—
17C2×M16×D43C2212yes—
18#14583456C2211yescharacteristic
19#14583454C411yescharacteristic
20#14583454C411yescharacteristic
21#14583447C411yescharacteristic
22#14583447C411yescharacteristic
23#14583431C2212yes—
24#14583431C2212yes—
25#14583430C412yes—
26#14583430C412yes—
27#14583428C412yes—
28#14583428C412yes—
29#14583409C412yes—
30#14583409C412yes—
31#14583406C2212yes—
32#41×Dic43C2212yes—
33C4×#10621900C2212yes—
34C4×#10621900C2212yes—
35C2×C42×D43C2211yescharacteristic
36#14583028C2214yescomplemented
37#14583028C2214yescomplemented
38#14583027C2214yescomplemented
39#14583027C2214yescomplemented
40#14582975C2214yes—
41#14582974C2214yes—
42#14582973C2214yes—
43#14582971C2214yescomplemented
44#14582971C2214yescomplemented
45#14582970C2214yes—
46#14582968C2214yes—
47#14582967C2214yes—
48C8×C22⋊D43C2214yes—
49(C22⋊D43)⋊C8C2214yes—
50#14582957C2214yescomplemented
51#14582957C2214yescomplemented
52#14582954C2212yes—
53#14582954C2212yes—
54#14582954C2212yes—
55#14582954C2212yes—
56#14582953C2214yescomplemented
57#14582949C2214yescomplemented
58#14582927C2212yes—
59#14582927C2214yescomplemented
60#14582925C2212yes—
61#14582925C2214yescomplemented
62#14582923C2211yescharacteristic
63#14582922C2212yes—
64#14582922C2214yescomplemented
65#14582921C2212yes—
66#14582921C2212yes—
67C2×Dic43⋊C8C2211yescharacteristic
68C2×Dic43⋊C8C2211yescharacteristic
69C2×Dic43⋊C8C2214yescomplemented
70C4⋊C8×D43C2212yes—
71C4⋊C8×D43C2212yes—
72#14582866C2212yes—
73C2×(C2×D43)⋊C8C2211yescharacteristic
74C2×(C2×D43)⋊C8C2211yescharacteristic
75#14582857C2212yes—
76#14582854C2212yes—
77C2×#13063236C2211yescharacteristic
78C2×#131×C43C2212yes—
79C43×#532C2211yescharacteristic
80C43×#435C2214yescomplemented
81C43×#435C2214yescomplemented
82C43×#423C2211yescharacteristic
83C43×#408C2212yes—
84C2×#97×C43C2211yescharacteristic
85C2×#10621900C2×C412yes—
86C2×#10621900C2×C412yes—
87C22×C4×D43C2×C411yescharacteristic
88C22×C4×D43C2×C411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90#13063332—44no—
91C2×#10621877C2312yes—
92C2×#10621877C2314yes—
93C2×#10621872C2314yes—
94M16×D43—44no—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2314yes—
98C2×C8×D43C2314yes—
99#13063325C2×C411yescharacteristic
100#13063325C2×C411yescharacteristic
101#13063318C2×C414yes—
102#13063318C2×C414yes—
103#13063317C2×C412yes—
104#13063316C2×C412yes—
105#13063316C2×C412yes—
106#13063312C2×C412yes—
107#13063312C2×C412yes—
108#13063307C2×C414yes—
109#13063307C2×C414yes—
110#13063306C2×C414yes—
111#13063305C2×C412yes—
112#13063305C2×C412yes—
113#13063304C2×C412yes—
114#13063304C2×C412yes—
115#13063301C2×C412yes—
116#13063301C2×C412yes—
117#13063296C2×C412yes—
118#13063296C2×C412yes—
119#13063296C2×C412yes—
120#13063296C2×C412yes—
121#13063293C2×C414yes—
122Q8×Dic43C2×C412yes—
123Q8×Dic43C2×C412yes—
124C4×Dic86C2312yes—
125C4×Dic86C2312yes—
126#13063290C2×C412yes—
127#13063290C2×C412yes—
128D4×Dic43C2×C412yes—
129D4×Dic43C2×C412yes—
130D4×Dic43C2×C414yes—
131D4×Dic43C2×C414yes—
132D4×Dic43C2×C412yes—
133D4×Dic43C2×C412yes—
134C4×C22⋊D43C2314yes—
135C4×C22⋊D43C2314yes—
136(C22⋊D43)⋊C4C2×C414yes—
137(C22⋊D43)⋊C4C2×C414yes—
138#13063284C2312yes—
139#13063284C2314yes—
140#13063283C2×C412yes—
141#13063283C2×C412yes—
142#13063281C2×C414yes—
143#13063281C2×C414yes—
144C2×C4×Dic43C2×C411yescharacteristic
145C2×C4×Dic43C2×C411yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147C2×C4×Dic43C2314yes—
148C42×D43C2×C411yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43C2×C411yescharacteristic
151C42×D43C2×C411yescharacteristic
152C42×D43C2311yescharacteristic
153C42×D43C2311yescharacteristic
154C42×D43C2311yescharacteristic
155C42×D43C2311yescharacteristic
156C4⋊(C43⋊C8)C2312yes—
157C4⋊(C43⋊C8)C2312yes—
158Dic43⋊C8C2314yes—
159Dic43⋊C8C2314yes—
160Dic43⋊C8C2312yes—
161Dic43⋊C8C2312yes—
162Dic43⋊C8C2312yes—
163Dic43⋊C8C2312yes—
164Dic43⋊C8C2314yes—
165Dic43⋊C8C2314yes—
166Dic43⋊C8C2314yes—
167Dic43⋊C8C2314yes—
168C22⋊(C43⋊C8)C2314yes—
169C22⋊(C43⋊C8)C2314yes—
170(C2×D43)⋊C8C2312yes—
171(C2×D43)⋊C8C2312yes—
172(C2×D43)⋊C8C2312yes—
173(C2×D43)⋊C8C2312yes—
174#13063236C2312yes—
175#13063236C2312yes—
176#13063235C2314yes—
177#13063235C2314yes—
178C8×Dic43C2314yes—
179C8×Dic43C2314yes—
180C2×#41×C43C2312yes—
181#131×C43—44no—
182C2×M16×C43C2312yes—
183C2×M16×C43C2314yes—
184C22×C8×C43C2311yescharacteristic
185C22×C8×C43C2311yescharacteristic
186C22×C8×C43C2314yes—
187C4⋊Q8×C43C2×C411yescharacteristic
188#127×C43C2×C411yescharacteristic
189#124×C43C2×C412yes—
190#121×C43C2×C412yes—
191#121×C43C2×C412yes—
192C4×D4×C43C2312yes—
193C4×D4×C43C2312yes—
194C2×C42×C43C2311yescharacteristic
195C4⋊C8×C43C2312yes—
196C4⋊C8×C43C2312yes—
197C22⋊C8×C43C2314yes—
198C22⋊C8×C43C2314yes—
199#97×C43C2312yes—
200#97×C43C2312yes—
201C23×D43C22×C411yescharacteristic
202#41×C43—24no—
203#41×C43—24no—
204C2×Q8×C43C22×C412yes—
205C2×D4×C43C22×C414yes—
206C2×D4×C43C22×C412yes—
207C2×D4×C43C22×C412yes—
208C2×D4×C43C22×C412yes—
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C2414yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43C22×C414yes—
214C2×C22⋊D43C22×C414yes—
215C22×Dic43C22×C411yescharacteristic
216C22×Dic43C22×C411yescharacteristic
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C414yes—
220#10621900—44no—
221#10621900—44no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×C4×D43C22×C411yescharacteristic
227C2×C4×D43C22×C411yescharacteristic
228C2×C4×D43C22×C411yescharacteristic
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C22×C411yescharacteristic
231C2×C4×D43C22×C411yescharacteristic
232C2×C4×D43C22×C411yescharacteristic
233C2×C4×D43C22×C411yescharacteristic
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C2411yescharacteristic
237C2×C4×D43C2411yescharacteristic
238C2×Dic86C22×C412yes—
239C2×Dic86C22×C412yes—
240M16×C43—24no—
241M16×C43—44no—
242C2×C8×C43—22no—
243C2×C8×C43—22no—
244C2×C8×C43—44no—
245C2×C8×C43C2412yes—
246C2×C8×C43C2412yes—
247C2×C8×C43C2414yes—
248C4⋊C4×C43C22×C412yes—
249C4⋊C4×C43C22×C412yes—
250C22⋊C4×C43C22×C414yes—
251C22⋊C4×C43C22×C414yes—
252C42×C43C22×C411yescharacteristic
253C42×C43C22×C411yescharacteristic
254C42×C43C2411yescharacteristic
255C42×C43C2411yescharacteristic
256C22⋊Dic43C22×C414yes—
257C22⋊Dic43C22×C414yes—
258C22⋊Dic43C22×C414yes—
259C22⋊Dic43C22×C414yes—
260C22⋊Dic43C22×C414yes—
261(C2×D43)⋊C4C22×C414yes—
262(C2×D43)⋊C4C22×C414yes—
263C4⋊Dic43C22×C412yes—
264C4⋊Dic43C22×C412yes—
265C4⋊Dic43C22×C412yes—
266C4⋊Dic43C22×C412yes—
267C4⋊Dic43C22×C414yes—
268C4⋊Dic43C22×C414yes—
269Dic43⋊C4C22×C414yes—
270Dic43⋊C4C22×C414yes—
271Dic43⋊C4C22×C414yes—
272Dic43⋊C4C22×C414yes—
273C4×Dic43C22×C411yescharacteristic
274C4×Dic43C22×C411yescharacteristic
275C4×Dic43C22×C411yescharacteristic
276C4×Dic43C22×C411yescharacteristic
277C4×Dic43C22×C411yescharacteristic
278C4×Dic43C22×C411yescharacteristic
279C4×Dic43C22×C411yescharacteristic
280C4×Dic43C22×C411yescharacteristic
281C4×Dic43C22×C411yescharacteristic
282C4×Dic43C22×C411yescharacteristic
283C4×Dic43C22×C414yes—
284C4×Dic43C22×C414yes—
285C4×Dic43C2414yes—
286C4×Dic43C2411yescharacteristic
287C4×Dic43C2411yescharacteristic
288#10621877—24no—
289#10621877—44no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—44no—
293C2×C43⋊C8C2412yes—
294C2×C43⋊C8C2414yes—
295C2×C43⋊C8C2412yes—
296#10621872—44no—
297C8×D43—44no—
298C23×C43C23×C414yes—
299C23×C43C23×C411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—41no—
303C22×D43C23×C411yescharacteristic
304C22×D43C23×C411yescharacteristic
305Q8×C43—24no—
306D4×C43—28no—
307D4×C43—24no—
308D4×C43—42no—
309D4×C43—42no—
310C2×C4×C43—24no—
311C2×C4×C43—24no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C23×C411yescharacteristic
316C2×C4×C43C23×C414yes—
317C2×C4×C43C23×C411yescharacteristic
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C43H(5,𝔽2)12yes—
321C2×C4×C432−1+412yes—
322C2×C4×C43C2511yescharacteristic
323C22⋊D43—28no—
324C22⋊D43—44no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—28no—
328C2×Dic43—41no—
329C2×Dic43—44no—
330C2×Dic43C23×C411yescharacteristic
331C2×Dic43C23×C411yescharacteristic
332C2×Dic43C23×C411yescharacteristic
333C2×Dic43C23×C411yescharacteristic
334C2×Dic43C23×C411yescharacteristic
335C2×Dic43C23×C414yes—
336C2×Dic43C23×C414yes—
337C2×Dic43C23×C411yescharacteristic
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—21no—
343C4×D43—21no—
344C4×D43—21no—
345C4×D43—21no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352Dic86—42no—
353Dic86—42no—
354C8×C43—24no—
355C8×C43—22no—
356C8×C43—22no—
357C43⋊C8—24no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360#60269—431nomaximal, Sylow
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—24no—
364C22×C43—24no—
365C22×C43—24no—
366C22×C43#52012yes—
367C22×C43C24×C411yescharacteristic
368C2×D43—21no—
369C2×D43—21no—
370C2×D43—21no—
371C2×D43—21no—
372C2×D43—21no—
373C2×D43—44no—
374C2×D43#56812yes—
375C4×C43—24no—
376C4×C43—21no—
377C4×C43—21no—
378C4×C43—21no—
379C4×C43—21no—
380C4×C43#52012yes—
381C4×C43C2×H(5,𝔽2)11yescharacteristic
382C4×C43C2×2−1+411yescharacteristic
383Dic43—21no—
384Dic43—21no—
385Dic43—24no—
386Dic43—24no—
387Dic43—21no—
388Dic43—21no—
389Dic43—21no—
390Dic43#56812yes—
391#3444—431no—
392#2995—434no—
393#2992—434no—
394#2990—434no—
395#2989—434no—
396#2961—431no—
397#2961—431no—
398#2933—432no—
399#2933—432no—
400#2932—431no—
401#2932D4311yescharacteristic, complemented
402#2925—432no—
403C2×#432—431no—
404#2906—432no—
405C2×#423—431no—
406C2×C43—22no—
407C2×C43—44no—
408C2×C43C2×#52011yescharacteristic
409C2×C43C2×#56811yescharacteristic
410C2×C43C2×#56811yescharacteristic
411D43—22no—
412D43—41no—
413C2×#131—432no—
414C2×#131C2×D4312yes—
415C22×M16—432no—
416#533—431no—
417#533—431no—
418#533—431no—
419#532—431no—
420#532—431no—
421#532C2×D4311yescharacteristic
422#529—432no—
423#529—432no—
424#529—432no—
425#529—432no—
426#529—432no—
427#529—432no—
428#525—432no—
429#525—432no—
430#525—432no—
431C4×#41—432no—
432C4×#41—432no—
433C4×#41—432no—
434C22×C42—431no—
435#446—434no—
436#446—434no—
437#446—434no—
438#446—434no—
439#436—434no—
440#436—434no—
441#435—434no—
442#435—434no—
443#435—434no—
444#435—434no—
445#435—434no—
446#435—434no—
447#435C2×D4314yescomplemented
448#435C2×D4314yescomplemented
449C8×D4—434no—
450C8×D4—434no—
451#433—434no—
452#433—434no—
453#432—434no—
454#432—432no—
455#432—432no—
456#432—432no—
457#432—432no—
458#431—434no—
459#424—432no—
460#424—434no—
461#424—432no—
462#424—434no—
463#423—432no—
464#423—434no—
465#423—431no—
466#423—432no—
467#423—432no—
468#423C2×D4311yescharacteristic
469C2×C4⋊C8—431no—
470C2×C4⋊C8—434no—
471C2×C4⋊C8—431no—
472C2×C4⋊C8—432no—
473C2×C4⋊C8—432no—
474#408—432no—
475#408C2×D4312yes—
476C2×C22⋊C8—431no—
477C2×C22⋊C8—431no—
478#405—432no—
479#405—432no—
480C2×#97—431no—
481C2×#97C2×D4311yescharacteristic
482C43#6026911yescharacteristic, complemented, Sylow
483C2×#41—432no—
484C2×#41—432no—
485C2×#41C22×D4312yes—
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—431no—
489#131—44no—
490#131—1724no—
491C2×M16—432no—
492C2×M16—434no—
493C2×M16—434no—
494C2×M16—1724no—
495C2×M16C22×D4312yes—
496C2×M16C22×D4314yes—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8—434no—
500C22×C8—434no—
501C22×C8C22×D4311yescharacteristic
502C22×C8C22×D4311yescharacteristic
503C22×C8C22×D4314yes—
504C4⋊Q8—431no—
505C4⋊Q8—431no—
506C4⋊Q8C4×D4311yescharacteristic
507#127C4×D4311yescharacteristic
508#126—434no—
509#126—434no—
510#125—432no—
511#125—432no—
512#125—432no—
513#124—432no—
514#124—432no—
515#124C4×D4312yes—
516#123—434no—
517#123—434no—
518#123—434no—
519C22⋊Q8—432no—
520C22⋊Q8—432no—
521C22⋊Q8—432no—
522C22⋊Q8—432no—
523C22⋊Q8—432no—
524C22⋊Q8—432no—
525#121—432no—
526#121—432no—
527#121—432no—
528#121—432no—
529#121C4×D4312yes—
530#121C4×D4312yes—
531#120—434no—
532C4×Q8—432no—
533C4×Q8—432no—
534C4×Q8—432no—
535C4×Q8—432no—
536C4×Q8—432no—
537C4×Q8—432no—
538C4×D4—434no—
539C4×D4—434no—
540C4×D4—432no—
541C4×D4—432no—
542C4×D4—432no—
543C4×D4—432no—
544C4×D4—434no—
545C4×D4—434no—
546C4×D4—434no—
547C4×D4—434no—
548C4×D4C22×D4312yes—
549C4×D4C22×D4312yes—
550#117—432no—
551#117—434no—
552#117—432no—
553#117—432no—
554#117—434no—
555#117—434no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—434no—
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×C42C22×D4311yescharacteristic
569C4⋊C8—432no—
570C4⋊C8—434no—
571C4⋊C8—434no—
572C4⋊C8—432no—
573C4⋊C8—434no—
574C4⋊C8—434no—
575C4⋊C8—432no—
576C4⋊C8—432no—
577C4⋊C8—434no—
578C4⋊C8—434no—
579C4⋊C8—432no—
580C4⋊C8—432no—
581C4⋊C8C22×D4312yes—
582C4⋊C8C22×D4312yes—
583C22⋊C8—434no—
584C22⋊C8—434no—
585C22⋊C8—432no—
586C22⋊C8—432no—
587C22⋊C8—432no—
588C22⋊C8—432no—
589C22⋊C8C22×D4314yes—
590C22⋊C8C22×D4314yes—
591#97—434no—
592#97—434no—
593#97—432no—
594#97—432no—
595#97C22×D4312yes—
596#97C22×D4312yes—
597C4×C8—434no—
598C4×C8—434no—
599C24—431no—
600#41—24no—
601#41—24no—
602#41—1724no—
603#41—1724no—
604C2×Q8—432no—
605C2×Q8—432no—
606C2×Q8C2×C4×D4312yes—
607C2×D4—434no—
608C2×D4—434no—
609C2×D4C2×C4×D4314yes—
610C2×D4C2×C4×D4312yes—
611C2×D4C2×C4×D4312yes—
612C2×D4C2×C4×D4312yes—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—434no—
616C22×C4—431no—
617C22×C4—434no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—1722no—
633C22×C4—1722no—
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4C2×C4×D4311yescharacteristic
636C22×C4C23×D4314yes—
637C22×C4C23×D4311yescharacteristic
638M16—24no—
639M16—44no—
640M16—864no—
641M16—1724no—
642M16—1724no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—44no—
646C2×C8—432no—
647C2×C8—434no—
648C2×C8—432no—
649C2×C8—862no—
650C2×C8—862no—
651C2×C8—1724no—
652C2×C8—1724no—
653C2×C8C23×D4312yes—
654C2×C8C23×D4314yes—
655C2×C8C23×D4312yes—
656C4⋊C4—432no—
657C4⋊C4—432no—
658C4⋊C4—432no—
659C4⋊C4—432no—
660C4⋊C4—434no—
661C4⋊C4—434no—
662C4⋊C4—434no—
663C4⋊C4—434no—
664C4⋊C4—434no—
665C4⋊C4—434no—
666C4⋊C4C2×C4×D4312yes—
667C4⋊C4C2×C4×D4312yes—
668C22⋊C4—434no—
669C22⋊C4—434no—
670C22⋊C4—434no—
671C22⋊C4—434no—
672C22⋊C4—434no—
673C22⋊C4—434no—
674C22⋊C4—434no—
675C22⋊C4C2×C4×D4314yes—
676C22⋊C4C2×C4×D4314yes—
677C42—431no—
678C42—431no—
679C42—431no—
680C42—431no—
681C42—431no—
682C42—431no—
683C42—431no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—434no—
688C42—434no—
689C42—434no—
690C42—431no—
691C42—431no—
692C42C2×C4×D4311yescharacteristic
693C42C2×C4×D4311yescharacteristic
694C42C23×D4311yescharacteristic
695C42C23×D4311yescharacteristic
696C23—431no—
697C23—431no—
698C23—862no—
699C23—862no—
700C23—1721no—
701C23C22×C4×D4314yes—
702C23C22×C4×D4311yescharacteristic
703Q8—24no—
704Q8—1722no—
705Q8—1722no—
706D4—28no—
707D4—24no—
708D4—42no—
709D4—42no—
710D4—868no—
711D4—1724no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—431no—
717C2×C4—431no—
718C2×C4—431no—
719C2×C4—431no—
720C2×C4—431no—
721C2×C4—431no—
722C2×C4—434no—
723C2×C4—434no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—868no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1724no—
743C2×C4C22×C4×D4311yescharacteristic
744C2×C4C22×C4×D4311yescharacteristic
745C2×C4C22×C4×D4311yescharacteristic
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C22×C4×D4314yes—
748C2×C4C22×C4×D4311yescharacteristic
749C2×C4#1306337012yes—
750C2×C4#1306337212yes—
751C2×C4C24×D4311yescharacteristic
752C8—22no—
753C8—24no—
754C8—22no—
755C8—862no—
756C8—864no—
757C8—862no—
758C22—21no—
759C22—21no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—432no—
764C22—861no—
765C22—861no—
766C22—861no—
767C22—861no—
768C22—861no—
769C22—1724no—
770C22#1458337812yes—
771C22C23×C4×D4311yescharacteristic
772C4—24no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—432no—
778C4—861no—
779C4—861no—
780C4—861no—
781C4—861no—
782C4—861no—
783C4—864no—
784C4—864no—
785C4#1458337812yes—
786C4C2×#1306337011yescharacteristic
787C4C2×#1306337211yescharacteristic
788C2—22no—
789C2—44no—
790C2—862no—
791C2—1721no—
792C2C2×#1458337811yescharacteristic
793C2#568×D4311yescharacteristic
794C2#568×D4311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2932C2
prime radical#19147890C2
cosocleC2×C4×C43C25
hypercenter#2932D43
hypocenterC43#60269
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #19143761C2semidirect
3. #19143730C2semidirect
4. #19143715C2semidirect
5. #19143707C2semidirect
6. #19143535C2semidirect
7. #19143532C2semidirect
8. #19143325C2semidirect
9. #19143317C2semidirect
10. #19143313C2semidirect
11. #19143257C2semidirect
12. C2×#14582954C2semidirect
13. #19143161C2semidirect
14. #423×D43C2semidirect
15. C43×#2932C2semidirect
36. #14583028C22semidirect
37. #14583028C22semidirect
38. #14583027C22semidirect
39. #14583027C22semidirect
43. #14582971C22semidirect
44. #14582971C22semidirect
50. #14582957C22semidirect
51. #14582957C22semidirect
56. #14582953C22semidirect
57. #14582949C22semidirect
59. #14582927C22semidirect
61. #14582925C22semidirect
64. #14582922C22semidirect
69. C2×Dic43⋊C8C22semidirect
80. C43×#435C22semidirect
81. C43×#435C22semidirect
401. #2932D43semidirect
447. #435C2×D43semidirect
448. #435C2×D43semidirect
482. C43#60269semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191437612
#191437302
#191437152
#191437072
#191435352
#191435322
#191433252
#191433172
#191433132
#191432572
C2×#145829542
#191431612
#423×D432
C43×#29322
#6026943