Finite Group Databasebeta

← C2×#19135141 #25098619

Subgroups — C2×#19135141 #25098619

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2C2×#14583468C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic, complemented
4C22×#13063241C211yesmaximal, characteristic, complemented
5C22×#13063241C211yesmaximal, characteristic, complemented
6#19135141C218yesmaximal, direct product factor
7C2×#14582669C211yesmaximal, characteristic, complemented
8C2×C43×#344C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×D172C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yescomplemented
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×M16×D43—22no—
20#14583468—22no—
21#14583468—22no—
22#14583468C414yes—
23#14583468C2214yes—
24C2×#13063322—21no—
25C2×#13063313—21no—
26C2×#13063300—22no—
27C2×#13063295C414yes—
28#14582881—22no—
29#14582881C2214yescomplemented
30C2×#13063243—21no—
31C2×#13063241—21no—
32C2×#13063241—22no—
33C2×#13063241—22no—
34C2×#13063241—22no—
35C2×#13063241—22no—
36C2×#13063241C2214yescomplemented
37C2×#13063241C2214yescomplemented
38#14582669C2214yescomplemented
39C22×M16×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C43×#344C2214yescomplemented
43C24×D43C2×C412yes—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898C2×C412yes—
53C2×#10621898D412yes—
54C2×#10621898D412yes—
55C2×#10621898C2312yes—
56C22×Dic86D411yescharacteristic
57C22×D172—21no—
58C22×D172—21no—
59C22×D172—21no—
60C22×D172—21no—
61C22×D172—21no—
62C22×D172—21no—
63C22×D172—21no—
64C22×D172—21no—
65C22×D172—21no—
66C22×D172—21no—
67C22×D172—21no—
68C22×D172—21no—
69C22×D172—24no—
70C22×D172C2×C412yes—
71C22×D172D411yescharacteristic
72C22×D172C2312yes—
73C22×C22⋊D43C2×C412yes—
74C22×C4×D43D412yes—
75#13063333—28no—
76#13063333—28no—
77#13063331—28no—
78#13063331—28no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877—21no—
87C2×#10621877D412yescomplemented
88C2×#10621877D412yescomplemented
89C2×#10621877C2312yes—
90C2×#10621877C2312yes—
91C2×#10621872—24no—
92M16×D43—28no—
93M16×D43—28no—
94C22×C43⋊C8—21no—
95C22×C43⋊C8—21no—
96C2×C8×D43—24no—
97#13063322—24no—
98#13063322—24no—
99#13063313—24no—
100#13063313—24no—
101#13063300—28no—
102#13063300—28no—
103#13063295—28no—
104#13063295C2×C4116yes—
105C2×(C2×D43)⋊C4—24no—
106#13063243—24no—
107#13063241—24no—
108#13063241—28no—
109#13063241—28no—
110C23×C4×C43C2311yescharacteristic
111C2×M16×C43—21no—
112C2×M16×C43—21no—
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43D412yescomplemented
120C2×M16×C43D412yescomplemented
121C2×M16×C43C2312yes—
122C2×M16×C43C2312yes—
123C22×C8×C43—21no—
124C22×C8×C43—21no—
125#117×C43—21no—
126#117×C43—21no—
127#117×C43C2×C412yes—
128#117×C43C2312yes—
129C2×C4⋊C4×C43—21no—
130C2×C22⋊C4×C43C2×C412yes—
131C2×C42×C43—21no—
132C24×C43C22×C411yescharacteristic
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—22no—
139C23×D43—84no—
140C23×D43C22⋊C412yes—
141C23×D43C22×C414yes—
142C22×C4×C43—22no—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43C22⋊C414yes—
162C2×C22⋊D43C22×C414yes—
163C22×Dic43C22⋊C412yes—
164#10621898—22no—
165#10621898—22no—
166#10621898—22no—
167#10621898—22no—
168#10621898—22no—
169#10621898—22no—
170#10621898—22no—
171#10621898—22no—
172#10621898—22no—
173#10621898—22no—
174#10621898—22no—
175#10621898—22no—
176#10621898—22no—
177#10621898—22no—
178#10621898—22no—
179#10621898—22no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—22no—
185C2×D172—22no—
186C2×D172—22no—
187C2×D172—22no—
188C2×D172—22no—
189C2×D172—22no—
190C2×D172—22no—
191C2×D172—22no—
192C2×D172—22no—
193C2×D172—22no—
194C2×D172—22no—
195C2×D172—22no—
196C2×D172—216no—
197C2×D172—41no—
198C2×D172—41no—
199C2×D172—41no—
200C2×D172—41no—
201C2×D172—41no—
202C2×D172—41no—
203C2×D172—41no—
204C2×D172—41no—
205C2×D172—41no—
206C2×D172—41no—
207C2×D172—41no—
208C2×D172—41no—
209C2×D172—41no—
210C2×D172—41no—
211C2×D172—41no—
212C2×D172—41no—
213C2×D172—88no—
214C2×D172C22⋊C412yes—
215C2×D172C2×D412yes—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43C22⋊C414yes—
221C2×C4×D43C2×D414yes—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86C22⋊C412yes—
227C2×Dic86C2×D412yes—
228M16×C43—22no—
229M16×C43—22no—
230M16×C43—22no—
231M16×C43—22no—
232M16×C43—22no—
233M16×C43—41no—
234M16×C43—41no—
235M16×C43C2×D414yescomplemented
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43—22no—
240C2×C8×C43—41no—
241C2×C8×C43—41no—
242C4⋊C4×C43—22no—
243C4⋊C4×C43—22no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43C22×C414yes—
246C42×C43—22no—
247C42×C43—22no—
248(C2×D43)⋊C4—216no—
249#10621877—22no—
250#10621877—22no—
251#10621877—22no—
252#10621877—22no—
253#10621877—22no—
254#10621877—41no—
255#10621877—41no—
256#10621877C2×D414yescomplemented
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—22no—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—41no—
262C2×C43⋊C8—41no—
263#10621872—216no—
264C8×D43—216no—
265C23×C43—42no—
266C23×C43C2×C22⋊C411yescharacteristic
267C23×C43C2×C22⋊C411yescharacteristic
268C23×C43C4×D411yescharacteristic
269C23×C43C4×D411yescharacteristic
270C23×C43C4×D411yescharacteristic
271C23×C43C4×D411yescharacteristic
272C23×C43C23×C411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—24no—
276C22×D43—24no—
277C22×D43—24no—
278C22×D43—44no—
279C22×D43—48no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—84no—
285C22×D43—84no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43C2×C22⋊C414yes—
291C2×C4×C43—24no—
292C2×C4×C43—44no—
293C2×C4×C43C2×C22⋊C411yescharacteristic
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C4×D411yescharacteristic
296C2×C4×C43C4×D411yescharacteristic
297C2×C4×C43C4×D411yescharacteristic
298C2×C4×C43C4×D411yescharacteristic
299C2×C4×C43#12011yescharacteristic
300C2×C4×C43#12011yescharacteristic
301C2×C4×C43#12011yescharacteristic
302C2×C4×C43#12011yescharacteristic
303C2×C4×C43#12111yescharacteristic
304C2×C4×C43#12111yescharacteristic
305C2×C4×C43#12111yescharacteristic
306C2×C4×C43#12111yescharacteristic
307C2×C4×C43#12111yescharacteristic
308C2×C4×C43#12111yescharacteristic
309C2×C4×C43#12111yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12311yescharacteristic
312C2×C4×C43#12311yescharacteristic
313C2×C4×C43#12311yescharacteristic
314C2×C4×C43#12311yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C22⋊D43—24no—
322C22⋊D43—24no—
323C22⋊D43—24no—
324C22⋊D43—24no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43C2×C22⋊C414yes—
328D172—22no—
329D172—22no—
330D172—22no—
331D172—22no—
332D172—42no—
333D172—42no—
334D172—42no—
335D172—42no—
336D172—42no—
337D172—42no—
338D172—42no—
339D172—42no—
340D172—816no—
341C4×D43—24no—
342C4×D43—24no—
343C4×D43—24no—
344C4×D43—24no—
345Dic86—22no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349C8×C43—24no—
350C8×C43—42no—
351C43⋊C8—24no—
352C43⋊C8—42no—
353C2×#1914—431nomaximal, Sylow
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43#38611yescharacteristic
362C22×C43#38611yescharacteristic
363C22×C43#38611yescharacteristic
364C22×C43#38611yescharacteristic
365C22×C43C22×C22⋊C411yescharacteristic
366C22×C43C2×C4×D411yescharacteristic
367C22×C43C2×C4×D411yescharacteristic
368C2×D43—24no—
369C2×D43—44no—
370C2×D43—44no—
371C2×D43—48no—
372C2×D43—44no—
373C2×D43—82no—
374C2×D43—84no—
375C2×D43—84no—
376C2×D43—84no—
377C2×D43—84no—
378C2×D43—84no—
379C2×D43—84no—
380C4×C43—44no—
381C4×C43#38611yescharacteristic
382C4×C43#38611yescharacteristic
383C4×C43#38611yescharacteristic
384C4×C43#38611yescharacteristic
385C4×C43C2×#12011yescharacteristic
386C4×C43C2×#12111yescharacteristic
387C4×C43C2×#12111yescharacteristic
388C4×C43C2×#12311yescharacteristic
389Dic43—24no—
390C2×#568—431no—
391C2×#535—431no—
392C2×#413—431no—
393C22×#100—431no—
394C22×#100—431no—
395#1914—438no—
396C2×#344—431no—
397C2×#344D4311yescharacteristic, complemented
398C2×C43—21no—
399C2×C43—21no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43#191412yescomplemented
405C2×C43C2×#38611yescharacteristic
406D43—44no—
407D43—84no—
408C22×#41—431no—
409C23×D4—431no—
410#568—434no—
411#568—862no—
412#568—862no—
413#568—862no—
414C2×#131—862no—
415C2×#131—862no—
416C22×M16—431no—
417C22×M16—431no—
418C22×M16—862no—
419C22×M16C2×D4311yescharacteristic
420C22×M16C2×D4311yescharacteristic
421#535—434no—
422#535—434no—
423#535—862no—
424#535—862no—
425C2×#127—861no—
426C2×#124—861no—
427C2×#121—862no—
428C2×#120—434no—
429C2×#117C2×D4311yescharacteristic
430#413—434no—
431#413—862no—
432C2×#101—861no—
433C2×#100—434no—
434C2×#100—434no—
435C2×#100—862no—
436C2×#100—862no—
437C2×#100—861no—
438C2×#100—862no—
439C2×#100—862no—
440#344—434no—
441#344C2×D4314yescomplemented
442C43C2×#191411yescharacteristic, complemented, Sylow
443C25—432no—
444C2×#41—432no—
445C2×#41—432no—
446C2×#41—432no—
447C2×#41—432no—
448C2×#41—861no—
449C2×#41—861no—
450C2×#41—861no—
451C2×#41—861no—
452C2×#41—861no—
453C2×#41—861no—
454C2×#41—861no—
455C2×#41—861no—
456C22×Q8—431no—
457C22×D4—432no—
458C22×D4—432no—
459C22×D4—431no—
460C22×D4—432no—
461C22×D4—864no—
462C22×D4—861no—
463C22×D4—861no—
464C22×D4—861no—
465C22×D4—861no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4—861no—
474C23×C4—432no—
475C23×C4C22×D4311yescharacteristic
476#131—868no—
477#131—868no—
478#131—868no—
479#131—868no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—432no—
489C2×M16—432no—
490C2×M16—432no—
491C2×M16—432no—
492C2×M16—864no—
493C2×M16—868no—
494C2×M16—868no—
495C2×M16—861no—
496C2×M16—861no—
497C2×M16—861no—
498C2×M16—861no—
499C2×M16—861no—
500C2×M16—861no—
501C2×M16—861no—
502C2×M16—861no—
503C2×M16D17212yescomplemented
504C2×M16D17212yescomplemented
505C2×M16C22×D4312yes—
506C2×M16C22×D4312yes—
507C22×C8—21no—
508C22×C8—21no—
509C22×C8—864no—
510C22×C8—861no—
511C22×C8—861no—
512#127—864no—
513#127—864no—
514#124—864no—
515#124—864no—
516#121—868no—
517#121—868no—
518#120—4316no—
519#120—868no—
520#117—21no—
521#117—21no—
522#117C4×D4312yes—
523#117C22×D4312yes—
524C2×C4⋊C4—21no—
525C2×C22⋊C4—864no—
526C2×C22⋊C4C4×D4312yes—
527C2×C42—21no—
528#101—864no—
529#100—868no—
530#100—864no—
531#100—868no—
532C24—432no—
533C24—434no—
534C24—862no—
535C24—862no—
536C24—862no—
537C24—862no—
538C24—862no—
539C24—862no—
540C24—3444no—
541C24C2×C4×D4311yescharacteristic
542#41—862no—
543#41—862no—
544#41—862no—
545#41—862no—
546#41—862no—
547#41—862no—
548#41—862no—
549#41—862no—
550#41—862no—
551#41—862no—
552#41—862no—
553#41—862no—
554#41—862no—
555#41—862no—
556#41—862no—
557#41—862no—
558C2×Q8—432no—
559C2×Q8—432no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×D4—434no—
565C2×D4—434no—
566C2×D4—432no—
567C2×D4—432no—
568C2×D4—8616no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—862no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—3448no—
590C2×D4—1721no—
591C2×D4—1721no—
592C2×D4—1721no—
593C2×D4—1721no—
594C2×D4—1721no—
595C2×D4—1721no—
596C2×D4—1721no—
597C2×D4—1721no—
598C2×D4—1721no—
599C2×D4—1721no—
600C2×D4—1721no—
601C2×D4—1721no—
602C2×D4—1721no—
603C2×D4—1721no—
604C2×D4—1721no—
605C2×D4—1721no—
606C22×C4—22no—
607C22×C4—432no—
608C22×C4—434no—
609C22×C4—434no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4C2×C4×D4311yescharacteristic
615C22×C4C2×D17211yescharacteristic
616C22×C4C2×D17211yescharacteristic
617C22×C4#1062189811yescharacteristic
618C22×C4#1062189811yescharacteristic
619C22×C4D4×D4311yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4#1062190211yescharacteristic
626C22×C4#1062190211yescharacteristic
627C22×C4C23×D4311yescharacteristic
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—41no—
634M16—41no—
635M16—434no—
636M16—8616no—
637M16—862no—
638M16—862no—
639M16—862no—
640M16—862no—
641M16—862no—
642M16—1721no—
643M16—1721no—
644M16C2×D17214yescomplemented
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—8616no—
652C2×C8—862no—
653C2×C8—862no—
654C2×C8—862no—
655C2×C8—862no—
656C2×C8—1721no—
657C2×C8—1721no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—8616no—
662C22⋊C4C2×C4×D4314yes—
663C42—22no—
664C42—22no—
665C23—42no—
666C23—434no—
667C23—862no—
668C23—862no—
669C23—864no—
670C23—864no—
671C23—864no—
672C23—3444no—
673C23—3444no—
674C23—3444no—
675C23—3444no—
676C23—3444no—
677C23—3444no—
678C23—1728no—
679C23—1724no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23C22⋊C4×D4311yescharacteristic
685C23C22⋊C4×D4311yescharacteristic
686C23#1306328711yescharacteristic
687C23#1306328711yescharacteristic
688C23C4×D17211yescharacteristic
689C23C4×D17211yescharacteristic
690C23C22×C4×D4311yescharacteristic
691Q8—862no—
692Q8—862no—
693Q8—862no—
694Q8—862no—
695D4—864no—
696D4—864no—
697D4—864no—
698D4—864no—
699D4—862no—
700D4—862no—
701D4—862no—
702D4—862no—
703D4—34416no—
704D4—1722no—
705D4—1722no—
706D4—1722no—
707D4—1722no—
708D4—1722no—
709D4—1722no—
710D4—1722no—
711D4—1722no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—434no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—864no—
718C2×C4—864no—
719C2×C4—864no—
720C2×C4—864no—
721C2×C4C22⋊C4×D4311yescharacteristic
722C2×C4C22⋊C4×D4311yescharacteristic
723C2×C4#1306328711yescharacteristic
724C2×C4#1306328711yescharacteristic
725C2×C4C4×D17211yescharacteristic
726C2×C4C4×D17211yescharacteristic
727C2×C4#1306329511yescharacteristic
728C2×C4#1306329511yescharacteristic
729C2×C4#1306329511yescharacteristic
730C2×C4#1306329511yescharacteristic
731C2×C4#1306329811yescharacteristic
732C2×C4#1306329811yescharacteristic
733C2×C4#1306329811yescharacteristic
734C2×C4#1306329811yescharacteristic
735C2×C4#1306330011yescharacteristic
736C2×C4#1306330011yescharacteristic
737C2×C4#1306330011yescharacteristic
738C2×C4#1306330011yescharacteristic
739C2×C4#1306331011yescharacteristic
740C2×C4#1306331011yescharacteristic
741C2×C4#1306331011yescharacteristic
742C2×C4#1306331011yescharacteristic
743C2×C4C2×D4×D4311yescharacteristic
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4C22×D17211yescharacteristic
747C2×C4C2×#1062189811yescharacteristic
748C2×C4C2×#1062190211yescharacteristic
749C8—24no—
750C8—42no—
751C8—864no—
752C8—1722no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—864no—
761C22—3444no—
762C22—3444no—
763C22—3444no—
764C22—3444no—
765C22—3444no—
766C22—3442no—
767C22—3444no—
768C22—1728no—
769C22—1724no—
770C22—1724no—
771C22—1724no—
772C22#1458277711yescharacteristic
773C22#1458277711yescharacteristic
774C22#1458277711yescharacteristic
775C22#1458277711yescharacteristic
776C22C2×C22⋊C4×D4311yescharacteristic
777C22C2×#1306328711yescharacteristic
778C22C2×C4×D17211yescharacteristic
779C4—44no—
780C4—864no—
781C4#1458277711yescharacteristic
782C4#1458277711yescharacteristic
783C4#1458277711yescharacteristic
784C4#1458277711yescharacteristic
785C4C2×#1306329511yescharacteristic
786C4C2×#1306329811yescharacteristic
787C4C2×#1306330011yescharacteristic
788C4C2×#1306331011yescharacteristic
789C2—21no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—3444no—
796C2—1724no—
797C2#1913514112yesdirect product factor
798C2C2×#1458277711yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC2×#14583468C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43C2×#1914
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582881C2semidirect
4. C22×#13063241C2semidirect
5. C22×#13063241C2semidirect
6. #19135141C2direct (N × H)
7. C2×#14582669C2semidirect
8. C2×C43×#344C2semidirect
14. #14583665C22semidirect
29. #14582881C22semidirect
36. C2×#13063241C22semidirect
37. C2×#13063241C22semidirect
38. #14582669C22semidirect
42. C43×#344C22semidirect
87. C2×#10621877D4semidirect
88. C2×#10621877D4semidirect
119. C2×M16×C43D4semidirect
120. C2×M16×C43D4semidirect
235. M16×C43C2×D4semidirect
256. #10621877C2×D4semidirect
397. C2×#344D43semidirect
404. C2×C43#1914semidirect
441. #344C2×D43semidirect
442. C43C2×#1914semidirect
503. C2×M16D172semidirect
504. C2×M16D172semidirect
644. M16C2×D172semidirect
797. C2#19135141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836652
C2×#145834682
C2×#145828812
C22×#130632412
#191351412
C2×#145826692
C2×C43×#3442
C2×#191443