Finite Group Databasebeta

← C2×#25363 #6447129

Subgroups — C2×#25363 #6447129

Order 512.

2082 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3142C211yesmaximal, characteristic
2C22×#479C211yesmaximal, characteristic, complemented
3C2×#3037C211yesmaximal, characteristic
4C2×#2935C211yesmaximal, characteristic
5#25363C2116yesmaximal, direct product factor
6C2×#2079C211yesmaximal, characteristic, complemented
7C2×#2078C211yesmaximal, characteristic, complemented
8C2×#2052C211yesmaximal, characteristic, complemented
9C2×#2052C211yesmaximal, characteristic, complemented
10C2×#1998C211yesmaximal, characteristic, complemented
11C2×#1950C211yesmaximal, characteristic, complemented
12C2×#1908C211yesmaximal, characteristic, complemented
13C2×#1908C211yesmaximal, characteristic, complemented
14C2×#1816C211yesmaximal, characteristic, complemented
15C2×#1815C211yesmaximal, characteristic, complemented
16C2×C4×#101C211yesmaximal, characteristic, complemented
17C22×#137C2211yescharacteristic
18C22×#137C2211yescharacteristic
19C22×#131C2211yescharacteristic
20C22×#131C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C22×#125C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24#3142—24no—
25#3142C2218yes—
26C2×#491—21no—
27C2×#490—21no—
28C2×#488—21no—
29C2×#488—21no—
30C2×#479—21no—
31C2×#479—21no—
32C2×#479—21no—
33C2×#479—21no—
34C2×#479—24no—
35C2×#479C2218yescomplemented
36#3037—24no—
37#3037C2218yes—
38C2×#464—21no—
39C2×#464—21no—
40C2×#462—21no—
41C2×#460—21no—
42#2935—24no—
43#2935C2218yes—
44C2×#436—21no—
45C2×#435—21no—
46C2×#435—21no—
47C2×C8×D4—21no—
48C22×#108C2211yescharacteristic
49C22×#108C2211yescharacteristic
50C22×#107C2211yescharacteristic
51C22×#106C2211yescharacteristic
52C2×#423C2211yescharacteristic
53C22×C4⋊C8C2211yescharacteristic
54C2×#417C2211yescharacteristic
55C2×#417C2211yescharacteristic
56C2×#417C2211yescharacteristic
57C2×#417C2211yescharacteristic
58C2×#417C2211yescharacteristic
59C2×#417C2211yescharacteristic
60C22×#103C2211yescharacteristic
61C22×#103C2211yescharacteristic
62C22×#101C2211yescharacteristic
63C22×#101C2211yescharacteristic
64C2×#408C2211yescharacteristic
65C2×#408C2211yescharacteristic
66C2×C4×M16C2211yescharacteristic
67C2×C4×M16C2211yescharacteristic
68#2079C2218yescomplemented
69#2078C2218yescomplemented
70#2052C2218yescomplemented
71#2052C2218yescomplemented
72#1998C2218yescomplemented
73#1950C2218yescomplemented
74#1908C2218yescomplemented
75#1908C2218yescomplemented
76#1816C2218yescomplemented
77#1815C2218yescomplemented
78C4×#101C2218yescomplemented
79C2×#343C2211yescharacteristic
80C2×#343C2211yescharacteristic
81C2×#343C2211yescharacteristic
82C2×#343C2211yescharacteristic
83C2×#343C2211yescharacteristic
84C2×#343C2211yescharacteristic
85C2×#341C2211yescharacteristic
86C2×#341C2211yescharacteristic
87C22×#41C2311yescharacteristic
88C22×#41C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C2×#137—22no—
91C2×#137—22no—
92C2×#137—24no—
93C2×#137—24no—
94C2×#137—42no—
95C2×#137—42no—
96C2×#137C2314yes—
97C2×#137C2314yes—
98C22×Q16—21no—
99C22×Q16—21no—
100C22×SD16—21no—
101C22×SD16—21no—
102C2×#131—22no—
103C2×#131—22no—
104C2×#131—24no—
105C2×#131—24no—
106C2×#131—42no—
107C2×#131—42no—
108C2×#131C2314yes—
109C2×#131C2314yes—
110C22×M16—21no—
111C22×M16—21no—
112C22×M16C2311yescharacteristic
113C22×M16C2311yescharacteristic
114C22×M16C2311yescharacteristic
115C22×M16C2311yescharacteristic
116C22×M16C2311yescharacteristic
117C22×M16C2311yescharacteristic
118C23×C8—21no—
119C23×C8—21no—
120C23×C8C2311yescharacteristic
121C23×C8C2311yescharacteristic
122#532—22no—
123#532—22no—
124#532D414yes—
125#532C2314yes—
126C2×C4⋊Q8D411yescharacteristic
127C2×#127D411yescharacteristic
128C2×#125—21no—
129C2×#125—21no—
130C2×#125—22no—
131C2×#125—21no—
132C2×#125—21no—
133C2×#125—22no—
134C2×#125—22no—
135C2×#125C2314yes—
136C2×#124D411yescharacteristic
137C2×#124D411yescharacteristic
138C2×#121—21no—
139C2×#121—21no—
140C2×C4×Q8—22no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—22no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—22no—
147C2×C4×Q8C2314yes—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C42—21no—
157C22×C42C2311yescharacteristic
158#491—28no—
159#490—28no—
160#488—28no—
161#488—28no—
162#479—28no—
163#479—28no—
164#479—28no—
165#479—28no—
166#464—28no—
167#464—28no—
168#462—28no—
169#460—28no—
170#436—28no—
171#435—28no—
172#435—28no—
173C8×D4—28no—
174C2×#108—42no—
175C2×#108—42no—
176C2×#108C2314yes—
177C2×#108C2314yes—
178C2×#107—21no—
179C2×#107—21no—
180C2×#107—22no—
181C2×#107C2314yes—
182C2×#106—21no—
183C2×#106—21no—
184C2×#106—22no—
185C2×#106C2314yes—
186#423—22no—
187#423C2314yes—
188C2×C4⋊C8—21no—
189C2×C4⋊C8—21no—
190C2×C4⋊C8D411yescharacteristic
191C2×C4⋊C8D411yescharacteristic
192C2×C4⋊C8D411yescharacteristic
193C2×C4⋊C8D411yescharacteristic
194C2×C4⋊C8D414yes—
195C2×C4⋊C8C2314yes—
196#417—22no—
197#417—22no—
198#417—22no—
199#417—22no—
200#417—22no—
201#417—22no—
202#417C2314yes—
203#417C2314yes—
204#417C2314yes—
205#417C2314yes—
206#417C2314yes—
207#417C2314yes—
208C2×#103—21no—
209C2×#103—21no—
210C2×#103—21no—
211C2×#103—21no—
212C2×#103—21no—
213C2×#103—21no—
214C2×#103—21no—
215C2×#103—21no—
216C2×#103—22no—
217C2×#103—21no—
218C2×#103—21no—
219C2×#103—22no—
220C2×#103C2314yes—
221C2×#103C2314yes—
222C2×#102—21no—
223C2×#102—21no—
224C2×#102—21no—
225C2×#102—21no—
226C2×#102—21no—
227C2×#102—21no—
228C2×#101—24no—
229C2×#101—24no—
230C2×#101C2314yes—
231C2×#101C2314yes—
232#408—22no—
233#408—22no—
234#408C2314yes—
235#408C2314yes—
236C2×C22⋊C8—21no—
237C2×C22⋊C8—21no—
238C2×C22⋊C8—21no—
239C2×C22⋊C8—21no—
240C4×M16—22no—
241C4×M16—22no—
242C4×M16C2314yes—
243C4×M16C2314yes—
244C2×#97—21no—
245C2×#97—21no—
246C2×C4×C8—21no—
247C2×C4×C8—21no—
248#343C2314yes—
249#343C2314yes—
250#343C2314yes—
251#343C2314yes—
252#343C2314yes—
253#343C2314yes—
254#341C2314yes—
255#341C2314yes—
256C2×#41—21no—
257C2×#41—21no—
258C2×#41—21no—
259C2×#41—21no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41C2×D412yes—
269C2×#41C2×D412yes—
270C2×#41C2412yes—
271C2×#41C2412yes—
272C22×Q8—21no—
273C22×Q8—22no—
274C22×Q8—21no—
275C22×Q8—21no—
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8C2×D411yescharacteristic
281C22×Q8C2×D411yescharacteristic
282C22×Q8#4114yes—
283C22×Q8C2412yes—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C2×D411yescharacteristic
289C22×D4C2×D411yescharacteristic
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4#4111yescharacteristic
297C23×C4#4111yescharacteristic
298C23×C4C2411yescharacteristic
299#137—28no—
300#137—28no—
301#137—44no—
302#137—44no—
303#137—48no—
304#137—48no—
305C2×Q16—24no—
306C2×Q16—24no—
307C2×Q16—44no—
308C2×Q16—44no—
309C2×SD16—24no—
310C2×SD16—24no—
311C2×SD16—44no—
312C2×SD16—44no—
313#131—28no—
314#131—28no—
315#131—44no—
316#131—44no—
317#131—48no—
318#131—48no—
319C2×M16—21no—
320C2×M16—22no—
321C2×M16—21no—
322C2×M16—21no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16—24no—
327C2×M16—24no—
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—44no—
339C2×M16—44no—
340C2×M16#4114yes—
341C2×M16C2412yes—
342C2×M16C2412yes—
343C2×M16C2412yes—
344C2×M16C2412yes—
345C2×M16C2412yes—
346C2×M16C2412yes—
347C22×C8—21no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—24no—
358C22×C8—24no—
359C22×C8—44no—
360C22×C8—44no—
361C22×C8C2×D411yescharacteristic
362C22×C8C2×D411yescharacteristic
363C22×C8C2×D411yescharacteristic
364C22×C8C2×D411yescharacteristic
365C22×C8C2×D412yes—
366C22×C8C2×D412yes—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C4⋊Q8—22no—
370C4⋊Q8C2×D414yes—
371#127—22no—
372#127C2×D414yes—
373#125—24no—
374#125—24no—
375#125—24no—
376#125—24no—
377#125—42no—
378#125—42no—
379#125—42no—
380#125—42no—
381#124—22no—
382#124—22no—
383#124C2×D414yes—
384#124C2×D414yes—
385#121—24no—
386#121—24no—
387#121—24no—
388#121—24no—
389C4×Q8—24no—
390C4×Q8—24no—
391C4×Q8—24no—
392C4×Q8—24no—
393C4×Q8—42no—
394C4×Q8—42no—
395C4×Q8—42no—
396C4×Q8—42no—
397C4×D4—24no—
398C4×D4—24no—
399C4×D4—24no—
400C4×D4—24no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C42—24no—
438C2×C42—42no—
439C2×C42—41no—
440C2×C42—41no—
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D412yes—
446C2×C42C2×D412yes—
447C2×C42#4112yes—
448C2×C42C2412yes—
449#108—44no—
450#108—44no—
451#107—24no—
452#107—24no—
453#106—24no—
454#106—24no—
455C4⋊C8—24no—
456C4⋊C8—24no—
457C4⋊C8C2×D414yes—
458C4⋊C8C2×D414yes—
459C4⋊C8C2×D414yes—
460C4⋊C8C2×D414yes—
461#103—24no—
462#103—24no—
463#103—24no—
464#103—24no—
465#103—24no—
466#103—24no—
467#103—24no—
468#103—24no—
469#103—24no—
470#103—24no—
471#102—24no—
472#102—24no—
473#102—24no—
474#102—24no—
475#102—24no—
476#102—24no—
477#101—28no—
478#101—28no—
479C22⋊C8—24no—
480C22⋊C8—24no—
481C22⋊C8—24no—
482C22⋊C8—24no—
483#97—24no—
484#97—24no—
485C4×C8—24no—
486C4×C8—24no—
487C24—21no—
488C24—21no—
489C24C2×#4111yescharacteristic
490#41—24no—
491#41—24no—
492#41—24no—
493#41—24no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—42no—
503#41—42no—
504#41—42no—
505#41—42no—
506#41—42no—
507#41—42no—
508#41—42no—
509#41—42no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—24no—
513C2×Q8—22no—
514C2×Q8—24no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—24no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—24no—
521C2×Q8—24no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8C22×D412yes—
534C2×Q8C22×D412yes—
535C2×Q8C2×#4114yes—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—24no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—24no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—82no—
554C2×D4C22×D412yes—
555C2×D4C22×D412yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4#12111yescharacteristic
586C22×C4#12111yescharacteristic
587C22×C4#12111yescharacteristic
588C22×C4#12111yescharacteristic
589C22×C4#12112yes—
590C22×C4#12112yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4111yescharacteristic
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C42−1+412yes—
602C22×C4C2511yescharacteristic
603Q16—48no—
604Q16—48no—
605SD16—48no—
606SD16—48no—
607M16—24no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—22no—
617M16—22no—
618M16—22no—
619M16—48no—
620M16—48no—
621M16—42no—
622M16—42no—
623M16—42no—
624M16—42no—
625M16—42no—
626M16C2×#4114yes—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—48no—
645C2×C8—48no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8—42no—
649C2×C8—42no—
650C2×C8—42no—
651C2×C8C22×D412yes—
652C2×C8C22×D412yes—
653C2×C8C22×D412yes—
654C2×C8C22×D412yes—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C42—44no—
680C42—44no—
681C42#12112yes—
682C42#12112yes—
683C42#12112yes—
684C42#12112yes—
685C42C22×D412yes—
686C42C22×D412yes—
687C42C22×D412yes—
688C42C22×D412yes—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23C2×#12111yescharacteristic
700C23C2×#12111yescharacteristic
701C23#52912yes—
702C23#54212yes—
703C23C22×#4111yescharacteristic
704Q8—24no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—24no—
710Q8—44no—
711Q8—44no—
712Q8—42no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—42no—
722D4—42no—
723D4—44no—
724D4—44no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—84no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4—82no—
763C2×C4—82no—
764C2×C4—82no—
765C2×C4C2×#12112yes—
766C2×C4C2×#12112yes—
767C2×C4C2×#12112yes—
768C2×C4C2×#12112yes—
769C2×C4C2×#12111yescharacteristic
770C2×C4C2×#12111yescharacteristic
771C2×C4#52912yes—
772C2×C4#54212yes—
773C2×C4#54612yes—
774C2×C4#54612yes—
775C2×C4#54612yes—
776C2×C4#54612yes—
777C2×C4#54712yes—
778C2×C4#54712yes—
779C2×C4#54812yes—
780C2×C4#54812yes—
781C2×C4C23×D411yescharacteristic
782C2×C4C23×D411yescharacteristic
783C2×C4C22×#4111yescharacteristic
784C2×C4C22×#4111yescharacteristic
785C2×C4C2×H(5,𝔽2)11yescharacteristic
786C2×C4C2×2−1+411yescharacteristic
787C8—22no—
788C8—22no—
789C8—22no—
790C8—22no—
791C8—24no—
792C8—42no—
793C8—42no—
794C8—42no—
795C8—42no—
796C8—42no—
797C22—24no—
798C22—24no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—84no—
811C22#242712yes—
812C22#242712yes—
813C22#306712yes—
814C22#306912yes—
815C22C22×#12111yescharacteristic
816C22C2×#52911yescharacteristic
817C22C2×#54211yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4#242712yes—
829C4#242712yes—
830C4C2×#54611yescharacteristic
831C4C2×#54611yescharacteristic
832C4C2×#54711yescharacteristic
833C4C2×#54811yescharacteristic
834C2—21no—
835C2—22no—
836C2—21no—
837C2—82no—
838C2—82no—
839C2#2536314yesdirect product factor
840C2C2×#242711yescharacteristic
841C2C2×#306711yescharacteristic
842C2C2×#306911yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#479C2semidirect
5. #25363C2direct (N × H)
6. C2×#2079C2semidirect
7. C2×#2078C2semidirect
8. C2×#2052C2semidirect
9. C2×#2052C2semidirect
10. C2×#1998C2semidirect
11. C2×#1950C2semidirect
12. C2×#1908C2semidirect
13. C2×#1908C2semidirect
14. C2×#1816C2semidirect
15. C2×#1815C2semidirect
16. C2×C4×#101C2semidirect
35. C2×#479C22semidirect
68. #2079C22semidirect
69. #2078C22semidirect
70. #2052C22semidirect
71. #2052C22semidirect
72. #1998C22semidirect
73. #1950C22semidirect
74. #1908C22semidirect
75. #1908C22semidirect
76. #1816C22semidirect
77. #1815C22semidirect
78. C4×#101C22semidirect
839. C2#25363direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31422
C22×#4792
C2×#30372
C2×#29352
#253632
C2×#20792
C2×#20782
C2×#20522
C2×#19982
C2×#19502
C2×#19082
C2×#18162
C2×#18152
C2×C4×#1012