Finite Group Databasebeta

← #25064055

Subgroups — #25064055

Order 11008.

1466 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582762C211yesmaximal, characteristic, complemented
3#19133152C214yesmaximal, complemented
4#19133129C212yesmaximal, complemented
5#19133125C212yesmaximal, complemented
6#19133100C214yesmaximal, complemented
7C2×C43×#407C211yesmaximal, characteristic, complemented
8C22×#10621898C411yescharacteristic, complemented
9#14583410—21no—
10#14583410—21no—
11#14583410—21no—
12#14583410—21no—
13#14583410C412yescomplemented
14#14583410C412yescomplemented
15#14583410C2212yes—
16#14583410C2212yes—
17C2×#13063308—21no—
18C2×#13063304C411yescharacteristic, complemented
19C2×#13063304C2211yescharacteristic
20C2×#13063299C411yescharacteristic, complemented
21C2×#13063299C2211yescharacteristic
22C2×#13063294—21no—
23C2×C4×C22⋊D43—21no—
24C2×C4×C22⋊D43—21no—
25C2×#13063284C411yescharacteristic, complemented
26C22×C22⋊Dic43—21no—
27#14582762—21no—
28#14582762—21no—
29#14582762C2212yes—
30#14582762C2212yescomplemented
31C2×C43⋊#95—21no—
32C2×C43⋊#95C2212yescomplemented
33#14582637C2218yescomplemented
34#14582634C2218yescomplemented
35C24×C4×C43C2211yescharacteristic
36C22×M16×C43—21no—
37C43×#407—21no—
38C43×#407—21no—
39C43×#407C2212yes—
40C43×#407C2212yescomplemented
41C2×C22⋊C8×C43—21no—
42C2×C22⋊C8×C43C2212yescomplemented
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—44no—
46C2×#10621898C2×C412yes—
47C2×#10621898C2×C412yescomplemented
48C22×Dic86C2×C411yescharacteristic, complemented
49C22×D172C2×C411yescharacteristic, complemented
50C22×C22⋊D43—21no—
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C23×Dic43—22no—
54C22×C4×D43—21no—
55#13063308—22no—
56#13063308—22no—
57#13063308—22no—
58#13063308—22no—
59#13063304—21no—
60#13063304—21no—
61#13063304—21no—
62#13063304—21no—
63#13063304C2×C412yes—
64#13063304C2×C412yescomplemented
65#13063304C2×C412yescomplemented
66#13063304C2312yes—
67#13063299—21no—
68#13063299—21no—
69#13063299—21no—
70#13063299—21no—
71#13063299C2×C412yes—
72#13063299C2×C412yescomplemented
73#13063299C2×C412yescomplemented
74#13063299C2312yes—
75#13063294—22no—
76#13063294—22no—
77#13063294—22no—
78#13063294—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82C4×C22⋊D43—22no—
83C4×C22⋊D43—22no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87#13063284—21no—
88#13063284—21no—
89#13063284C2×C412yes—
90#13063284C2×C412yescomplemented
91C2×C4⋊Dic43C2×C411yescharacteristic, complemented
92C2×C4⋊Dic43C2×C411yescharacteristic, complemented
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—44no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C43⋊#95—22no—
105C43⋊#95—22no—
106C43⋊#95—22no—
107C43⋊#95C2314yes—
108C25×C43D411yescharacteristic
109C23×C4×C43—44no—
110C23×C4×C43C2×C411yescharacteristic
111C23×C4×C43C2×C411yescharacteristic
112C23×C4×C43C2×C411yescharacteristic
113C23×C4×C43C2×C411yescharacteristic
114C23×C4×C43D411yescharacteristic
115C23×C4×C43D411yescharacteristic
116C23×C4×C43D411yescharacteristic
117C23×C4×C43D411yescharacteristic
118C23×C4×C43D411yescharacteristic
119C23×C4×C43D411yescharacteristic
120C23×C4×C43D411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—22no—
126C2×M16×C43—44no—
127C22×C8×C43—22no—
128C22⋊C8×C43—22no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131C22⋊C8×C43C2314yes—
132C24×C43—24no—
133C24×C43—42no—
134C24×C43—42no—
135C24×C43C22⋊C411yescharacteristic
136C24×C43C22⋊C411yescharacteristic
137C24×C43C22⋊C411yescharacteristic
138C24×C43C22⋊C411yescharacteristic
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—24no—
144C22×C4×C43—24no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43C22⋊C411yescharacteristic
158C22×C4×C43C22⋊C411yescharacteristic
159C22×C4×C43C22⋊C411yescharacteristic
160C22×C4×C43C22⋊C411yescharacteristic
161C22×C4×C43C22⋊C411yescharacteristic
162C22×C4×C43C22⋊C411yescharacteristic
163C22×C4×C43C22⋊C411yescharacteristic
164C22×C4×C43C22⋊C411yescharacteristic
165C22×C4×C43C22⋊C411yescharacteristic
166C22×C4×C43C22⋊C411yescharacteristic
167C22×C4×C43C22⋊C411yescharacteristic
168C22×C4×C43C22⋊C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—22no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—44no—
192C2×C22⋊D43—44no—
193C2×C22⋊D43—44no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—24no—
198C22×Dic43—44no—
199C22×Dic43—44no—
200C22×Dic43—44no—
201#10621898—44no—
202#10621898—44no—
203#10621898—44no—
204#10621898—44no—
205C2×D172—21no—
206C2×D172—42no—
207C2×D172C22×C412yes—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—44no—
211C2×Dic86—21no—
212C2×Dic86—42no—
213C2×Dic86C22×C412yes—
214M16×C43—44no—
215M16×C43—44no—
216C2×C8×C43—24no—
217C2×C8×C43—44no—
218C22⋊Dic43—22no—
219C22⋊Dic43—22no—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224C22⋊Dic43—44no—
225C22⋊Dic43—44no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43C22×C412yes—
233C4⋊Dic43C22×C412yes—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238C4×Dic43—22no—
239C4×Dic43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—416no—
261C23×C43#9914yes—
262C23×C43C2×C22⋊C411yescharacteristic
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43C2×C22⋊C411yescharacteristic
267C23×C43C2×C22⋊C411yescharacteristic
268C23×C43C22×D411yescharacteristic
269C22×D43—22no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—42no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C2×C22⋊C411yescharacteristic
304C2×C4×C43C2×C22⋊C411yescharacteristic
305C2×C4×C43C2×C22⋊C411yescharacteristic
306C2×C4×C43C2×C22⋊C411yescharacteristic
307C2×C4×C43C23×C411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C22⋊D43—44no—
310C22⋊D43—44no—
311C22⋊D43—44no—
312C22⋊D43—44no—
313C22⋊D43—44no—
314C22⋊D43—44no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—44no—
322C2×Dic43—44no—
323C2×Dic43—44no—
324C2×Dic43—88no—
325D172—42no—
326D172—42no—
327C4×D43—44no—
328C4×D43—44no—
329Dic86—42no—
330Dic86—42no—
331C8×C43—44no—
332#17587—431nomaximal, Sylow
333C22×C43—28no—
334C22×C43—21no—
335C22×C43—21no—
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—44no—
351C22×C43—44no—
352C22×C43—44no—
353C22×C43—44no—
354C22×C43—44no—
355C22×C43—44no—
356C22×C43C2×#9912yes—
357C22×C43C2×#9912yes—
358C22×C43C2×#9912yes—
359C22×C43#42112yes—
360C22×C43C22×C22⋊C411yescharacteristic
361C22×C43#57512yes—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—84no—
366C4×C43—21no—
367C4×C43—21no—
368C4×C43—21no—
369C4×C43—21no—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—21no—
373C4×C43—21no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—84no—
378C2×#525—431no—
379C2×#407D4311yescharacteristic, complemented
380C2×#381—431no—
381#1516—434no—
382#1511—432no—
383#1510—432no—
384#1504—434no—
385C2×C43—22no—
386C2×C43—22no—
387C2×C43—22no—
388C2×C43—22no—
389C2×C43—22no—
390C2×C43—41no—
391C2×C43—41no—
392C2×C43C22×#9911yescharacteristic
393C2×C43#289611yescharacteristic
394C2×C43C2×#42111yescharacteristic
395D43—82no—
396C22×#41—431no—
397C24×C4C2×D4311yescharacteristic
398C22×M16—21no—
399#525—432no—
400#525—432no—
401#525—432no—
402#525—432no—
403#525—861no—
404#525—861no—
405#525—861no—
406#525—861no—
407C2×#123—861no—
408C2×C22⋊Q8—431no—
409C2×C22⋊Q8—431no—
410C2×#121—431no—
411C2×#121—431no—
412C2×#120—861no—
413C2×C4×D4—861no—
414C2×C4×D4—861no—
415C2×#117—431no—
416C22×C22⋊C4—861no—
417#407—21no—
418#407—21no—
419#407C2×D4312yes—
420#407C2×D4312yescomplemented
421C2×C22⋊C8—21no—
422C2×C22⋊C8C2×D4312yescomplemented
423#381—432no—
424#381—432no—
425#381—861no—
426#381—861no—
427C2×#95—432no—
428C2×#95—861no—
429#328—438no—
430#327—438no—
431C43#1758711yescharacteristic, complemented, Sylow
432C25D17211yescharacteristic
433C2×#41—432no—
434C2×#41—432no—
435C2×#41—861no—
436C2×#41—861no—
437C2×#41—1724no—
438C22×Q8—431no—
439C22×D4—431no—
440C22×D4—861no—
441C22×D4—861no—
442C22×D4—861no—
443C23×C4—44no—
444C23×C4—861no—
445C23×C4—862no—
446C23×C4C4×D4311yescharacteristic
447C23×C4C4×D4311yescharacteristic
448C23×C4C4×D4311yescharacteristic
449C23×C4C4×D4311yescharacteristic
450C23×C4D17211yescharacteristic
451C23×C4D17211yescharacteristic
452C23×C4D17211yescharacteristic
453C23×C4C22⋊D4311yescharacteristic
454C23×C4C22⋊D4311yescharacteristic
455C23×C4C22⋊D4311yescharacteristic
456C23×C4C22⋊D4311yescharacteristic
457C23×C4C22×D4311yescharacteristic
458C23×C4C22×D4311yescharacteristic
459C23×C4C22×D4311yescharacteristic
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—44no—
463C22×C8—22no—
464#123—862no—
465#123—862no—
466#123—862no—
467#123—862no—
468C22⋊Q8—432no—
469C22⋊Q8—432no—
470C22⋊Q8—432no—
471C22⋊Q8—432no—
472C22⋊Q8—861no—
473C22⋊Q8—861no—
474C22⋊Q8—861no—
475C22⋊Q8—861no—
476#121—432no—
477#121—432no—
478#121—432no—
479#121—432no—
480#121—861no—
481#121—861no—
482#121—861no—
483#121—861no—
484#120—862no—
485#120—862no—
486#120—862no—
487#120—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—862no—
495C4×D4—862no—
496#117—432no—
497#117—432no—
498#117—861no—
499#117—861no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—862no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—1724no—
512C2×C42—861no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8C22×D4314yes—
517#95—434no—
518#95—862no—
519#95—862no—
520#95—862no—
521C24—24no—
522C24—42no—
523C24—42no—
524C24—861no—
525C24(C2×D43)⋊C411yescharacteristic
526C24(C2×D43)⋊C411yescharacteristic
527C24(C2×D43)⋊C411yescharacteristic
528C24(C2×D43)⋊C411yescharacteristic
529C24C2×D17211yescharacteristic
530C24C2×D17211yescharacteristic
531C24C2×D17211yescharacteristic
532#41—1724no—
533#41—1724no—
534#41—1724no—
535#41—1724no—
536C2×Q8—432no—
537C2×Q8—861no—
538C2×Q8—1722no—
539C2×D4—432no—
540C2×D4—862no—
541C2×D4—862no—
542C2×D4—862no—
543C2×D4—862no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—861no—
547C2×D4—1722no—
548C2×D4—1724no—
549C2×D4—1724no—
550C2×D4—1724no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—864no—
571C22×C4—1724no—
572C22×C4—1724no—
573C22×C4—1724no—
574C22×C4—1724no—
575C22×C4(C2×D43)⋊C411yescharacteristic
576C22×C4(C2×D43)⋊C411yescharacteristic
577C22×C4(C2×D43)⋊C411yescharacteristic
578C22×C4(C2×D43)⋊C411yescharacteristic
579C22×C4(C2×D43)⋊C411yescharacteristic
580C22×C4(C2×D43)⋊C411yescharacteristic
581C22×C4(C2×D43)⋊C411yescharacteristic
582C22×C4(C2×D43)⋊C411yescharacteristic
583C22×C4(C2×D43)⋊C411yescharacteristic
584C22×C4(C2×D43)⋊C411yescharacteristic
585C22×C4(C2×D43)⋊C411yescharacteristic
586C22×C4(C2×D43)⋊C411yescharacteristic
587C22×C4C2×C4×D4311yescharacteristic
588C22×C4C2×C4×D4311yescharacteristic
589C22×C4C2×C4×D4311yescharacteristic
590C22×C4C2×C4×D4311yescharacteristic
591C22×C4C2×C4×D4311yescharacteristic
592C22×C4C2×C4×D4311yescharacteristic
593C22×C4C2×D17211yescharacteristic
594C22×C4C2×D17211yescharacteristic
595C22×C4C2×D17211yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C2×C22⋊D4311yescharacteristic
600C22×C4C2×C22⋊D4311yescharacteristic
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603M16—44no—
604M16—44no—
605C2×C8—24no—
606C2×C8—44no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—862no—
612C4⋊C4—862no—
613C4⋊C4—862no—
614C4⋊C4—862no—
615C22⋊C4—862no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—862no—
621C22⋊C4—862no—
622C22⋊C4—862no—
623C22⋊C4—862no—
624C22⋊C4—862no—
625C22⋊C4—1724no—
626C22⋊C4—1724no—
627C42—862no—
628C42—862no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—862no—
651C23—1722no—
652C23—1722no—
653C23—1722no—
654C23#1306323914yes—
655C23C2×(C2×D43)⋊C411yescharacteristic
656C23C2×(C2×D43)⋊C411yescharacteristic
657C23C2×(C2×D43)⋊C411yescharacteristic
658C23C2×(C2×D43)⋊C411yescharacteristic
659C23C2×(C2×D43)⋊C411yescharacteristic
660C23C2×(C2×D43)⋊C411yescharacteristic
661C23C22×D17211yescharacteristic
662Q8—1722no—
663Q8—1722no—
664D4—1722no—
665D4—1722no—
666D4—1724no—
667D4—1724no—
668D4—1724no—
669D4—1724no—
670D4—1724no—
671D4—1724no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—3448no—
704C2×C4—1724no—
705C2×C4—1724no—
706C2×C4—1724no—
707C2×C4—1724no—
708C2×C4—1724no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4C2×(C2×D43)⋊C411yescharacteristic
713C2×C4C2×(C2×D43)⋊C411yescharacteristic
714C2×C4C2×(C2×D43)⋊C411yescharacteristic
715C2×C4C2×(C2×D43)⋊C411yescharacteristic
716C2×C4C2×(C2×D43)⋊C411yescharacteristic
717C2×C4C2×(C2×D43)⋊C411yescharacteristic
718C2×C4C22×C4×D4311yescharacteristic
719C2×C4C22×C22⋊D4311yescharacteristic
720C8—44no—
721C22—28no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—3444no—
745C22—1722no—
746C22—1722no—
747C22—1722no—
748C22C2×#1306323912yes—
749C22C2×#1306323912yes—
750C22C2×#1306323912yes—
751C22#1458291512yes—
752C22C22×(C2×D43)⋊C411yescharacteristic
753C22#1458369912yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—3444no—
763C4—1722no—
764C4—1722no—
765C4—1722no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—22no—
770C2—22no—
771C2—41no—
772C2—41no—
773C2—3442no—
774C2C22×#1306323911yescharacteristic
775C2#1914311511yescharacteristic
776C2C2×#1458291511yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC2×#407D43
hypocenterC43#17587
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#14582762C2semidirect
3. #19133152C2semidirect
4. #19133129C2semidirect
5. #19133125C2semidirect
6. #19133100C2semidirect
7. C2×C43×#407C2semidirect
8. C22×#10621898C4semidirect
13. #14583410C4semidirect
14. #14583410C4semidirect
18. C2×#13063304C4semidirect
20. C2×#13063299C4semidirect
25. C2×#13063284C4semidirect
30. #14582762C22semidirect
32. C2×C43⋊#95C22semidirect
33. #14582637C22semidirect
34. #14582634C22semidirect
40. C43×#407C22semidirect
42. C2×C22⋊C8×C43C22semidirect
47. C2×#10621898C2×C4semidirect
48. C22×Dic86C2×C4semidirect
49. C22×D172C2×C4semidirect
64. #13063304C2×C4semidirect
65. #13063304C2×C4semidirect
72. #13063299C2×C4semidirect
73. #13063299C2×C4semidirect
90. #13063284C2×C4semidirect
91. C2×C4⋊Dic43C2×C4semidirect
92. C2×C4⋊Dic43C2×C4semidirect
379. C2×#407D43semidirect
420. #407C2×D43semidirect
422. C2×C22⋊C8C2×D43semidirect
431. C43#17587semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145827622
#191331522
#191331292
#191331252
#191331002
C2×C43×#4072
#1758743