Finite Group Databasebeta

← C2×#495242 #72321013

Subgroups — C2×#495242 #72321013

Order 1024.

7957 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#509C211yesmaximal, characteristic
2C22×#2155C211yesmaximal, characteristic, complemented
3C23×#361C211yesmaximal, characteristic, complemented
4C22×#2145C211yesmaximal, characteristic, complemented
5C22×#2110C211yesmaximal, characteristic, complemented
6C2×#21240C211yesmaximal, characteristic, complemented
7C2×#21233C211yesmaximal, characteristic, complemented
8#495242C2116yesmaximal, direct product factor
9C2×#13249C218yesmaximal, complemented
10C23×#135C2211yescharacteristic
11C24×D8C2211yescharacteristic
12C22×#509—28no—
13C22×#509—28no—
14C22×#509C414yescomplemented
15C22×#509C418yescomplemented
16C22×#509C2214yes—
17C22×#509C2218yes—
18C23×SD32C412yescomplemented
19C23×D16C412yescomplemented
20C23×M32C2211yescharacteristic
21C23×M32C2211yescharacteristic
22C23×#108C2211yescharacteristic
23C22×#427C2211yescharacteristic
24C22×#421—21no—
25C22×#418—21no—
26C2×#2879—21no—
27C22×#405C2211yescharacteristic
28C2×#2309—21no—
29C2×#2155—28no—
30C2×#2155C2218yescomplemented
31C22×#365C2214yescomplemented
32C22×#361—28no—
33C22×#361C2214yescomplemented
34C22×#361C2218yescomplemented
35C2×#2145—28no—
36C2×#2145C2218yescomplemented
37C22×#360C2214yescomplemented
38C2×#2110—28no—
39C2×#2110C2218yescomplemented
40C22×#347C2214yescomplemented
41#21240—24no—
42#21240C2218yescomplemented
43C2×#1975C2214yescomplemented
44C2×#1974—22no—
45#21233—24no—
46#21233C2218yescomplemented
47C2×#1972C2214yescomplemented
48C2×#1970—22no—
49#13249C22164yescomplemented
50C23×#41—21no—
51C24×D4—21no—
52C22×#135—21no—
53C22×#135—22no—
54C22×#135—24no—
55C22×#135—24no—
56C22×#135—24no—
57C22×#135—21no—
58C22×#135—22no—
59C22×#135—24no—
60C22×#135C2×C412yes—
61C22×#135C2×C414yes—
62C22×#135C2312yes—
63C22×#135C2314yes—
64C23×Q16C2×C411yescharacteristic
65C23×SD16—21no—
66C23×D8—24no—
67C23×D8—24no—
68C23×D8—24no—
69C23×D8—21no—
70C23×D8—22no—
71C23×D8—24no—
72C23×D8—21no—
73C23×D8—21no—
74C23×D8—22no—
75C23×D8C2×C412yes—
76C23×D8C2×C412yes—
77C23×D8C2×C414yes—
78C23×D8C2×C411yescharacteristic
79C23×D8C2312yes—
80C23×D8C2314yes—
81C23×M16—21no—
82C23×M16D411yescharacteristic
83C24×C8C2311yescharacteristic
84C22×#117—21no—
85C22×#117D411yescharacteristic
86C2×#509—232no—
87C2×#509—264no—
88C2×#509—216no—
89C2×#509—216no—
90C2×#509—232no—
91C2×#509—232no—
92C2×#509C2×C4116yes—
93C2×#509C2×C4132yescomplemented
94C2×#509C23116yes—
95C22×SD32—216no—
96C22×SD32C2×C418yes—
97C22×SD32C2×C4116yescomplemented
98C22×D16—216no—
99C22×D16C2×C418yes—
100C22×D16C2×C4116yescomplemented
101C22×M32—24no—
102C22×M32—21no—
103C22×M32—22no—
104C22×M32C2×C412yes—
105C22×M32C2×C414yes—
106C22×M32D418yes—
107C22×M32D418yes—
108C22×M32D418yes—
109C22×M32C2312yes—
110C22×M32C2314yes—
111C22×M32C2312yes—
112C22×M32C2314yes—
113C23×C16—21no—
114C23×C16C2×C412yes—
115C22×#108—21no—
116C22×#108—22no—
117C22×#108—24no—
118C22×#108—24no—
119C22×#108C2312yes—
120C22×#108C2314yes—
121C2×#427—22no—
122C2×#427—24no—
123C2×#427—24no—
124C2×#427C2314yes—
125C22×#107—21no—
126C22×#106C2312yes—
127C2×#421—28no—
128C2×#421—48no—
129C22×#104—24no—
130C2×#418—28no—
131C2×#418—48no—
132C22×#102—24no—
133#2879—28no—
134#2879—44no—
135C2×#408—24no—
136C2×#408—42no—
137C2×#407—42no—
138C2×#405—24no—
139C2×#405—24no—
140C2×#405D414yes—
141C2×#405C2314yes—
142C22×#97C2312yes—
143C22×C4×C8D412yes—
144#2309—28no—
145#2309—44no—
146C2×#390—24no—
147C2×#390—42no—
148C2×#379—42no—
149#2155—232no—
150C2×#365—216no—
151C2×#365C23116yescomplemented
152C2×#361—216no—
153C2×#361—232no—
154C2×#361C23116yescomplemented
155#2145—232no—
156C2×#360—216no—
157C2×#360C23116yescomplemented
158#2110—232no—
159C2×#347—216no—
160C2×#347C23116yescomplemented
161#1975—28no—
162#1975C23116yescomplemented
163#1974—216no—
164#1972—28no—
165#1972C23116yescomplemented
166#1970—216no—
167C26—41no—
168C22×#41—24no—
169C22×#41—22no—
170C22×#41—22no—
171C22×#41—24no—
172C22×#41—41no—
173C22×#41—42no—
174C22×#41—41no—
175C22×#41—42no—
176C22×#41—44no—
177C22×#41—44no—
178C22×#41—44no—
179C22×#41—44no—
180C23×Q8—21no—
181C23×D4—22no—
182C23×D4—24no—
183C23×D4—22no—
184C23×D4—21no—
185C23×D4—24no—
186C23×D4—22no—
187C23×D4—41no—
188C23×D4—44no—
189C23×D4—44no—
190C23×D4—44no—
191C23×D4—44no—
192C23×D4—41no—
193C23×D4—41no—
194C23×D4—42no—
195C23×D4—42no—
196C23×D4—41no—
197C24×C4—41no—
198C24×C4C2×D411yescharacteristic
199C2×#135—28no—
200C2×#135—216no—
201C2×#135—24no—
202C2×#135—24no—
203C2×#135—24no—
204C2×#135—28no—
205C2×#135—216no—
206C2×#135—24no—
207C2×#135—22no—
208C2×#135—24no—
209C2×#135—28no—
210C2×#135—24no—
211C2×#135—28no—
212C2×#135—24no—
213C2×#135—28no—
214C2×#135—24no—
215C2×#135—22no—
216C2×#135—24no—
217C2×#135—28no—
218C2×#135—44no—
219C2×#135—48no—
220C2×#135—44no—
221C2×#135—48no—
222C2×#135—44no—
223C2×#135—48no—
224C2×#135—44no—
225C2×#135—48no—
226C2×#135C22×C414yes—
227C2×#135C22×C418yes—
228C2×#135C2414yes—
229C22×Q16—24no—
230C22×Q16—24no—
231C22×Q16—21no—
232C22×Q16—22no—
233C22×Q16C22×C412yes—
234C22×Q16C22×C414yes—
235C22×SD16—22no—
236C22×SD16—24no—
237C22×SD16—22no—
238C22×SD16—24no—
239C22×SD16—44no—
240C22×SD16—44no—
241C22×D8—24no—
242C22×D8—28no—
243C22×D8—28no—
244C22×D8—216no—
245C22×D8—28no—
246C22×D8—28no—
247C22×D8—216no—
248C22×D8—24no—
249C22×D8—22no—
250C22×D8—24no—
251C22×D8—22no—
252C22×D8—24no—
253C22×D8—24no—
254C22×D8—24no—
255C22×D8—24no—
256C22×D8—21no—
257C22×D8—22no—
258C22×D8—24no—
259C22×D8—28no—
260C22×D8—24no—
261C22×D8—28no—
262C22×D8—24no—
263C22×D8—28no—
264C22×D8—24no—
265C22×D8—22no—
266C22×D8—24no—
267C22×D8—28no—
268C22×D8—22no—
269C22×D8—24no—
270C22×D8—24no—
271C22×D8—22no—
272C22×D8—44no—
273C22×D8—44no—
274C22×D8—48no—
275C22×D8—44no—
276C22×D8—48no—
277C22×D8—44no—
278C22×D8—44no—
279C22×D8—48no—
280C22×D8—44no—
281C22×D8—48no—
282C22×D8C22×C412yes—
283C22×D8C22×C414yes—
284C22×D8C22×C414yes—
285C22×D8C22×C418yes—
286C22×D8C22×C414yes—
287C22×D8C22×C418yes—
288C22×D8C2414yes—
289C22×M16—24no—
290C22×M16—21no—
291C22×M16—21no—
292C22×M16—22no—
293C22×M16—24no—
294C22×M16—22no—
295C22×M16—24no—
296C22×M16—41no—
297C22×M16—42no—
298C22×M16—44no—
299C22×M16—44no—
300C22×M16C2×D414yes—
301C23×C8—41no—
302C23×C8C22×C411yescharacteristic
303C23×C8C22×C411yescharacteristic
304C23×C8C22×C412yes—
305C23×C8C2×D412yes—
306C23×C8C2×D414yes—
307C23×C8C2×D414yes—
308C23×C8C2×D411yescharacteristic
309C23×C8C2×D412yes—
310C23×C8C2×D414yes—
311C23×C8#4114yes—
312C23×C8#4111yescharacteristic
313C23×C8#4111yescharacteristic
314C23×C8#4112yes—
315C23×C8C2411yescharacteristic
316C23×C8C2412yes—
317C2×#117—22no—
318C2×#117—24no—
319C2×#117—24no—
320C2×#117—24no—
321C2×#117—42no—
322C2×#117—44no—
323C2×#117—44no—
324C2×#117C2×D414yes—
325C22×C4⋊C4—21no—
326C22×C4⋊C4—22no—
327C22×C22⋊C4—21no—
328C22×C22⋊C4—41no—
329C22×C22⋊C4—48no—
330C22×C42—41no—
331C22×C42C2×D412yes—
332#509—264no—
333#509—2128no—
334#509—232no—
335#509—232no—
336C2×SD32—232no—
337C2×SD32—264no—
338C2×SD32C22×C4132yes—
339C2×D16—232no—
340C2×D16—264no—
341C2×D16C22×C4132yes—
342C2×M32—28no—
343C2×M32—216no—
344C2×M32—24no—
345C2×M32—28no—
346C2×M32—24no—
347C2×M32—22no—
348C2×M32C22⋊C4116yescomplemented
349C2×M32C22⋊C4132yescomplemented
350C2×M32C22×C414yes—
351C2×M32C22×C418yes—
352C2×M32C2×D418yes—
353C2×M32C2×D4116yes—
354C2×M32C2×D418yes—
355C2×M32C2×D418yes—
356C2×M32C2×D4116yes—
357C2×M32C2×D4116yes—
358C2×M32C2414yes—
359C2×M32C2414yes—
360C22×C16—28no—
361C22×C16—22no—
362C22×C16—24no—
363C22×C16C22⋊C4116yescomplemented
364C22×C16C22×C414yes—
365C22×C16C22×C418yes—
366C2×#108—24no—
367C2×#108—28no—
368C2×#108—24no—
369C2×#108—28no—
370C2×#108—24no—
371C2×#108—22no—
372C2×#108—44no—
373C2×#108—48no—
374C2×#108C2414yes—
375#427—28no—
376#427—28no—
377#427—48no—
378C2×#107—24no—
379C2×#107—44no—
380C2×#106—24no—
381C2×#106—24no—
382C2×#106—22no—
383C2×#106C2414yes—
384#421—432no—
385C2×#104—216no—
386C2×#104—416no—
387#418—432no—
388C2×#102—216no—
389C2×#102—416no—
390#408—216no—
391#408—48no—
392#408—416no—
393#407—416no—
394C2×C22⋊C8—48no—
395#405—216no—
396#405—28no—
397#405—28no—
398C2×#97—24no—
399C2×#97—24no—
400C2×#97C2×D414yes—
401C2×#97C2414yes—
402C2×C4×C8—28no—
403C2×C4×C8C2×D418yes—
404#390—216no—
405#390—48no—
406#390—416no—
407#379—416no—
408#365—232no—
409#361—232no—
410#360—232no—
411#347—232no—
412C25—42no—
413C25—44no—
414C25—41no—
415C25—44no—
416C25—42no—
417C25—42no—
418C25—84no—
419C25—84no—
420C25—168no—
421C25AGL(1,ℤ/8)11yescharacteristic
422C2×#41—24no—
423C2×#41—28no—
424C2×#41—24no—
425C2×#41—42no—
426C2×#41—44no—
427C2×#41—42no—
428C2×#41—44no—
429C2×#41—44no—
430C2×#41—44no—
431C2×#41—44no—
432C2×#41—44no—
433C2×#41—48no—
434C2×#41—44no—
435C2×#41—48no—
436C2×#41—44no—
437C2×#41—48no—
438C2×#41—44no—
439C2×#41—48no—
440C2×#41—48no—
441C2×#41—416no—
442C2×#41—48no—
443C2×#41—416no—
444C2×#41—84no—
445C2×#41—88no—
446C2×#41—84no—
447C2×#41—88no—
448C2×#41—84no—
449C2×#41—88no—
450C2×#41—84no—
451C2×#41—88no—
452C22×Q8—24no—
453C22×Q8—22no—
454C22×Q8—42no—
455C22×Q8—41no—
456C22×Q8—44no—
457C22×Q8—44no—
458C22×D4—28no—
459C22×D4—24no—
460C22×D4—28no—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—22no—
464C22×D4—24no—
465C22×D4—44no—
466C22×D4—42no—
467C22×D4—44no—
468C22×D4—42no—
469C22×D4—44no—
470C22×D4—48no—
471C22×D4—44no—
472C22×D4—48no—
473C22×D4—44no—
474C22×D4—48no—
475C22×D4—44no—
476C22×D4—48no—
477C22×D4—42no—
478C22×D4—44no—
479C22×D4—44no—
480C22×D4—42no—
481C22×D4—42no—
482C22×D4—44no—
483C22×D4—48no—
484C22×D4—48no—
485C22×D4—416no—
486C22×D4—44no—
487C22×D4—48no—
488C22×D4—48no—
489C22×D4—416no—
490C22×D4—44no—
491C22×D4—44no—
492C22×D4—44no—
493C22×D4—44no—
494C22×D4—44no—
495C22×D4—44no—
496C22×D4—42no—
497C22×D4—42no—
498C22×D4—42no—
499C22×D4—41no—
500C22×D4—84no—
501C22×D4—84no—
502C22×D4—84no—
503C22×D4—88no—
504C22×D4—84no—
505C22×D4—84no—
506C22×D4—88no—
507C22×D4—84no—
508C22×D4—84no—
509C22×D4—88no—
510C22×D4—84no—
511C22×D4—88no—
512C23×C4—22no—
513C23×C4—41no—
514C23×C4—42no—
515C23×C4—44no—
516C23×C4—44no—
517C23×C4—42no—
518C23×C4—42no—
519C23×C4—84no—
520C23×C4—84no—
521C23×C4C4×D411yescharacteristic
522C23×C4C4×D412yes—
523C23×C4C4×D411yescharacteristic
524C23×C4#12114yes—
525C23×C4#12714yes—
526C23×C4AGL(1,ℤ/8)14yes—
527C23×C4AGL(1,ℤ/8)14yes—
528C23×C4AGL(1,ℤ/8)11yescharacteristic
529C23×C4AGL(1,ℤ/8)11yescharacteristic
530C23×C4AGL(1,ℤ/8)12yes—
531C23×C4AGL(1,ℤ/8)11yescharacteristic
532C23×C4AGL(1,ℤ/8)12yes—
533C23×C4C22×D411yescharacteristic
534C23×C4C22×D412yes—
535#135—28no—
536#135—216no—
537#135—28no—
538#135—216no—
539#135—24no—
540#135—24no—
541#135—24no—
542#135—24no—
543#135—48no—
544#135—44no—
545#135—48no—
546#135—44no—
547#135—44no—
548#135—48no—
549#135—44no—
550#135—48no—
551#135—416no—
552#135—416no—
553#135—416no—
554C2×Q16—24no—
555C2×Q16—28no—
556C2×Q16—24no—
557C2×Q16—28no—
558C2×Q16—22no—
559C2×Q16—24no—
560C2×Q16—44no—
561C2×Q16—48no—
562C2×Q16C23×C414yes—
563C2×SD16—28no—
564C2×SD16—24no—
565C2×SD16—24no—
566C2×SD16—44no—
567C2×SD16—48no—
568C2×SD16—44no—
569C2×SD16—48no—
570C2×SD16—48no—
571C2×SD16—416no—
572C2×D8—28no—
573C2×D8—216no—
574C2×D8—28no—
575C2×D8—216no—
576C2×D8—24no—
577C2×D8—28no—
578C2×D8—28no—
579C2×D8—216no—
580C2×D8—28no—
581C2×D8—216no—
582C2×D8—24no—
583C2×D8—28no—
584C2×D8—28no—
585C2×D8—24no—
586C2×D8—28no—
587C2×D8—24no—
588C2×D8—22no—
589C2×D8—24no—
590C2×D8—24no—
591C2×D8—24no—
592C2×D8—24no—
593C2×D8—24no—
594C2×D8—24no—
595C2×D8—44no—
596C2×D8—48no—
597C2×D8—48no—
598C2×D8—44no—
599C2×D8—48no—
600C2×D8—44no—
601C2×D8—44no—
602C2×D8—48no—
603C2×D8—44no—
604C2×D8—48no—
605C2×D8—44no—
606C2×D8—48no—
607C2×D8—48no—
608C2×D8—416no—
609C2×D8—48no—
610C2×D8—416no—
611C2×D8—416no—
612C2×D8—416no—
613C2×D8—416no—
614C2×D8—44no—
615C2×D8—48no—
616C2×D8C23×C418yes—
617C2×D8C23×C414yes—
618C2×M16—28no—
619C2×M16—24no—
620C2×M16—24no—
621C2×M16—28no—
622C2×M16—24no—
623C2×M16—44no—
624C2×M16—44no—
625C2×M16—48no—
626C2×M16—44no—
627C2×M16—42no—
628C2×M16—44no—
629C2×M16—48no—
630C2×M16—44no—
631C2×M16—48no—
632C2×M16—84no—
633C2×M16—88no—
634C22×C8—24no—
635C22×C8—22no—
636C22×C8—22no—
637C22×C8—24no—
638C22×C8—42no—
639C22×C8—44no—
640C22×C8—84no—
641C22×C8C2×C22⋊C414yes—
642C22×C8C2×C22⋊C414yes—
643C22×C8C2×C22⋊C418yes—
644C22×C8C4×D414yes—
645C22×C8C4×D414yes—
646C22×C8C4×D418yes—
647C22×C8C4×D412yes—
648C22×C8C4×D411yescharacteristic
649C22×C8C4×D412yes—
650C22×C8C4×D411yescharacteristic
651C22×C8C4×D412yes—
652C22×C8C4×D412yes—
653C22×C8C4×D412yes—
654C22×C8#12114yes—
655C22×C8#12114yes—
656C22×C8#12118yes—
657C22×C8#12114yes—
658C22×C8#12118yes—
659C22×C8#12414yes—
660C22×C8#12414yes—
661C22×C8#12418yes—
662C22×C8#12714yes—
663C22×C8#12718yes—
664C22×C8C23×C411yescharacteristic
665C22×C8C23×C412yes—
666C22×C8C23×C411yescharacteristic
667C22×C8C23×C412yes—
668C22×C8C22×D414yes—
669C22×C8C22×D412yes—
670C22×C8C22×D414yes—
671C22×C8C22×D412yes—
672C22×C8C22×D414yes—
673C22×C8C22×D412yes—
674C22×C8C22×D411yescharacteristic
675C22×C8C22×D412yes—
676C22×C8C22×D414yes—
677C22×C8C2×#4112yes—
678C22×C8C2×#4114yes—
679C22×C8C2×#4111yescharacteristic
680C22×C8C2×#4112yes—
681C22×C8C2×#4112yes—
682C22×C8C2×#4111yescharacteristic
683C22×C8C2511yescharacteristic
684#117—28no—
685#117—28no—
686#117—48no—
687#117—48no—
688#117—48no—
689#117—88no—
690C2×C4⋊C4—24no—
691C2×C4⋊C4—24no—
692C2×C4⋊C4—44no—
693C2×C4⋊C4—44no—
694C2×C4⋊C4—44no—
695C2×C4⋊C4—42no—
696C2×C22⋊C4—24no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—432no—
700C2×C22⋊C4—84no—
701C2×C22⋊C4—1616no—
702C2×C42—24no—
703C2×C42—24no—
704C2×C42—22no—
705C2×C42—44no—
706C2×C42—84no—
707C2×C42C22×D414yes—
708SD32—264no—
709D16—264no—
710M32—216no—
711M32—28no—
712M32—24no—
713M32C2×C22⋊C4116yes—
714M32C2×C22⋊C4132yescomplemented
715M32C22×D418yes—
716M32C22×D418yes—
717M32C22×D418yes—
718C2×C16—28no—
719C2×C16—216no—
720C2×C16—24no—
721C2×C16C2×C22⋊C4116yes—
722C2×C16C2×C22⋊C4132yescomplemented
723C2×C16C23×C418yes—
724#108—24no—
725#108—24no—
726#108—44no—
727#108—48no—
728#107—48no—
729#106—24no—
730#106—24no—
731#106—44no—
732#104—432no—
733#102—432no—
734C22⋊C8—432no—
735#97—28no—
736#97—24no—
737#97—24no—
738C4×C8—216no—
739C24—44no—
740C24—44no—
741C24—42no—
742C24—44no—
743C24—44no—
744C24—44no—
745C24—48no—
746C24—48no—
747C24—816no—
748C24—84no—
749C24—88no—
750C24—84no—
751C24—88no—
752C24—88no—
753C24—816no—
754C24—84no—
755C24—88no—
756C24—164no—
757C24—168no—
758C24—168no—
759C24—1616no—
760C24—1616no—
761C24—1632no—
762C24—1632no—
763C24#44211yescharacteristic
764C24#44211yescharacteristic
765C24#44212yes—
766C24#46914yes—
767C24#49614yes—
768C24C2×AGL(1,ℤ/8)11yescharacteristic
769C24C2×AGL(1,ℤ/8)12yes—
770#41—44no—
771#41—44no—
772#41—48no—
773#41—416no—
774#41—48no—
775#41—416no—
776#41—44no—
777#41—44no—
778#41—88no—
779#41—84no—
780#41—88no—
781#41—84no—
782#41—816no—
783#41—816no—
784#41—816no—
785#41—84no—
786#41—88no—
787#41—84no—
788#41—88no—
789C2×Q8—24no—
790C2×Q8—44no—
791C2×Q8—42no—
792C2×Q8—44no—
793C2×Q8—48no—
794C2×Q8—48no—
795C2×Q8—44no—
796C2×Q8—88no—
797C2×Q8—84no—
798C2×D4—28no—
799C2×D4—24no—
800C2×D4—44no—
801C2×D4—48no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—48no—
806C2×D4—416no—
807C2×D4—48no—
808C2×D4—416no—
809C2×D4—44no—
810C2×D4—48no—
811C2×D4—44no—
812C2×D4—48no—
813C2×D4—48no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—42no—
817C2×D4—416no—
818C2×D4—48no—
819C2×D4—48no—
820C2×D4—416no—
821C2×D4—48no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—84no—
827C2×D4—88no—
828C2×D4—88no—
829C2×D4—816no—
830C2×D4—84no—
831C2×D4—88no—
832C2×D4—84no—
833C2×D4—88no—
834C2×D4—88no—
835C2×D4—84no—
836C2×D4—88no—
837C2×D4—84no—
838C2×D4—816no—
839C2×D4—88no—
840C2×D4—816no—
841C2×D4—88no—
842C2×D4—816no—
843C2×D4—816no—
844C2×D4—816no—
845C2×D4—88no—
846C2×D4—84no—
847C2×D4—84no—
848C2×D4—84no—
849C2×D4—88no—
850C2×D4—88no—
851C2×D4—84no—
852C2×D4—88no—
853C22×C4—24no—
854C22×C4—48no—
855C22×C4—44no—
856C22×C4—42no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—88no—
865C22×C4—816no—
866C22×C4—88no—
867C22×C4—84no—
868C22×C4—88no—
869C22×C4—88no—
870C22×C4—84no—
871C22×C4#39014yes—
872C22×C4#39014yes—
873C22×C4#39018yes—
874C22×C4#44214yes—
875C22×C4#44214yes—
876C22×C4#44218yes—
877C22×C4#44212yes—
878C22×C4#44212yes—
879C22×C4#44212yes—
880C22×C4#44212yes—
881C22×C4#44212yes—
882C22×C4#44211yescharacteristic
883C22×C4#44211yescharacteristic
884C22×C4#46914yes—
885C22×C4#46918yes—
886C22×C4#46914yes—
887C22×C4#46914yes—
888C22×C4#46918yes—
889C22×C4#49614yes—
890C22×C4#49614yes—
891C22×C4#49618yes—
892C22×C4#49614yes—
893C22×C4#49618yes—
894C22×C4C2×C4×D412yes—
895C22×C4C2×C4×D412yes—
896C22×C4C2×C4×D411yescharacteristic
897C22×C4C2×C4×D411yescharacteristic
898C22×C4C2×#12112yes—
899C22×C4C2×#12114yes—
900C22×C4C2×#12712yes—
901C22×C4C2×#12714yes—
902C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
903C22×C4C2×AGL(1,ℤ/8)12yes—
904C22×C4C2×AGL(1,ℤ/8)12yes—
905C22×C4C2×AGL(1,ℤ/8)14yes—
906C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
907C22×C4C2×AGL(1,ℤ/8)12yes—
908C22×C4C2×AGL(1,ℤ/8)12yes—
909C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
910C22×C4C2×AGL(1,ℤ/8)12yes—
911C22×C4C2×AGL(1,ℤ/8)14yes—
912C22×C4C23×D411yescharacteristic
913Q16—24no—
914Q16—24no—
915Q16—44no—
916Q16—48no—
917SD16—44no—
918SD16—44no—
919SD16—48no—
920SD16—416no—
921D8—24no—
922D8—28no—
923D8—28no—
924D8—24no—
925D8—44no—
926D8—44no—
927D8—48no—
928D8—416no—
929D8—48no—
930D8—416no—
931D8—44no—
932D8—48no—
933M16—48no—
934M16—48no—
935M16—44no—
936M16—44no—
937M16—88no—
938M16—84no—
939C2×C8—24no—
940C2×C8—24no—
941C2×C8—24no—
942C2×C8—44no—
943C2×C8—44no—
944C2×C8—44no—
945C2×C8—84no—
946C2×C8—88no—
947C2×C8#39014yes—
948C2×C8#39018yes—
949C2×C8#39014yes—
950C2×C8#39018yes—
951C2×C8#39018yes—
952C2×C8#39018yes—
953C2×C8#39018yes—
954C2×C8C22×C22⋊C412yes—
955C2×C8C22×C22⋊C414yes—
956C2×C8C22×C22⋊C412yes—
957C2×C8C22×C22⋊C414yes—
958C2×C8C2×C4×D412yes—
959C2×C8C2×C4×D414yes—
960C2×C8C2×C4×D412yes—
961C2×C8C2×C4×D414yes—
962C2×C8C2×C4×D412yes—
963C2×C8C2×C4×D411yescharacteristic
964C2×C8C2×C4×D412yes—
965C2×C8C2×C4×D411yescharacteristic
966C2×C8C2×#12112yes—
967C2×C8C2×#12114yes—
968C2×C8C2×#12114yes—
969C2×C8C2×#12112yes—
970C2×C8C2×#12114yes—
971C2×C8C2×#12112yes—
972C2×C8C2×#12412yes—
973C2×C8C2×#12414yes—
974C2×C8C2×#12412yes—
975C2×C8C2×#12414yes—
976C2×C8C2×#12712yes—
977C2×C8C2×#12714yes—
978C2×C8C24×C411yescharacteristic
979C2×C8C23×D411yescharacteristic
980C2×C8C23×D411yescharacteristic
981C2×C8C23×D411yescharacteristic
982C2×C8C22×#4111yescharacteristic
983C2×C8C22×#4111yescharacteristic
984C4⋊C4—48no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—84no—
988C22⋊C4—48no—
989C22⋊C4—88no—
990C22⋊C4—1632no—
991C42—24no—
992C42—24no—
993C42—44no—
994C42—88no—
995C16—28no—
996C16C22×C22⋊C4116yes—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—44no—
1001C23—44no—
1002C23—48no—
1003C23—48no—
1004C23—44no—
1005C23—48no—
1006C23—816no—
1007C23—816no—
1008C23—84no—
1009C23—816no—
1010C23—88no—
1011C23—84no—
1012C23—88no—
1013C23—84no—
1014C23—88no—
1015C23—816no—
1016C23—816no—
1017C23—88no—
1018C23—168no—
1019C23—1616no—
1020C23—1616no—
1021C23—1616no—
1022C23—1616no—
1023C23—1616no—
1024C23—1632no—
1025C23—1632no—
1026C23—1632no—
1027C23—1664no—
1028C23—1632no—
1029C23#197214yes—
1030C23#197214yes—
1031C23#197218yes—
1032C23C2×#44212yes—
1033C23C2×#44211yescharacteristic
1034C23C2×#44212yes—
1035C23C2×#44211yescharacteristic
1036C23C2×#46912yes—
1037C23C2×#46914yes—
1038C23C2×#49612yes—
1039C23C2×#49614yes—
1040C23C22×AGL(1,ℤ/8)11yescharacteristic
1041Q8—44no—
1042Q8—44no—
1043Q8—88no—
1044Q8—84no—
1045D4—48no—
1046D4—44no—
1047D4—48no—
1048D4—44no—
1049D4—84no—
1050D4—84no—
1051D4—816no—
1052D4—88no—
1053D4—84no—
1054D4—84no—
1055D4—88no—
1056D4—816no—
1057D4—816no—
1058D4—88no—
1059D4—88no—
1060D4—84no—
1061C2×C4—48no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4—84no—
1067C2×C4—84no—
1068C2×C4—84no—
1069C2×C4—88no—
1070C2×C4—816no—
1071C2×C4—88no—
1072C2×C4—84no—
1073C2×C4—168no—
1074C2×C4#197218yes—
1075C2×C4#197214yes—
1076C2×C4#197218yes—
1077C2×C4#197214yes—
1078C2×C4#197218yes—
1079C2×C4#197218yes—
1080C2×C4#197218yes—
1081C2×C4C2×#39014yes—
1082C2×C4C2×#39012yes—
1083C2×C4C2×#39012yes—
1084C2×C4C2×#39014yes—
1085C2×C4C2×#44211yescharacteristic
1086C2×C4C2×#44212yes—
1087C2×C4C2×#44212yes—
1088C2×C4C2×#44211yescharacteristic
1089C2×C4C2×#44214yes—
1090C2×C4C2×#44212yes—
1091C2×C4C2×#44212yes—
1092C2×C4C2×#44214yes—
1093C2×C4C2×#46912yes—
1094C2×C4C2×#46912yes—
1095C2×C4C2×#46914yes—
1096C2×C4C2×#46914yes—
1097C2×C4C2×#46912yes—
1098C2×C4C2×#46914yes—
1099C2×C4C2×#49612yes—
1100C2×C4C2×#49614yes—
1101C2×C4C2×#49614yes—
1102C2×C4C2×#49612yes—
1103C2×C4C2×#49614yes—
1104C2×C4C2×#49612yes—
1105C2×C4C22×C4×D411yescharacteristic
1106C2×C4C22×#12111yescharacteristic
1107C2×C4C22×#12711yescharacteristic
1108C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1109C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1110C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1111C8—44no—
1112C8—84no—
1113C8C2×#39012yes—
1114C8C2×#39014yes—
1115C8C2×#39012yes—
1116C8C2×#39014yes—
1117C8C23×C22⋊C411yescharacteristic
1118C8C22×C4×D411yescharacteristic
1119C8C22×#12111yescharacteristic
1120C8C22×#12411yescharacteristic
1121C22—24no—
1122C22—24no—
1123C22—28no—
1124C22—28no—
1125C22—22no—
1126C22—22no—
1127C22—24no—
1128C22—24no—
1129C22—44no—
1130C22—48no—
1131C22—44no—
1132C22—84no—
1133C22—88no—
1134C22—816no—
1135C22—88no—
1136C22—168no—
1137C22—168no—
1138C22—1616no—
1139C22—1616no—
1140C22—1632no—
1141C22—1632no—
1142C22—168no—
1143C22—1616no—
1144C22C2×#197214yes—
1145C22C2×#197214yes—
1146C22C2×#197212yes—
1147C22C2×#197212yes—
1148C22#3347114yes—
1149C22C22×#44211yescharacteristic
1150C22C22×#46911yescharacteristic
1151C22C22×#49611yescharacteristic
1152C4—84no—
1153C4—84no—
1154C4—164no—
1155C4C2×#197212yes—
1156C4C2×#197214yes—
1157C4C2×#197214yes—
1158C4C2×#197212yes—
1159C4C22×#39011yescharacteristic
1160C4C22×#44211yescharacteristic
1161C4C22×#46911yescharacteristic
1162C4C22×#49611yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—24no—
1166C2—22no—
1167C2—24no—
1168C2—164no—
1169C2—168no—
1170C2#49524214yesdirect product factor
1171C2C22×#197211yescharacteristic
1172C2C2×#3347112yes—
subgroupG/H
center, socleC23C2×#442
commutatorC2×C8C24×C4
Frattini, cosocleC22×C8C25
prime radicalC23×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#405 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#2155C2semidirect
3. C23×#361C2semidirect
4. C22×#2145C2semidirect
5. C22×#2110C2semidirect
6. C2×#21240C2semidirect
7. C2×#21233C2semidirect
8. #495242C2direct (N × H)
9. C2×#13249C2semidirect
14. C22×#509C4semidirect
15. C22×#509C4semidirect
18. C23×SD32C4semidirect
19. C23×D16C4semidirect
30. C2×#2155C22semidirect
31. C22×#365C22semidirect
33. C22×#361C22semidirect
34. C22×#361C22semidirect
36. C2×#2145C22semidirect
37. C22×#360C22semidirect
39. C2×#2110C22semidirect
40. C22×#347C22semidirect
42. #21240C22semidirect
43. C2×#1975C22semidirect
46. #21233C22semidirect
47. C2×#1972C22semidirect
49. #13249C22semidirect
93. C2×#509C2×C4semidirect
97. C22×SD32C2×C4semidirect
100. C22×D16C2×C4semidirect
151. C2×#365C23semidirect
154. C2×#361C23semidirect
157. C2×#360C23semidirect
160. C2×#347C23semidirect
162. #1975C23semidirect
165. #1972C23semidirect
348. C2×M32C22⋊C4semidirect
349. C2×M32C22⋊C4semidirect
363. C22×C16C22⋊C4semidirect
714. M32C2×C22⋊C4semidirect
722. C2×C16C2×C22⋊C4semidirect
1170. C2#495242direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5092
C22×#21552
C23×#3612
C22×#21452
C22×#21102
C2×#212402
C2×#212332
#4952422
C2×#132492