Finite Group Databasebeta

← C2×#495897 #72320646

Subgroups — C2×#495897 #72320646

Order 1024.

4035 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#33605C211yesmaximal, characteristic
2C22×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
3C22×#2110C211yesmaximal, characteristic, complemented
4C2×#21547C211yesmaximal, characteristic, complemented
5C2×#21529C211yesmaximal, characteristic, complemented
6#495897C2116yesmaximal, direct product factor
7C2×#13249C211yesmaximal, characteristic, complemented
8C2×#13174C211yesmaximal, characteristic, complemented
9C2×#13155C211yesmaximal, characteristic, complemented
10C2×#13153C211yesmaximal, characteristic, complemented
11C2×#13067C211yesmaximal, characteristic, complemented
12C2×#13065C211yesmaximal, characteristic, complemented
13C2×#12831C211yesmaximal, characteristic, complemented
14C2×#12677C211yesmaximal, characteristic, complemented
15C2×#12650C211yesmaximal, characteristic, complemented
16C2×#12647C211yesmaximal, characteristic, complemented
17C22×#509C2211yescharacteristic
18C23×M32C2211yescharacteristic
19C23×M32C2211yescharacteristic
20C2×#3050C2211yescharacteristic
21C22×#466C2211yescharacteristic
22C22×#444C2211yescharacteristic
23C22×#442C2211yescharacteristic
24C2×#2930—21no—
25C22×#405C2211yescharacteristic
26C2×#2324—21no—
27#33605C418yescomplemented
28#33605C2218yes—
29C2×#2220C412yescomplemented
30C2×#2218C412yescomplemented
31C2×#2217C412yescomplemented
32C2×#2215C412yescomplemented
33C2×AGL(1,ℤ/16)—28no—
34C2×AGL(1,ℤ/16)C2218yescomplemented
35C2×#2159C2211yescharacteristic
36C22×#365C2211yescharacteristic
37C22×#365C2211yescharacteristic
38C22×#361C2211yescharacteristic
39C22×#361C2211yescharacteristic
40C22×#360C2211yescharacteristic
41C22×#360C2211yescharacteristic
42C2×#2139C2211yescharacteristic
43C2×#2140C2211yescharacteristic
44C2×#2110—28no—
45C2×#2110C2218yescomplemented
46C22×#347C2211yescharacteristic
47C22×#347C2211yescharacteristic
48C22×#347C2211yescharacteristic
49C22×#347C2211yescharacteristic
50#21547—24no—
51#21547C2218yescomplemented
52#21529—24no—
53#21529C2218yescomplemented
54C2×#1975C2211yescharacteristic
55C2×#1972C2211yescharacteristic
56C2×#1946C2211yescharacteristic
57C2×#1943C2211yescharacteristic
58C2×#1937—21no—
59C2×#1934—21no—
60C2×#1897—21no—
61C2×#1895—21no—
62C2×#1810C2211yescharacteristic
63C2×#1807C2211yescharacteristic
64C2×#1776C2211yescharacteristic
65C2×#1773C2211yescharacteristic
66C2×#1764—21no—
67C2×C4×#102—21no—
68#13249C2218yescomplemented
69#13174C2218yescomplemented
70#13155C2218yescomplemented
71#13153C2218yescomplemented
72#13067C2218yescomplemented
73#13065C2218yescomplemented
74#12831C2218yescomplemented
75#12677C2218yescomplemented
76#12650C2218yescomplemented
77#12647C2218yescomplemented
78C2×#1387C2211yescharacteristic
79C2×#1387C2211yescharacteristic
80C2×#1386C2211yescharacteristic
81C2×#1386C2211yescharacteristic
82C2×#1383C2211yescharacteristic
83C2×#1383C2211yescharacteristic
84C22×#135C2311yescharacteristic
85C23×D8C2311yescharacteristic
86C22×#131—21no—
87C23×M16D411yescharacteristic
88C24×C8C2311yescharacteristic
89C2×#525—21no—
90C22×#121—21no—
91C22×C4×D4—21no—
92C22×#117D411yescharacteristic
93C2×#509—24no—
94C2×#509—24no—
95C2×#509C2×C414yes—
96C2×#509C2314yes—
97C22×SD32C2×C412yes—
98C22×D16C2×C412yes—
99C22×M32—24no—
100C22×M32—24no—
101C22×M32—24no—
102C22×M32—24no—
103C22×M32—21no—
104C22×M32—22no—
105C22×M32C2×C412yescomplemented
106C22×M32C2×C414yescomplemented
107C22×M32C2314yes—
108C22×M32C2311yescharacteristic
109C22×M32C2311yescharacteristic
110C22×M32C2311yescharacteristic
111C22×M32C2311yescharacteristic
112C22×M32C2314yes—
113C23×C16—21no—
114C23×C16C2×C412yescomplemented
115#3050—22no—
116#3050—22no—
117#3050C2×C414yescomplemented
118#3050C2314yes—
119C2×#467C2×C411yescharacteristic, complemented
120C2×#467C2×C411yescharacteristic, complemented
121C2×#466—22no—
122C2×#466—21no—
123C2×#466—21no—
124C2×#466—22no—
125C2×#466C2×C412yes—
126C2×#466C2×C412yes—
127C2×#466C2×C414yes—
128C2×#466C2×C411yescharacteristic, complemented
129C2×#466C2×C411yescharacteristic, complemented
130C2×#466C2314yes—
131C2×#465—21no—
132C2×#465—21no—
133C2×#444—22no—
134C2×#444—24no—
135C2×#444—24no—
136C2×#444C2314yes—
137C2×#442—22no—
138C2×#442—24no—
139C2×#442—24no—
140C2×#442C2314yes—
141#2930—28no—
142#2930—44no—
143C2×#436—41no—
144C2×#436—41no—
145C2×#435—41no—
146C2×#435—41no—
147C22×#108C2311yescharacteristic
148C22×#108C2311yescharacteristic
149C2×#427C2311yescharacteristic
150C22×#107C2311yescharacteristic
151C22×#106C2311yescharacteristic
152C22×#106C2311yescharacteristic
153C2×#424—21no—
154C22×#104—21no—
155C22×#104—21no—
156C2×#416—21no—
157C22×#102—21no—
158C22×#102—21no—
159C22×#102—21no—
160C2×#408—21no—
161C2×#407—21no—
162C2×#405—24no—
163C2×#405—24no—
164C2×#405—21no—
165C2×#405D414yes—
166C2×#405C2314yes—
167C22×#97C2311yescharacteristic
168C22×#97C2311yescharacteristic
169C22×C4×C8D411yescharacteristic
170C22×C4×C8D411yescharacteristic
171#2324—28no—
172#2324—44no—
173C2×#390—21no—
174C2×#390—41no—
175C2×#389—21no—
176C2×#388—41no—
177C2×#386—41no—
178C2×#385—41no—
179C2×#380—21no—
180C2×C4×C4⋊C4—21no—
181#2220C2×C4116yescomplemented
182#2218C2×C4116yescomplemented
183#2217C2×C4116yescomplemented
184#2215C2×C4116yescomplemented
185AGL(1,ℤ/16)—232no—
186#2159C2×C414yescomplemented
187#2159C2314yes—
188C2×#367C2×C412yescomplemented
189C2×#366C2×C412yescomplemented
190C2×#365—24no—
191C2×#365—24no—
192C2×#365C2314yes—
193C2×#365C2314yes—
194C2×#361—24no—
195C2×#361—24no—
196C2×#361C2314yes—
197C2×#361C2314yes—
198C2×#360—24no—
199C2×#360—24no—
200C2×#360C2314yes—
201C2×#360C2314yes—
202#2140C2×C414yes—
203#2140C2314yes—
204#2139C2×C414yescomplemented
205#2139C2314yes—
206C2×#358C2×C412yescomplemented
207C2×#357C2×C412yes—
208C2×#357C2×C412yes—
209C2×#357C2×C412yescomplemented
210#2110—232no—
211C2×#347—24no—
212C2×#347—24no—
213C2×#347—24no—
214C2×#347D418yescomplemented
215C2×#347C2314yes—
216C2×#347C2314yes—
217C2×#347C2314yes—
218C2×#347C2314yes—
219#1975—22no—
220#1975C2314yes—
221#1972—22no—
222#1972C2314yes—
223#1946—22no—
224#1946C2314yes—
225#1943—22no—
226#1943C2314yes—
227#1937—28no—
228#1934—28no—
229#1897—28no—
230#1895—28no—
231#1810—22no—
232#1810C2314yes—
233#1807—22no—
234#1807C2314yes—
235#1776—22no—
236#1776C2314yes—
237#1773—22no—
238#1773C2314yes—
239#1764—28no—
240C4×#102—28no—
241C2×#341—21no—
242C2×#340—21no—
243C2×#340—21no—
244C2×#340—21no—
245C2×#339—21no—
246C2×#339—21no—
247#1387C2314yes—
248#1387C2314yes—
249#1386C2314yes—
250#1386C2314yes—
251#1383C2314yes—
252#1383C2314yes—
253C22×#41—21no—
254C23×D4—21no—
255C23×D4—41no—
256C24×C4—41no—
257C24×C4C2×D411yescharacteristic
258C2×#135—21no—
259C2×#135—22no—
260C2×#135—21no—
261C2×#135—22no—
262C2×#135—22no—
263C2×#135—22no—
264C2×#135C22×C412yes—
265C2×#135C2412yes—
266C22×Q16C22×C411yescharacteristic
267C22×SD16—21no—
268C22×D8—22no—
269C22×D8—21no—
270C22×D8—22no—
271C22×D8—22no—
272C22×D8—22no—
273C22×D8—21no—
274C22×D8—21no—
275C22×D8C22×C411yescharacteristic
276C22×D8C22×C412yes—
277C22×D8C22×C412yes—
278C22×D8C2412yes—
279C2×#131—24no—
280C2×#131—42no—
281C2×#131—44no—
282C2×#131—44no—
283C22×M16—21no—
284C22×M16—21no—
285C22×M16—22no—
286C22×M16—24no—
287C22×M16—21no—
288C22×M16—21no—
289C22×M16—42no—
290C22×M16—41no—
291C22×M16C2×D414yes—
292C23×C8—22no—
293C23×C8—22no—
294C23×C8—22no—
295C23×C8—22no—
296C23×C8—41no—
297C23×C8C22×C411yescharacteristic
298C23×C8C22×C411yescharacteristic
299C23×C8C22×C412yes—
300C23×C8C2×D411yescharacteristic
301C23×C8C2×D412yes—
302C23×C8C2×D411yescharacteristic
303C23×C8C2×D411yescharacteristic
304C23×C8#4111yescharacteristic
305C23×C8#4111yescharacteristic
306C23×C8#4112yes—
307C23×C8C2412yes—
308C23×C8C2411yescharacteristic
309#525—24no—
310#525—24no—
311#525—42no—
312#525—42no—
313C2×#123—41no—
314C2×C22⋊Q8—21no—
315C2×C22⋊Q8—21no—
316C2×#121—22no—
317C2×#121—22no—
318C2×#121—24no—
319C2×#121—21no—
320C2×#121—21no—
321C2×#121—24no—
322C2×#121—42no—
323C2×#121—41no—
324C2×#121—41no—
325C2×#121—42no—
326C2×#120—41no—
327C2×C4×D4—24no—
328C2×C4×D4—42no—
329C2×C4×D4—44no—
330C2×C4×D4—41no—
331C2×C4×D4—41no—
332C2×C4×D4—44no—
333C2×#117—22no—
334C2×#117—24no—
335C2×#117—21no—
336C2×#117—42no—
337C2×#117C2×D414yes—
338C22×C4⋊C4—21no—
339C22×C4⋊C4—21no—
340C22×C4⋊C4—21no—
341C22×C4⋊C4—21no—
342C22×C4⋊C4—41no—
343C22×C22⋊C4—21no—
344C22×C22⋊C4—41no—
345C22×C22⋊C4—41no—
346C22×C22⋊C4—41no—
347C22×C22⋊C4—41no—
348C22×C22⋊C4—41no—
349C22×C42—41no—
350C22×C42C2×D411yescharacteristic
351C22×C42C2×D411yescharacteristic
352#509—216no—
353#509—28no—
354#509—28no—
355C2×SD32—28no—
356C2×SD32C22×C418yes—
357C2×D16—28no—
358C2×D16C22×C418yes—
359C2×M32—216no—
360C2×M32—28no—
361C2×M32—22no—
362C2×M32—22no—
363C2×M32—22no—
364C2×M32—22no—
365C2×M32—24no—
366C2×M32—21no—
367C2×M32—21no—
368C2×M32—216no—
369C2×M32—28no—
370C2×M32—28no—
371C2×M32—28no—
372C2×M32—28no—
373C2×M32—28no—
374C2×M32C22×C412yes—
375C2×M32C22×C412yes—
376C2×M32C22×C418yescomplemented
377C2×M32C2×D414yes—
378C2×M32C2×D414yes—
379C2×M32#4114yes—
380C2×M32#4114yes—
381C2×M32C2412yes—
382C2×M32C2412yes—
383C2×M32C2412yes—
384C2×M32C2412yes—
385C22×C16—28no—
386C22×C16—24no—
387C22×C16—21no—
388C22×C16—21no—
389C22×C16—28no—
390C22×C16C22×C412yes—
391C22×C16C22×C412yes—
392C22×C16C22×C418yescomplemented
393#467—22no—
394#467—22no—
395#467C22×C414yescomplemented
396#467C22×C414yescomplemented
397#466—24no—
398#466—24no—
399#466—24no—
400#466—24no—
401#466—22no—
402#466—22no—
403#466—24no—
404#466—24no—
405#466C22×C418yes—
406#466C22×C418yes—
407#466C22×C414yescomplemented
408#466C22×C414yescomplemented
409#465—24no—
410#465—24no—
411#465—24no—
412#465—24no—
413#444—28no—
414#444—28no—
415#444—48no—
416#442—28no—
417#442—28no—
418#442—48no—
419#436—48no—
420#436—48no—
421#435—48no—
422#435—48no—
423C2×#108—22no—
424C2×#108—22no—
425C2×#108—22no—
426C2×#108—22no—
427C2×#108—21no—
428C2×#108—21no—
429C2×#108C2412yes—
430C2×#108C2412yes—
431#427—21no—
432#427—21no—
433#427C22×C412yes—
434#427C2412yes—
435C2×#107—21no—
436C2×#107—21no—
437C2×#107—21no—
438C2×#107C22×C411yescharacteristic
439C2×#107C22×C411yescharacteristic
440C2×#107C22×C412yes—
441C2×#107C22×C412yes—
442C2×#107C2412yes—
443C2×#106—21no—
444C2×#106—22no—
445C2×#106—22no—
446C2×#106—22no—
447C2×#106—22no—
448C2×#106—21no—
449C2×#106—21no—
450C2×#106C2412yes—
451C2×#106C2412yes—
452#424—24no—
453#424—42no—
454C2×C4⋊C8—41no—
455C2×C4⋊C8—41no—
456C2×#104—24no—
457C2×#104—24no—
458C2×#104—44no—
459C2×#104—44no—
460#416—24no—
461#416—24no—
462C2×#103—21no—
463C2×#103—21no—
464C2×#102—22no—
465C2×#102—22no—
466C2×#102—24no—
467C2×#102—21no—
468C2×#102—21no—
469C2×#102—24no—
470C2×#102—24no—
471C2×#102—24no—
472C2×#102—44no—
473C2×#102—44no—
474#408—24no—
475#408—42no—
476#407—24no—
477#407—42no—
478C2×C22⋊C8—41no—
479C2×C22⋊C8—41no—
480C2×C22⋊C8—41no—
481C2×C22⋊C8—41no—
482#405—216no—
483#405—28no—
484#405—28no—
485#405—24no—
486#405—42no—
487C2×#97—22no—
488C2×#97—22no—
489C2×#97—41no—
490C2×#97C2×D412yes—
491C2×#97C2×D412yes—
492C2×#97C2×D414yes—
493C2×#97#4114yes—
494C2×#97C2412yes—
495C2×#97C2412yes—
496C2×C4×C8—24no—
497C2×C4×C8—24no—
498C2×C4×C8—41no—
499C2×C4×C8C2×D414yes—
500C2×C4×C8C2×D414yes—
501#390—24no—
502#390—42no—
503#390—48no—
504#389—24no—
505#389—42no—
506#388—48no—
507#386—48no—
508#385—48no—
509#380—24no—
510#380—42no—
511C4×C4⋊C4—24no—
512C4×C4⋊C4—42no—
513C2×#95—41no—
514C2×#95—41no—
515C2×#95—41no—
516#367C22×C418yescomplemented
517#366C22×C418yescomplemented
518#365—28no—
519#365—28no—
520#361—28no—
521#361—28no—
522#360—28no—
523#360—28no—
524#358C22×C418yescomplemented
525#357C22×C418yes—
526#357C22×C418yes—
527#357C22×C418yescomplemented
528#347—28no—
529#347—28no—
530#347—28no—
531#347C2×D4116yescomplemented
532#341—24no—
533#340—24no—
534#340—24no—
535#340—24no—
536#339—24no—
537#339—24no—
538C25—41no—
539C25AGL(1,ℤ/8)11yescharacteristic
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—41no—
543C2×#41—41no—
544C2×#41—42no—
545C2×#41—42no—
546C2×#41—42no—
547C2×#41—42no—
548C22×Q8—21no—
549C22×D4—22no—
550C22×D4—22no—
551C22×D4—21no—
552C22×D4—22no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—41no—
556C22×D4—41no—
557C22×D4—44no—
558C22×D4—42no—
559C22×D4—42no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4—41no—
565C22×D4—42no—
566C22×D4—42no—
567C22×D4—162no—
568C22×D4—162no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4—44no—
576C23×C4—41no—
577C23×C4—41no—
578C23×C4—41no—
579C23×C4—41no—
580C23×C4—84no—
581C23×C4—162no—
582C23×C4—162no—
583C23×C4C4×D411yescharacteristic
584C23×C4C4×D411yescharacteristic
585C23×C4C4×D412yes—
586C23×C4AGL(1,ℤ/8)11yescharacteristic
587C23×C4AGL(1,ℤ/8)11yescharacteristic
588C23×C4AGL(1,ℤ/8)12yes—
589C23×C4AGL(1,ℤ/8)11yescharacteristic
590C23×C4AGL(1,ℤ/8)12yes—
591C23×C4C22×D412yes—
592C23×C4C22×D411yescharacteristic
593#135—24no—
594#135—24no—
595#135—22no—
596#135—22no—
597#135—22no—
598#135—22no—
599#135—42no—
600#135—42no—
601#135—42no—
602#135—42no—
603C2×Q16—22no—
604C2×Q16—21no—
605C2×Q16—22no—
606C2×Q16C23×C412yes—
607C2×SD16—22no—
608C2×SD16—22no—
609C2×SD16—42no—
610C2×SD16—42no—
611C2×D8—24no—
612C2×D8—24no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—21no—
617C2×D8—24no—
618C2×D8—24no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—42no—
626C2×D8—42no—
627C2×D8—42no—
628C2×D8—42no—
629C2×D8—42no—
630C2×D8—42no—
631C2×D8C23×C414yes—
632C2×D8C23×C412yes—
633#131—48no—
634#131—48no—
635#131—88no—
636C2×M16—24no—
637C2×M16—24no—
638C2×M16—28no—
639C2×M16—22no—
640C2×M16—22no—
641C2×M16—44no—
642C2×M16—44no—
643C2×M16—44no—
644C2×M16—48no—
645C2×M16—44no—
646C2×M16—41no—
647C2×M16—41no—
648C2×M16—42no—
649C2×M16—42no—
650C2×M16—42no—
651C2×M16—42no—
652C2×M16—84no—
653C22×C8—22no—
654C22×C8—22no—
655C22×C8—21no—
656C22×C8—21no—
657C22×C8—22no—
658C22×C8—22no—
659C22×C8—24no—
660C22×C8—22no—
661C22×C8—22no—
662C22×C8—22no—
663C22×C8—24no—
664C22×C8—24no—
665C22×C8—22no—
666C22×C8—24no—
667C22×C8—22no—
668C22×C8—22no—
669C22×C8—22no—
670C22×C8—24no—
671C22×C8—24no—
672C22×C8—22no—
673C22×C8—22no—
674C22×C8—22no—
675C22×C8—22no—
676C22×C8—22no—
677C22×C8—21no—
678C22×C8—21no—
679C22×C8—22no—
680C22×C8—44no—
681C22×C8—41no—
682C22×C8—41no—
683C22×C8—84no—
684C22×C8C4×D411yescharacteristic
685C22×C8C4×D411yescharacteristic
686C22×C8C4×D412yes—
687C22×C8C4×D412yes—
688C22×C8C4×D412yes—
689C22×C8C4×D412yes—
690C22×C8C4×D412yes—
691C22×C8#12114yes—
692C22×C8C23×C412yes—
693C22×C8C23×C412yes—
694C22×C8C23×C411yescharacteristic
695C22×C8C23×C411yescharacteristic
696C22×C8C22×D412yes—
697C22×C8C22×D412yes—
698C22×C8C22×D412yes—
699C22×C8C22×D411yescharacteristic
700C22×C8C22×D412yes—
701C22×C8C2×#4112yes—
702C22×C8C2×#4112yes—
703C22×C8C2×#4112yes—
704C22×C8C2×#4111yescharacteristic
705C22×C8C2×#4111yescharacteristic
706C22×C8C2×#4112yes—
707C22×C8C2×#4112yes—
708C22×C8C2511yescharacteristic
709#123—44no—
710#123—44no—
711C22⋊Q8—24no—
712C22⋊Q8—24no—
713C22⋊Q8—42no—
714C22⋊Q8—42no—
715#121—28no—
716#121—28no—
717#121—24no—
718#121—24no—
719#121—44no—
720#121—44no—
721#121—44no—
722#121—44no—
723#121—44no—
724#121—44no—
725#121—42no—
726#121—42no—
727#120—44no—
728#120—44no—
729C4×D4—48no—
730C4×D4—44no—
731C4×D4—44no—
732C4×D4—44no—
733C4×D4—44no—
734C4×D4—48no—
735C4×D4—88no—
736#117—28no—
737#117—22no—
738#117—22no—
739#117—44no—
740#117—48no—
741#117—41no—
742#117—41no—
743C2×C4⋊C4—22no—
744C2×C4⋊C4—22no—
745C2×C4⋊C4—21no—
746C2×C4⋊C4—21no—
747C2×C4⋊C4—22no—
748C2×C4⋊C4—24no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—44no—
752C2×C4⋊C4—41no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—42no—
758C2×C4⋊C4—42no—
759C2×C4⋊C4—42no—
760C2×C4⋊C4—42no—
761C2×C4⋊C4—41no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—44no—
764C2×C4⋊C4—162no—
765C2×C22⋊C4—24no—
766C2×C22⋊C4—44no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—44no—
771C2×C22⋊C4—44no—
772C2×C22⋊C4—42no—
773C2×C22⋊C4—42no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—44no—
777C2×C22⋊C4—44no—
778C2×C22⋊C4—44no—
779C2×C22⋊C4—44no—
780C2×C22⋊C4—84no—
781C2×C22⋊C4—162no—
782C2×C22⋊C4—162no—
783C2×C22⋊C4—162no—
784C2×C42—21no—
785C2×C42—22no—
786C2×C42—22no—
787C2×C42—22no—
788C2×C42—21no—
789C2×C42—41no—
790C2×C42—44no—
791C2×C42—162no—
792C2×C42#12114yes—
793C2×C42C22×D412yes—
794C2×C42C22×D412yes—
795SD32—216no—
796D16—216no—
797M32—216no—
798M32—24no—
799M32—24no—
800M32—24no—
801M32—22no—
802M32—22no—
803M32—22no—
804M32—22no—
805M32—216no—
806M32C4×D418yes—
807M32C22×D414yes—
808M32C22×D414yes—
809M32C2×#4114yes—
810M32C2×#4114yes—
811C2×C16—216no—
812C2×C16—24no—
813C2×C16—24no—
814C2×C16—24no—
815C2×C16—22no—
816C2×C16—22no—
817C2×C16—216no—
818C2×C16C4×D418yes—
819C2×C16C23×C414yes—
820C2×C16C23×C414yes—
821#108—22no—
822#108—22no—
823#108—22no—
824#108—22no—
825#108—42no—
826#108—42no—
827#107—22no—
828#107—22no—
829#107—21no—
830#107—21no—
831#107—22no—
832#107C23×C412yes—
833#107C23×C412yes—
834#107C23×C414yes—
835#106—22no—
836#106—22no—
837#106—22no—
838#106—22no—
839#106—22no—
840#106—22no—
841#106—42no—
842#106—42no—
843C4⋊C8—44no—
844C4⋊C8—44no—
845#104—48no—
846#104—48no—
847#103—24no—
848#103—24no—
849#102—28no—
850#102—28no—
851#102—24no—
852#102—24no—
853#102—48no—
854#102—48no—
855C22⋊C8—44no—
856C22⋊C8—44no—
857C22⋊C8—44no—
858C22⋊C8—44no—
859#97—24no—
860#97—22no—
861#97—22no—
862#97—44no—
863#97#12118yes—
864#97C22×D414yes—
865#97C2×#4114yes—
866C4×C8—28no—
867C4×C8—28no—
868C4×C8—44no—
869#95—44no—
870#95—44no—
871#95—44no—
872C24—22no—
873C24—22no—
874C24—42no—
875C24—42no—
876C24—42no—
877C24—41no—
878C24—42no—
879C24—42no—
880C24—82no—
881C24—82no—
882C24—82no—
883C24—82no—
884C24—82no—
885C24—82no—
886C24#44211yescharacteristic
887C24#44211yescharacteristic
888C24#44212yes—
889C24C2×AGL(1,ℤ/8)11yescharacteristic
890C24C2×AGL(1,ℤ/8)12yes—
891#41—42no—
892#41—42no—
893#41—44no—
894#41—44no—
895#41—42no—
896#41—42no—
897#41—82no—
898#41—82no—
899#41—82no—
900#41—82no—
901C2×Q8—22no—
902C2×Q8—41no—
903C2×Q8—42no—
904C2×Q8—42no—
905C2×D4—24no—
906C2×D4—22no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—48no—
912C2×D4—48no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—41no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—82no—
928C2×D4—82no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—82no—
932C2×D4—82no—
933C2×D4—82no—
934C2×D4—82no—
935C2×D4—162no—
936C2×D4—162no—
937C2×D4—164no—
938C2×D4—164no—
939C2×D4—164no—
940C2×D4—164no—
941C2×D4—168no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—24no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—24no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—24no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—42no—
973C22×C4—41no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—88no—
981C22×C4—82no—
982C22×C4—82no—
983C22×C4—82no—
984C22×C4—82no—
985C22×C4—82no—
986C22×C4—82no—
987C22×C4—82no—
988C22×C4—82no—
989C22×C4—82no—
990C22×C4—82no—
991C22×C4—164no—
992C22×C4—164no—
993C22×C4—1616no—
994C22×C4#44212yes—
995C22×C4#44212yes—
996C22×C4#44212yes—
997C22×C4#44212yes—
998C22×C4#44212yes—
999C22×C4#44211yescharacteristic
1000C22×C4#44211yescharacteristic
1001C22×C4C2×C4×D412yes—
1002C22×C4C2×C4×D412yes—
1003C22×C4C2×C4×D411yescharacteristic
1004C22×C4C2×C4×D411yescharacteristic
1005C22×C4C2×#12112yes—
1006C22×C4#53212yes—
1007C22×C4C2×AGL(1,ℤ/8)12yes—
1008C22×C4C2×AGL(1,ℤ/8)12yes—
1009C22×C4C2×AGL(1,ℤ/8)12yes—
1010C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1011C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1012C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
1013C22×C4#57512yes—
1014C22×C4#57512yes—
1015C22×C4C23×D411yescharacteristic
1016Q16—22no—
1017Q16—22no—
1018Q16—42no—
1019SD16—42no—
1020SD16—42no—
1021SD16—44no—
1022D8—22no—
1023D8—24no—
1024D8—24no—
1025D8—22no—
1026D8—42no—
1027D8—42no—
1028D8—44no—
1029D8—44no—
1030D8—42no—
1031M16—48no—
1032M16—48no—
1033M16—42no—
1034M16—42no—
1035M16—42no—
1036M16—42no—
1037M16—88no—
1038M16—82no—
1039M16—82no—
1040C2×C8—22no—
1041C2×C8—22no—
1042C2×C8—24no—
1043C2×C8—24no—
1044C2×C8—22no—
1045C2×C8—22no—
1046C2×C8—22no—
1047C2×C8—24no—
1048C2×C8—22no—
1049C2×C8—22no—
1050C2×C8—22no—
1051C2×C8—22no—
1052C2×C8—22no—
1053C2×C8—22no—
1054C2×C8—22no—
1055C2×C8—22no—
1056C2×C8—22no—
1057C2×C8—24no—
1058C2×C8—24no—
1059C2×C8—24no—
1060C2×C8—24no—
1061C2×C8—22no—
1062C2×C8—22no—
1063C2×C8—22no—
1064C2×C8—42no—
1065C2×C8—42no—
1066C2×C8—42no—
1067C2×C8—42no—
1068C2×C8—88no—
1069C2×C8—82no—
1070C2×C8—82no—
1071C2×C8C2×C4×D412yes—
1072C2×C8C2×C4×D412yes—
1073C2×C8C2×C4×D412yes—
1074C2×C8C2×C4×D412yes—
1075C2×C8C2×C4×D411yescharacteristic
1076C2×C8C2×C4×D411yescharacteristic
1077C2×C8C4×#4112yes—
1078C2×C8C4×#4112yes—
1079C2×C8C2×#12114yes—
1080C2×C8C2×#12112yes—
1081C2×C8#52512yes—
1082C2×C8#52512yes—
1083C2×C8#52912yes—
1084C2×C8#52912yes—
1085C2×C8#53212yes—
1086C2×C8C24×C411yescharacteristic
1087C2×C8C23×D411yescharacteristic
1088C2×C8C22×#4111yescharacteristic
1089C2×C8C22×#4111yescharacteristic
1090C2×C8C22×#4111yescharacteristic
1091C2×C8C22×#4111yescharacteristic
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—48no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—82no—
1108C4⋊C4—82no—
1109C4⋊C4—164no—
1110C22⋊C4—48no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—42no—
1115C22⋊C4—48no—
1116C22⋊C4—48no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—88no—
1120C22⋊C4—164no—
1121C22⋊C4—164no—
1122C22⋊C4—164no—
1123C42—24no—
1124C42—22no—
1125C42—22no—
1126C42—22no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—164no—
1131C42C2×#12114yes—
1132C16—24no—
1133C16—24no—
1134C16—24no—
1135C16C2×C4×D418yes—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—24no—
1146C23—22no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—42no—
1151C23—42no—
1152C23—44no—
1153C23—84no—
1154C23—84no—
1155C23—82no—
1156C23—82no—
1157C23—82no—
1158C23—84no—
1159C23—82no—
1160C23—84no—
1161C23—82no—
1162C23—82no—
1163C23—84no—
1164C23—84no—
1165C23—82no—
1166C23—82no—
1167C23—84no—
1168C23—84no—
1169C23—82no—
1170C23—164no—
1171C23—164no—
1172C23—164no—
1173C23—164no—
1174C23C2×#44212yes—
1175C23C2×#44212yes—
1176C23C2×#44211yescharacteristic
1177C23C2×#44211yescharacteristic
1178C23#305512yes—
1179C23#318012yes—
1180C23C22×AGL(1,ℤ/8)11yescharacteristic
1181Q8—42no—
1182Q8—42no—
1183Q8—82no—
1184D4—44no—
1185D4—42no—
1186D4—44no—
1187D4—42no—
1188D4—82no—
1189D4—84no—
1190D4—82no—
1191D4—82no—
1192D4—84no—
1193D4—84no—
1194D4—82no—
1195D4—82no—
1196D4—164no—
1197D4—164no—
1198D4—168no—
1199D4—168no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—42no—
1219C2×C4—48no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—44no—
1227C2×C4—42no—
1228C2×C4—82no—
1229C2×C4—82no—
1230C2×C4—84no—
1231C2×C4—84no—
1232C2×C4—82no—
1233C2×C4—82no—
1234C2×C4—84no—
1235C2×C4—82no—
1236C2×C4—82no—
1237C2×C4—84no—
1238C2×C4—82no—
1239C2×C4—82no—
1240C2×C4—82no—
1241C2×C4—82no—
1242C2×C4—82no—
1243C2×C4—82no—
1244C2×C4—82no—
1245C2×C4—1616no—
1246C2×C4—164no—
1247C2×C4—164no—
1248C2×C4C4×#12112yes—
1249C2×C4C4×#12112yes—
1250C2×C4C2×#44212yes—
1251C2×C4C2×#44212yes—
1252C2×C4C2×#44211yescharacteristic
1253C2×C4C2×#44211yescharacteristic
1254C2×C4#294312yes—
1255C2×C4#294312yes—
1256C2×C4#305512yes—
1257C2×C4#305512yes—
1258C2×C4#305512yes—
1259C2×C4#318012yes—
1260C2×C4#318012yes—
1261C2×C4#318012yes—
1262C2×C4C22×C4×D411yescharacteristic
1263C2×C4C22×#12111yescharacteristic
1264C2×C4C2×#53211yescharacteristic
1265C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1266C2×C4C2×#57511yescharacteristic
1267C2×C4C2×#57511yescharacteristic
1268C8—24no—
1269C8—22no—
1270C8—22no—
1271C8—42no—
1272C8—82no—
1273C8—82no—
1274C8C4×#12112yes—
1275C8C4×#12112yes—
1276C8C22×C4×D411yescharacteristic
1277C8C2×C4×#4111yescharacteristic
1278C8C2×#52511yescharacteristic
1279C8C2×#52911yescharacteristic
1280C22—24no—
1281C22—24no—
1282C22—21no—
1283C22—21no—
1284C22—21no—
1285C22—21no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—44no—
1293C22—44no—
1294C22—82no—
1295C22—82no—
1296C22—84no—
1297C22—82no—
1298C22—84no—
1299C22—84no—
1300C22—82no—
1301C22—82no—
1302C22—84no—
1303C22—162no—
1304C22—162no—
1305C22—162no—
1306C22—162no—
1307C22—168no—
1308C22—164no—
1309C22—168no—
1310C22#2152612yes—
1311C22#2152612yes—
1312C22#3346912yes—
1313C22#3347112yes—
1314C22C22×#44211yescharacteristic
1315C22C2×#305511yescharacteristic
1316C22C2×#318011yescharacteristic
1317C4—22no—
1318C4—22no—
1319C4—44no—
1320C4—82no—
1321C4—82no—
1322C4—84no—
1323C4—82no—
1324C4—82no—
1325C4—162no—
1326C4—162no—
1327C4#2152612yes—
1328C4#2152612yes—
1329C4C2×C4×#12111yescharacteristic
1330C4C2×#294311yescharacteristic
1331C4C2×#305511yescharacteristic
1332C4C2×#318011yescharacteristic
1333C2—21no—
1334C2—21no—
1335C2—22no—
1336C2—42no—
1337C2—42no—
1338C2—162no—
1339C2—164no—
1340C2#49589714yesdirect product factor
1341C2C2×#2152611yescharacteristic
1342C2C2×#3346911yescharacteristic
1343C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC23C2×#442
commutatorC2×C8C24×C4
Frattini, cosocleC22×C8C25
prime radicalC2×#33605C2
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×AGL(1,ℤ/16)C2semidirect
3. C22×#2110C2semidirect
4. C2×#21547C2semidirect
5. C2×#21529C2semidirect
6. #495897C2direct (N × H)
7. C2×#13249C2semidirect
8. C2×#13174C2semidirect
9. C2×#13155C2semidirect
10. C2×#13153C2semidirect
11. C2×#13067C2semidirect
12. C2×#13065C2semidirect
13. C2×#12831C2semidirect
14. C2×#12677C2semidirect
15. C2×#12650C2semidirect
16. C2×#12647C2semidirect
27. #33605C4semidirect
29. C2×#2220C4semidirect
30. C2×#2218C4semidirect
31. C2×#2217C4semidirect
32. C2×#2215C4semidirect
34. C2×AGL(1,ℤ/16)C22semidirect
45. C2×#2110C22semidirect
51. #21547C22semidirect
53. #21529C22semidirect
68. #13249C22semidirect
69. #13174C22semidirect
70. #13155C22semidirect
71. #13153C22semidirect
72. #13067C22semidirect
73. #13065C22semidirect
74. #12831C22semidirect
75. #12677C22semidirect
76. #12650C22semidirect
77. #12647C22semidirect
105. C22×M32C2×C4semidirect
106. C22×M32C2×C4semidirect
114. C23×C16C2×C4semidirect
117. #3050C2×C4semidirect
119. C2×#467C2×C4semidirect
120. C2×#467C2×C4semidirect
128. C2×#466C2×C4semidirect
129. C2×#466C2×C4semidirect
181. #2220C2×C4semidirect
182. #2218C2×C4semidirect
183. #2217C2×C4semidirect
184. #2215C2×C4semidirect
186. #2159C2×C4semidirect
188. C2×#367C2×C4semidirect
189. C2×#366C2×C4semidirect
204. #2139C2×C4semidirect
206. C2×#358C2×C4semidirect
209. C2×#357C2×C4semidirect
214. C2×#347D4semidirect
376. C2×M32C22×C4semidirect
392. C22×C16C22×C4semidirect
395. #467C22×C4semidirect
396. #467C22×C4semidirect
407. #466C22×C4semidirect
408. #466C22×C4semidirect
516. #367C22×C4semidirect
517. #366C22×C4semidirect
524. #358C22×C4semidirect
527. #357C22×C4semidirect
531. #347C2×D4semidirect
1340. C2#495897direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#336052
C22×AGL(1,ℤ/16)2
C22×#21102
C2×#215472
C2×#215292
#4958972
C2×#132492
C2×#131742
C2×#131552
C2×#131532
C2×#130672
C2×#130652
C2×#128312
C2×#126772
C2×#126502
C2×#126472