Finite Group Databasebeta

← #25102351

Subgroups — #25102351

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×#14583380C211yesmaximal, characteristic, complemented
2C2×#14583042C211yesmaximal, characteristic
3C2×#14582996C211yesmaximal, characteristic, complemented
4C2×#14582979C211yesmaximal, characteristic, complemented
5#19137290C211yesmaximal, characteristic, complemented
6#19134947C211yesmaximal, characteristic, complemented
7#19134940C211yesmaximal, characteristic, complemented
8#19134850C211yesmaximal, characteristic, complemented
9#19134843C211yesmaximal, characteristic, complemented
10#19134783C211yesmaximal, characteristic, complemented
11#19134536C211yesmaximal, characteristic, complemented
12#19134419C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19#14583380—24no—
20#14583380—24no—
21C2×#13063290C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×C4×C22⋊D43—21no—
28C2×#13063284C2211yescharacteristic
29C2×#13063283—21no—
30C2×C4⋊C4×D43—21no—
31#14583042C418yescomplemented
32#14582996—24no—
33#14582979—24no—
34C2×#13063258C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582802—21no—
46#14582802C2211yescharacteristic
47#14582798C2211yescharacteristic
48#14582792—21no—
49#14582779—21no—
50#14582774—21no—
51#14582759C2211yescharacteristic
52C4⋊C4×Dic43C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
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
85#13063290—22no—
86#13063290—22no—
87#13063290—22no—
88#13063290D414yescomplemented
89D4×Dic43—22no—
90D4×Dic43—22no—
91#13063287—22no—
92#13063287—22no—
93#13063287—22no—
94#13063287D414yescomplemented
95C4×C22⋊D43—28no—
96C4×C22⋊D43—28no—
97#13063284—22no—
98#13063284—22no—
99#13063283—28no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43D411yescharacteristic
102C2×C4⋊Dic43D411yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C4⋊C4×D43—28no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43D411yescharacteristic
113C2×C22⋊Dic43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43C2311yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121#13063258—22no—
122#13063258—22no—
123#13063250—22no—
124#13063250—22no—
125#13063248C2×C414yescomplemented
126#13063247—22no—
127#13063247—22no—
128#13063245C2×C414yescomplemented
129C22⋊(C43⋊C8)C2×C414yescomplemented
130#13063235—22no—
131C8×Dic43—22no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×D4×C43—21no—
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141#121×C43—22no—
142#121×C43C2×C414yescomplemented
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43—22no—
145C2×C4⋊C4×C43—22no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150#102×C43—22no—
151#102×C43—22no—
152C22⋊C8×C43—22no—
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—24no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—81no—
174C22×C4×C43—81no—
175C22×C4×C43C22×C412yes—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43#4112yes—
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C2×C22⋊D43—24no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—42no—
186C22×Dic43—81no—
187C22×Dic43—81no—
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
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—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C4⋊C4×C43—24no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43C22×C412yes—
228C4⋊C4×C43C2×D412yes—
229C4⋊C4×C43C2×D412yes—
230C22⋊C4×C43—24no—
231C22⋊Dic43—22no—
232C22⋊Dic43—22no—
233C22⋊Dic43—42no—
234C22⋊Dic43—81no—
235C22⋊Dic43—81no—
236C22⋊Dic43—81no—
237#10621883—28no—
238#10621882—28no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241C4⋊Dic43—22no—
242C4⋊Dic43—22no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—81no—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250C4×Dic43—24no—
251C4×Dic43—21no—
252C4×Dic43—21no—
253C4×Dic43—24no—
254C4×Dic43—81no—
255C4×Dic43C2×D412yes—
256C4×Dic43C2×D412yes—
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—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—84no—
306C2×C4×C43C4×D412yes—
307C2×C4×C43C23×C411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C22⋊D43—216no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—84no—
334C2×Dic43#12012yes—
335C2×Dic43#12012yes—
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—
347C8×C43—41no—
348C8×C43—41no—
349C43⋊C8—22no—
350C43⋊C8—22no—
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—42no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43C2×C4×D411yescharacteristic
385C4×C43C2×C4×D411yescharacteristic
386C4×C43#52511yescharacteristic
387C4×C43#52511yescharacteristic
388Dic43—22no—
389Dic43—22no—
390Dic43—24no—
391Dic43—41no—
392Dic43—41no—
393Dic43—81no—
394Dic43—81no—
395C2×#520—431no—
396C2×#449—431no—
397C2×#440—431no—
398C2×C4×D8—431no—
399#2324—431no—
400#1880—431no—
401#1879—431no—
402#1874D4311yescharacteristic, complemented
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—431no—
431C2×C4×D4—861no—
432C2×C4×D4—861no—
433C2×#117—431no—
434C2×#117—861no—
435C22×C4⋊C4—861no—
436C22×C4⋊C4C2×D4311yescharacteristic
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×#102C2×D4311yescharacteristic
449C2×#102C2×D4311yescharacteristic
450C2×C22⋊C8—431no—
451C2×C22⋊C8C2×D4311yescharacteristic
452C2×#97—431no—
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#340C2×D4311yescharacteristic
465#340C2×D4311yescharacteristic
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×C8C22×D4311yescharacteristic
495C22×C8C22×D4311yescharacteristic
496#121—22no—
497#121C4×D4314yescomplemented
498C4×Q8—434no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×Q8—862no—
502C4×D4—434no—
503C4×D4—862no—
504C4×D4—862no—
505C4×D4—862no—
506C4×D4—862no—
507C4×D4—868no—
508C4×D4—868no—
509C4×D4—862no—
510#117—862no—
511#117—862no—
512#117—868no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—868no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22×D4311yescharacteristic
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—431no—
537C2×C42—431no—
538C2×C42—861no—
539C2×C42—861no—
540C2×C42—861no—
541#107—862no—
542#107—862no—
543#103—434no—
544#103—862no—
545#103—862no—
546#102—22no—
547#102—22no—
548#102—434no—
549#102—862no—
550#102—862no—
551C22⋊C8—22no—
552C22⋊C8—434no—
553#97—862no—
554C4×C8—862no—
555#95—861no—
556#95—861no—
557#95—861no—
558C24—21no—
559C24—861no—
560C24D4×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—24no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—861no—
608C22×C4—864no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—3441no—
614C22×C4—3441no—
615C22×C4—3441no—
616C22×C4—3441no—
617C22×C4—1722no—
618C22×C4C2×C4×D4312yes—
619C22×C4D4×D4311yescharacteristic
620C22×C4#1062190012yes—
621C22×C4C23×D4311yescharacteristic
622SD16—868no—
623D8—868no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—432no—
631C2×C8—432no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—862no—
641C4⋊C4—862no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—3441no—
649C4⋊C4C2×C4×D4312yes—
650C4⋊C4D4×D4312yes—
651C4⋊C4D4×D4312yes—
652C22⋊C4—24no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—3441no—
658C22⋊C4—3441no—
659C22⋊C4—3441no—
660C22⋊C4—1722no—
661C42—432no—
662C42—432no—
663C42—864no—
664C42—864no—
665C42—861no—
666C42—861no—
667C42—3441no—
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—
688C23(C22⋊D43)⋊C412yes—
689C23C2×D4×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—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—84no—
720C2×C4—432no—
721C2×C4—432no—
722C2×C4—8616no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—3444no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4(C22⋊D43)⋊C412yes—
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4#41×D4311yescharacteristic
750C2×C4#41×D4311yescharacteristic
751C2×C4C2×#1062190011yescharacteristic
752C8—41no—
753C8—41no—
754C8—862no—
755C8—862no—
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×(C22⋊D43)⋊C411yescharacteristic
778C22#120×D4311yescharacteristic
779C22#1458340711yescharacteristic
780C22#1458370011yescharacteristic
781C22#1458370311yescharacteristic
782C22#1458370511yescharacteristic
783C22#1458371511yescharacteristic
784C4—22no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—864no—
789C4—862no—
790C4—862no—
791C4—3441no—
792C4—3441no—
793C4—1721no—
794C4—1721no—
795C4C4×D4×D4311yescharacteristic
796C4C4×D4×D4311yescharacteristic
797C4#1458340911yescharacteristic
798C4#1458340911yescharacteristic
799C2—42no—
800C2—82no—
801C2—1724no—
802C2#1913710011yescharacteristic
803C2#1914342111yescharacteristic
804C2#1914346611yescharacteristic
805C2#1914385811yescharacteristic
806C2#1914390511yescharacteristic
807C2#1914478911yescharacteristic
808C2#1914485211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583042C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43#21460
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#14583380C2semidirect
3. C2×#14582996C2semidirect
4. C2×#14582979C2semidirect
5. #19137290C2semidirect
6. #19134947C2semidirect
7. #19134940C2semidirect
8. #19134850C2semidirect
9. #19134843C2semidirect
10. #19134783C2semidirect
11. #19134536C2semidirect
12. #19134419C2semidirect
13. #19134414C2semidirect
14. #19134363C2semidirect
15. C43×#1874C2semidirect
31. #14583042C4semidirect
69. C2×#10621898C2×C4semidirect
79. C2×#10621883C2×C4semidirect
82. C2×#10621882C2×C4semidirect
88. #13063290D4semidirect
94. #13063287D4semidirect
125. #13063248C2×C4semidirect
128. #13063245C2×C4semidirect
129. C22⋊(C43⋊C8)C2×C4semidirect
142. #121×C43C2×C4semidirect
402. #1874D43semidirect
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×#145833802
C2×#145830422
C2×#145829962
C2×#145829792
#191372902
#191349472
#191349402
#191348502
#191348432
#191347832
#191345362
#191344192
#191344142
#191343632
C43×#18742
#2146043