Finite Group Databasebeta

← C2×#72225077 #72320424

Subgroups — C2×#72225077 #72320424

Order 2048.

2290 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×#93996C211yesmaximal, characteristic, complemented
2C2×#140357C211yesmaximal, characteristic, complemented
3C2×#483596C211yesmaximal, characteristic
4#72225077C218yesmaximal, direct product factor
5C2×#94056C211yesmaximal, characteristic, complemented
6C22×#7390C211yesmaximal, characteristic
7C2×#151024C211yesmaximal, characteristic, complemented
8C2×#151969C211yesmaximal, characteristic
9C22×#2177C2211yescharacteristic
10C2×#17854—21no—
11C22×#1419C411yescharacteristic
12C2×#13617C411yescharacteristic
13C22×#1398C2211yescharacteristic
14C22×#1398C2211yescharacteristic
15C2×#13164—21no—
16C2×#12671C2211yescharacteristic
17#483596—22no—
18#483596—22no—
19#483596—22no—
20#483596C2214yes—
21C2×#12067—22no—
22C2×#12067—22no—
23C22×#1369C2211yescharacteristic
24C2×#11999C2211yescharacteristic
25C2×#11599—21no—
26C2×#11405C2211yescharacteristic
27#151969C414yes—
28#151969C2214yes—
29C2×#7477C411yescharacteristic
30C2×#7474C411yescharacteristic
31#151024—22no—
32#151024C2214yescomplemented
33C2×#7457—22no—
34C2×#7390—22no—
35C2×#7390—22no—
36C2×#7390C2214yes—
37#140357—22no—
38#140357C2214yescomplemented
39C2×#7180—21no—
40#94056C2214yescomplemented
41#93996C2214yescomplemented
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×#2177D412yes—
56C2×#2177D412yes—
57C2×#2177Q812yes—
58C2×#2177Q812yes—
59C2×#2177C2312yes—
60C22×#368C2×C411yescharacteristic
61C2×#2158C2×C411yescharacteristic
62C22×#367C2×C411yescharacteristic
63C2×#2153—41no—
64C22×#364—21no—
65C22×#357—21no—
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×#1419C814yescomplemented
79C2×#1419C814yescomplemented
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×#1398—21no—
92C2×#1398—21no—
93C2×#1398C2×C412yes—
94C2×#1398C2312yes—
95C2×#1398C2312yes—
96#13164—24no—
97#13164—42no—
98#12671—21no—
99#12671—21no—
100#12671C2×C412yes—
101#12671C2312yes—
102C2×#1382—21no—
103C2×#1378—41no—
104#12067—28no—
105#12067—28no—
106#12067—28no—
107#12067—28no—
108C2×#1369—21no—
109C2×#1369—21no—
110C2×#1369—21no—
111C2×#1369—21no—
112C2×#1369—21no—
113C2×#1369C2312yes—
114#11999—21no—
115#11999—21no—
116#11999D412yes—
117#11999C2312yes—
118C2×#1368—21no—
119C2×#1368D412yes—
120#11599—24no—
121#11599—24no—
122C2×#1333—24no—
123#11405—21no—
124#11405—21no—
125#11405D412yes—
126#11405C2312yes—
127C2×#1313—21no—
128C2×#1313—21no—
129#7477C2×C414yes—
130#7474C2×C414yes—
131#7457—28no—
132#7390—28no—
133#7180—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×D16C4⋊C412yes—
144C22×D16C4⋊C412yes—
145C22×D16C2×C812yes—
146C22×D16C2×C812yes—
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—21no—
182C2×M64—21no—
183C2×M64—21no—
184C2×M64—21no—
185C2×M64—22no—
186C2×M64—22no—
187C2×M64—21no—
188C2×M64—21no—
189C2×M64—21no—
190C2×M64—21no—
191C2×M64—22no—
192C2×M64—41no—
193C2×M64—41no—
194C2×M64—41no—
195C2×M64C2×C812yescomplemented
196C2×M64C2×C812yescomplemented
197C2×M64C22×C412yes—
198C2×M64C22×C412yes—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—41no—
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#2177C4⋊C414yes—
215#2177C4⋊C414yes—
216#2177C2×D414yes—
217#2177C2×Q814yes—
218C2×#368—21no—
219C2×#368—21no—
220C2×#368—21no—
221C2×#368C2×C812yescomplemented
222C2×#368C2×C812yescomplemented
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×#367C4⋊C412yes—
233C2×#367C4⋊C412yes—
234C2×#367C22×C412yes—
235C2×#366—21no—
236#2153—44no—
237#2153—82no—
238C2×#364—22no—
239C2×#364—41no—
240C2×#364—41no—
241C2×#364—41no—
242C2×#364—41no—
243C2×#364—41no—
244C2×#364—82no—
245C2×#357—22no—
246C2×#357—22no—
247C2×#357—22no—
248C2×#357—22no—
249C2×#357—22no—
250C2×#357—22no—
251C4×M32—21no—
252C4×M32—21no—
253C4×M32—21no—
254C4×M32C2×D412yes—
255C2×#346—21no—
256C2×#346C22×C411yescharacteristic
257C2×#346C2×D411yescharacteristic
258C2×#346C2×D411yescharacteristic
259C2×#346C2×D411yescharacteristic
260C2×#346C2×D411yescharacteristic
261C2×#346C2×D411yescharacteristic
262C2×#346C2×Q811yescharacteristic
263C2×#346C2×Q811yescharacteristic
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#1450SD1612yes—
290#1450C2×D412yes—
291C2×#322—21no—
292C2×C82SD1612yes—
293#1419C2×C8116yescomplemented
294#1415—28no—
295#1398—22no—
296#1398—22no—
297#1398—22no—
298#1398—22no—
299#1398—22no—
300#1398—22no—
301#1398—41no—
302#1398—41no—
303#1382—22no—
304#1382—22no—
305#1378—44no—
306#1369—22no—
307#1369—22no—
308#1369—41no—
309#1369—41no—
310#1368—22no—
311#1368—22no—
312#1368—22no—
313#1368C2×D414yes—
314#1333—216no—
315#1313—22no—
316#1313—22no—
317#1313—22no—
318#1313—22no—
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×D16C4⋊C814yes—
377C2×D16C4⋊C814yes—
378C2×D16C4⋊C814yes—
379C2×D16C4⋊C814yes—
380C2×D16C2×C4⋊C414yes—
381C2×D16C22×C814yes—
382C2×D16C2×M1614yes—
383C2×M32—22no—
384C2×M32—41no—
385C2×M32—41no—
386C2×M32—41no—
387C2×M32—41no—
388C2×M32—41no—
389C2×M32—42no—
390C2×M32—81no—
391C2×M32—81no—
392C2×M32—81no—
393C2×M32—81no—
394C2×M32—81no—
395C22×C16—21no—
396C22×C16—21no—
397C22×C16—21no—
398C22×C16—21no—
399C22×C16—41no—
400C22×C16—81no—
401C22×C16C2×C4⋊C411yescharacteristic
402C22×C16C2×C4⋊C411yescharacteristic
403C22×C16C4×D411yescharacteristic
404C22×C16C4×D411yescharacteristic
405C22×C16C4×D411yescharacteristic
406C22×C16C4×D411yescharacteristic
407C22×C16C22⋊Q811yescharacteristic
408C22×C16C22⋊Q811yescharacteristic
409C22×C16#12311yescharacteristic
410C22×C16#12311yescharacteristic
411C22×C16C22×C811yescharacteristic
412C22×C16C22×C811yescharacteristic
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—22no—
451C2×#108—22no—
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×C8C4×D411yescharacteristic
489C2×C4×C8#12011yescharacteristic
490C2×C4×C8#12011yescharacteristic
491C2×C4×C8C22⋊Q811yescharacteristic
492C2×C4×C8C22⋊Q811yescharacteristic
493C2×C4×C8C2×SD1611yescharacteristic
494C2×C4×C8C2×SD1611yescharacteristic
495C2×C4×C8#13511yescharacteristic
496C2×C4×C8#13511yescharacteristic
497C2×C4×C8AGL(1,ℤ/8)11yescharacteristic
498C2×C4×C8AGL(1,ℤ/8)11yescharacteristic
499C2×C4×C8C22×D411yescharacteristic
500M64—22no—
501M64—22no—
502M64—22no—
503M64—24no—
504M64—22no—
505M64—22no—
506M64—42no—
507M64—42no—
508M64—42no—
509M64—41no—
510M64—41no—
511M64C22×C814yescomplemented
512C2×C32—22no—
513C2×C32—22no—
514C2×C32—22no—
515C2×C32—22no—
516C2×C32—42no—
517C2×C32—42no—
518C2×C32—42no—
519C2×C32—41no—
520C2×C32—41no—
521#368—22no—
522#368—22no—
523#368—22no—
524#368C22×C814yescomplemented
525#367—22no—
526#367—22no—
527#367—22no—
528#367—22no—
529#367—41no—
530#367C2×C4⋊C414yes—
531#366—22no—
532#366—41no—
533#364—42no—
534#364—42no—
535#364—88no—
536#364—81no—
537#364—81no—
538#357—24no—
539#357—24no—
540#357—24no—
541#357—24no—
542#346—22no—
543#346—41no—
544#346C2×C4⋊C411yescharacteristic
545#346C2×C4⋊C411yescharacteristic
546#346C4×D411yescharacteristic
547#346C4×D411yescharacteristic
548#346#12011yescharacteristic
549#346#12011yescharacteristic
550#346C22⋊Q811yescharacteristic
551#346C22⋊Q811yescharacteristic
552#346C22⋊Q811yescharacteristic
553#346C22⋊Q811yescharacteristic
554#346#12311yescharacteristic
555#346#12311yescharacteristic
556#346C22×D411yescharacteristic
557#346C22×D411yescharacteristic
558#346C22×Q811yescharacteristic
559#346C2×#4111yescharacteristic
560C4×C16—22no—
561C4×C16—41no—
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#322—22no—
571C82—22no—
572C82C2×SD1614yes—
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—42no—
628C2×M16—42no—
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—81no—
639C22×C8—82no—
640C22×C8—328no—
641C22×C8#38511yescharacteristic
642C22×C8#38511yescharacteristic
643C22×C8C8×D411yescharacteristic
644C22×C8C8×D411yescharacteristic
645C22×C8#43511yescharacteristic
646C22×C8#43511yescharacteristic
647C22×C8C4×SD1611yescharacteristic
648C22×C8C4×SD1611yescharacteristic
649C22×C8#44211yescharacteristic
650C22×C8#44211yescharacteristic
651C22×C8#44311yescharacteristic
652C22×C8#44311yescharacteristic
653C22×C8#44411yescharacteristic
654C22×C8#44411yescharacteristic
655C22×C8#44911yescharacteristic
656C22×C8#44911yescharacteristic
657C22×C8#47611yescharacteristic
658C22×C8#47611yescharacteristic
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#44211yescharacteristic
700C2×C42#45011yescharacteristic
701C2×C42#45011yescharacteristic
702C2×C42#47811yescharacteristic
703C2×C42#47811yescharacteristic
704C2×C42C2×AGL(1,ℤ/8)11yescharacteristic
705D16—24no—
706D16—24no—
707D16—24no—
708D16—24no—
709D16—24no—
710D16—24no—
711D16—24no—
712D16C2×C4⋊C818yes—
713M32—42no—
714M32—42no—
715M32—81no—
716M32—81no—
717M32—82no—
718M32—82no—
719M32—161no—
720M32—161no—
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—42no—
734C2×C16—81no—
735C2×C16—81no—
736C2×C16—82no—
737C2×C16—161no—
738C2×C16—161no—
739C2×C16#38511yescharacteristic
740C2×C16#38511yescharacteristic
741C2×C16#38511yescharacteristic
742C2×C16#38511yescharacteristic
743C2×C16C2×C4⋊C811yescharacteristic
744C2×C16C2×C4⋊C811yescharacteristic
745C2×C16C2×C4⋊C811yescharacteristic
746C2×C16C2×C4⋊C811yescharacteristic
747C2×C16#42411yescharacteristic
748C2×C16#42411yescharacteristic
749C2×C16#42411yescharacteristic
750C2×C16#42411yescharacteristic
751C2×C16C8×D411yescharacteristic
752C2×C16C8×D411yescharacteristic
753C2×C16C8×D411yescharacteristic
754C2×C16C8×D411yescharacteristic
755C2×C16C8×D411yescharacteristic
756C2×C16C8×D411yescharacteristic
757C2×C16#43511yescharacteristic
758C2×C16#43511yescharacteristic
759C2×C16#43511yescharacteristic
760C2×C16#43511yescharacteristic
761C2×C16#43511yescharacteristic
762C2×C16#43511yescharacteristic
763C2×C16C22×C4⋊C411yescharacteristic
764C2×C16C2×C4×D411yescharacteristic
765C2×C16C2×C22⋊Q811yescharacteristic
766C2×C16C2×#12311yescharacteristic
767C2×C16C23×C811yescharacteristic
768C2×C16C22×M1611yescharacteristic
769C2×C16C2×#13111yescharacteristic
770C2×C16C2×#13111yescharacteristic
771#108—24no—
772#108—42no—
773#108—42no—
774#108—42no—
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×C8#38511yescharacteristic
805C4×C8#38511yescharacteristic
806C4×C8C4×SD1611yescharacteristic
807C4×C8C4×SD1611yescharacteristic
808C4×C8#44911yescharacteristic
809C4×C8#44911yescharacteristic
810C4×C8#45011yescharacteristic
811C4×C8#45011yescharacteristic
812C4×C8#47611yescharacteristic
813C4×C8#47611yescharacteristic
814C4×C8#47811yescharacteristic
815C4×C8#47811yescharacteristic
816C4×C8C2×#12011yescharacteristic
817C4×C8C2×C22⋊Q811yescharacteristic
818C4×C8C22×SD1611yescharacteristic
819C4×C8C2×#13511yescharacteristic
820C32—24no—
821C32—44no—
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#158011yescharacteristic
884C22×C4#158011yescharacteristic
885C22×C4#158611yescharacteristic
886C22×C4#158611yescharacteristic
887C22×C4#186411yescharacteristic
888C22×C4#186411yescharacteristic
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—44no—
906M16—82no—
907M16—82no—
908M16—82no—
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—82no—
924C2×C8—82no—
925C2×C8—82no—
926C2×C8—84no—
927C2×C8—164no—
928C2×C8—3216no—
929C2×C8C8×SD1611yescharacteristic
930C2×C8C8×SD1611yescharacteristic
931C2×C8C8×SD1611yescharacteristic
932C2×C8C8×SD1611yescharacteristic
933C2×C8#158011yescharacteristic
934C2×C8#158011yescharacteristic
935C2×C8#158211yescharacteristic
936C2×C8#158211yescharacteristic
937C2×C8#158211yescharacteristic
938C2×C8#158211yescharacteristic
939C2×C8#158611yescharacteristic
940C2×C8#158611yescharacteristic
941C2×C8#185011yescharacteristic
942C2×C8#185011yescharacteristic
943C2×C8#185011yescharacteristic
944C2×C8#185011yescharacteristic
945C2×C8#186411yescharacteristic
946C2×C8#186411yescharacteristic
947C2×C8#186411yescharacteristic
948C2×C8#186411yescharacteristic
949C2×C8#186611yescharacteristic
950C2×C8#186611yescharacteristic
951C2×C8#186611yescharacteristic
952C2×C8#186611yescharacteristic
953C2×C8C2×#38511yescharacteristic
954C2×C8C2×C8×D411yescharacteristic
955C2×C8C2×#43511yescharacteristic
956C2×C8C2×C4×SD1611yescharacteristic
957C2×C8C2×#44311yescharacteristic
958C2×C8C2×#44411yescharacteristic
959C2×C8C2×#44911yescharacteristic
960C2×C8C2×#47611yescharacteristic
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#186411yescharacteristic
982C42#186411yescharacteristic
983C42C2×#45011yescharacteristic
984C42C2×#47811yescharacteristic
985C16—21no—
986C16—21no—
987C16—21no—
988C16—21no—
989C16—82no—
990C16—162no—
991C16#185011yescharacteristic
992C16#185011yescharacteristic
993C16#185011yescharacteristic
994C16#185011yescharacteristic
995C16C22×C4⋊C811yescharacteristic
996C16C2×#42411yescharacteristic
997C16C2×C8×D411yescharacteristic
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#1206511yescharacteristic
1018C23#1206511yescharacteristic
1019C23#1207811yescharacteristic
1020C23#1207811yescharacteristic
1021C23#1295611yescharacteristic
1022C23#1295611yescharacteristic
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#884511yescharacteristic
1053C2×C4#884511yescharacteristic
1054C2×C4#884511yescharacteristic
1055C2×C4#884511yescharacteristic
1056C2×C4#1206511yescharacteristic
1057C2×C4#1206511yescharacteristic
1058C2×C4#1206711yescharacteristic
1059C2×C4#1206711yescharacteristic
1060C2×C4#1206711yescharacteristic
1061C2×C4#1206711yescharacteristic
1062C2×C4#1207711yescharacteristic
1063C2×C4#1207711yescharacteristic
1064C2×C4#1207711yescharacteristic
1065C2×C4#1207711yescharacteristic
1066C2×C4#1207811yescharacteristic
1067C2×C4#1207811yescharacteristic
1068C2×C4#1295511yescharacteristic
1069C2×C4#1295511yescharacteristic
1070C2×C4#1295511yescharacteristic
1071C2×C4#1295511yescharacteristic
1072C2×C4#1295611yescharacteristic
1073C2×C4#1295611yescharacteristic
1074C2×C4C2×#158011yescharacteristic
1075C2×C4C2×#158611yescharacteristic
1076C2×C4C2×#186411yescharacteristic
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—84no—
1086C8—164no—
1087C8#884511yescharacteristic
1088C8#884511yescharacteristic
1089C8#884511yescharacteristic
1090C8#884511yescharacteristic
1091C8C2×C8×SD1611yescharacteristic
1092C8C2×#158211yescharacteristic
1093C8C2×#185011yescharacteristic
1094C8C2×#186611yescharacteristic
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#13590811yescharacteristic
1112C22#13590811yescharacteristic
1113C22#13590811yescharacteristic
1114C22#13590811yescharacteristic
1115C22C2×#1206511yescharacteristic
1116C22C2×#1207811yescharacteristic
1117C22C2×#1295611yescharacteristic
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—164no—
1123C4—322no—
1124C4#13590811yescharacteristic
1125C4#13590811yescharacteristic
1126C4#13590811yescharacteristic
1127C4#13590811yescharacteristic
1128C4C2×#884511yescharacteristic
1129C4C2×#1206711yescharacteristic
1130C4C2×#1207711yescharacteristic
1131C4C2×#1295511yescharacteristic
1132C2—21no—
1133C2—21no—
1134C2—21no—
1135C2—21no—
1136C2—21no—
1137C2—21no—
1138C2—168no—
1139C2#7222507712yesdirect product factor
1140C2C2×#13590811yescharacteristic
subgroupG/H
center, socleC22#135908
commutatorC2×C16C23×C8
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×#93996C2semidirect
2. C2×#140357C2semidirect
4. #72225077C2direct (N × H)
5. C2×#94056C2semidirect
7. C2×#151024C2semidirect
32. #151024C22semidirect
38. #140357C22semidirect
40. #94056C22semidirect
41. #93996C22semidirect
78. C2×#1419C8semidirect
79. C2×#1419C8semidirect
195. C2×M64C2×C8semidirect
196. C2×M64C2×C8semidirect
221. C2×#368C2×C8semidirect
222. C2×#368C2×C8semidirect
293. #1419C2×C8semidirect
511. M64C22×C8semidirect
524. #368C22×C8semidirect
1139. C2#72225077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#939962
C2×#1403572
C2×#4835962
#722250772
C2×#940562
C22×#73902
C2×#1510242
C2×#1519692