Finite Group Databasebeta

← #25102342

Subgroups — #25102342

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×#14583379C211yesmaximal, characteristic, complemented
2C2×#14583042C211yesmaximal, characteristic
3C2×#14582999C211yesmaximal, characteristic, complemented
4C2×C4×#10621882C211yesmaximal, characteristic, complemented
5#19134953C211yesmaximal, characteristic, complemented
6#19134946C211yesmaximal, characteristic, complemented
7#19134913C211yesmaximal, characteristic, complemented
8#19134848C211yesmaximal, characteristic, complemented
9#19134841C211yesmaximal, characteristic, complemented
10#19134782C211yesmaximal, characteristic, complemented
11#19134533C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic, complemented
13C4×#13063248C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2324C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19#14583379—24no—
20#14583379—24no—
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×(C22⋊D43)⋊C4—21no—
26C2×(C22⋊D43)⋊C4—21no—
27C2×#13063283—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C2×C4⋊C4×D43—21no—
30#14583042C418yescomplemented
31#14582999—24no—
32C4×#10621882—24no—
33C2×#13063258C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×#13063236C2211yescharacteristic
46C2×C4×C43⋊C8C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582654C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#390—21no—
57C43×#390C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#388—21no—
60C43×#386—21no—
61C43×#385—21no—
62C43×#380C2211yescharacteristic
63C4×C4⋊C4×C43C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C2×#10621883—22no—
78C2×#10621883—22no—
79C2×#10621883C2×C414yescomplemented
80C2×#10621882—22no—
81C2×#10621882—22no—
82C2×#10621882C2×C414yescomplemented
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86D414yescomplemented
91C4×D172—22no—
92C4×D172—22no—
93C4×D172—22no—
94C4×D172D414yescomplemented
95(C22⋊D43)⋊C4—28no—
96(C22⋊D43)⋊C4—28no—
97#13063283—28no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43—22no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C4⋊C4×D43—28no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110#13063258—22no—
111#13063258—22no—
112#13063248—22no—
113#13063248—22no—
114#13063248C2×C414yescomplemented
115#13063246—22no—
116#13063246—22no—
117#13063245—22no—
118#13063245—22no—
119#13063245C2×C414yescomplemented
120C22⋊(C43⋊C8)—22no—
121C22⋊(C43⋊C8)C2×C414yescomplemented
122#13063236—22no—
123C4×C43⋊C8—22no—
124C22×D4×C43—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128#121×C43—22no—
129#121×C43C2×C414yescomplemented
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132#117×C43—22no—
133#117×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C23×D43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—24no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43C22×C412yes—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—42no—
173C22×C4×C43—81no—
174C22×C4×C43—81no—
175C22×C4×C43C22×C412yes—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43#4112yes—
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—24no—
184C2×C22⋊D43—24no—
185C2×C22⋊D43—24no—
186C22×Dic43—24no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—81no—
191C22×Dic43—81no—
192#10621898—28no—
193#10621898—28no—
194#10621898—28no—
195#10621898—28no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172C22×C412yes—
200C2×D172C2×D412yes—
201C2×D172#4112yes—
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—24no—
207C2×C4×D43—81no—
208C2×C4×D43—81no—
209C2×C4×D43—81no—
210C2×C4×D43—81no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86C22×C412yes—
215C2×Dic86C2×D412yes—
216C2×Dic86#4112yes—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—81no—
225C4⋊C4×C43C22×C412yes—
226C22⋊C4×C43—24no—
227C22⋊C4×C43—22no—
228C22⋊C4×C43—22no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—81no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43—81no—
233C42×C43—21no—
234C42×C43—21no—
235C42×C43—81no—
236C42×C43C2×D412yes—
237C42×C43C2×D412yes—
238#10621883—28no—
239#10621882—28no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242C4⋊Dic43—24no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43C2×D412yes—
246C4⋊Dic43C2×D412yes—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249C4×Dic43—24no—
250C4×Dic43—24no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8C22×C412yes—
262C2×C43⋊C8C22×C412yes—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43C4×D412yes—
277C23×C43C22×D411yescharacteristic
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—84no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—84no—
316C2×C4×C43C4×D412yes—
317C2×C4×C43#12012yes—
318C2×C4×C43#12012yes—
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C22⋊D43—216no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—84no—
336D172—22no—
337D172—22no—
338D172—22no—
339D172C4×D414yes—
340C4×D43—216no—
341C4×D43—84no—
342C4×D43—84no—
343Dic86—22no—
344Dic86—22no—
345Dic86—22no—
346Dic86C4×D414yes—
347C43⋊C8—22no—
348C43⋊C8—22no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351#21460—431nomaximal, Sylow
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43C2×C4×D411yescharacteristic
367C22×C43C2×#12011yescharacteristic
368C22×C43#52511yescharacteristic
369C22×C43#57611yescharacteristic
370C22×C43#57611yescharacteristic
371C22×C43#57711yescharacteristic
372C22×C43#57811yescharacteristic
373C2×D43—24no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—22no—
383C4×C43—42no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—81no—
387C4×C43—81no—
388C4×C43C2×C4×D411yescharacteristic
389C4×C43C2×C4×D411yescharacteristic
390C4×C43#52511yescharacteristic
391C4×C43#52511yescharacteristic
392Dic43—24no—
393Dic43—42no—
394Dic43—42no—
395C2×#520—431no—
396C2×#449—431no—
397C2×#440—431no—
398C2×C4×D8—431no—
399#2324D4311yescharacteristic, complemented
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—42no—
411C2×C43—82no—
412C2×C43C4×#12011yescharacteristic
413C2×C43#294611yescharacteristic
414C2×C43#295111yescharacteristic
415C2×C43#300811yescharacteristic
416C2×C43#301311yescharacteristic
417C2×C43#311911yescharacteristic
418C2×C43#312411yescharacteristic
419D43—44no—
420C22×#41—431no—
421C22×SD16—431no—
422C22×D8—431no—
423C2×#121C2×D4311yescharacteristic
424#520—864no—
425#520—864no—
426C2×C4×Q8—431no—
427C2×C4×Q8—431no—
428C2×C4×D4—431no—
429C2×C4×D4—431no—
430C2×C4×D4—861no—
431C2×C4×D4—861no—
432C2×C4×D4C2×D4311yescharacteristic
433C2×#117—861no—
434C2×#117C2×D4311yescharacteristic
435C22×C4⋊C4—431no—
436C22×C4⋊C4—861no—
437#449—438no—
438#440—864no—
439C4×D8—864no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×C22⋊C8—431no—
451C2×C22⋊C8—431no—
452C2×#97—431no—
453C2×C4×C8—431no—
454#390—21no—
455#390C2×D4311yescharacteristic
456#389C2×D4311yescharacteristic
457#388—21no—
458#386—21no—
459#385—21no—
460#380C2×D4311yescharacteristic
461C4×C4⋊C4C2×D4311yescharacteristic
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×Q8—431no—
476C22×D4—21no—
477C22×D4—431no—
478C22×D4—861no—
479C22×D4C22×D4311yescharacteristic
480C23×C4—21no—
481C23×C4—861no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4C22×D4311yescharacteristic
486C2×SD16—434no—
487C2×SD16—862no—
488C2×SD16—862no—
489C2×D8—434no—
490C2×D8—862no—
491C2×D8—862no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—431no—
495C22×C8—431no—
496#121—22no—
497#121C4×D4314yescomplemented
498C4×Q8—434no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×Q8—862no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—434no—
505C4×D4—862no—
506C4×D4—862no—
507C4×D4—868no—
508C4×D4—868no—
509C4×D4—862no—
510#117—22no—
511#117—22no—
512#117—868no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—868no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—862no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C22⋊D4311yescharacteristic
523C2×C4⋊C4C22⋊D4311yescharacteristic
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4C22⋊D4311yescharacteristic
535C2×C22⋊C4C22⋊D4311yescharacteristic
536C2×C42—21no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540C2×C42C22×D4311yescharacteristic
541#107—862no—
542#107—862no—
543#103—434no—
544#103—862no—
545#103—862no—
546#102—434no—
547#102—862no—
548#102—862no—
549#102—862no—
550#102—862no—
551C22⋊C8—434no—
552C22⋊C8—862no—
553#97—862no—
554C4×C8—862no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—861no—
560C24C2×C22⋊D4311yescharacteristic
561#41—868no—
562#41—868no—
563#41—868no—
564#41—868no—
565C2×Q8—432no—
566C2×Q8—432no—
567C2×Q8—432no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—432no—
580C2×D4—432no—
581C2×D4—432no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—864no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4C2×C4×D4312yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4—864no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—861no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—864no—
608C22×C4—3441no—
609C22×C4—3441no—
610C22×C4—3441no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—3441no—
614C22×C4C2×C4×D4312yes—
615C22×C4#1062189812yes—
616C22×C4C2×C22⋊D4311yescharacteristic
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C2×C22⋊D4311yescharacteristic
619C22×C4C2×C22⋊D4311yescharacteristic
620C22×C4C2×C22⋊D4311yescharacteristic
621C22×C4C23×D4311yescharacteristic
622SD16—868no—
623D8—868no—
624C2×C8—432no—
625C2×C8—432no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—81no—
644C4⋊C4—432no—
645C4⋊C4—432no—
646C4⋊C4—864no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4C2×C4×D4312yes—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42—864no—
665C42—864no—
666C42D4×D4312yes—
667C42D4×D4312yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23—1721no—
688C23C4×C22⋊D4312yes—
689C23C22×C22⋊D4311yescharacteristic
690Q8—434no—
691Q8—862no—
692Q8—862no—
693Q8—862no—
694D4—22no—
695D4—22no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—434no—
700D4—8616no—
701D4—862no—
702D4—862no—
703D4—862no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—84no—
730C2×C4—8616no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—3444no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4C4×C22⋊D4312yes—
744C2×C4#1306329312yes—
745C2×C4#1306329312yes—
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4#41×D4311yescharacteristic
750C2×C4#41×D4311yescharacteristic
751C2×C4C2×#1062189811yescharacteristic
752C8—862no—
753C8—862no—
754C8—1721no—
755C8—1721no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—864no—
771C22—1722no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22C2×C4×C22⋊D4311yescharacteristic
778C22C2×#1306329311yescharacteristic
779C22#1458340611yescharacteristic
780C22#1458370211yescharacteristic
781C22#1458370211yescharacteristic
782C22#1458371011yescharacteristic
783C22#1458371411yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—42no—
788C4—41no—
789C4—41no—
790C4—81no—
791C4—81no—
792C4—864no—
793C4—1722no—
794C4—1722no—
795C4C4×D4×D4311yescharacteristic
796C4C4×D4×D4311yescharacteristic
797C4#1458340811yescharacteristic
798C4#1458340811yescharacteristic
799C2—42no—
800C2—82no—
801C2—1724no—
802C2C4×#1306329311yescharacteristic
803C2#1914342711yescharacteristic
804C2#1914346811yescharacteristic
805C2#1914386111yescharacteristic
806C2#1914390711yescharacteristic
807C2#1914478811yescharacteristic
808C2#1914485111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2324C2
socleC23×C43C22×D4
prime radicalC2×#14583042C2
cosocleC22×C4×C43C24
hypercenter#2324D43
hypocenterC43#21460
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#14583379C2semidirect
3. C2×#14582999C2semidirect
4. C2×C4×#10621882C2semidirect
5. #19134953C2semidirect
6. #19134946C2semidirect
7. #19134913C2semidirect
8. #19134848C2semidirect
9. #19134841C2semidirect
10. #19134782C2semidirect
11. #19134533C2semidirect
12. #19134423C2semidirect
13. C4×#13063248C2semidirect
14. #19134361C2semidirect
15. C43×#2324C2semidirect
30. #14583042C4semidirect
69. C2×#10621898C2×C4semidirect
79. C2×#10621883C2×C4semidirect
82. C2×#10621882C2×C4semidirect
90. C4×Dic86D4semidirect
94. C4×D172D4semidirect
114. #13063248C2×C4semidirect
119. #13063245C2×C4semidirect
121. C22⋊(C43⋊C8)C2×C4semidirect
129. #121×C43C2×C4semidirect
399. #2324D43semidirect
468. C43#21460semidirect
497. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
C2×#145830422
C2×#145829992
C2×C4×#106218822
#191349532
#191349462
#191349132
#191348482
#191348412
#191347822
#191345332
#191344232
C4×#130632482
#191343612
C43×#23242
#2146043