Finite Group Databasebeta

← #72287186

Subgroups — #72287186

Order 1024.

2412 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623099C211yesmaximal, characteristic
2#6344817C211yesmaximal, characteristic, complemented
3C2×#17899C211yesmaximal, characteristic, complemented
4#483931C218yesmaximal, complemented
5#483922C214yesmaximal, complemented
6#483921C214yesmaximal, complemented
7#483839C214yesmaximal, complemented
8#483807C214yesmaximal, complemented
9#483421C211yesmaximal, characteristic, complemented
10C2×#11654C211yesmaximal, characteristic, complemented
11#481274C211yesmaximal, characteristic, complemented
12#479969C211yesmaximal, characteristic, complemented
13C2×#3169C2211yescharacteristic
14C2×#2989—21no—
15#60236—21no—
16C2×C4×#135C2211yescharacteristic
17#33675C2214yes—
18#33672C2212yes—
19#33669C2212yes—
20#33666C414yes—
21#33663C412yes—
22#33660C412yes—
23#33648C412yes—
24#33629C412yes—
25#33582C412yes—
26#33520C412yes—
27C4×#509C2214yes—
28#33418C2211yescharacteristic
29C2×#2163C2211yescharacteristic
30#17970—22no—
31#17970C2214yescomplemented
32#17962C2214yes—
33#17956—22no—
34#17899—22no—
35#17899—21no—
36#17899—21no—
37#17899C2212yes—
38#17899C2212yes—
39#17899C2214yescomplemented
40#17895—21no—
41#17895C2212yescomplemented
42C2×#1594C2212yescomplemented
43C2×#1593C2212yescomplemented
44C2×#1590—22no—
45#17854—21no—
46#17854C2212yescomplemented
47#17793C2211yescharacteristic
48C22×#334C2211yescharacteristic
49#17478—21no—
50C2×#1477—21no—
51C2×#1450C2211yescharacteristic
52#12089C22116yescomplemented
53#12087C22116yescomplemented
54#12078C22116yescomplemented
55#12077C22116yescomplemented
56#12030C2214yescomplemented
57#12028C2214yescomplemented
58#12000C2214yescomplemented
59#11665C2214yescomplemented
60#11664C2212yescomplemented
61#11663C2212yescomplemented
62#11654C2214yes—
63#11654C2214yescomplemented
64#11597C2214yes—
65C2×#1333C2214yescomplemented
66#11416C2214yescomplemented
67#11415C2214yescomplemented
68#11406C2212yescomplemented
69#11405C2212yescomplemented
70C22×#135C2×C411yescharacteristic
71C2×#532—21no—
72C2×C4×#41—21no—
73C2×#509C2×C414yes—
74#3169—21no—
75#3169—21no—
76#3169—21no—
77#3169—21no—
78#3169C2×C412yes—
79#3169C2×C412yes—
80#3169C2312yes—
81#3169C2312yes—
82C2×#500C2×C411yescharacteristic
83C2×#493C2×C411yescharacteristic
84C2×#486—21no—
85C2×#466—21no—
86C2×#466C2×C412yes—
87#2989—22no—
88#2989—22no—
89#2989—24no—
90#2989—42no—
91#2989—41no—
92#2989—41no—
93#2981—24no—
94#2979—42no—
95#2975—22no—
96#2974—42no—
97#2972—22no—
98C2×#446—22no—
99C4×#135—21no—
100C4×#135—21no—
101C4×#135—21no—
102C4×#135—21no—
103C4×#135C2×C412yes—
104C4×#135C2×C412yes—
105C4×#135C2312yes—
106C4×#135C2312yes—
107C2×C4×Q16C2×C411yescharacteristic
108C2×C4×Q16C2311yescharacteristic
109C2×C4×SD16—21no—
110C2×C4×SD16—21no—
111C2×C4×D8—21no—
112C2×C4×D8C2×C411yescharacteristic
113C2×C4×D8C2312yes—
114C2×C4×D8C2311yescharacteristic
115#2935—42no—
116#2931—24no—
117C2×#436—22no—
118C2×#435—42no—
119#2920—21no—
120C2×#432—41no—
121C2×#431D411yescharacteristic
122C2×#431D411yescharacteristic
123C2×#427C2×C411yescharacteristic
124C2×#423—41no—
125C22×C4⋊C8—21no—
126C2×#416—21no—
127#2880—42no—
128C22×C4×C8C2311yescharacteristic
129#2234C2×C418yes—
130#2233C2×C414yes—
131#2232C2×C414yes—
132#2227C2×C414yes—
133#2226C2×C414yes—
134#2225C2×C414yes—
135#2224C2×C414yes—
136#2207C2×C414yes—
137#2207C2×C414yes—
138#2206C2×C414yes—
139#2206C2×C414yes—
140#2186C2×C418yes—
141#2185C2×C414yes—
142#2184C2×C414yes—
143#2177C2318yes—
144#2175C2318yes—
145C4×SD32C2×C418yes—
146C4×D16C2×C418yes—
147#2163—21no—
148#2163—21no—
149#2163C2312yes—
150#2163C2312yes—
151#2163C2312yes—
152#2163C2312yes—
153#2162C2×C412yes—
154#2162C2×C412yes—
155#2159C2×C414yes—
156#2150C2×C412yes—
157C2×C4⋊C16—21no—
158#2140C2×C414yes—
159#2139C2×C414yes—
160#2112C2×C412yes—
161C2×C22⋊C16—21no—
162C4×M32C2312yes—
163C2×#346C2312yes—
164#1594—24no—
165#1594—22no—
166#1594—22no—
167#1594C2318yes—
168#1594C2314yes—
169#1594C2314yes—
170#1593—22no—
171#1593—22no—
172#1593C2314yes—
173#1593C2314yes—
174#1590—24no—
175#1590—24no—
176#1590—24no—
177#1590—24no—
178#1589—24no—
179#1589—24no—
180#1580—24no—
181#1580C2318yes—
182C8×D8—24no—
183C8×D8—24no—
184#1568—21no—
185#1568C2312yes—
186#1567—21no—
187#1566C2312yes—
188#1564—21no—
189#1564C2312yes—
190C2×#334—21no—
191C2×#334—21no—
192C2×#334—21no—
193C2×#334C2312yes—
194C2×#334C2312yes—
195C2×#334C2312yes—
196#1496—24no—
197#1492—24no—
198#1478—22no—
199#1478—22no—
200#1477—22no—
201#1477—22no—
202#1477—24no—
203C2×Q8⋊C8—22no—
204C2×D4⋊C8—22no—
205#1450D412yes—
206#1450D411yescharacteristic
207#1450D411yescharacteristic
208#1450C2312yes—
209#1450C2311yescharacteristic
210#1450C2311yescharacteristic
211C2×#322C2312yes—
212C2×C82D412yes—
213#1368C23116yes—
214#1334C2318yes—
215#1333C23116yes—
216#1333C2318yes—
217#1313C2318yes—
218#1313C2318yes—
219C22×#41—21no—
220C22×#41—41no—
221C2×#135—21no—
222C2×#135—21no—
223C2×#135—44no—
224C2×#135C22×C412yes—
225C2×#135C22×C412yes—
226C22×Q16C22×C411yescharacteristic
227C22×SD16—21no—
228C22×D8—21no—
229C22×D8C22×C412yes—
230C22×D8C22×C411yescharacteristic
231C2×#131—44no—
232C22×M16—42no—
233C23×C8—41no—
234C23×C8C22×C411yescharacteristic
235C23×C8#4111yescharacteristic
236#532—22no—
237#532—22no—
238#532—22no—
239#532—22no—
240#532—41no—
241#532—41no—
242#532—41no—
243#532—41no—
244C2×C4⋊Q8—21no—
245C2×#127—21no—
246C2×#124—41no—
247C2×#121—22no—
248C2×#121—41no—
249C4×#41—22no—
250C4×#41—22no—
251C4×#41—22no—
252C4×#41—22no—
253C4×#41—41no—
254C4×#41—41no—
255C4×#41—41no—
256C4×#41—41no—
257C2×C4×Q8—21no—
258C2×C4×Q8—21no—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4—22no—
262C2×C4×D4—41no—
263C2×C4×D4—41no—
264C2×C4×D4—41no—
265C2×#117—21no—
266C2×#117—41no—
267C22×C42—41no—
268C22×C42C2×D411yescharacteristic
269#509—48no—
270C2×SD32C22×C418yes—
271C2×D16C22×C418yes—
272C2×M32C22×C414yes—
273C22×C16—22no—
274#500—21no—
275#500—21no—
276#500C22×C412yes—
277#500C22×C412yes—
278#493—21no—
279#493—21no—
280#493C22×C412yes—
281#493C22×C412yes—
282#486—22no—
283#486—22no—
284#486—22no—
285#486—22no—
286#466—22no—
287#466—22no—
288#466—22no—
289#466—22no—
290#466—22no—
291#466—22no—
292#466C22×C414yes—
293#466C22×C414yes—
294#446—24no—
295#446—24no—
296#446—42no—
297#446—42no—
298C4×Q16—21no—
299C4×Q16—21no—
300C4×Q16—21no—
301C4×Q16—21no—
302C4×Q16C22×C412yes—
303C4×Q16C22×C412yes—
304C4×Q16C22×C412yes—
305C4×Q16C2412yes—
306C4×SD16—22no—
307C4×SD16—22no—
308C4×SD16—22no—
309C4×SD16—22no—
310C4×SD16—22no—
311C4×SD16—22no—
312C4×SD16—22no—
313C4×SD16—22no—
314C4×D8—22no—
315C4×D8—22no—
316C4×D8—21no—
317C4×D8—21no—
318C4×D8—22no—
319C4×D8—22no—
320C4×D8—22no—
321C4×D8—21no—
322C4×D8—22no—
323C4×D8—21no—
324C4×D8C22×C414yes—
325C4×D8C22×C412yes—
326C4×D8C22×C412yes—
327C4×D8C22×C412yes—
328C4×D8C2414yes—
329C4×D8C2412yes—
330#436—28no—
331#436—24no—
332#436—24no—
333#436—42no—
334#436—42no—
335#436—44no—
336#436—44no—
337#435—44no—
338#435—44no—
339#435—44no—
340#435—44no—
341#435—48no—
342C8×D4—28no—
343C8×D4—44no—
344C8×D4—44no—
345#432—22no—
346#432—42no—
347#432—42no—
348#432—44no—
349#432—41no—
350#431—21no—
351#431—21no—
352#431—21no—
353#431—21no—
354#431—22no—
355#431—41no—
356#431C2×D411yescharacteristic
357#431C2×D411yescharacteristic
358#431C2×D412yes—
359#431C2×D411yescharacteristic
360#431C2×D411yescharacteristic
361#431C2×D412yes—
362#427—21no—
363#427—21no—
364#427C22×C412yes—
365#427C22×C412yes—
366C2×#107—21no—
367C2×#107C22×C412yes—
368C2×#107C22×C411yescharacteristic
369C2×#107C22×C411yescharacteristic
370C2×#106—21no—
371#423—22no—
372#423—42no—
373#423—42no—
374#423—44no—
375C2×C4⋊C8—21no—
376C2×C4⋊C8—21no—
377C2×C4⋊C8—22no—
378C2×C4⋊C8—22no—
379C2×C4⋊C8—22no—
380C2×C4⋊C8—42no—
381C2×C4⋊C8—41no—
382C2×C4⋊C8—41no—
383C2×C4⋊C8—41no—
384#416—22no—
385#416—22no—
386#416—22no—
387#416—22no—
388C2×#103—21no—
389C2×#103—21no—
390C2×#102—22no—
391C2×#102—21no—
392C2×#102—22no—
393C2×#102—21no—
394#408—48no—
395#408—44no—
396#407—44no—
397#407—41no—
398C2×C22⋊C8—21no—
399C2×C22⋊C8—21no—
400C2×C22⋊C8—44no—
401C2×C22⋊C8—42no—
402C4×M16—41no—
403C2×#97—42no—
404C2×C4×C8C22×C411yescharacteristic
405C2×C4×C8C22×C411yescharacteristic
406C2×C4×C8C22×C411yescharacteristic
407C2×C4×C8C2×D412yes—
408C2×C4×C8C2×D412yes—
409C2×C4×C8C2×D411yescharacteristic
410C2×C4×C8C2×D411yescharacteristic
411C2×C4×C8C2×D411yescharacteristic
412C2×C4×C8#4111yescharacteristic
413C2×C4×C8#4111yescharacteristic
414C2×C4×C8#4111yescharacteristic
415C2×C4×C8C2411yescharacteristic
416C2×C4×C8C2411yescharacteristic
417C2×C4×C8C2411yescharacteristic
418#367C22×C418yes—
419#366C22×C418yes—
420C4⋊C16—22no—
421C4⋊C16—22no—
422C4⋊C16C22×C414yes—
423C4⋊C16C22×C414yes—
424#358C22×C418yes—
425#357C22×C418yes—
426#357C22×C418yes—
427#357C22×C418yes—
428C22⋊C16—22no—
429C22⋊C16—22no—
430C22⋊C16C22×C414yes—
431C22⋊C16C22×C414yes—
432#346—22no—
433#346C2414yes—
434#346C2414yes—
435C4×C16C22×C414yes—
436#335—22no—
437#335—22no—
438#334—22no—
439#334—22no—
440#334—22no—
441#334—22no—
442#334C2414yes—
443#334C2414yes—
444Q8⋊C8—24no—
445Q8⋊C8—24no—
446D4⋊C8—28no—
447D4⋊C8—28no—
448D4⋊C8—24no—
449D4⋊C8—24no—
450#322C2×D412yes—
451#322C2×D412yes—
452#322C2412yes—
453#322C2412yes—
454C82C2×D412yes—
455C82C2×D412yes—
456C82C2×D412yes—
457C82C2×D412yes—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—44no—
461C2×#41—44no—
462C2×#41—42no—
463C2×#41—42no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41—42no—
467C2×#41—42no—
468C2×#41—164no—
469C22×Q8—21no—
470C22×Q8—41no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—41no—
474C22×D4—42no—
475C22×D4—41no—
476C22×D4—41no—
477C23×C4—41no—
478C23×C4—41no—
479C23×C4—42no—
480C23×C4—41no—
481C23×C4C4×D411yescharacteristic
482C23×C4AGL(1,ℤ/8)11yescharacteristic
483C23×C4AGL(1,ℤ/8)11yescharacteristic
484#135—24no—
485#135—24no—
486#135—42no—
487#135—42no—
488#135—44no—
489#135—44no—
490C2×Q16—21no—
491C2×Q16—42no—
492C2×Q16C23×C412yes—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—44no—
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—21no—
499C2×D8—22no—
500C2×D8—28no—
501C2×D8—42no—
502C2×D8—44no—
503C2×D8C23×C412yes—
504C2×D8C23×C414yes—
505#131—168no—
506C2×M16—44no—
507C2×M16—44no—
508C2×M16—48no—
509C2×M16—42no—
510C2×M16—164no—
511C22×C8—24no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—42no—
515C22×C8—48no—
516C22×C8—42no—
517C22×C8—42no—
518C22×C8—42no—
519C22×C8—162no—
520C22×C8C4×D411yescharacteristic
521C22×C8C4×D411yescharacteristic
522C22×C8C4×D411yescharacteristic
523C22×C8C4×D411yescharacteristic
524C22×C8C4×D411yescharacteristic
525C22×C8C4×D411yescharacteristic
526C22×C8C23×C411yescharacteristic
527C22×C8C23×C411yescharacteristic
528C22×C8C23×C411yescharacteristic
529C22×C8C2×#4111yescharacteristic
530C22×C8C2×#4111yescharacteristic
531C22×C8C2×#4111yescharacteristic
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#127—22no—
537#127—22no—
538#127—41no—
539#127—41no—
540#124—42no—
541#124—42no—
542#124—42no—
543#124—42no—
544#121—24no—
545#121—24no—
546#121—42no—
547#121—42no—
548#121—42no—
549#121—42no—
550#121—42no—
551#121—42no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—24no—
564C4×D4—22no—
565C4×D4—24no—
566C4×D4—42no—
567C4×D4—42no—
568C4×D4—42no—
569C4×D4—42no—
570C4×D4—42no—
571C4×D4—42no—
572C4×D4—42no—
573C4×D4—42no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—42no—
577C4×D4—42no—
578C4×D4—42no—
579C4×D4—42no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—42no—
583C4×D4—42no—
584#117—22no—
585#117—22no—
586#117—41no—
587#117—41no—
588#117—42no—
589#117—42no—
590#117—42no—
591#117—42no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—42no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—42no—
607C2×C42—42no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42C4×D411yescharacteristic
611C2×C42C4×D411yescharacteristic
612C2×C42C4×D411yescharacteristic
613C2×C42AGL(1,ℤ/8)11yescharacteristic
614C2×C42AGL(1,ℤ/8)11yescharacteristic
615C2×C42AGL(1,ℤ/8)11yescharacteristic
616C2×C42AGL(1,ℤ/8)11yescharacteristic
617C2×C42AGL(1,ℤ/8)11yescharacteristic
618C2×C42AGL(1,ℤ/8)11yescharacteristic
619C2×C42C22×D411yescharacteristic
620C2×C42C22×D411yescharacteristic
621C2×C42C22×D411yescharacteristic
622SD32—48no—
623D16—48no—
624M32—28no—
625C2×C16—24no—
626C2×C16—44no—
627C2×C16C23×C418yes—
628#107—22no—
629#107—22no—
630#107—21no—
631#107—21no—
632#107—22no—
633#107C23×C412yes—
634#107C23×C412yes—
635#107C23×C414yes—
636#106—22no—
637#106—22no—
638C4⋊C8—21no—
639C4⋊C8—21no—
640C4⋊C8—22no—
641C4⋊C8—21no—
642C4⋊C8—22no—
643C4⋊C8—21no—
644C4⋊C8—24no—
645C4⋊C8—24no—
646C4⋊C8—44no—
647C4⋊C8—44no—
648C4⋊C8—42no—
649C4⋊C8—42no—
650C4⋊C8—42no—
651C4⋊C8—42no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—24no—
660#102—24no—
661#102—24no—
662#102—22no—
663#102—24no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—22no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—22no—
670C22⋊C8—48no—
671C22⋊C8—44no—
672C22⋊C8—44no—
673C22⋊C8—48no—
674C22⋊C8—42no—
675C22⋊C8—42no—
676#97—44no—
677#97—44no—
678#97—42no—
679C4×C8—22no—
680C4×C8—22no—
681C4×C8—42no—
682C4×C8C4×D411yescharacteristic
683C4×C8C4×D411yescharacteristic
684C4×C8C4×D411yescharacteristic
685C4×C8C4×D411yescharacteristic
686C4×C8C4×D411yescharacteristic
687C4×C8C4×D411yescharacteristic
688C4×C8C23×C411yescharacteristic
689C4×C8C23×C411yescharacteristic
690C4×C8C23×C411yescharacteristic
691C4×C8C22×D412yes—
692C4×C8C22×D412yes—
693C4×C8C22×D412yes—
694C4×C8C22×D412yes—
695C4×C8C22×D411yescharacteristic
696C4×C8C22×D411yescharacteristic
697C4×C8C22×D411yescharacteristic
698C4×C8C2×#4111yescharacteristic
699C4×C8C2×#4111yescharacteristic
700C4×C8C2×#4111yescharacteristic
701C4×C8C2511yescharacteristic
702C24—41no—
703C24—42no—
704C24#44211yescharacteristic
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709#41—88no—
710#41—84no—
711#41—84no—
712#41—164no—
713#41—164no—
714#41—164no—
715C2×Q8—22no—
716C2×Q8—42no—
717C2×Q8—42no—
718C2×Q8—41no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—162no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—41no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—84no—
739C2×D4—162no—
740C2×D4—162no—
741C2×D4—164no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—44no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—44no—
758C22×C4—82no—
759C22×C4—82no—
760C22×C4—84no—
761C22×C4—162no—
762C22×C4—164no—
763C22×C4#44211yescharacteristic
764C22×C4#44211yescharacteristic
765C22×C4#44211yescharacteristic
766C22×C4#44211yescharacteristic
767C22×C4#44211yescharacteristic
768C22×C4#44211yescharacteristic
769C22×C4#44211yescharacteristic
770C22×C4#44211yescharacteristic
771C22×C4#44211yescharacteristic
772C22×C4C2×C4×D411yescharacteristic
773C22×C4C2×C4×D411yescharacteristic
774C22×C4C2×C4×D411yescharacteristic
775C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
776C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
777C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
778C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
779C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
780C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
781Q16—22no—
782Q16—22no—
783Q16—42no—
784SD16—44no—
785SD16—44no—
786D8—22no—
787D8—28no—
788D8—22no—
789D8—44no—
790D8—44no—
791D8—42no—
792D8—44no—
793M16—84no—
794M16—164no—
795M16—164no—
796M16—168no—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8—22no—
803C2×C8—22no—
804C2×C8—22no—
805C2×C8—22no—
806C2×C8—22no—
807C2×C8—22no—
808C2×C8—41no—
809C2×C8—41no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—44no—
813C2×C8—44no—
814C2×C8—44no—
815C2×C8—44no—
816C2×C8—84no—
817C2×C8—168no—
818C2×C8—162no—
819C2×C8—162no—
820C2×C8C2×C4×D411yescharacteristic
821C2×C8C2×C4×D411yescharacteristic
822C2×C8C2×C4×D411yescharacteristic
823C2×C8C2×C4×D411yescharacteristic
824C2×C8C2×C4×D411yescharacteristic
825C2×C8C2×C4×D411yescharacteristic
826C2×C8#56814yes—
827C2×C8C24×C411yescharacteristic
828C2×C8C22×#4111yescharacteristic
829C4⋊C4—24no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—42no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—42no—
850C22⋊C4—44no—
851C42—42no—
852C42—42no—
853C42—42no—
854C42—42no—
855C42—42no—
856C42—42no—
857C42#44211yescharacteristic
858C42#44211yescharacteristic
859C42#44211yescharacteristic
860C42#44211yescharacteristic
861C42#44211yescharacteristic
862C42#44211yescharacteristic
863C42C2×C4×D411yescharacteristic
864C42C2×C4×D411yescharacteristic
865C42C2×C4×D411yescharacteristic
866C42C2×AGL(1,ℤ/8)11yescharacteristic
867C42C2×AGL(1,ℤ/8)11yescharacteristic
868C42C2×AGL(1,ℤ/8)11yescharacteristic
869C42C2×AGL(1,ℤ/8)11yescharacteristic
870C42C2×AGL(1,ℤ/8)11yescharacteristic
871C42C2×AGL(1,ℤ/8)11yescharacteristic
872C42C23×D411yescharacteristic
873C16—28no—
874C16—44no—
875C23—22no—
876C23—22no—
877C23—41no—
878C23—42no—
879C23—44no—
880C23—82no—
881C23—82no—
882C23—82no—
883C23—84no—
884C23—162no—
885C23—162no—
886C23C2×#44211yescharacteristic
887C23C2×#44211yescharacteristic
888C23C2×#44211yescharacteristic
889Q8—42no—
890Q8—42no—
891Q8—82no—
892Q8—84no—
893Q8—162no—
894D4—44no—
895D4—42no—
896D4—42no—
897D4—44no—
898D4—82no—
899D4—84no—
900D4—84no—
901D4—84no—
902D4—88no—
903D4—84no—
904D4—84no—
905D4—162no—
906D4—162no—
907D4—164no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—44no—
931C2×C4—88no—
932C2×C4—82no—
933C2×C4—82no—
934C2×C4—84no—
935C2×C4—82no—
936C2×C4—82no—
937C2×C4—82no—
938C2×C4—84no—
939C2×C4—84no—
940C2×C4—162no—
941C2×C4—162no—
942C2×C4—164no—
943C2×C4—162no—
944C2×C4#293012yes—
945C2×C4C2×#44211yescharacteristic
946C2×C4C2×#44211yescharacteristic
947C2×C4C2×#44211yescharacteristic
948C2×C4C2×#44211yescharacteristic
949C2×C4C2×#44211yescharacteristic
950C2×C4C2×#44211yescharacteristic
951C2×C4C2×#44211yescharacteristic
952C2×C4C2×#44211yescharacteristic
953C2×C4C2×#44211yescharacteristic
954C2×C4#295512yes—
955C2×C4C22×C4×D411yescharacteristic
956C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
957C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
958C8—21no—
959C8—21no—
960C8—21no—
961C8—21no—
962C8—21no—
963C8—21no—
964C8—42no—
965C8—42no—
966C8—42no—
967C8—42no—
968C8—84no—
969C8—84no—
970C8#293012yes—
971C8C2×#56812yes—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—44no—
980C22—82no—
981C22—84no—
982C22—84no—
983C22—82no—
984C22—82no—
985C22—84no—
986C22—164no—
987C22—324no—
988C22#1793512yes—
989C22#3347112yes—
990C22C22×#44211yescharacteristic
991C4—21no—
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—82no—
1001C4—82no—
1002C4—84no—
1003C4—82no—
1004C4#1793512yes—
1005C4#3346912yes—
1006C4C2×#293011yescharacteristic
1007C4C2×#295511yescharacteristic
1008C2—22no—
1009C2—22no—
1010C2—41no—
1011C2—162no—
1012C2—164no—
1013C2C2×#1793511yescharacteristic
1014C2C2×#3346911yescharacteristic
1015C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623099C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#1450 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6344817C2semidirect
3. C2×#17899C2semidirect
4. #483931C2semidirect
5. #483922C2semidirect
6. #483921C2semidirect
7. #483839C2semidirect
8. #483807C2semidirect
9. #483421C2semidirect
10. C2×#11654C2semidirect
11. #481274C2semidirect
12. #479969C2semidirect
31. #17970C22semidirect
39. #17899C22semidirect
41. #17895C22semidirect
42. C2×#1594C22semidirect
43. C2×#1593C22semidirect
46. #17854C22semidirect
52. #12089C22semidirect
53. #12087C22semidirect
54. #12078C22semidirect
55. #12077C22semidirect
56. #12030C22semidirect
57. #12028C22semidirect
58. #12000C22semidirect
59. #11665C22semidirect
60. #11664C22semidirect
61. #11663C22semidirect
63. #11654C22semidirect
65. C2×#1333C22semidirect
66. #11416C22semidirect
67. #11415C22semidirect
68. #11406C22semidirect
69. #11405C22semidirect

Maximal subgroups

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

subgroupindex
#76230992
#63448172
C2×#178992
#4839312
#4839222
#4839212
#4838392
#4838072
#4834212
C2×#116542
#4812742
#4799692