Finite Group Databasebeta

← #25102344

Subgroups — #25102344

Order 11008.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583381C211yesmaximal, characteristic, complemented
2C2×#14583043C211yesmaximal, characteristic
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19137282C211yesmaximal, characteristic, complemented
5#19134952C211yesmaximal, characteristic, complemented
6#19134940C211yesmaximal, characteristic, complemented
7#19134909C211yesmaximal, characteristic, complemented
8#19134847C211yesmaximal, characteristic, complemented
9#19134839C211yesmaximal, characteristic, complemented
10#19134781C211yesmaximal, characteristic, complemented
11#19134534C211yesmaximal, characteristic, complemented
12#19134421C211yesmaximal, characteristic, complemented
13C4×#13063249C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19#14583381—24no—
20#14583381—24no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×C4×D172—21no—
23C2×C4×D172C2211yescharacteristic
24C2×#13063287—21no—
25C2×#13063287C2211yescharacteristic
26C2×#13063282—21no—
27C2×#13063282C2211yescharacteristic
28C2×C4⋊C4×D43—21no—
29C2×C4⋊C4×D43C2211yescharacteristic
30#14583043C418yescomplemented
31C4×#10621882—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582799—21no—
44#14582795C2211yescharacteristic
45#14582793—21no—
46#14582778—21no—
47#14582772—21no—
48#14582756C2211yescharacteristic
49C4×C4⋊Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#440—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#97×C43C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—22no—
69C2×#10621902C2×C414yescomplemented
70C22×D172—21no—
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621882—22no—
79C2×#10621882—22no—
80C2×#10621882C2×C414yescomplemented
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063296—22no—
84#13063296C2×C414yescomplemented
85Q8×Dic43—22no—
86Q8×Dic43—22no—
87C4×D172—28no—
88C4×D172—22no—
89C4×D172D414yescomplemented
90#13063287—28no—
91#13063287—22no—
92#13063287—22no—
93#13063282—28no—
94#13063282—22no—
95#13063282—22no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C2×Dic43⋊C4D411yescharacteristic
104C4⋊C4×D43—28no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118#13063258—22no—
119#13063249—22no—
120#13063249C2×C414yescomplemented
121#13063247—22no—
122#13063247C2×C414yescomplemented
123#13063246—22no—
124#13063245—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8C2×C414yescomplemented
127C4×C43⋊C8—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C2×SD16×C43—22no—
135C2×SD16×C43—22no—
136C2×SD16×C43C2×C414yescomplemented
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C4×Q8×C43—22no—
140C4×Q8×C43D414yescomplemented
141C4×D4×C43—22no—
142C4×D4×C43—22no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#107×C43—22no—
150#103×C43—22no—
151#102×C43—22no—
152#97×C43—22no—
153C24×C43—21no—
154C23×D43—21no—
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C22×C412yes—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43#4112yes—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—42no—
172C22×C4×C43—81no—
173C22×C4×C43—81no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—24no—
178C2×C22⋊D43—81no—
179C2×C22⋊D43—81no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186#10621902—28no—
187#10621902—28no—
188#10621902—28no—
189#10621902—28no—
190C2×D172—24no—
191C2×D172—24no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—24no—
196C2×D172C22×C412yes—
197C2×D172C2×D412yes—
198C2×D172#4112yes—
199C2×C4×D43—24no—
200C2×C4×D43—24no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—24no—
206C2×C4×D43—24no—
207C2×C4×D43—24no—
208C2×C4×D43—24no—
209C2×C4×D43—81no—
210C2×C4×D43—81no—
211C2×C4×D43—81no—
212C2×C4×D43—81no—
213C2×C4×D43—81no—
214C2×C4×D43—81no—
215C2×C4×D43C22×C412yes—
216C2×C4×D43#4112yes—
217SD16×C43—28no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43C22×C412yes—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C2×D412yes—
229C22⋊C4×C43—42no—
230C42×C43—24no—
231C42×C43C2×D412yes—
232C42×C43C2×D412yes—
233C22⋊Dic43—24no—
234C22⋊Dic43—81no—
235C22⋊Dic43—81no—
236#10621882—28no—
237(C2×D43)⋊C4—24no—
238(C2×D43)⋊C4—24no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—81no—
242C4⋊Dic43—24no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43C22×C412yes—
248C4⋊Dic43C2×D412yes—
249Dic43⋊C4—24no—
250Dic43⋊C4—22no—
251Dic43⋊C4—22no—
252Dic43⋊C4—81no—
253C4×Dic43—24no—
254C4×Dic43—21no—
255C4×Dic43—21no—
256C4×Dic43—81no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8C22×C412yes—
263C23×C43—22no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C22×D411yescharacteristic
271C22×D43—22no—
272C22×D43—21no—
273C22×D43—22no—
274C22×D43—21no—
275C22×D43—22no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43C4×D412yes—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43C4×D414yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—41no—
292D4×C43—41no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—84no—
307C2×C4×C43#12012yes—
308C2×C4×C43#12012yes—
309C2×C4×C43C23×C411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C22⋊D43—84no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—22no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—22no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43C4×D412yes—
334D172—216no—
335D172—22no—
336D172—22no—
337D172—22no—
338D172C4×D414yes—
339C4×D43—216no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—84no—
345C4×D43—84no—
346C4×D43—84no—
347C8×C43—22no—
348C8×C43—41no—
349C43⋊C8—22no—
350C43⋊C8—41no—
351#21460—431nomaximal, Sylow
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43C2×C4×D411yescharacteristic
360C22×C43C2×#12011yescharacteristic
361C22×C43#52511yescharacteristic
362C22×C43#57611yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57711yescharacteristic
365C22×C43#57811yescharacteristic
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—24no—
369C2×D43—22no—
370C2×D43—41no—
371C2×D43—42no—
372C2×D43—41no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—41no—
377C2×D43—42no—
378C2×D43—41no—
379C2×D43—42no—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—24no—
383C4×C43—42no—
384C4×C43—81no—
385C4×C43C2×C4×D411yescharacteristic
386C4×C43C2×C4×D411yescharacteristic
387C4×C43#52511yescharacteristic
388C4×C43#52511yescharacteristic
389Dic43—22no—
390Dic43—42no—
391Dic43—41no—
392Dic43—42no—
393Dic43—41no—
394Dic43—81no—
395C2×#520—431no—
396C2×#449—431no—
397C2×#440D4311yescharacteristic, complemented
398C2×C4×D8—431no—
399#2324—431no—
400#1880—431no—
401#1879—431no—
402#1874—431no—
403#1863—431no—
404#1862—431no—
405#1852—431no—
406#1788—431no—
407#1762—431no—
408C4×#103—431no—
409#1750—431no—
410C2×C43—82no—
411C2×C43C4×#12011yescharacteristic
412C2×C43#294611yescharacteristic
413C2×C43#295111yescharacteristic
414C2×C43#300811yescharacteristic
415C2×C43#301311yescharacteristic
416C2×C43#311911yescharacteristic
417C2×C43#312411yescharacteristic
418D43—42no—
419D43—44no—
420C22×#41—431no—
421C22×SD16C2×D4311yescharacteristic
422C22×D8—431no—
423C2×#121—431no—
424#520—864no—
425#520—864no—
426C2×C4×Q8—431no—
427C2×C4×Q8C2×D4311yescharacteristic
428C2×C4×D4—431no—
429C2×C4×D4—431no—
430C2×C4×D4—861no—
431C2×C4×D4—861no—
432C2×C4×D4C2×D4311yescharacteristic
433C2×#117—431no—
434C2×#117—861no—
435C22×C4⋊C4—431no—
436C22×C4⋊C4—861no—
437#449—438no—
438#440—24no—
439C4×D8—864no—
440C2×#107—431no—
441C2×#107C2×D4311yescharacteristic
442C2×#103—431no—
443C2×#103—431no—
444C2×#103C2×D4311yescharacteristic
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102C2×D4311yescharacteristic
450C2×C22⋊C8—431no—
451C2×C22⋊C8—431no—
452C2×#97C2×D4311yescharacteristic
453C2×C4×C8—431no—
454#390—431no—
455#390—861no—
456#389—431no—
457#388—861no—
458#386—861no—
459#385—861no—
460#380—431no—
461C4×C4⋊C4—431no—
462#340—431no—
463#340—431no—
464#340—431no—
465#340—431no—
466#336—431no—
467#336—431no—
468C43#2146011yescharacteristic, complemented, Sylow
469C2×#41—434no—
470C2×#41—862no—
471C2×#41—862no—
472C2×#41—862no—
473C2×#41—862no—
474C2×#41—862no—
475C22×Q8C22×D4311yescharacteristic
476C22×D4—431no—
477C22×D4—861no—
478C22×D4—861no—
479C22×D4C22×D4311yescharacteristic
480C23×C4—21no—
481C23×C4—431no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4—861no—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16C4×D4314yescomplemented
489C2×D8—434no—
490C2×D8—862no—
491C2×D8—862no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8C22×D4311yescharacteristic
495C22×C8C22×D4311yescharacteristic
496#121—434no—
497#121—862no—
498C4×Q8—22no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×Q8C22⋊D4314yescomplemented
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—434no—
505C4×D4—868no—
506C4×D4—862no—
507C4×D4—868no—
508C4×D4—862no—
509C4×D4—862no—
510#117—868no—
511#117—862no—
512#117—862no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—868no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—862no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C42—21no—
537C2×C42—431no—
538C2×C42—861no—
539C2×C42—861no—
540C2×C42C22×D4311yescharacteristic
541#107—22no—
542#107—862no—
543#103—22no—
544#103—434no—
545#103—862no—
546#102—22no—
547#102—434no—
548#102—862no—
549#102—862no—
550#102—862no—
551C22⋊C8—434no—
552C22⋊C8—862no—
553#97—22no—
554C4×C8—862no—
555#95—861no—
556#95—861no—
557#95—861no—
558C24—21no—
559C24—431no—
560C24—861no—
561#41—868no—
562#41—868no—
563#41—868no—
564#41—868no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C2×C4×D4312yes—
569C2×Q8#1062189812yes—
570C2×Q8C2×C22⋊D4312yes—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—432no—
577C2×D4—432no—
578C2×D4—432no—
579C2×D4—864no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—864no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—3441no—
587C2×D4—3441no—
588C2×D4C2×C4×D4312yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—431no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—864no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—864no—
612C22×C4—861no—
613C22×C4—3441no—
614C22×C4—3441no—
615C22×C4—3441no—
616C22×C4—3441no—
617C22×C4—3441no—
618C22×C4—3441no—
619C22×C4D4×D4311yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4C23×D4311yescharacteristic
622SD16—28no—
623D8—868no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—432no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8C2×C4×D4312yes—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—432no—
641C4⋊C4—432no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—862no—
645C4⋊C4—862no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—3441no—
651C4⋊C4C2×C22⋊D4312yes—
652C22⋊C4—42no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—864no—
658C22⋊C4—3441no—
659C22⋊C4—3441no—
660C22⋊C4—3441no—
661C42—24no—
662C42—864no—
663C42—861no—
664C42—861no—
665C42—3441no—
666C42D4×D4312yes—
667C42C2×C22⋊D4312yes—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—432no—
676C23—862no—
677C23—862no—
678C23—861no—
679C23—862no—
680C23—861no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—1721no—
686C23—1721no—
687C23—1721no—
688C23—1721no—
689C23C2×D4×D4311yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×C22⋊D4314yes—
694D4—22no—
695D4—22no—
696D4—41no—
697D4—41no—
698D4—434no—
699D4—8616no—
700D4—862no—
701D4—862no—
702D4—862no—
703D4—3444no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—84no—
718C2×C4—432no—
719C2×C4—8616no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—861no—
728C2×C4—862no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—3444no—
735C2×C4—3444no—
736C2×C4—3444no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4#1306329312yes—
745C2×C4#1306329312yes—
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C22×C22⋊D4311yescharacteristic
749C2×C4#41×D4311yescharacteristic
750C2×C4#41×D4311yescharacteristic
751C2×C4C2×#1062189811yescharacteristic
752C8—22no—
753C8—41no—
754C8—862no—
755C8—1721no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—862no—
764C22—862no—
765C22—864no—
766C22—862no—
767C22—1722no—
768C22—1722no—
769C22—1721no—
770C22—1722no—
771C22—1721no—
772C22—1722no—
773C22—1721no—
774C22—1722no—
775C22—1721no—
776C22—1722no—
777C22C4×D4×D4311yescharacteristic
778C22C2×#1306329311yescharacteristic
779C22#1458340811yescharacteristic
780C22#1458370311yescharacteristic
781C22#1458370311yescharacteristic
782C22#1458370811yescharacteristic
783C22#1458371511yescharacteristic
784C4—24no—
785C4—22no—
786C4—22no—
787C4—42no—
788C4—81no—
789C4—862no—
790C4—3441no—
791C4—1722no—
792C4—1721no—
793C4—1722no—
794C4—1721no—
795C4C4×D4×D4311yescharacteristic
796C4C2×C4×C22⋊D4311yescharacteristic
797C4#1458340611yescharacteristic
798C4#1458340811yescharacteristic
799C2—82no—
800C2—1722no—
801C2—1724no—
802C2C4×#1306329311yescharacteristic
803C2#1914342611yescharacteristic
804C2#1914346711yescharacteristic
805C2#1914386211yescharacteristic
806C2#1914390911yescharacteristic
807C2#1914479211yescharacteristic
808C2#1914485511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC2×#14583043C2
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#21460
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#14583381C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19137282C2semidirect
5. #19134952C2semidirect
6. #19134940C2semidirect
7. #19134909C2semidirect
8. #19134847C2semidirect
9. #19134839C2semidirect
10. #19134781C2semidirect
11. #19134534C2semidirect
12. #19134421C2semidirect
13. C4×#13063249C2semidirect
14. #19134364C2semidirect
15. C2×C43×#440C2semidirect
30. #14583043C4semidirect
69. C2×#10621902C2×C4semidirect
80. C2×#10621882C2×C4semidirect
84. #13063296C2×C4semidirect
89. C4×D172D4semidirect
120. #13063249C2×C4semidirect
122. #13063247C2×C4semidirect
126. (C2×D43)⋊C8C2×C4semidirect
136. C2×SD16×C43C2×C4semidirect
140. C4×Q8×C43D4semidirect
397. C2×#440D43semidirect
468. C43#21460semidirect
488. C2×SD16C4×D43semidirect
501. C4×Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833812
C2×#145830432
C2×C4×#106218822
#191372822
#191349522
#191349402
#191349092
#191348472
#191348392
#191347812
#191345342
#191344212
C4×#130632492
#191343642
C2×C43×#4402
#2146043