Finite Group Databasebeta

← #72322423

Subgroups — #72322423

Order 1024.

2563 conjugacy classes of subgroups.

The subgroup lattice has 1001 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623096C211yesmaximal, characteristic
2#6344823C211yesmaximal, characteristic, complemented
3C2×#17854C211yesmaximal, characteristic, complemented
4#483888C214yesmaximal, complemented
5#483886C214yesmaximal, complemented
6#483878C218yesmaximal, complemented
7#483807C214yesmaximal, complemented
8#483592C214yesmaximal, complemented
9#483423C211yesmaximal, characteristic, complemented
10#481309C211yesmaximal, characteristic, complemented
11C2×#11667C211yesmaximal, characteristic, complemented
12#479969C211yesmaximal, characteristic, complemented
13#60673C2211yescharacteristic
14#60294—21no—
15C2×#2972—21no—
16C22×C4×D8C2211yescharacteristic
17#33674C2214yes—
18#33670C2212yes—
19#33669C2212yes—
20#33665C414yes—
21#33661C412yes—
22#33660C412yes—
23#33646C412yes—
24#33627C412yes—
25#33580C412yes—
26#33517C412yes—
27C4×#509C2214yes—
28#33418C2211yescharacteristic
29C2×#2163C2211yescharacteristic
30#17972C2212yescomplemented
31#17971—22no—
32#17970C2212yescomplemented
33#17963C2214yescomplemented
34#17959—22no—
35#17899C2212yescomplemented
36#17898—21no—
37#17858C2212yescomplemented
38#17857—21no—
39#17854—22no—
40#17854—21no—
41#17854—21no—
42#17854C2212yes—
43#17854C2214yes—
44#17854C2212yes—
45C2×#1580C2214yes—
46C2×C8×D8—22no—
47C2×#1568C2211yescharacteristic
48C2×#1564C2211yescharacteristic
49#17482—21no—
50C2×#1478—21no—
51C2×#1450C2211yescharacteristic
52#12078C22116yescomplemented
53#12077C22116yescomplemented
54#12067C22116yescomplemented
55#12065C22116yescomplemented
56#12031C2214yescomplemented
57#12028C2214yescomplemented
58#12000C2214yescomplemented
59#11667C2214yes—
60#11667C2214yes—
61#11653C2212yescomplemented
62#11652C2212yescomplemented
63#11651C2214yescomplemented
64#11597C2214yescomplemented
65C2×#1333C2214yes—
66#11416C2214yescomplemented
67#11415C2214yescomplemented
68#11406C2212yescomplemented
69#11405C2212yescomplemented
70C23×D8C2×C411yescharacteristic
71#3444—21no—
72C22×C4×D4—21no—
73C2×#509C2×C414yes—
74#3170C2×C411yescharacteristic
75#3170C2311yescharacteristic
76#3169C2×C411yescharacteristic
77#3169C2311yescharacteristic
78#3168—21no—
79#3168—21no—
80#3168C2×C412yes—
81#3168C2312yes—
82#3167—21no—
83#3167—21no—
84#3160C2×C411yescharacteristic
85#3147C2×C411yescharacteristic
86#3131—21no—
87#3050—21no—
88#3050C2×C412yes—
89#2990—42no—
90#2989—22no—
91#2988—22no—
92#2985—22no—
93#2981—22no—
94#2977—42no—
95#2972—22no—
96#2972—22no—
97#2972—24no—
98#2972—42no—
99#2972—42no—
100#2968—42no—
101#2966—24no—
102C4×#135—21no—
103C4×#135C2312yes—
104C2×C4×D8—21no—
105C2×C4×D8—21no—
106C2×C4×D8—21no—
107C2×C4×D8—21no—
108C2×C4×D8—21no—
109C2×C4×D8—21no—
110C2×C4×D8C2×C412yes—
111C2×C4×D8C2×C412yes—
112C2×C4×D8C2×C412yes—
113C2×C4×D8C2312yes—
114C2×C4×D8C2312yes—
115C2×C4×D8C2312yes—
116C2×C8×D4—24no—
117C2×C8×D4—42no—
118#2925—42no—
119C2×#432—21no—
120C2×#431—21no—
121C2×#431D411yescharacteristic
122C2×#431D411yescharacteristic
123C22×#107C2×C411yescharacteristic
124C22×#102—21no—
125C22×C22⋊C8—42no—
126C22×C4×C8C2311yescharacteristic
127#2236C2×C414yes—
128#2235C2×C414yes—
129#2233C2×C414yes—
130#2232C2×C414yes—
131#2228C2×C418yes—
132#2226C2×C414yes—
133#2224C2×C414yes—
134#2210C2×C418yes—
135#2208C2×C414yes—
136#2206C2×C414yes—
137#2187C2×C414yes—
138#2187C2×C414yes—
139#2184C2×C414yes—
140#2184C2×C414yes—
141#2177C2318yes—
142#2175C2318yes—
143C4×SD32C2×C418yes—
144C4×D16C2×C418yes—
145#2163—21no—
146#2163—21no—
147#2163C2312yes—
148#2163C2312yes—
149#2163C2312yes—
150#2163C2312yes—
151#2162C2×C412yes—
152#2162C2×C412yes—
153#2159C2×C414yes—
154#2150C2×C412yes—
155C2×C4⋊C16—21no—
156#2140C2×C414yes—
157#2139C2×C414yes—
158#2112C2×C412yes—
159C2×C22⋊C16—21no—
160C4×M32C2312yes—
161C2×#346C2312yes—
162#1594C2314yescomplemented
163#1593C2314yescomplemented
164#1592—24no—
165#1591—22no—
166#1590—24no—
167#1589—22no—
168#1580—24no—
169#1580—24no—
170#1580C2318yes—
171#1580C2318yes—
172#1580C2314yescomplemented
173#1579C2314yescomplemented
174SD16⋊C8—24no—
175C8×Q16—22no—
176C8×SD16—24no—
177C8×D8—22no—
178C8×D8—24no—
179C8×D8—24no—
180C8×D8—24no—
181C8×D8—24no—
182#1568—21no—
183#1568—21no—
184#1568C2312yes—
185#1568C2312yes—
186#1564—21no—
187#1564—21no—
188#1564C2312yes—
189#1564C2312yes—
190C2×#335—21no—
191C2×#335—21no—
192C2×#334C2312yes—
193C2×#334C2312yes—
194#1497—22no—
195#1496—22no—
196#1494—24no—
197#1478—24no—
198#1478—22no—
199#1478—22no—
200#1477—22no—
201#1477—22no—
202C2×D4⋊C8—24no—
203#1450D412yes—
204#1450D411yescharacteristic
205#1450D411yescharacteristic
206#1450C2312yes—
207#1450C2311yescharacteristic
208#1450C2311yescharacteristic
209C2×#322C2312yes—
210C2×C82D412yes—
211#1368C23116yescomplemented
212#1334C2318yescomplemented
213#1333C23116yes—
214#1333C2318yescomplemented
215#1313C2318yescomplemented
216#1313C2318yescomplemented
217C23×D4—21no—
218C24×C4—41no—
219C2×#135—21no—
220C2×#135C22×C412yes—
221C22×D8—28no—
222C22×D8—21no—
223C22×D8—21no—
224C22×D8—21no—
225C22×D8C22×C412yes—
226C22×D8C22×C412yes—
227C22×D8C22×C412yes—
228C23×C8—44no—
229C23×C8C22×C411yescharacteristic
230C23×C8#4111yescharacteristic
231#533—21no—
232#533—21no—
233#533—21no—
234#532—21no—
235#532—21no—
236#532—21no—
237#529—22no—
238#529—22no—
239#529—41no—
240#529—41no—
241#529—41no—
242#529—41no—
243#525—22no—
244#525—41no—
245#525—41no—
246C4×#41—22no—
247C4×#41—41no—
248C4×#41—41no—
249C2×C4×D4—22no—
250C2×C4×D4—22no—
251C2×C4×D4—22no—
252C2×C4×D4—22no—
253C2×C4×D4—22no—
254C2×C4×D4—22no—
255C2×C4×D4—41no—
256C2×C4×D4—41no—
257C2×C4×D4—41no—
258C2×C4×D4—41no—
259C2×C4×D4—41no—
260C2×C4×D4—41no—
261C22×C4⋊C4—21no—
262C22×C22⋊C4—41no—
263C22×C42C2×D411yescharacteristic
264#509—216no—
265C2×SD32C22×C418yes—
266C2×D16C22×C418yes—
267C2×M32C22×C414yes—
268C22×C16—22no—
269#500C22×C411yescharacteristic
270#500C22×C411yescharacteristic
271#499—21no—
272#499C22×C412yes—
273#498—21no—
274#495—21no—
275#495C22×C412yes—
276#494C22×C411yescharacteristic
277#493C22×C411yescharacteristic
278#492—21no—
279#488—22no—
280#488—22no—
281#487—21no—
282#487—21no—
283#486—21no—
284#486—21no—
285#467—21no—
286#467—21no—
287#467C22×C412yes—
288#467C22×C412yes—
289#466—21no—
290#466—21no—
291#466C22×C412yes—
292#466C22×C412yes—
293#465—22no—
294#465—22no—
295#465—22no—
296#465—22no—
297#446—24no—
298#446—44no—
299C8×Q8—24no—
300C4×Q16—21no—
301C4×Q16—21no—
302C4×Q16C22×C412yes—
303C4×Q16C2412yes—
304C4×SD16—22no—
305C4×SD16—22no—
306C4×SD16—22no—
307C4×SD16—22no—
308C4×D8—21no—
309C4×D8—22no—
310C4×D8—22no—
311C4×D8—22no—
312C4×D8—22no—
313C4×D8—22no—
314C4×D8—22no—
315C4×D8—22no—
316C4×D8—22no—
317C4×D8—21no—
318C4×D8—22no—
319C4×D8—22no—
320C4×D8—22no—
321C4×D8—22no—
322C4×D8C22×C412yes—
323C4×D8C22×C414yes—
324C4×D8C22×C414yes—
325C4×D8C22×C414yes—
326C4×D8C2414yes—
327C4×D8C2412yes—
328#436—24no—
329#435—44no—
330#435—44no—
331#435—44no—
332C8×D4—28no—
333C8×D4—28no—
334C8×D4—24no—
335C8×D4—44no—
336C8×D4—44no—
337C8×D4—44no—
338C8×D4—44no—
339C8×D4—44no—
340C8×D4—48no—
341C8×D4—44no—
342#433—44no—
343#433—44no—
344#432—22no—
345#432—22no—
346#432—42no—
347#432—41no—
348#432—41no—
349#431—21no—
350#431—21no—
351#431—21no—
352#431—21no—
353#431—22no—
354#431—22no—
355#431—42no—
356#431—41no—
357#431—41no—
358#431C2×D411yescharacteristic
359#431C2×D411yescharacteristic
360#431C2×D412yes—
361#431C2×D412yes—
362#431C2×D411yescharacteristic
363#431C2×D411yescharacteristic
364#427—21no—
365#427C22×C412yes—
366C2×#107—21no—
367C2×#107—21no—
368C2×#107—21no—
369C2×#107C22×C412yes—
370C2×#107C22×C412yes—
371C2×#107C22×C412yes—
372#423—42no—
373C2×C4⋊C8—21no—
374C2×C4⋊C8—21no—
375C2×C4⋊C8—22no—
376C2×C4⋊C8—22no—
377C2×C4⋊C8—42no—
378#416—22no—
379#416—22no—
380C2×#102—22no—
381C2×#102—22no—
382C2×#102—22no—
383C2×#102—22no—
384C2×#102—22no—
385C2×#102—22no—
386#408—44no—
387C2×C22⋊C8—21no—
388C2×C22⋊C8—21no—
389C2×C22⋊C8—44no—
390C2×C22⋊C8—44no—
391C2×C22⋊C8—48no—
392C2×C22⋊C8—44no—
393C2×C22⋊C8—41no—
394C2×C22⋊C8—41no—
395#405—44no—
396C2×#97—41no—
397C2×C4×C8—41no—
398C2×C4×C8C22×C411yescharacteristic
399C2×C4×C8C22×C411yescharacteristic
400C2×C4×C8C22×C411yescharacteristic
401C2×C4×C8C2×D412yes—
402C2×C4×C8C2×D412yes—
403C2×C4×C8C2×D411yescharacteristic
404C2×C4×C8C2×D411yescharacteristic
405C2×C4×C8C2×D411yescharacteristic
406C2×C4×C8#4111yescharacteristic
407C2×C4×C8#4111yescharacteristic
408C2×C4×C8#4111yescharacteristic
409C2×C4×C8C2411yescharacteristic
410C2×C4×C8C2411yescharacteristic
411C2×C4×C8C2411yescharacteristic
412#367C22×C418yes—
413#366C22×C418yes—
414C4⋊C16—22no—
415C4⋊C16—22no—
416C4⋊C16C22×C414yes—
417C4⋊C16C22×C414yes—
418#358C22×C418yes—
419#357C22×C418yes—
420#357C22×C418yes—
421#357C22×C418yes—
422C22⋊C16—22no—
423C22⋊C16—22no—
424C22⋊C16C22×C414yes—
425C22⋊C16C22×C414yes—
426#346—22no—
427#346C2414yes—
428#346C2414yes—
429C4×C16C22×C414yes—
430#335—22no—
431#335—22no—
432#335—22no—
433#335—22no—
434#334—22no—
435#334—22no—
436#334C2414yes—
437#334C2414yes—
438Q8⋊C8—24no—
439Q8⋊C8—24no—
440D4⋊C8—28no—
441D4⋊C8—28no—
442D4⋊C8—24no—
443D4⋊C8—24no—
444#322C2×D412yes—
445#322C2×D412yes—
446#322C2412yes—
447#322C2412yes—
448C82C2×D412yes—
449C82C2×D412yes—
450C82C2×D412yes—
451C82C2×D412yes—
452C25—41no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C22×D4—28no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—44no—
461C22×D4—41no—
462C22×D4—41no—
463C22×D4—41no—
464C23×C4—41no—
465C23×C4—42no—
466C23×C4—42no—
467C23×C4—42no—
468C23×C4—42no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4—164no—
472C23×C4C4×D411yescharacteristic
473C23×C4AGL(1,ℤ/8)11yescharacteristic
474C23×C4AGL(1,ℤ/8)11yescharacteristic
475#135—28no—
476#135—44no—
477C2×Q16—21no—
478C2×Q16C23×C412yes—
479C2×SD16—22no—
480C2×SD16—22no—
481C2×D8—28no—
482C2×D8—28no—
483C2×D8—28no—
484C2×D8—28no—
485C2×D8—28no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—21no—
490C2×D8—24no—
491C2×D8#13118yes—
492C2×D8C23×C412yes—
493C2×D8C23×C414yes—
494C2×M16—44no—
495C22×C8—24no—
496C22×C8—22no—
497C22×C8—22no—
498C22×C8—42no—
499C22×C8—48no—
500C22×C8—48no—
501C22×C8—44no—
502C22×C8—42no—
503C22×C8—42no—
504C22×C8—168no—
505C22×C8C4×D411yescharacteristic
506C22×C8C4×D411yescharacteristic
507C22×C8C4×D411yescharacteristic
508C22×C8C4×D411yescharacteristic
509C22×C8C4×D411yescharacteristic
510C22×C8C4×D411yescharacteristic
511C22×C8C23×C411yescharacteristic
512C22×C8C23×C411yescharacteristic
513C22×C8C23×C411yescharacteristic
514C22×C8C2×#4111yescharacteristic
515C22×C8C2×#4111yescharacteristic
516C22×C8C2×#4111yescharacteristic
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8—21no—
520#127—21no—
521#126—42no—
522#126—42no—
523#125—22no—
524#125—41no—
525#125—41no—
526#124—22no—
527#124—41no—
528#124—41no—
529#123—42no—
530#123—42no—
531#123—42no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—41no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C22⋊Q8—41no—
538#121—22no—
539#121—22no—
540#121—41no—
541#121—41no—
542#121—41no—
543#121—41no—
544#120—42no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×D4—24no—
552C4×D4—24no—
553C4×D4—24no—
554C4×D4—22no—
555C4×D4—24no—
556C4×D4—22no—
557C4×D4—42no—
558C4×D4—42no—
559C4×D4—42no—
560C4×D4—42no—
561C4×D4—42no—
562C4×D4—42no—
563C4×D4—42no—
564C4×D4—42no—
565C4×D4—42no—
566C4×D4—42no—
567C4×D4—42no—
568C4×D4—42no—
569C4×D4—41no—
570C4×D4—42no—
571C4×D4—42no—
572C4×D4—42no—
573C4×D4—42no—
574C4×D4—42no—
575C4×D4—42no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579#117—22no—
580#117—41no—
581#117—41no—
582#117—42no—
583#117—42no—
584#117—42no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C42—42no—
598C2×C42C4×D411yescharacteristic
599C2×C42C4×D411yescharacteristic
600C2×C42C4×D411yescharacteristic
601C2×C42AGL(1,ℤ/8)11yescharacteristic
602C2×C42AGL(1,ℤ/8)11yescharacteristic
603C2×C42AGL(1,ℤ/8)11yescharacteristic
604C2×C42AGL(1,ℤ/8)11yescharacteristic
605C2×C42AGL(1,ℤ/8)11yescharacteristic
606C2×C42AGL(1,ℤ/8)11yescharacteristic
607C2×C42C22×D411yescharacteristic
608C2×C42C22×D411yescharacteristic
609C2×C42C22×D411yescharacteristic
610SD32—216no—
611D16—216no—
612M32—28no—
613C2×C16—24no—
614C2×C16—44no—
615C2×C16C23×C418yes—
616#107—22no—
617#107—22no—
618#107—22no—
619#107—21no—
620#107—21no—
621#107C23×C412yes—
622#107C23×C412yes—
623#107C23×C414yes—
624#106—22no—
625#106—22no—
626C4⋊C8—21no—
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—22no—
631C4⋊C8—22no—
632C4⋊C8—24no—
633C4⋊C8—24no—
634C4⋊C8—44no—
635C4⋊C8—44no—
636C4⋊C8—42no—
637C4⋊C8—42no—
638#103—22no—
639#103—22no—
640#103—22no—
641#103—22no—
642#102—24no—
643#102—24no—
644#102—24no—
645#102—22no—
646#102—22no—
647#102—22no—
648#102—24no—
649#102—22no—
650C22⋊C8—21no—
651C22⋊C8—21no—
652C22⋊C8—22no—
653C22⋊C8—22no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—48no—
657C22⋊C8—48no—
658C22⋊C8—44no—
659C22⋊C8—44no—
660C22⋊C8—42no—
661C22⋊C8—42no—
662C22⋊C8—42no—
663C22⋊C8—42no—
664#97—44no—
665#97—42no—
666#97—42no—
667C4×C8—22no—
668C4×C8—22no—
669C4×C8—44no—
670C4×C8—42no—
671C4×C8—42no—
672C4×C8C4×D411yescharacteristic
673C4×C8C4×D411yescharacteristic
674C4×C8C4×D411yescharacteristic
675C4×C8C4×D411yescharacteristic
676C4×C8C4×D411yescharacteristic
677C4×C8C4×D411yescharacteristic
678C4×C8C23×C411yescharacteristic
679C4×C8C23×C411yescharacteristic
680C4×C8C23×C411yescharacteristic
681C4×C8C22×D412yes—
682C4×C8C22×D412yes—
683C4×C8C22×D412yes—
684C4×C8C22×D412yes—
685C4×C8C22×D411yescharacteristic
686C4×C8C22×D411yescharacteristic
687C4×C8C22×D411yescharacteristic
688C4×C8C2×#4111yescharacteristic
689C4×C8C2×#4111yescharacteristic
690C4×C8C2×#4111yescharacteristic
691C4×C8C2511yescharacteristic
692C24—48no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—162no—
697C24—162no—
698C24#44211yescharacteristic
699#41—44no—
700#41—44no—
701#41—162no—
702#41—162no—
703C2×Q8—22no—
704C2×Q8—41no—
705C2×Q8—41no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—24no—
709C2×D4—22no—
710C2×D4—28no—
711C2×D4—48no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—41no—
723C2×D4—41no—
724C2×D4—44no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—44no—
733C22×C4—42no—
734C22×C4—44no—
735C22×C4—42no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—88no—
739C22×C4—81no—
740C22×C4—164no—
741C22×C4—164no—
742C22×C4—164no—
743C22×C4—164no—
744C22×C4—164no—
745C22×C4—162no—
746C22×C4#44211yescharacteristic
747C22×C4#44211yescharacteristic
748C22×C4#44211yescharacteristic
749C22×C4#44211yescharacteristic
750C22×C4#44211yescharacteristic
751C22×C4#44211yescharacteristic
752C22×C4#44211yescharacteristic
753C22×C4#44211yescharacteristic
754C22×C4#44211yescharacteristic
755C22×C4C2×C4×D411yescharacteristic
756C22×C4C2×C4×D411yescharacteristic
757C22×C4C2×C4×D411yescharacteristic
758C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
759C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
760C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
761C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
762C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
763C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
764Q16—24no—
765Q16—42no—
766SD16—44no—
767SD16—44no—
768D8—28no—
769D8—28no—
770D8—28no—
771D8—24no—
772D8—24no—
773D8—42no—
774D8C2×#13118yes—
775M16—164no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—22no—
779C2×C8—22no—
780C2×C8—22no—
781C2×C8—22no—
782C2×C8—22no—
783C2×C8—22no—
784C2×C8—22no—
785C2×C8—22no—
786C2×C8—22no—
787C2×C8—41no—
788C2×C8—41no—
789C2×C8—41no—
790C2×C8—41no—
791C2×C8—44no—
792C2×C8—44no—
793C2×C8—44no—
794C2×C8—82no—
795C2×C8—84no—
796C2×C8—164no—
797C2×C8—168no—
798C2×C8—168no—
799C2×C8—162no—
800C2×C8C2×C4×D411yescharacteristic
801C2×C8C2×C4×D411yescharacteristic
802C2×C8C2×C4×D411yescharacteristic
803C2×C8C2×C4×D411yescharacteristic
804C2×C8C2×C4×D411yescharacteristic
805C2×C8C2×C4×D411yescharacteristic
806C2×C8C2×#13114yes—
807C2×C8C24×C411yescharacteristic
808C2×C8C22×#4111yescharacteristic
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—41no—
817C4⋊C4—41no—
818C4⋊C4—41no—
819C4⋊C4—41no—
820C4⋊C4—42no—
821C4⋊C4—42no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—42no—
825C22⋊C4—42no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—42no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—42no—
836C22⋊C4—44no—
837C22⋊C4—42no—
838C42—42no—
839C42—42no—
840C42—42no—
841C42#44211yescharacteristic
842C42#44211yescharacteristic
843C42#44211yescharacteristic
844C42#44211yescharacteristic
845C42#44211yescharacteristic
846C42#44211yescharacteristic
847C42C2×C4×D411yescharacteristic
848C42C2×C4×D411yescharacteristic
849C42C2×C4×D411yescharacteristic
850C42C2×AGL(1,ℤ/8)11yescharacteristic
851C42C2×AGL(1,ℤ/8)11yescharacteristic
852C42C2×AGL(1,ℤ/8)11yescharacteristic
853C42C2×AGL(1,ℤ/8)11yescharacteristic
854C42C2×AGL(1,ℤ/8)11yescharacteristic
855C42C2×AGL(1,ℤ/8)11yescharacteristic
856C42C23×D411yescharacteristic
857C16—28no—
858C16—44no—
859C23—22no—
860C23—22no—
861C23—41no—
862C23—48no—
863C23—48no—
864C23—44no—
865C23—48no—
866C23—42no—
867C23—84no—
868C23—84no—
869C23—162no—
870C23—162no—
871C23—162no—
872C23—162no—
873C23—1616no—
874C23C2×#44211yescharacteristic
875C23C2×#44211yescharacteristic
876C23C2×#44211yescharacteristic
877Q8—42no—
878Q8—42no—
879Q8—161no—
880Q8—161no—
881D4—28no—
882D4—48no—
883D4—48no—
884D4—44no—
885D4—42no—
886D4—42no—
887D4—48no—
888D4—84no—
889D4—84no—
890D4—161no—
891D4—161no—
892D4—162no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—44no—
916C2×C4—88no—
917C2×C4—82no—
918C2×C4—82no—
919C2×C4—88no—
920C2×C4—84no—
921C2×C4—84no—
922C2×C4—164no—
923C2×C4—164no—
924C2×C4—162no—
925C2×C4—162no—
926C2×C4—162no—
927C2×C4#292912yes—
928C2×C4C2×#44211yescharacteristic
929C2×C4C2×#44211yescharacteristic
930C2×C4C2×#44211yescharacteristic
931C2×C4C2×#44211yescharacteristic
932C2×C4C2×#44211yescharacteristic
933C2×C4C2×#44211yescharacteristic
934C2×C4C2×#44211yescharacteristic
935C2×C4C2×#44211yescharacteristic
936C2×C4C2×#44211yescharacteristic
937C2×C4#295512yes—
938C2×C4C22×C4×D411yescharacteristic
939C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
940C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
941C8—21no—
942C8—21no—
943C8—21no—
944C8—21no—
945C8—21no—
946C8—21no—
947C8—42no—
948C8—42no—
949C8—42no—
950C8—42no—
951C8—84no—
952C8—84no—
953C8#292912yes—
954C8C22×#13112yes—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—44no—
963C22—48no—
964C22—816no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—82no—
969C22—82no—
970C22—168no—
971C22—168no—
972C22#1790712yes—
973C22#3347112yes—
974C22C22×#44211yescharacteristic
975C4—21no—
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—82no—
986C4—84no—
987C4—82no—
988C4—82no—
989C4#1790712yes—
990C4C2×#292911yescharacteristic
991C4C2×#295511yescharacteristic
992C2—22no—
993C2—22no—
994C2—41no—
995C2—88no—
996C2—162no—
997C2C2×#1790711yescharacteristic
998C2C2×#3347111yescharacteristic
999C2#762263511yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623096C2
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. #6344823C2semidirect
3. C2×#17854C2semidirect
4. #483888C2semidirect
5. #483886C2semidirect
6. #483878C2semidirect
7. #483807C2semidirect
8. #483592C2semidirect
9. #483423C2semidirect
10. #481309C2semidirect
11. C2×#11667C2semidirect
12. #479969C2semidirect
30. #17972C22semidirect
32. #17970C22semidirect
33. #17963C22semidirect
35. #17899C22semidirect
37. #17858C22semidirect
52. #12078C22semidirect
53. #12077C22semidirect
54. #12067C22semidirect
55. #12065C22semidirect
56. #12031C22semidirect
57. #12028C22semidirect
58. #12000C22semidirect
61. #11653C22semidirect
62. #11652C22semidirect
63. #11651C22semidirect
64. #11597C22semidirect
66. #11416C22semidirect
67. #11415C22semidirect
68. #11406C22semidirect
69. #11405C22semidirect
162. #1594C23semidirect
163. #1593C23semidirect
172. #1580C23semidirect
173. #1579C23semidirect
211. #1368C23semidirect
212. #1334C23semidirect
214. #1333C23semidirect
215. #1313C23semidirect
216. #1313C23semidirect

Maximal subgroups

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

subgroupindex
#76230962
#63448232
C2×#178542
#4838882
#4838862
#4838782
#4838072
#4835922
#4834232
#4813092
C2×#116672
#4799692