Finite Group Databasebeta

← #72309881

Subgroups — #72309881

Order 1024.

3503 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21546C211yesmaximal, characteristic
2C22×#1776C211yesmaximal, characteristic, complemented
3C2×#13001C211yesmaximal, characteristic
4#494443C211yesmaximal, characteristic
5C2×#12650C212yesmaximal, complemented
6C2×#12605C211yesmaximal, characteristic, complemented
7#147466C212yesmaximal, complemented
8#147245C212yesmaximal, complemented
9#146520C211yesmaximal, characteristic, complemented
10#146510C211yesmaximal, characteristic, complemented
11#146344C212yesmaximal, complemented
12C2×#3050C2211yescharacteristic
13C22×#444C2211yescharacteristic
14C2×#2929—21no—
15C23×#107C2211yescharacteristic
16C23×#106C2211yescharacteristic
17C23×#97C2211yescharacteristic
18C22×C4×C4⋊C4—21no—
19C22×#360C2212yes—
20C2×#2139C2212yes—
21C2×#2112C2211yescharacteristic
22C2×#2112C2211yescharacteristic
23C22×#347C2212yes—
24#21546—24no—
25#21546C418yescomplemented
26C2×#1975C2211yescharacteristic
27C2×#1946C2211yescharacteristic
28C2×#1938—21no—
29C2×#1896—21no—
30C2×#1810C2211yescharacteristic
31C2×#1776—28no—
32C2×#1776—21no—
33C2×#1776—21no—
34C2×#1776C2212yes—
35C2×#1776C2212yes—
36C2×#1773C2211yescharacteristic
37C2×#1765—21no—
38C22×#340—21no—
39#13001C418yescomplemented
40#12993C414yescomplemented
41#12991C414yescomplemented
42#12650—28no—
43#12605—24no—
44C2×#1387C2212yes—
45C2×#1387C2212yes—
46C2×#1386C2212yes—
47C2×#1383C2212yes—
48C2×#1383C2212yes—
49#12557C2212yes—
50C2×#1375C2212yes—
51C22×#135C2311yescharacteristic
52C22×#131—21no—
53C24×C8D411yescharacteristic
54C24×C8C2311yescharacteristic
55C2×#525—21no—
56C23×C4⋊C4—21no—
57C23×C4⋊C4—21no—
58C23×C42—41no—
59C23×C42D411yescharacteristic
60C22×M32C2312yes—
61C22×M32C2312yes—
62#3050—22no—
63#3050—22no—
64#3050C2×C414yes—
65#3050C2×C414yes—
66C2×#467C2×C412yes—
67C2×#466C2×C412yes—
68C2×#465—22no—
69C2×#444—22no—
70C2×#444—24no—
71C2×#444—24no—
72C2×#444C2×C414yescomplemented
73#2929—28no—
74#2929—44no—
75C2×#435—42no—
76C2×C8×D4—42no—
77C22×#108C2311yescharacteristic
78C22×#108C2311yescharacteristic
79C2×#427C2311yescharacteristic
80C22×#107—24no—
81C22×#107—24no—
82C22×#107—21no—
83C22×#107—22no—
84C22×#107C2×C414yes—
85C22×#107C2312yes—
86C22×#106—24no—
87C22×#106—24no—
88C22×#106—21no—
89C22×#106—22no—
90C22×#106C2×C414yes—
91C22×#106C2312yes—
92C2×#424—21no—
93C22×#104—21no—
94C22×#104—21no—
95C2×#416—21no—
96C2×#408—21no—
97C2×#407—21no—
98C2×#405—21no—
99C22×#97—24no—
100C22×#97—24no—
101C22×#97C2×C414yes—
102C22×#97D414yes—
103C22×#97D411yescharacteristic
104C22×#97D411yescharacteristic
105C22×#97C2311yescharacteristic
106C22×#97C2311yescharacteristic
107C2×C4×C4⋊C4—28no—
108C2×C4×C4⋊C4—22no—
109C2×C4×C4⋊C4—22no—
110C2×C4×C4⋊C4—44no—
111C2×C4×C4⋊C4—41no—
112C2×C4×C4⋊C4—41no—
113C22×#95—41no—
114C2×#360—24no—
115C2×#360—24no—
116C2×#360C2×C418yescomplemented
117#2139—24no—
118#2139—24no—
119C2×#358C2×C414yescomplemented
120C2×#357C2×C414yescomplemented
121#2112—22no—
122#2112—22no—
123#2112—22no—
124#2112C2×C414yes—
125C2×C22⋊C16—22no—
126C2×C22⋊C16C2×C414yes—
127C2×#347—24no—
128C2×#347—24no—
129C2×#347—24no—
130#1975—22no—
131#1975C2×C414yescomplemented
132#1946—22no—
133#1946C2×C414yescomplemented
134#1938—28no—
135#1896—28no—
136#1810—22no—
137#1810C2×C414yes—
138#1776—28no—
139#1776—28no—
140#1776—24no—
141#1776—24no—
142#1776—24no—
143#1776D418yescomplemented
144#1773—22no—
145#1773C2×C414yescomplemented
146#1765—28no—
147C2×#341—21no—
148C2×#340—28no—
149C2×#340—22no—
150C2×#340—22no—
151C2×#339—21no—
152C2×#339—21no—
153#1387—24no—
154#1387—24no—
155#1386C2×C418yescomplemented
156#1383—24no—
157#1383—24no—
158#1380C2×C418yescomplemented
159#1375—24no—
160C22×#41—21no—
161C24×C4—21no—
162C24×C4—41no—
163C24×C4—41no—
164C24×C4C2×D411yescharacteristic
165C2×#135—21no—
166C2×#135—22no—
167C2×#135—21no—
168C2×#135—22no—
169C2×#135—22no—
170C2×#135—22no—
171C2×#135C22×C412yes—
172C2×#135C22×C412yes—
173C22×Q16C22×C411yescharacteristic
174C22×SD16—21no—
175C22×D8C22×C411yescharacteristic
176C2×#131—24no—
177C2×#131—42no—
178C2×#131—42no—
179C2×#131—42no—
180C2×#131—42no—
181C2×#131—42no—
182C22×M16—21no—
183C22×M16—21no—
184C22×M16—41no—
185C23×C8—22no—
186C23×C8—22no—
187C23×C8—22no—
188C23×C8—22no—
189C23×C8—22no—
190C23×C8—22no—
191C23×C8—22no—
192C23×C8—22no—
193C23×C8—41no—
194C23×C8—41no—
195C23×C8—41no—
196C23×C8C22⋊C414yes—
197C23×C8C22×C412yes—
198C23×C8C22×C412yes—
199C23×C8C22×C412yes—
200C23×C8C2×D411yescharacteristic
201C23×C8C2×D411yescharacteristic
202C23×C8C2×D411yescharacteristic
203C23×C8C2×D412yes—
204C23×C8#4112yes—
205C23×C8#4112yes—
206C23×C8C2411yescharacteristic
207#525—24no—
208#525—24no—
209#525—42no—
210#525—42no—
211C2×#123—41no—
212C2×C22⋊Q8—22no—
213C2×#121—22no—
214C2×#120—41no—
215C2×C4×D4—42no—
216C2×#117—21no—
217C22×C4⋊C4—24no—
218C22×C4⋊C4—24no—
219C22×C4⋊C4—24no—
220C22×C4⋊C4—24no—
221C22×C4⋊C4—24no—
222C22×C4⋊C4—24no—
223C22×C4⋊C4—22no—
224C22×C4⋊C4—22no—
225C22×C4⋊C4—42no—
226C22×C4⋊C4—42no—
227C22×C4⋊C4—42no—
228C22×C4⋊C4—42no—
229C22×C4⋊C4—42no—
230C22×C4⋊C4—42no—
231C22×C4⋊C4—41no—
232C22×C4⋊C4—41no—
233C22×C42—21no—
234C22×C42—22no—
235C22×C42—22no—
236C22×C42—22no—
237C22×C42—22no—
238C22×C42—22no—
239C22×C42—48no—
240C22×C42—42no—
241C22×C42—42no—
242C22×C42—88no—
243C22×C42C22⋊C414yes—
244C22×C42C2×D411yescharacteristic
245C22×C42C2×D411yescharacteristic
246C2×M32—22no—
247C2×M32—22no—
248C2×M32—22no—
249C2×M32—22no—
250C2×M32—22no—
251C2×M32—22no—
252C2×M32—22no—
253C2×M32—22no—
254C2×M32—22no—
255C2×M32—22no—
256C2×M32—22no—
257C2×M32C22×C414yes—
258C22×C16—22no—
259C22×C16C22×C414yes—
260#467—24no—
261#467C4218yescomplemented
262#466—24no—
263#466C4218yescomplemented
264#465—28no—
265#465—28no—
266#444—216no—
267#444—48no—
268#435—416no—
269C8×D4—416no—
270C2×#108—22no—
271C2×#108—22no—
272C2×#108—22no—
273C2×#108—22no—
274C2×#108—21no—
275C2×#108—21no—
276C2×#108C22×C412yes—
277C2×#108C22×C412yes—
278#427—21no—
279#427—21no—
280#427C22×C412yes—
281#427C22×C412yes—
282C2×#107—24no—
283C2×#107—216no—
284C2×#107—24no—
285C2×#107—24no—
286C2×#107—22no—
287C2×#107—22no—
288C2×#107—22no—
289C2×#107—216no—
290C2×#107C22×C412yes—
291C2×#107C22×C414yes—
292C2×#107C2×D414yes—
293C2×#107#4114yes—
294C2×#106—24no—
295C2×#106—216no—
296C2×#106—24no—
297C2×#106—24no—
298C2×#106—22no—
299C2×#106—22no—
300C2×#106—22no—
301C2×#106—21no—
302C2×#106—216no—
303C2×#106C22×C414yes—
304C2×#106C2×D414yes—
305C2×#106#4114yes—
306#424—24no—
307#424—42no—
308C2×C4⋊C8—42no—
309C2×#104—24no—
310C2×#104—24no—
311C2×#104—42no—
312C2×#104—42no—
313C2×#104—42no—
314C2×#104—42no—
315#416—24no—
316#416—24no—
317C2×#103—22no—
318C2×#102—22no—
319#408—24no—
320#408—42no—
321#407—24no—
322#407—42no—
323C2×C22⋊C8—42no—
324C2×C22⋊C8—42no—
325#405—24no—
326#405—42no—
327C2×#97—22no—
328C2×#97—22no—
329C2×#97—22no—
330C2×#97—22no—
331C2×#97—22no—
332C2×#97—22no—
333C2×#97—216no—
334C2×#97—216no—
335C2×#97—41no—
336C2×#97C22⋊C414yes—
337C2×#97C22⋊C414yes—
338C2×#97C22×C412yes—
339C2×#97C22×C412yes—
340C2×#97C2×D412yes—
341C2×#97C2×D414yes—
342C2×#97C2×D412yes—
343C2×#97#4114yes—
344C2×C4×C8—41no—
345C4×C4⋊C4—28no—
346C4×C4⋊C4—28no—
347C4×C4⋊C4—48no—
348C4×C4⋊C4—48no—
349C4×C4⋊C4—44no—
350C4×C4⋊C4—44no—
351C2×#95—48no—
352C2×#95—42no—
353C2×#95—42no—
354#360—216no—
355#358—28no—
356#357—28no—
357C22⋊C16—28no—
358C22⋊C16—28no—
359#347—48no—
360#341—24no—
361#340—28no—
362#340—28no—
363#339—24no—
364#339—24no—
365C25AGL(1,ℤ/8)11yescharacteristic
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—41no—
369C2×#41—41no—
370C2×#41—41no—
371C2×#41—41no—
372C2×#41—41no—
373C2×#41—41no—
374C2×#41—41no—
375C2×#41—41no—
376C2×#41—41no—
377C2×#41—41no—
378C22×Q8—21no—
379C22×D4—21no—
380C22×D4—41no—
381C22×D4—42no—
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—24no—
395C23×C4—44no—
396C23×C4—44no—
397C23×C4—44no—
398C23×C4—44no—
399C23×C4—44no—
400C23×C4—44no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—44no—
404C23×C4—44no—
405C23×C4—41no—
406C23×C4—84no—
407C23×C4—84no—
408C23×C4—84no—
409C23×C4—84no—
410C23×C4C2×C22⋊C412yes—
411C23×C4C4×D412yes—
412C23×C4C4×D412yes—
413C23×C4AGL(1,ℤ/8)12yes—
414C23×C4AGL(1,ℤ/8)12yes—
415C23×C4AGL(1,ℤ/8)11yescharacteristic
416C23×C4#13712yes—
417C23×C4C22×D411yescharacteristic
418#135—24no—
419#135—24no—
420#135—24no—
421#135—24no—
422#135—42no—
423#135—42no—
424#135—42no—
425#135—42no—
426C2×Q16—22no—
427C2×Q16—21no—
428C2×Q16—22no—
429C2×Q16C2×C4212yescomplemented
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—42no—
433C2×SD16—42no—
434C2×D8—22no—
435C2×D8—21no—
436C2×D8—22no—
437C2×D8C2×C4212yescomplemented
438#131—48no—
439#131—48no—
440#131—84no—
441#131—84no—
442C2×M16—22no—
443C2×M16—22no—
444C2×M16—44no—
445C2×M16—41no—
446C2×M16—41no—
447C2×M16—41no—
448C2×M16—41no—
449C2×M16—41no—
450C2×M16—41no—
451C2×M16—41no—
452C2×M16—41no—
453C2×M16—41no—
454C2×M16—41no—
455C2×M16—82no—
456C2×M16—82no—
457C22×C8—21no—
458C22×C8—21no—
459C22×C8—21no—
460C22×C8—21no—
461C22×C8—21no—
462C22×C8—21no—
463C22×C8—21no—
464C22×C8—21no—
465C22×C8—24no—
466C22×C8—24no—
467C22×C8—24no—
468C22×C8—24no—
469C22×C8—24no—
470C22×C8—24no—
471C22×C8—24no—
472C22×C8—24no—
473C22×C8—24no—
474C22×C8—24no—
475C22×C8—24no—
476C22×C8—24no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—28no—
484C22×C8—28no—
485C22×C8—44no—
486C22×C8—44no—
487C22×C8—44no—
488C22×C8—44no—
489C22×C8—44no—
490C22×C8—44no—
491C22×C8—41no—
492C22×C8—41no—
493C22×C8—82no—
494C22×C8—82no—
495C22×C8C2×C4214yes—
496C22×C8C2×C22⋊C412yes—
497C22×C8C2×C22⋊C412yes—
498C22×C8C2×C22⋊C412yes—
499C22×C8#11714yes—
500C22×C8C4×D414yes—
501C22×C8C4×D414yes—
502C22×C8C4×D412yes—
503C22×C8C4×D412yes—
504C22×C8#12012yes—
505C22×C8#12312yes—
506C22×C8C23×C411yescharacteristic
507C22×C8C23×C411yescharacteristic
508C22×C8C23×C411yescharacteristic
509C22×C8C22×D412yes—
510C22×C8C22×D411yescharacteristic
511C22×C8C2×#4111yescharacteristic
512C22×C8C2×#4111yescharacteristic
513C22×C8C2×#4112yes—
514C22×C8C2×#4112yes—
515C22×C8C2×#4112yes—
516#123—44no—
517#123—44no—
518C22⋊Q8—28no—
519C22⋊Q8—44no—
520#121—28no—
521#121—44no—
522#120—44no—
523#120—44no—
524C4×D4—48no—
525C4×D4—48no—
526#117—22no—
527#117—22no—
528#117—41no—
529#117—41no—
530C2×C4⋊C4—216no—
531C2×C4⋊C4—216no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—44no—
540C2×C4⋊C4—44no—
541C2×C4⋊C4—48no—
542C2×C4⋊C4—48no—
543C2×C4⋊C4—48no—
544C2×C4⋊C4—48no—
545C2×C4⋊C4—48no—
546C2×C4⋊C4—48no—
547C2×C4⋊C4—44no—
548C2×C4⋊C4—44no—
549C2×C4⋊C4—42no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—42no—
552C2×C4⋊C4—42no—
553C2×C4⋊C4—42no—
554C2×C4⋊C4—42no—
555C2×C4⋊C4—44no—
556C2×C4⋊C4—44no—
557C2×C4⋊C4—42no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C42—24no—
562C2×C42—24no—
563C2×C42—28no—
564C2×C42—28no—
565C2×C42—21no—
566C2×C42—21no—
567C2×C42—21no—
568C2×C42—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—24no—
572C2×C42—28no—
573C2×C42—28no—
574C2×C42—41no—
575C2×C42—48no—
576C2×C42—48no—
577C2×C42—832no—
578C2×C42—88no—
579C2×C42—88no—
580C2×C42C2×C22⋊C412yes—
581C2×C42C2×C22⋊C412yes—
582C2×C42#12012yes—
583C2×C42#12312yes—
584C2×C42AGL(1,ℤ/8)12yes—
585C2×C42#13712yes—
586M32—24no—
587M32—24no—
588M32—42no—
589M32—42no—
590M32—42no—
591M32—42no—
592M32—42no—
593M32—42no—
594C2×C16—24no—
595C2×C16—24no—
596C2×C16—24no—
597C2×C16—24no—
598C2×C16—42no—
599C2×C16—42no—
600#108—24no—
601#108—24no—
602#108—42no—
603#108—42no—
604#107—216no—
605#107—24no—
606#107—22no—
607#107—24no—
608#107—24no—
609#107C2×C4214yescomplemented
610#107C4×D418yes—
611#106—216no—
612#106—22no—
613#106—24no—
614#106—22no—
615#106—24no—
616#106—24no—
617#106C4×D418yes—
618C4⋊C8—48no—
619#104—48no—
620#104—48no—
621#103—28no—
622#102—28no—
623C22⋊C8—48no—
624C22⋊C8—48no—
625#97—24no—
626#97—24no—
627#97—28no—
628#97—28no—
629#97—44no—
630#97C4×D418yes—
631#97#12118yes—
632C4×C8—44no—
633#95—48no—
634#95—48no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—24no—
639C24—24no—
640C24—21no—
641C24—41no—
642C24#41712yes—
643C24#44212yes—
644C24#44212yes—
645C24C2×AGL(1,ℤ/8)11yescharacteristic
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—42no—
653#41—42no—
654#41—81no—
655#41—81no—
656#41—81no—
657#41—81no—
658#41—81no—
659#41—81no—
660#41—81no—
661#41—81no—
662C2×Q8—22no—
663C2×Q8—41no—
664C2×Q8—41no—
665C2×Q8—41no—
666C2×Q8—41no—
667C2×Q8—41no—
668C2×D4—22no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—48no—
672C2×D4—41no—
673C2×D4—41no—
674C2×D4—41no—
675C2×D4—41no—
676C2×D4—41no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4—84no—
681C2×D4—84no—
682C2×D4—81no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—216no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—48no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—48no—
722C22×C4—416no—
723C22×C4—416no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—416no—
727C22×C4—416no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—42no—
732C22×C4—41no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—88no—
739C22×C4—88no—
740C22×C4—84no—
741C22×C4—84no—
742C22×C4—88no—
743C22×C4—88no—
744C22×C4—816no—
745C22×C4—816no—
746C22×C4—816no—
747C22×C4—84no—
748C22×C4—84no—
749C22×C4—88no—
750C22×C4—88no—
751C22×C4—81no—
752C22×C4—81no—
753C22×C4—81no—
754C22×C4—81no—
755C22×C4C4×C22⋊C414yes—
756C22×C4#41712yes—
757C22×C4#41814yes—
758C22×C4#44014yes—
759C22×C4#44014yes—
760C22×C4#44212yes—
761C22×C4#44212yes—
762C22×C4C22×C22⋊C411yescharacteristic
763C22×C4C2×C4×D411yescharacteristic
764C22×C4C2×C4×D411yescharacteristic
765C22×C4C2×#12011yescharacteristic
766C22×C4C2×#12311yescharacteristic
767C22×C4#52511yescharacteristic
768C22×C4#52511yescharacteristic
769C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
770C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
771C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
772C22×C4C2×#13711yescharacteristic
773C22×C4C2×#13711yescharacteristic
774C22×C4#57511yescharacteristic
775C22×C4#57511yescharacteristic
776Q16—24no—
777Q16—42no—
778SD16—44no—
779SD16—44no—
780D8—24no—
781D8—42no—
782M16—42no—
783M16—42no—
784M16—42no—
785M16—42no—
786M16—88no—
787M16—81no—
788M16—81no—
789M16—81no—
790M16—81no—
791C2×C8—22no—
792C2×C8—22no—
793C2×C8—22no—
794C2×C8—22no—
795C2×C8—22no—
796C2×C8—22no—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8—22no—
803C2×C8—28no—
804C2×C8—28no—
805C2×C8—28no—
806C2×C8—28no—
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—22no—
810C2×C8—416no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8—41no—
814C2×C8—41no—
815C2×C8—42no—
816C2×C8—42no—
817C2×C8—88no—
818C2×C8—81no—
819C2×C8—81no—
820C2×C8—81no—
821C2×C8—81no—
822C2×C8C4×C22⋊C414yes—
823C2×C8#38614yes—
824C2×C8C22×C4211yescharacteristic
825C2×C8C2×#11711yescharacteristic
826C2×C8C2×C4×D412yes—
827C2×C8C2×C4×D412yes—
828C2×C8C2×C4×D412yes—
829C2×C8C2×C4×D411yescharacteristic
830C2×C8C2×C4×D411yescharacteristic
831C2×C8C4×#4112yes—
832C2×C8C4×#4112yes—
833C2×C8C4×#4112yes—
834C2×C8C2×#12112yes—
835C2×C8#52512yes—
836C2×C8#52512yes—
837C2×C8#52912yes—
838C2×C8#52912yes—
839C2×C8#53212yes—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—416no—
844C4⋊C4—416no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—42no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C22⋊C4—42no—
854C22⋊C4—42no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C42—216no—
858C42—22no—
859C42—22no—
860C42—22no—
861C42—22no—
862C42—22no—
863C42—22no—
864C42—42no—
865C42—42no—
866C42—816no—
867C42—816no—
868C42#38614yes—
869C42#41714yes—
870C16—44no—
871C16—44no—
872C23—24no—
873C23—24no—
874C23—28no—
875C23—24no—
876C23—28no—
877C23—24no—
878C23—22no—
879C23—22no—
880C23—28no—
881C23—28no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—42no—
891C23—81no—
892C23—82no—
893C23—82no—
894C23—81no—
895C23#176214yes—
896C23#218014yes—
897C23AGL(1,ℤ/16)14yes—
898C23C2×#41711yescharacteristic
899C23C2×#44211yescharacteristic
900C23C2×#44211yescharacteristic
901C23#300311yescharacteristic
902C23#309211yescharacteristic
903C23#311411yescharacteristic
904C23#311411yescharacteristic
905Q8—42no—
906Q8—42no—
907Q8—81no—
908Q8—81no—
909D4—42no—
910D4—42no—
911D4—82no—
912D4—816no—
913D4—82no—
914D4—82no—
915D4—82no—
916D4—81no—
917D4—81no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—432no—
937C2×C4—44no—
938C2×C4—44no—
939C2×C4—44no—
940C2×C4—44no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—44no—
944C2×C4—42no—
945C2×C4—48no—
946C2×C4—48no—
947C2×C4—84no—
948C2×C4—84no—
949C2×C4—832no—
950C2×C4—88no—
951C2×C4—88no—
952C2×C4—84no—
953C2×C4—84no—
954C2×C4—88no—
955C2×C4—832no—
956C2×C4—81no—
957C2×C4—82no—
958C2×C4—88no—
959C2×C4—82no—
960C2×C4—81no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4—82no—
964C2×C4—82no—
965C2×C4#176214yes—
966C2×C4C2×C4×C22⋊C411yescharacteristic
967C2×C4C2×#38611yescharacteristic
968C2×C4#229711yescharacteristic
969C2×C4C4×#12011yescharacteristic
970C2×C4C4×#12011yescharacteristic
971C2×C4C4×#12311yescharacteristic
972C2×C4C4×#12311yescharacteristic
973C2×C4C2×#41811yescharacteristic
974C2×C4C2×#41711yescharacteristic
975C2×C4#289611yescharacteristic
976C2×C4C2×#44011yescharacteristic
977C2×C4C2×#44011yescharacteristic
978C2×C4C4×AGL(1,ℤ/8)11yescharacteristic
979C2×C4C4×AGL(1,ℤ/8)11yescharacteristic
980C2×C4C4×#13711yescharacteristic
981C2×C4C4×#13711yescharacteristic
982C2×C4#300411yescharacteristic
983C2×C4#300611yescharacteristic
984C2×C4#300611yescharacteristic
985C2×C4#309211yescharacteristic
986C2×C4#309411yescharacteristic
987C2×C4#309411yescharacteristic
988C2×C4#310911yescharacteristic
989C2×C4#310911yescharacteristic
990C2×C4#311211yescharacteristic
991C2×C4#311211yescharacteristic
992C2×C4#311711yescharacteristic
993C2×C4#311711yescharacteristic
994C8—24no—
995C8—24no—
996C8—42no—
997C8—82no—
998C8—82no—
999C8C42×D412yes—
1000C8#229012yes—
1001C8C4×#12112yes—
1002C8C4×#12112yes—
1003C22—28no—
1004C22—28no—
1005C22—28no—
1006C22—28no—
1007C22—22no—
1008C22—22no—
1009C22—24no—
1010C22—22no—
1011C22—22no—
1012C22—24no—
1013C22—24no—
1014C22—21no—
1015C22—21no—
1016C22—24no—
1017C22—21no—
1018C22—21no—
1019C22—24no—
1020C22—24no—
1021C22—84no—
1022C22—82no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22#1265018yescomplemented
1027C22C2×#176211yescharacteristic
1028C22#2090911yescharacteristic
1029C22#2139111yescharacteristic
1030C22#2145211yescharacteristic
1031C22#2145211yescharacteristic
1032C22#2157811yescharacteristic
1033C22#2157811yescharacteristic
1034C22C2×#218012yes—
1035C22C2×AGL(1,ℤ/16)12yes—
1036C4—24no—
1037C4—44no—
1038C4—44no—
1039C4—88no—
1040C4—84no—
1041C4—88no—
1042C4—82no—
1043C4C4×#38611yescharacteristic
1044C4C4×#41711yescharacteristic
1045C4#2091211yescharacteristic
1046C4#2139511yescharacteristic
1047C4#2145411yescharacteristic
1048C4#2145411yescharacteristic
1049C4#2158011yescharacteristic
1050C4#2158011yescharacteristic
1051C2—21no—
1052C2—21no—
1053C2—21no—
1054C2—28no—
1055C2—21no—
1056C2—162no—
1057C2#35421411yescharacteristic
1058C2C2×#1265012yes—
1059C2#49572511yescharacteristic
1060C2#49572611yescharacteristic
1061C2#49594912yes—
subgroupG/H
center, socleC23C2×#442
commutatorC2×C8C22×C42
Frattini, cosocleC23×C8C24
prime radicalC2×#3050C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×#97 ◁ G
LECSG ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#1776C2semidirect
5. C2×#12650C2semidirect
6. C2×#12605C2semidirect
7. #147466C2semidirect
8. #147245C2semidirect
9. #146520C2semidirect
10. #146510C2semidirect
11. #146344C2semidirect
25. #21546C4semidirect
39. #13001C4semidirect
40. #12993C4semidirect
41. #12991C4semidirect
72. C2×#444C2×C4semidirect
116. C2×#360C2×C4semidirect
119. C2×#358C2×C4semidirect
120. C2×#357C2×C4semidirect
131. #1975C2×C4semidirect
133. #1946C2×C4semidirect
143. #1776D4semidirect
145. #1773C2×C4semidirect
155. #1386C2×C4semidirect
158. #1380C2×C4semidirect
261. #467C42semidirect
263. #466C42semidirect
429. C2×Q16C2×C42semidirect
437. C2×D8C2×C42semidirect
609. #107C2×C42semidirect
1026. C22#12650semidirect

Maximal subgroups

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

subgroupindex
C2×#215462
C22×#17762
C2×#130012
#4944432
C2×#126502
C2×#126052
#1474662
#1472452
#1465202
#1465102
#1463442