Finite Group Databasebeta

← C2×#72225082 #72320139

Subgroups — C2×#72225082 #72320139

Order 2048.

2346 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#129176C211yesmaximal, characteristic, complemented
2C2×#483596C211yesmaximal, characteristic
3#72225082C218yesmaximal, direct product factor
4C2×#149504C211yesmaximal, characteristic, complemented
5C2×#94031C211yesmaximal, characteristic, complemented
6C2×#94056C211yesmaximal, characteristic, complemented
7C22×#7390C211yesmaximal, characteristic
8C2×#151969C211yesmaximal, characteristic
9C22×#2177C2211yescharacteristic
10C2×#17854—21no—
11C22×#1419C411yescharacteristic
12C2×#13617C411yescharacteristic
13C22×#1398C2211yescharacteristic
14C22×#1398C2211yescharacteristic
15C2×#12671C2211yescharacteristic
16C2×#12667—21no—
17#483596—22no—
18#483596—22no—
19#483596C414yescomplemented
20#483596C2214yes—
21C2×#12067—22no—
22C2×#12067C414yescomplemented
23C22×#1369C2211yescharacteristic
24C2×#11999C2211yescharacteristic
25C2×#11599—21no—
26C2×#11405C2211yescharacteristic
27#151969C414yes—
28#151969C2214yes—
29C2×#7477C411yescharacteristic
30C2×#7474C411yescharacteristic
31C2×#7390C414yescomplemented
32C2×#7390C414yescomplemented
33C2×#7390C2214yes—
34#149504—22no—
35#149504C2214yescomplemented
36C2×#7333—22no—
37#129176—22no—
38#129176C2214yescomplemented
39C2×#7181—21no—
40#94056C2214yescomplemented
41#94031C2214yescomplemented
42C23×D16C2×C411yescharacteristic
43C2×#2972—41no—
44C22×C4×D8—21no—
45C22×M64—21no—
46C22×M64C2×C411yescharacteristic
47C22×M64C2×C411yescharacteristic
48C2×#2177—21no—
49C2×#2177—21no—
50C2×#2177—21no—
51C2×#2177—21no—
52C2×#2177—21no—
53C2×#2177—21no—
54C2×#2177C2×C412yes—
55C2×#2177C2×C412yes—
56C2×#2177C2×C412yes—
57C2×#2177C2×C412yes—
58C2×#2177C2×C412yes—
59C2×#2177C2312yes—
60C22×#368C2×C411yescharacteristic
61C2×#2158C2×C411yescharacteristic
62C22×#367C2×C411yescharacteristic
63C22×#364—21no—
64C22×#357—21no—
65C2×#2110—41no—
66C2×C4×M32D411yescharacteristic
67C22×#346C2311yescharacteristic
68C2×#1772—21no—
69#17854—24no—
70#17854—24no—
71#17854—42no—
72#17854—42no—
73C2×#1580—24no—
74C2×C8×D8—42no—
75C2×#1564—21no—
76C2×#1478—41no—
77C2×#1450D411yescharacteristic
78C2×#1419—22no—
79C2×#1419—22no—
80C2×#1419C2×C414yes—
81#13617—22no—
82#13617C2×C414yes—
83C2×#1415—22no—
84C2×#1398—21no—
85C2×#1398—21no—
86C2×#1398—21no—
87C2×#1398—21no—
88C2×#1398—21no—
89C2×#1398—21no—
90C2×#1398—21no—
91C2×#1398C2×C412yes—
92C2×#1398C2×C412yes—
93C2×#1398C2×C412yes—
94C2×#1398C2312yes—
95C2×#1398C2312yes—
96#12671—21no—
97#12671—21no—
98#12671C2×C412yes—
99#12671C2312yes—
100#12667—24no—
101#12667—42no—
102C2×#1382—21no—
103C2×#1378—41no—
104#12067—28no—
105#12067—28no—
106#12067—28no—
107#12067C2×C4116yescomplemented
108C2×#1369—21no—
109C2×#1369—21no—
110C2×#1369—21no—
111C2×#1369C2×C412yes—
112C2×#1369C2×C412yes—
113C2×#1369C2312yes—
114#11999—21no—
115#11999—21no—
116#11999C2×C412yes—
117#11999C2312yes—
118C2×#1368—21no—
119C2×#1368C2×C412yes—
120#11599—24no—
121#11599—24no—
122C2×#1333—24no—
123#11405C2×C412yes—
124#11405D412yes—
125#11405D412yes—
126#11405C2312yes—
127C2×#1313C2×C412yes—
128C2×#1313D412yes—
129#7477C2×C414yes—
130#7474C2×C414yes—
131#7390C2×C4116yescomplemented
132#7333—28no—
133#7181—24no—
134C23×D8—21no—
135C22×C4×D4—41no—
136C22×D16—21no—
137C22×D16—21no—
138C22×D16—21no—
139C22×D16—21no—
140C22×D16—21no—
141C22×D16—21no—
142C22×D16—21no—
143C22×D16C4212yes—
144C22×D16C4212yes—
145C22×D16M1612yes—
146C22×D16M1612yes—
147C22×D16M1612yes—
148C22×D16M1612yes—
149C22×D16C22×C412yes—
150C22×M32—21no—
151C22×M32—41no—
152C23×C16C22×C411yescharacteristic
153C23×C16#4111yescharacteristic
154#2972—44no—
155#2972—44no—
156#2972—82no—
157#2972—82no—
158C2×C4×D8—22no—
159C2×C4×D8—22no—
160C2×C4×D8—22no—
161C2×C4×D8—22no—
162C2×C4×D8—22no—
163C2×C4×D8—22no—
164C2×C4×D8—41no—
165C2×C4×D8—41no—
166C2×C4×D8—41no—
167C2×C4×D8—41no—
168C2×C4×D8—41no—
169C2×C4×D8—41no—
170C2×C8×D4—44no—
171C2×C8×D4—82no—
172C2×#431—21no—
173C2×#431—41no—
174C22×#108—21no—
175C2×#427—21no—
176C22×#107—21no—
177C22×#102—41no—
178C22×C22⋊C8—82no—
179C2×#405—41no—
180C22×C4×C8C2×D411yescharacteristic
181C2×M64—22no—
182C2×M64—22no—
183C2×M64—22no—
184C2×M64—22no—
185C2×M64—22no—
186C2×M64—22no—
187C2×M64—21no—
188C2×M64—21no—
189C2×M64—21no—
190C2×M64—21no—
191C2×M64—21no—
192C2×M64—21no—
193C2×M64—21no—
194C2×M64—21no—
195C2×M64—21no—
196C2×M64—21no—
197C2×M64C22×C412yes—
198C2×M64C22×C412yes—
199C22×C32—22no—
200C22×C32—21no—
201C22×C32—21no—
202#2177—22no—
203#2177—22no—
204#2177—22no—
205#2177—22no—
206#2177—22no—
207#2177—22no—
208#2177—22no—
209#2177—22no—
210#2177—22no—
211#2177—22no—
212#2177—22no—
213#2177—22no—
214#2177C4214yes—
215#2177C4214yes—
216#2177C22×C414yes—
217#2177C22×C414yes—
218C2×#368—21no—
219C2×#368—21no—
220C2×#368—21no—
221C2×#368—21no—
222C2×#368—21no—
223C2×#368C22×C412yes—
224#2158—21no—
225#2158—21no—
226#2158—21no—
227#2158C22×C412yes—
228C2×#367—21no—
229C2×#367—21no—
230C2×#367—21no—
231C2×#367—21no—
232C2×#367C4212yes—
233C2×#367C4212yes—
234C2×#367C22×C412yes—
235C2×#366—21no—
236C2×#364—22no—
237C2×#364—22no—
238C2×#364—22no—
239C2×#364—41no—
240C2×#364—41no—
241C2×#364—41no—
242C2×#357—22no—
243C2×#357—22no—
244C2×#357—22no—
245C2×#357—22no—
246C2×#357—22no—
247C2×#357—22no—
248#2110—44no—
249#2110—82no—
250C2×#347—82no—
251C4×M32—21no—
252C4×M32—21no—
253C4×M32C22⋊C412yes—
254C4×M32C2×D412yes—
255C2×#346C22⋊C412yes—
256C2×#346C22×C411yescharacteristic
257C2×#346C22×C411yescharacteristic
258C2×#346C22×C411yescharacteristic
259C2×#346C22×C411yescharacteristic
260C2×#346C22×C411yescharacteristic
261C2×#346C2×D411yescharacteristic
262C2×#346C2×D411yescharacteristic
263C2×#346C2×D411yescharacteristic
264C2×#346#4111yescharacteristic
265C2×#346#4111yescharacteristic
266C2×#346#4111yescharacteristic
267C2×#346C2411yescharacteristic
268C2×C4×C16—21no—
269#1772—22no—
270#1772—22no—
271#1772—41no—
272#1772—41no—
273C2×#339—41no—
274#1580—216no—
275#1580—48no—
276C8×D8—48no—
277C8×D8—48no—
278#1564—22no—
279#1564—22no—
280#1564—41no—
281#1564—41no—
282C2×#335—41no—
283C2×#334—22no—
284#1478—44no—
285#1478—44no—
286C2×D4⋊C8—44no—
287#1450—21no—
288#1450—21no—
289#1450C22⋊C412yes—
290#1450C2×D412yes—
291C2×#322C22⋊C412yes—
292C2×C82—21no—
293#1419—28no—
294#1415—28no—
295#1398—22no—
296#1398—22no—
297#1398—22no—
298#1398—22no—
299#1398—22no—
300#1398—22no—
301#1398—22no—
302#1398C22×C414yes—
303#1382—22no—
304#1382—22no—
305#1378—44no—
306#1369—22no—
307#1369—22no—
308#1369—22no—
309#1369C22×C414yes—
310#1368—22no—
311#1368—22no—
312#1368—22no—
313#1368C22×C414yes—
314#1333—216no—
315#1313C22⋊C414yes—
316#1313C22⋊C414yes—
317#1313C22×C414yes—
318#1313C2×D414yes—
319C23×D4—41no—
320C24×C4—81no—
321C22×D8—22no—
322C22×D8—22no—
323C22×D8—22no—
324C22×D8—22no—
325C22×D8—22no—
326C22×D8—22no—
327C22×D8—22no—
328C22×D8—41no—
329C22×D8—41no—
330C22×D8—41no—
331C22×D8—41no—
332C22×D8—41no—
333C22×D8—41no—
334C22×D8—41no—
335C22×M16—41no—
336C23×C8—84no—
337C23×C8C4×D411yescharacteristic
338C23×C8AGL(1,ℤ/8)11yescharacteristic
339C2×C4×D4—42no—
340C2×C4×D4—42no—
341C2×C4×D4—42no—
342C2×C4×D4—42no—
343C2×C4×D4—42no—
344C2×C4×D4—42no—
345C2×C4×D4—81no—
346C2×C4×D4—81no—
347C2×C4×D4—81no—
348C2×C4×D4—81no—
349C2×C4×D4—81no—
350C2×C4×D4—81no—
351C2×#117—41no—
352C22×C4⋊C4—41no—
353C22×C22⋊C4—81no—
354C22×C42AGL(1,ℤ/8)11yescharacteristic
355C2×D16—22no—
356C2×D16—22no—
357C2×D16—22no—
358C2×D16—22no—
359C2×D16—22no—
360C2×D16—22no—
361C2×D16—22no—
362C2×D16—22no—
363C2×D16—22no—
364C2×D16—22no—
365C2×D16—22no—
366C2×D16—22no—
367C2×D16—22no—
368C2×D16—22no—
369C2×D16—22no—
370C2×D16—22no—
371C2×D16—22no—
372C2×D16—22no—
373C2×D16—22no—
374C2×D16—22no—
375C2×D16—22no—
376C2×D16#9714yes—
377C2×D16#9714yes—
378C2×D16#9714yes—
379C2×D16#9714yes—
380C2×D16C2×C4214yes—
381C2×D16C2×M1614yes—
382C2×D16C2×M1614yes—
383C2×M32—22no—
384C2×M32—22no—
385C2×M32—41no—
386C2×M32—41no—
387C2×M32—41no—
388C2×M32—41no—
389C2×M32—42no—
390C2×M32—42no—
391C2×M32—42no—
392C2×M32—81no—
393C2×M32—81no—
394C2×M32—81no—
395C22×C16—21no—
396C22×C16—21no—
397C22×C16—21no—
398C22×C16—21no—
399C22×C16—22no—
400C22×C16—81no—
401C22×C16C2×C4211yescharacteristic
402C22×C16C2×C4211yescharacteristic
403C22×C16#11711yescharacteristic
404C22×C16#11711yescharacteristic
405C22×C16C4×D411yescharacteristic
406C22×C16C4×D411yescharacteristic
407C22×C16C4×D411yescharacteristic
408C22×C16C4×D411yescharacteristic
409C22×C16C4×D411yescharacteristic
410C22×C16C4×D411yescharacteristic
411C22×C16C2×M1611yescharacteristic
412C22×C16C2×M1611yescharacteristic
413C22×C16C2×M1611yescharacteristic
414C22×C16C2×M1611yescharacteristic
415C22×C16#13111yescharacteristic
416C22×C16#13111yescharacteristic
417C22×C16#13111yescharacteristic
418C22×C16#13111yescharacteristic
419C22×C16C23×C411yescharacteristic
420C22×C16C2×#4111yescharacteristic
421C4×D8—24no—
422C4×D8—24no—
423C4×D8—24no—
424C4×D8—24no—
425C4×D8—42no—
426C4×D8—42no—
427C4×D8—42no—
428C4×D8—42no—
429C4×D8—42no—
430C4×D8—42no—
431C4×D8—42no—
432C4×D8—42no—
433C4×D8—42no—
434C4×D8—42no—
435C4×D8—42no—
436C4×D8—42no—
437C8×D4—416no—
438C8×D4—88no—
439C8×D4—88no—
440C8×D4—88no—
441#431—22no—
442#431—22no—
443#431—41no—
444#431—41no—
445#431—42no—
446#431—42no—
447#431—81no—
448#431—81no—
449C2×#108—22no—
450C2×#108—41no—
451C2×#108—41no—
452C2×#108—41no—
453C2×#108—41no—
454C2×#108—41no—
455#427—22no—
456#427—41no—
457#427—41no—
458#427—41no—
459C2×#107—22no—
460C2×#107—22no—
461C2×#107—22no—
462C2×#107—41no—
463C2×#107—41no—
464C2×#107—41no—
465C2×#107—41no—
466C2×#106—41no—
467C2×C4⋊C8—41no—
468C2×C4⋊C8—42no—
469C2×#102—42no—
470C2×#102—42no—
471C2×#102—42no—
472C2×#102—42no—
473C2×#102—42no—
474C2×#102—42no—
475C2×C22⋊C8—41no—
476C2×C22⋊C8—88no—
477C2×C22⋊C8—88no—
478C2×C22⋊C8—84no—
479C2×C22⋊C8—81no—
480#405—42no—
481#405—42no—
482#405—81no—
483#405—81no—
484C2×#97—81no—
485C2×C4×C8—22no—
486C2×C4×C8—81no—
487C2×C4×C8—81no—
488C2×C4×C8C2×C22⋊C411yescharacteristic
489C2×C4×C8C2×C22⋊C411yescharacteristic
490C2×C4×C8C4×D411yescharacteristic
491C2×C4×C8C4×D411yescharacteristic
492C2×C4×C8C4×D411yescharacteristic
493C2×C4×C8AGL(1,ℤ/8)11yescharacteristic
494C2×C4×C8AGL(1,ℤ/8)11yescharacteristic
495C2×C4×C8AGL(1,ℤ/8)11yescharacteristic
496C2×C4×C8AGL(1,ℤ/8)11yescharacteristic
497C2×C4×C8#13711yescharacteristic
498C2×C4×C8#13711yescharacteristic
499C2×C4×C8C22×D411yescharacteristic
500M64—24no—
501M64—24no—
502M64—24no—
503M64—24no—
504M64—22no—
505M64—22no—
506M64—22no—
507M64—22no—
508M64—41no—
509M64—41no—
510M64—41no—
511M64—41no—
512C2×C32—24no—
513C2×C32—24no—
514C2×C32—24no—
515C2×C32—22no—
516C2×C32—22no—
517C2×C32—41no—
518C2×C32—41no—
519C2×C32—41no—
520C2×C32—41no—
521#368—22no—
522#368—22no—
523#368—41no—
524#368—41no—
525#367—22no—
526#367—22no—
527#367—22no—
528#367—22no—
529#367—41no—
530#367C2×C4214yes—
531#366—22no—
532#366—41no—
533#364—24no—
534#364—42no—
535#364—42no—
536#364—42no—
537#357—24no—
538#357—24no—
539#357—24no—
540#357—24no—
541#347—88no—
542#346—22no—
543#346C2×C4211yescharacteristic
544#346C2×C4211yescharacteristic
545#346C2×C22⋊C414yes—
546#346C2×C22⋊C411yescharacteristic
547#346C2×C22⋊C411yescharacteristic
548#346#11711yescharacteristic
549#346#11711yescharacteristic
550#346C4×D411yescharacteristic
551#346C4×D411yescharacteristic
552#346C4×D411yescharacteristic
553#346C4×D411yescharacteristic
554#346C4×D411yescharacteristic
555#346C4×D411yescharacteristic
556#346C23×C411yescharacteristic
557#346C23×C411yescharacteristic
558#346C22×D411yescharacteristic
559#346C2×#4111yescharacteristic
560C4×C16—22no—
561C4×C16—22no—
562#339—42no—
563#339—42no—
564#335—42no—
565#335—42no—
566#334—24no—
567#334—42no—
568D4⋊C8—416no—
569#322—22no—
570#322C2×C22⋊C414yes—
571C82—22no—
572C82—22no—
573C25—81no—
574C22×D4—42no—
575C22×D4—42no—
576C22×D4—42no—
577C22×D4—42no—
578C22×D4—42no—
579C22×D4—42no—
580C22×D4—42no—
581C22×D4—81no—
582C22×D4—81no—
583C22×D4—81no—
584C22×D4—81no—
585C22×D4—81no—
586C22×D4—81no—
587C22×D4—81no—
588C23×C4—21no—
589C23×C4—82no—
590C23×C4—82no—
591C23×C4—82no—
592C23×C4—82no—
593C23×C4—82no—
594C23×C4—82no—
595C23×C4—81no—
596C23×C4—324no—
597C23×C4#44211yescharacteristic
598C2×D8—24no—
599C2×D8—24no—
600C2×D8—24no—
601C2×D8—24no—
602C2×D8—24no—
603C2×D8—24no—
604C2×D8—24no—
605C2×D8—42no—
606C2×D8—42no—
607C2×D8—42no—
608C2×D8—42no—
609C2×D8—42no—
610C2×D8—42no—
611C2×D8—42no—
612C2×D8—42no—
613C2×D8—42no—
614C2×D8—42no—
615C2×D8—42no—
616C2×D8—42no—
617C2×D8—42no—
618C2×D8—42no—
619C2×D8—42no—
620C2×D8—42no—
621C2×D8—42no—
622C2×D8—42no—
623C2×D8—42no—
624C2×D8—42no—
625C2×D8—42no—
626C2×M16—42no—
627C2×M16—81no—
628C2×M16—81no—
629C2×M16—81no—
630C2×M16—81no—
631C2×M16—81no—
632C22×C8—21no—
633C22×C8—21no—
634C22×C8—21no—
635C22×C8—21no—
636C22×C8—42no—
637C22×C8—816no—
638C22×C8—82no—
639C22×C8—81no—
640C22×C8—328no—
641C22×C8C4×C22⋊C411yescharacteristic
642C22×C8C4×C22⋊C411yescharacteristic
643C22×C8#41711yescharacteristic
644C22×C8#41711yescharacteristic
645C22×C8#43511yescharacteristic
646C22×C8#43511yescharacteristic
647C22×C8#43511yescharacteristic
648C22×C8#43511yescharacteristic
649C22×C8#44011yescharacteristic
650C22×C8#44011yescharacteristic
651C22×C8#44211yescharacteristic
652C22×C8#44211yescharacteristic
653C22×C8#44211yescharacteristic
654C22×C8#44211yescharacteristic
655C22×C8#44311yescharacteristic
656C22×C8#44311yescharacteristic
657C22×C8#44311yescharacteristic
658C22×C8#44311yescharacteristic
659C22×C8C2×C4×D411yescharacteristic
660C22×C8C2×AGL(1,ℤ/8)11yescharacteristic
661C4×D4—44no—
662C4×D4—44no—
663C4×D4—44no—
664C4×D4—44no—
665C4×D4—82no—
666C4×D4—82no—
667C4×D4—82no—
668C4×D4—82no—
669C4×D4—82no—
670C4×D4—82no—
671C4×D4—82no—
672C4×D4—82no—
673C4×D4—82no—
674C4×D4—82no—
675C4×D4—82no—
676C4×D4—82no—
677#117—42no—
678#117—81no—
679#117—81no—
680#117—81no—
681C2×C4⋊C4—42no—
682C2×C4⋊C4—42no—
683C2×C4⋊C4—42no—
684C2×C4⋊C4—81no—
685C2×C4⋊C4—81no—
686C2×C4⋊C4—81no—
687C2×C4⋊C4—81no—
688C2×C22⋊C4—82no—
689C2×C22⋊C4—82no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4—82no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4—81no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—81no—
699C2×C42#41811yescharacteristic
700C2×C42#41811yescharacteristic
701C2×C42#44011yescharacteristic
702C2×C42#44011yescharacteristic
703C2×C42#44211yescharacteristic
704C2×C42C2×AGL(1,ℤ/8)11yescharacteristic
705D16—24no—
706D16—24no—
707D16—24no—
708D16—24no—
709D16—24no—
710D16—24no—
711D16—24no—
712D16C2×#9718yes—
713M32—42no—
714M32—42no—
715M32—42no—
716M32—42no—
717M32—44no—
718M32—82no—
719M32—82no—
720M32—82no—
721C2×C16—21no—
722C2×C16—21no—
723C2×C16—21no—
724C2×C16—21no—
725C2×C16—21no—
726C2×C16—21no—
727C2×C16—21no—
728C2×C16—21no—
729C2×C16—21no—
730C2×C16—21no—
731C2×C16—21no—
732C2×C16—21no—
733C2×C16—24no—
734C2×C16—42no—
735C2×C16—42no—
736C2×C16—82no—
737C2×C16—82no—
738C2×C16—82no—
739C2×C16C4×C22⋊C411yescharacteristic
740C2×C16C4×C22⋊C411yescharacteristic
741C2×C16C4×C22⋊C411yescharacteristic
742C2×C16C4×C22⋊C411yescharacteristic
743C2×C16C2×#9711yescharacteristic
744C2×C16C2×#9711yescharacteristic
745C2×C16C2×#9711yescharacteristic
746C2×C16C2×#9711yescharacteristic
747C2×C16#40511yescharacteristic
748C2×C16#40511yescharacteristic
749C2×C16#40511yescharacteristic
750C2×C16#40511yescharacteristic
751C2×C16#43511yescharacteristic
752C2×C16#43511yescharacteristic
753C2×C16#43511yescharacteristic
754C2×C16#43511yescharacteristic
755C2×C16#43511yescharacteristic
756C2×C16#43511yescharacteristic
757C2×C16#43511yescharacteristic
758C2×C16#43511yescharacteristic
759C2×C16#43511yescharacteristic
760C2×C16#43511yescharacteristic
761C2×C16#43511yescharacteristic
762C2×C16#43511yescharacteristic
763C2×C16C22×C4211yescharacteristic
764C2×C16C2×#11711yescharacteristic
765C2×C16C2×C4×D411yescharacteristic
766C2×C16C2×C4×D411yescharacteristic
767C2×C16C22×M1611yescharacteristic
768C2×C16C22×M1611yescharacteristic
769C2×C16C2×#13111yescharacteristic
770C2×C16C2×#13111yescharacteristic
771#108—42no—
772#108—42no—
773#108—81no—
774#108—81no—
775#107—24no—
776#107—42no—
777#107—42no—
778#107—42no—
779#107—42no—
780#107—81no—
781#106—42no—
782#106—81no—
783C4⋊C8—42no—
784C4⋊C8—42no—
785C4⋊C8—44no—
786C4⋊C8—82no—
787#102—44no—
788#102—44no—
789#102—44no—
790#102—44no—
791C22⋊C8—42no—
792C22⋊C8—42no—
793C22⋊C8—816no—
794C22⋊C8—82no—
795C22⋊C8—82no—
796#97—82no—
797#97—82no—
798C4×C8—24no—
799C4×C8—42no—
800C4×C8—82no—
801C4×C8—82no—
802C4×C8—82no—
803C4×C8—82no—
804C4×C8C4×C22⋊C411yescharacteristic
805C4×C8C4×C22⋊C411yescharacteristic
806C4×C8#41711yescharacteristic
807C4×C8#41711yescharacteristic
808C4×C8#41811yescharacteristic
809C4×C8#41811yescharacteristic
810C4×C8#44011yescharacteristic
811C4×C8#44011yescharacteristic
812C4×C8#44011yescharacteristic
813C4×C8#44011yescharacteristic
814C4×C8#44211yescharacteristic
815C4×C8#44211yescharacteristic
816C4×C8C22×C22⋊C411yescharacteristic
817C4×C8C2×C4×D411yescharacteristic
818C4×C8C2×AGL(1,ℤ/8)11yescharacteristic
819C4×C8C2×#13711yescharacteristic
820C32—28no—
821C32—42no—
822C32—42no—
823C24—82no—
824C24—82no—
825C24—82no—
826C24—82no—
827C24—82no—
828C24—82no—
829C24—82no—
830C24—322no—
831C24—322no—
832C24AGL(1,ℤ/16)11yescharacteristic
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—82no—
841C2×D4—82no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—82no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—82no—
849C2×D4—82no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—82no—
855C2×D4—82no—
856C2×D4—82no—
857C2×D4—82no—
858C2×D4—82no—
859C2×D4—82no—
860C2×D4—82no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—82no—
872C22×C4—82no—
873C22×C4—82no—
874C22×C4—82no—
875C22×C4—168no—
876C22×C4—161no—
877C22×C4—324no—
878C22×C4—324no—
879C22×C4—324no—
880C22×C4—324no—
881C22×C4—324no—
882C22×C4—322no—
883C22×C4#158611yescharacteristic
884C22×C4#158611yescharacteristic
885C22×C4#158611yescharacteristic
886C22×C4#158611yescharacteristic
887C22×C4#176211yescharacteristic
888C22×C4#176211yescharacteristic
889C22×C4#218011yescharacteristic
890C22×C4#218011yescharacteristic
891C22×C4AGL(1,ℤ/16)11yescharacteristic
892C22×C4AGL(1,ℤ/16)11yescharacteristic
893C22×C4AGL(1,ℤ/16)11yescharacteristic
894C22×C4AGL(1,ℤ/16)11yescharacteristic
895C22×C4AGL(1,ℤ/16)11yescharacteristic
896C22×C4C2×#44211yescharacteristic
897D8—28no—
898D8—44no—
899D8—44no—
900D8—44no—
901D8—44no—
902D8—44no—
903D8—44no—
904D8—44no—
905M16—82no—
906M16—82no—
907M16—161no—
908M16—161no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—44no—
922C2×C8—84no—
923C2×C8—84no—
924C2×C8—82no—
925C2×C8—164no—
926C2×C8—161no—
927C2×C8—161no—
928C2×C8—3216no—
929C2×C8#158511yescharacteristic
930C2×C8#158511yescharacteristic
931C2×C8#158511yescharacteristic
932C2×C8#158511yescharacteristic
933C2×C8#158511yescharacteristic
934C2×C8#158511yescharacteristic
935C2×C8#158511yescharacteristic
936C2×C8#158511yescharacteristic
937C2×C8#158611yescharacteristic
938C2×C8#158611yescharacteristic
939C2×C8#158611yescharacteristic
940C2×C8#158611yescharacteristic
941C2×C8#175211yescharacteristic
942C2×C8#175211yescharacteristic
943C2×C8#175211yescharacteristic
944C2×C8#175211yescharacteristic
945C2×C8#176211yescharacteristic
946C2×C8#176211yescharacteristic
947C2×C8#176211yescharacteristic
948C2×C8#176211yescharacteristic
949C2×C8#176411yescharacteristic
950C2×C8#176411yescharacteristic
951C2×C8#176411yescharacteristic
952C2×C8#176411yescharacteristic
953C2×C8C2×C4×C22⋊C411yescharacteristic
954C2×C8C2×#41711yescharacteristic
955C2×C8C2×#43511yescharacteristic
956C2×C8C2×#43511yescharacteristic
957C2×C8C2×#44011yescharacteristic
958C2×C8C2×#44211yescharacteristic
959C2×C8C2×#44311yescharacteristic
960C2×C8C2×#44311yescharacteristic
961C4⋊C4—44no—
962C4⋊C4—82no—
963C4⋊C4—82no—
964C4⋊C4—82no—
965C4⋊C4—82no—
966C4⋊C4—161no—
967C22⋊C4—84no—
968C22⋊C4—84no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—82no—
972C22⋊C4—161no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—82no—
980C42—161no—
981C42#176211yescharacteristic
982C42#176211yescharacteristic
983C42C2×#41811yescharacteristic
984C42C2×#44011yescharacteristic
985C16—21no—
986C16—21no—
987C16—21no—
988C16—21no—
989C16—44no—
990C16—84no—
991C16#175211yescharacteristic
992C16#175211yescharacteristic
993C16#175211yescharacteristic
994C16#175211yescharacteristic
995C16C22×#9711yescharacteristic
996C16C2×#40511yescharacteristic
997C16C2×#43511yescharacteristic
998C16C2×#43511yescharacteristic
999C23—42no—
1000C23—84no—
1001C23—84no—
1002C23—84no—
1003C23—84no—
1004C23—84no—
1005C23—84no—
1006C23—84no—
1007C23—164no—
1008C23—164no—
1009C23—324no—
1010C23—324no—
1011C23—322no—
1012C23—322no—
1013C23—322no—
1014C23—322no—
1015C23—324no—
1016C23—324no—
1017C23#1207711yescharacteristic
1018C23#1207711yescharacteristic
1019C23#1207811yescharacteristic
1020C23#1207811yescharacteristic
1021C23#1264711yescharacteristic
1022C23#1264711yescharacteristic
1023C23C2×AGL(1,ℤ/16)11yescharacteristic
1024D4—48no—
1025D4—84no—
1026D4—84no—
1027D4—84no—
1028D4—84no—
1029D4—84no—
1030D4—84no—
1031D4—84no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—81no—
1039C2×C4—81no—
1040C2×C4—81no—
1041C2×C4—81no—
1042C2×C4—84no—
1043C2×C4—168no—
1044C2×C4—168no—
1045C2×C4—164no—
1046C2×C4—162no—
1047C2×C4—324no—
1048C2×C4—324no—
1049C2×C4—322no—
1050C2×C4—322no—
1051C2×C4—322no—
1052C2×C4#820411yescharacteristic
1053C2×C4#820411yescharacteristic
1054C2×C4#820411yescharacteristic
1055C2×C4#820411yescharacteristic
1056C2×C4#1207711yescharacteristic
1057C2×C4#1207711yescharacteristic
1058C2×C4#1207711yescharacteristic
1059C2×C4#1207711yescharacteristic
1060C2×C4#1207711yescharacteristic
1061C2×C4#1207711yescharacteristic
1062C2×C4#1207811yescharacteristic
1063C2×C4#1207811yescharacteristic
1064C2×C4#1207811yescharacteristic
1065C2×C4#1207811yescharacteristic
1066C2×C4#1207811yescharacteristic
1067C2×C4#1207811yescharacteristic
1068C2×C4#1264711yescharacteristic
1069C2×C4#1264711yescharacteristic
1070C2×C4#1265011yescharacteristic
1071C2×C4#1265011yescharacteristic
1072C2×C4#1265011yescharacteristic
1073C2×C4#1265011yescharacteristic
1074C2×C4C2×#158611yescharacteristic
1075C2×C4C2×#158611yescharacteristic
1076C2×C4C2×#176211yescharacteristic
1077C2×C4C2×#218011yescharacteristic
1078C2×C4C2×AGL(1,ℤ/16)11yescharacteristic
1079C2×C4C2×AGL(1,ℤ/16)11yescharacteristic
1080C8—21no—
1081C8—21no—
1082C8—21no—
1083C8—21no—
1084C8—84no—
1085C8—164no—
1086C8—162no—
1087C8#820411yescharacteristic
1088C8#820411yescharacteristic
1089C8#820411yescharacteristic
1090C8#820411yescharacteristic
1091C8C2×#158511yescharacteristic
1092C8C2×#158511yescharacteristic
1093C8C2×#175211yescharacteristic
1094C8C2×#176411yescharacteristic
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—88no—
1103C22—164no—
1104C22—164no—
1105C22—168no—
1106C22—168no—
1107C22—324no—
1108C22—324no—
1109C22—324no—
1110C22—324no—
1111C22#12871911yescharacteristic
1112C22#12871911yescharacteristic
1113C22#12871911yescharacteristic
1114C22#12871911yescharacteristic
1115C22C2×#1207711yescharacteristic
1116C22C2×#1207811yescharacteristic
1117C22C2×#1264711yescharacteristic
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—164no—
1123C4—322no—
1124C4#12871911yescharacteristic
1125C4#12871911yescharacteristic
1126C4#12871911yescharacteristic
1127C4#12871911yescharacteristic
1128C4C2×#820411yescharacteristic
1129C4C2×#1207711yescharacteristic
1130C4C2×#1207811yescharacteristic
1131C4C2×#1265011yescharacteristic
1132C2—21no—
1133C2—21no—
1134C2—21no—
1135C2—21no—
1136C2—21no—
1137C2—21no—
1138C2—168no—
1139C2#7222508212yesdirect product factor
1140C2C2×#12871911yescharacteristic
subgroupG/H
center, socleC22#128719
commutatorC2×C16C22×C42
Frattini, cosocleC2×#346C24
prime radicalC23×D16C2×C4
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4×C8 ◁ C2×#11405 ◁ G
LECSG ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#129176C2semidirect
3. #72225082C2direct (N × H)
4. C2×#149504C2semidirect
5. C2×#94031C2semidirect
6. C2×#94056C2semidirect
19. #483596C4semidirect
22. C2×#12067C4semidirect
31. C2×#7390C4semidirect
32. C2×#7390C4semidirect
35. #149504C22semidirect
38. #129176C22semidirect
40. #94056C22semidirect
41. #94031C22semidirect
107. #12067C2×C4semidirect
131. #7390C2×C4semidirect
1139. C2#72225082direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1291762
C2×#4835962
#722250822
C2×#1495042
C2×#940312
C2×#940562
C22×#73902
C2×#1519692