Finite Group Databasebeta

← C2×#24918559 #36275761

Subgroups — C2×#24918559 #36275761

Order 21248.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128322C211yesmaximal, characteristic, complemented
2C2×#19128270C211yesmaximal, characteristic, complemented
3#24918559C2116yesmaximal, direct product factor
4C2×#19128090C211yesmaximal, characteristic, complemented
5C2×#19128085C211yesmaximal, characteristic, complemented
6C2×#19128061C211yesmaximal, characteristic, complemented
7C2×#19128048C211yesmaximal, characteristic, complemented
8C2×#19127924C211yesmaximal, characteristic, complemented
9C2×#19127902C211yesmaximal, characteristic, complemented
10C2×#19127917C211yesmaximal, characteristic, complemented
11C2×#19127897C211yesmaximal, characteristic, complemented
12C2×#19127865C211yesmaximal, characteristic, complemented
13C2×#19127848C211yesmaximal, characteristic, complemented
14C2×#19127854C211yesmaximal, characteristic, complemented
15C2×#19127837C211yesmaximal, characteristic, complemented
16C2×#433×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C22×Dic332C2211yescharacteristic, complemented
20C22×#13050579C2211yescharacteristic
21C22×#13050579C2211yescharacteristic
22C22×#13050579C2211yescharacteristic, complemented
23C22×#13050579C2211yescharacteristic, complemented
24C22×D664C2211yescharacteristic
25C22×D664C2211yescharacteristic
26C22×D664C2211yescharacteristic, complemented
27#19128322—24no—
28#19128322C2218yescomplemented
29#19128270—24no—
30#19128270C2218yescomplemented
31C2×#14581792C2211yescharacteristic, complemented
32C2×#14581789C2211yescharacteristic
33C2×#14581789C2211yescharacteristic
34C2×#14581787—21no—
35C2×#14581780C2211yescharacteristic
36C2×#14581780C2211yescharacteristic
37C2×#14581780C2211yescharacteristic, complemented
38C2×#14581778—21no—
39C2×#14581774—21no—
40C2×#14581771C2211yescharacteristic
41C2×#14581770—21no—
42C2×#14581767—21no—
43C2×#14581767—21no—
44C2×#14581766C2211yescharacteristic
45C2×#14581762—21no—
46C2×#14581762—21no—
47C2×C4×Dic166C2211yescharacteristic, complemented
48C2×C4×D332C2211yescharacteristic, complemented
49#19128090C2218yescomplemented
50#19128085C2218yescomplemented
51#19128061C2218yescomplemented
52#19128048C2218yescomplemented
53#19127924C2218yescomplemented
54#19127917C2218yescomplemented
55#19127902C2218yescomplemented
56#19127897C2218yescomplemented
57#19127865C2218yescomplemented
58#19127854C2218yescomplemented
59#19127848C2218yescomplemented
60#19127837C2218yescomplemented
61C2×#14581717C2211yescharacteristic, complemented
62C2×#14581717C2211yescharacteristic, complemented
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic, complemented
68C2×#14581714C2211yescharacteristic, complemented
69C2×#117×C83C2211yescharacteristic
70#433×C83C2218yescomplemented
71C2×C4⋊C8×C83C2211yescharacteristic, complemented
72C2×C4⋊C8×C83C2211yescharacteristic, complemented
73C2×C22⋊C8×C83C2211yescharacteristic
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×#97×C83C2211yescharacteristic, complemented
76C2×C4×C8×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050590—22no—
79C2×#13050590—42no—
80C2×#13050590—42no—
81C2×#13050590C2314yes—
82C22×Dic166—21no—
83C22×Dic166C2311yescharacteristic
84C22×Dic166C2311yescharacteristic
85C22×D332—21no—
86C22×D332—22no—
87C22×D332—21no—
88C22×D332—21no—
89C22×D332—21no—
90C22×D332—21no—
91C22×D332—42no—
92C22×D332—42no—
93C22×D332C2311yescharacteristic
94C22×D332C2311yescharacteristic
95C22×D332C2311yescharacteristic
96C22×D332C2311yescharacteristic
97C22×D332C2314yes—
98C22×C22⋊D83—21no—
99C22×C22⋊D83—21no—
100C22×C4×D83—21no—
101C22×C4×D83—21no—
102C2×Dic332—42no—
103C2×Dic332C2314yescomplemented
104C2×#13050579—42no—
105C2×#13050579—42no—
106C2×#13050579—42no—
107C2×#13050579—42no—
108C2×#13050579C2314yes—
109C2×#13050579C2314yes—
110C2×#13050579C2314yescomplemented
111C2×#13050579C2314yescomplemented
112C2×D664—42no—
113C2×D664—42no—
114C2×D664—42no—
115C2×D664C2314yes—
116C2×D664C2314yes—
117C2×D664C2314yescomplemented
118#14581792—22no—
119#14581792C2314yescomplemented
120#14581789—22no—
121#14581789—22no—
122#14581789C2314yes—
123#14581789C2314yes—
124#14581787—28no—
125#14581780—22no—
126#14581780—22no—
127#14581780—22no—
128#14581780C2314yes—
129#14581780C2314yes—
130#14581780C2314yescomplemented
131#14581778—28no—
132#14581774—28no—
133#14581771—22no—
134#14581771C2314yes—
135#14581770—28no—
136#14581767—28no—
137#14581767—28no—
138#14581766—22no—
139#14581766C2314yes—
140#14581762—28no—
141#14581762—28no—
142C4×Dic166—22no—
143C4×Dic166C2314yescomplemented
144C4×D332—22no—
145C4×D332C2314yescomplemented
146C2×C4⋊Dic83—21no—
147C2×C4⋊Dic83C2311yescharacteristic
148C2×C4⋊Dic83C2311yescharacteristic
149C2×Dic83⋊C4—21no—
150C2×Dic83⋊C4—21no—
151C2×C22⋊Dic83—21no—
152C2×(C2×D83)⋊C4—21no—
153C2×(C2×D83)⋊C4—21no—
154C2×(C2×D83)⋊C4—21no—
155C2×(C2×D83)⋊C4—21no—
156C2×(C2×D83)⋊C4—21no—
157C2×(C2×D83)⋊C4—21no—
158C2×(C2×D83)⋊C4—21no—
159C2×(C2×D83)⋊C4—21no—
160C2×C4×Dic83—21no—
161#14581717C2314yescomplemented
162#14581717C2314yescomplemented
163#14581714C2314yes—
164#14581714C2314yes—
165#14581714C2314yes—
166#14581714C2314yes—
167#14581714C2314yescomplemented
168#14581714C2314yescomplemented
169C23×C4×C83C2311yescharacteristic
170C22×C8×C83C2311yescharacteristic
171C22×C8×C83C2311yescharacteristic
172C22×C8×C83C2311yescharacteristic
173C22×C8×C83C2311yescharacteristic
174#117×C83D414yes—
175#117×C83C2314yes—
176C2×C4⋊C4×C83D411yescharacteristic
177C2×C4⋊C4×C83D411yescharacteristic
178C2×C22⋊C4×C83D411yescharacteristic
179C2×C22⋊C4×C83D411yescharacteristic
180C2×C42×C83C2311yescharacteristic
181C2×C42×C83C2311yescharacteristic
182C4⋊C8×C83C2314yescomplemented
183C4⋊C8×C83C2314yescomplemented
184C22⋊C8×C83C2314yes—
185C22⋊C8×C83C2314yes—
186#97×C83C2314yescomplemented
187C4×C8×C83C2314yescomplemented
188C23×D83—21no—
189C23×D83—21no—
190C23×D83—21no—
191C23×D83—21no—
192C23×D83—24no—
193C23×D83—44no—
194C23×D83—82no—
195C23×D83—82no—
196#13050590—44no—
197#13050590—44no—
198#13050590—48no—
199C2×Dic166—22no—
200C2×Dic166—22no—
201C2×Dic166—22no—
202C2×Dic166—22no—
203C2×Dic166—21no—
204C2×Dic166—21no—
205C2×Dic166—24no—
206C2×Dic166—82no—
207C2×Dic166C2412yes—
208C2×Dic166C2412yes—
209C2×D332—22no—
210C2×D332—22no—
211C2×D332—22no—
212C2×D332—22no—
213C2×D332—22no—
214C2×D332—22no—
215C2×D332—22no—
216C2×D332—22no—
217C2×D332—21no—
218C2×D332—24no—
219C2×D332—21no—
220C2×D332—21no—
221C2×D332—21no—
222C2×D332—24no—
223C2×D332—24no—
224C2×D332—24no—
225C2×D332—24no—
226C2×D332—44no—
227C2×D332—44no—
228C2×D332—44no—
229C2×D332—48no—
230C2×D332—82no—
231C2×D332—82no—
232C2×D332—82no—
233C2×D332—82no—
234C2×D332C2412yes—
235C2×D332C2412yes—
236C2×D332C2412yes—
237C2×D332C2412yes—
238C2×C22⋊D83—24no—
239C2×C22⋊D83—24no—
240C2×C22⋊D83—44no—
241C2×C22⋊D83—82no—
242C22×Dic83—21no—
243C22×Dic83—21no—
244C22×Dic83—21no—
245C22×Dic83—21no—
246C2×C4×D83—24no—
247C2×C4×D83—24no—
248C2×C4×D83—44no—
249C2×C4×D83—82no—
250Dic332—44no—
251#13050579—44no—
252#13050579—44no—
253#13050579—44no—
254#13050579—44no—
255D664—44no—
256D664—44no—
257D664—44no—
258C4⋊Dic83—21no—
259C4⋊Dic83—21no—
260C4⋊Dic83—24no—
261C4⋊Dic83C2412yes—
262C4⋊Dic83C2412yes—
263Dic83⋊C4—24no—
264Dic83⋊C4—24no—
265C22⋊Dic83—24no—
266(C2×D83)⋊C4—24no—
267(C2×D83)⋊C4—24no—
268(C2×D83)⋊C4—24no—
269(C2×D83)⋊C4—24no—
270(C2×D83)⋊C4—24no—
271(C2×D83)⋊C4—24no—
272(C2×D83)⋊C4—24no—
273(C2×D83)⋊C4—24no—
274C4×Dic83—24no—
275C24×C83C2×D411yescharacteristic
276C22×C4×C83—22no—
277C22×C4×C83—22no—
278C22×C4×C83C2×D412yes—
279C22×C4×C83C2×D411yescharacteristic
280C22×C4×C83C2×D411yescharacteristic
281C22×C4×C83C2×D411yescharacteristic
282C22×C4×C83C2×D411yescharacteristic
283C22×C4×C83C2×D411yescharacteristic
284C22×C4×C83C2412yes—
285C22×C4×C83C2411yescharacteristic
286C2×C8×C83—22no—
287C2×C8×C83—22no—
288C2×C8×C83—22no—
289C2×C8×C83—22no—
290C2×C8×C83C2412yes—
291C2×C8×C83C2412yes—
292C2×C8×C83C2412yes—
293C2×C8×C83C2412yes—
294C4⋊C4×C83C2×D414yes—
295C4⋊C4×C83C2×D414yes—
296C22⋊C4×C83C2×D414yes—
297C22⋊C4×C83C2×D414yes—
298C42×C83C2×D412yes—
299C42×C83C2×D412yes—
300C42×C83C2412yes—
301C42×C83C2412yes—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83C22×D412yes—
306C23×C83C22×D411yescharacteristic
307C22×D83—22no—
308C22×D83—22no—
309C22×D83—22no—
310C22×D83—22no—
311C22×D83—48no—
312C22×D83—42no—
313C22×D83—42no—
314C22×D83—42no—
315C22×D83—42no—
316C22×D83—42no—
317C22×D83—42no—
318C22×D83—42no—
319C22×D83—42no—
320C22×D83—42no—
321C22×D83—42no—
322C22×D83—42no—
323C22×D83—42no—
324C22×D83—84no—
325C22×D83—84no—
326C22×D83—816no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—24no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83C22×D412yes—
336C2×C4×C83C22×D412yes—
337C2×C4×C83C22×D412yes—
338C2×C4×C83C22×D412yes—
339C2×C4×C83C22×D412yes—
340C2×C4×C83C22×D411yescharacteristic
341C2×C4×C83H(5,𝔽2)12yes—
342C2×C4×C83H(5,𝔽2)12yes—
343C2×C4×C83C2511yescharacteristic
344C22⋊D83—48no—
345C22⋊D83—84no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—42no—
351C2×Dic83—42no—
352C2×Dic83—42no—
353C2×Dic83—42no—
354D332—22no—
355D332—22no—
356D332—22no—
357D332—22no—
358D332—22no—
359D332—22no—
360D332—22no—
361D332—22no—
362D332—48no—
363D332—42no—
364D332—42no—
365D332—42no—
366D332—42no—
367D332—84no—
368D332—84no—
369D332—84no—
370D332—84no—
371C4×D83—48no—
372C4×D83—84no—
373Dic166—22no—
374Dic166—22no—
375Dic166—22no—
376Dic166—22no—
377Dic166—42no—
378Dic166—42no—
379Dic166—84no—
380C8×C83—22no—
381C8×C83—22no—
382C8×C83—22no—
383C8×C83—22no—
384C22×C83—22no—
385C22×C83—22no—
386C22×C83—22no—
387C22×C83—44no—
388C22×C83#53512yes—
389C22×C83#57612yes—
390C22×C83#57712yes—
391C22×C83C23×D411yescharacteristic
392C2×D83—42no—
393C2×D83—42no—
394C2×D83—42no—
395C2×D83—42no—
396C2×D83—42no—
397C2×D83—42no—
398C2×D83—42no—
399C2×D83—42no—
400C2×D83—42no—
401C2×D83—42no—
402C2×D83—42no—
403C2×D83—42no—
404C2×D83—816no—
405C2×D83—84no—
406C2×D83—84no—
407C2×D83—84no—
408C2×D83—84no—
409C4×C83—22no—
410C4×C83—22no—
411C4×C83—22no—
412C4×C83—22no—
413C4×C83—22no—
414C4×C83#53512yes—
415C4×C83C2×H(5,𝔽2)11yescharacteristic
416C4×C83C2×H(5,𝔽2)11yescharacteristic
417Dic83—42no—
418Dic83—42no—
419Dic83—42no—
420Dic83—42no—
421C2×#3224—831nomaximal, Sylow
422C2×C83—42no—
423C2×C83#322414yescomplemented
424C2×C83C2×#53511yescharacteristic
425C2×C83C2×#57611yescharacteristic
426C2×C83C2×#57711yescharacteristic
427D83—82no—
428D83—82no—
429D83—82no—
430D83—82no—
431C2×#542—831no—
432C2×#535—831no—
433#3224—8316no—
434C2×#496—831no—
435C2×#495—831no—
436C2×#489—831no—
437C2×#486—831no—
438C2×#464—831no—
439C2×#460—831no—
440C2×#463—831no—
441C2×#459—831no—
442C2×#452—831no—
443C2×#449—831no—
444C2×#450—831no—
445C2×#447—831no—
446C2×#433D8311yescharacteristic, complemented
447C83C2×#322411yescharacteristic, complemented, Sylow
448C22×#41—831no—
449C23×D4—831no—
450C22×Q16—831no—
451C22×SD16—831no—
452C22×SD16—831no—
453C22×SD16—831no—
454C22×SD16—831no—
455C22×D8—831no—
456C22×D8—831no—
457C22×D8—831no—
458#542—838no—
459#542—1664no—
460#535—838no—
461#535—1664no—
462C2×C4⋊Q8—831no—
463C2×#127—831no—
464C2×#127—831no—
465C2×#126—1661no—
466C2×#124—831no—
467C2×#124—831no—
468C2×#124—831no—
469C2×#124—1661no—
470C2×#123—1661no—
471C2×C22⋊Q8—831no—
472C2×C22⋊Q8—1661no—
473C2×#121—831no—
474C2×#121—1661no—
475C2×#121—1661no—
476C2×#120—1661no—
477C2×#120—1661no—
478C2×C4×Q8—831no—
479C2×C4×D4—831no—
480C2×#117C2×D8311yescharacteristic
481#496—838no—
482#495—838no—
483#489—838no—
484#486—838no—
485#464—838no—
486#463—838no—
487#460—838no—
488#459—838no—
489#452—838no—
490#450—838no—
491#449—838no—
492#447—838no—
493#433C2×D8318yescomplemented
494C2×C4⋊C8C2×D8311yescharacteristic, complemented
495C2×C4⋊C8C2×D8311yescharacteristic, complemented
496C2×#103—831no—
497C2×#103—831no—
498C2×#102—831no—
499C2×#102—831no—
500C2×#102—831no—
501C2×#102—831no—
502C2×#102—831no—
503C2×#102—831no—
504C2×C22⋊C8C2×D8311yescharacteristic
505C2×C22⋊C8C2×D8311yescharacteristic
506C2×#97C2×D8311yescharacteristic, complemented
507C2×C4×C8C2×D8311yescharacteristic, complemented
508C25—1661no—
509C2×#41—3322no—
510C2×#41—3322no—
511C2×#41—834no—
512C2×#41—1662no—
513C22×Q8—831no—
514C22×Q8—831no—
515C22×Q8—1661no—
516C22×D4—3322no—
517C22×D4—3322no—
518C22×D4—834no—
519C22×D4—831no—
520C22×D4—831no—
521C22×D4—831no—
522C22×D4—831no—
523C22×D4—1661no—
524C22×D4—1661no—
525C22×D4—1661no—
526C22×D4—1662no—
527C22×D4—1661no—
528C22×D4—1661no—
529C22×D4—1661no—
530C22×D4—1661no—
531C23×C4—1661no—
532C23×C4—1661no—
533C23×C4C22×D8311yescharacteristic
534C2×Q16—3322no—
535C2×Q16—834no—
536C2×SD16—3322no—
537C2×SD16—3322no—
538C2×SD16—3322no—
539C2×SD16—3322no—
540C2×SD16—834no—
541C2×SD16—834no—
542C2×SD16—834no—
543C2×SD16—834no—
544C2×D8—3322no—
545C2×D8—3322no—
546C2×D8—3322no—
547C2×D8—834no—
548C2×D8—834no—
549C2×D8—834no—
550C22×C8C22×D8311yescharacteristic
551C22×C8C22×D8311yescharacteristic
552C22×C8C22×D8311yescharacteristic
553C22×C8C22×D8311yescharacteristic
554C4⋊Q8—834no—
555C4⋊Q8—1662no—
556#127—834no—
557#127—834no—
558#127—1662no—
559#127—1662no—
560#126—1668no—
561#124—834no—
562#124—834no—
563#124—834no—
564#124—1668no—
565#124—1662no—
566#124—1662no—
567#124—1662no—
568#123—1668no—
569C22⋊Q8—834no—
570C22⋊Q8—1662no—
571C22⋊Q8—1668no—
572#121—834no—
573#121—1662no—
574#121—1668no—
575#121—1668no—
576#120—1668no—
577#120—1668no—
578C4×Q8—834no—
579C4×Q8—1662no—
580C4×D4—834no—
581C4×D4—1662no—
582#117D33214yes—
583#117C22×D8314yes—
584C2×C4⋊C4—831no—
585C2×C4⋊C4—831no—
586C2×C4⋊C4—1661no—
587C2×C4⋊C4—1661no—
588C2×C4⋊C4—1661no—
589C2×C4⋊C4D33211yescharacteristic
590C2×C4⋊C4D33211yescharacteristic
591C2×C22⋊C4—1661no—
592C2×C22⋊C4—1661no—
593C2×C22⋊C4—1661no—
594C2×C22⋊C4—1661no—
595C2×C22⋊C4—1661no—
596C2×C22⋊C4—1661no—
597C2×C22⋊C4—1661no—
598C2×C22⋊C4—1661no—
599C2×C22⋊C4—1661no—
600C2×C22⋊C4D33211yescharacteristic
601C2×C22⋊C4D33211yescharacteristic
602C2×C42—1661no—
603C2×C42C22×D8311yescharacteristic
604C2×C42C22×D8311yescharacteristic
605C4⋊C8C22×D8314yescomplemented
606C4⋊C8C22×D8314yescomplemented
607#103—834no—
608#103—834no—
609#102—834no—
610#102—834no—
611#102—834no—
612#102—834no—
613#102—834no—
614#102—834no—
615C22⋊C8C22×D8314yes—
616C22⋊C8C22×D8314yes—
617#97C22×D8314yescomplemented
618C4×C8C22×D8314yescomplemented
619C24—3324no—
620C24—6642no—
621C24—6642no—
622C24—1661no—
623C24—1661no—
624C24—1661no—
625C24—1661no—
626C24—1664no—
627C24C2×D33211yescharacteristic
628#41—3328no—
629#41—3324no—
630#41—3324no—
631C2×Q8—832no—
632C2×Q8—832no—
633C2×Q8—6642no—
634C2×Q8—1662no—
635C2×Q8—1662no—
636C2×Q8—1662no—
637C2×Q8—1662no—
638C2×Q8—1661no—
639C2×Q8—1661no—
640C2×Q8—1664no—
641C2×D4—3324no—
642C2×D4—3328no—
643C2×D4—3324no—
644C2×D4—3324no—
645C2×D4—3324no—
646C2×D4—832no—
647C2×D4—832no—
648C2×D4—832no—
649C2×D4—832no—
650C2×D4—6642no—
651C2×D4—6642no—
652C2×D4—6642no—
653C2×D4—6642no—
654C2×D4—6642no—
655C2×D4—1664no—
656C2×D4—1664no—
657C2×D4—1661no—
658C2×D4—1664no—
659C2×D4—1661no—
660C2×D4—1661no—
661C2×D4—1661no—
662C2×D4—1664no—
663C2×D4—1664no—
664C2×D4—1664no—
665C2×D4—1664no—
666C2×D4—1662no—
667C2×D4—1662no—
668C2×D4—1662no—
669C2×D4—1662no—
670C2×D4—1662no—
671C2×D4—1662no—
672C2×D4—1662no—
673C2×D4—1662no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—3324no—
677C22×C4—6642no—
678C22×C4—1661no—
679C22×C4—1661no—
680C22×C4—1661no—
681C22×C4—1661no—
682C22×C4—1664no—
683C22×C4—1664no—
684C22×C4C2×D33212yes—
685C22×C4C2×D33211yescharacteristic
686C22×C4C2×D33211yescharacteristic
687C22×C4C2×D33211yescharacteristic
688C22×C4C2×D33211yescharacteristic
689C22×C4C2×D33211yescharacteristic
690C22×C4C23×D8312yes—
691C22×C4C23×D8311yescharacteristic
692Q16—3324no—
693SD16—3324no—
694SD16—3324no—
695SD16—3324no—
696SD16—3324no—
697D8—3324no—
698D8—3324no—
699D8—3324no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8C23×D8312yes—
705C2×C8C23×D8312yes—
706C2×C8C23×D8312yes—
707C2×C8C23×D8312yes—
708C4⋊C4—832no—
709C4⋊C4—832no—
710C4⋊C4—1661no—
711C4⋊C4—1661no—
712C4⋊C4—1664no—
713C4⋊C4—1664no—
714C4⋊C4—1664no—
715C4⋊C4C2×D33214yes—
716C4⋊C4C2×D33214yes—
717C22⋊C4—1664no—
718C22⋊C4—1664no—
719C22⋊C4—1664no—
720C22⋊C4—1664no—
721C22⋊C4—1664no—
722C22⋊C4—1664no—
723C22⋊C4—1664no—
724C22⋊C4—1664no—
725C22⋊C4—1664no—
726C22⋊C4C2×D33214yes—
727C22⋊C4C2×D33214yes—
728C42—1664no—
729C42C2×D33212yes—
730C42C2×D33212yes—
731C42C23×D8312yes—
732C42C23×D8312yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—3328no—
737C23—3322no—
738C23—3322no—
739C23—3322no—
740C23—3322no—
741C23—3322no—
742C23—3322no—
743C23—3322no—
744C23—3322no—
745C23—3322no—
746C23—3322no—
747C23—3322no—
748C23—3322no—
749C23—6644no—
750C23—6644no—
751C23—66416no—
752C23—1662no—
753C23—1662no—
754C23—1662no—
755C23—1662no—
756C23C22×D33212yes—
757C23C22×D33211yescharacteristic
758Q8—3322no—
759Q8—3322no—
760Q8—6644no—
761Q8—1662no—
762Q8—1662no—
763Q8—1662no—
764Q8—1662no—
765D4—3328no—
766D4—3328no—
767D4—3322no—
768D4—3322no—
769D4—3322no—
770D4—3322no—
771D4—6644no—
772D4—6644no—
773D4—6644no—
774D4—6644no—
775D4—6644no—
776D4—1662no—
777D4—1662no—
778D4—1662no—
779D4—1662no—
780D4—1662no—
781D4—1662no—
782D4—1662no—
783D4—1662no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—3328no—
793C2×C4—3322no—
794C2×C4—3322no—
795C2×C4—3322no—
796C2×C4—3322no—
797C2×C4—6644no—
798C2×C4—1662no—
799C2×C4—1662no—
800C2×C4—1662no—
801C2×C4—1662no—
802C2×C4C22×D33212yes—
803C2×C4C22×D33212yes—
804C2×C4C22×D33212yes—
805C2×C4C22×D33212yes—
806C2×C4C22×D33212yes—
807C2×C4C22×D33211yescharacteristic
808C2×C4#1458183812yes—
809C2×C4#1458183812yes—
810C2×C4C24×D8311yescharacteristic
811C8—22no—
812C8—22no—
813C8—22no—
814C8—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—3322no—
820C22—3322no—
821C22—3322no—
822C22—3322no—
823C22—3322no—
824C22—3322no—
825C22—3322no—
826C22—3322no—
827C22—3322no—
828C22—3322no—
829C22—3322no—
830C22—3322no—
831C22—66416no—
832C22—6644no—
833C22—6644no—
834C22—6644no—
835C22—6644no—
836C22#1912827012yes—
837C22#1912850612yes—
838C22#1912851312yes—
839C22C23×D33211yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—3322no—
846C4—3322no—
847C4—3322no—
848C4—3322no—
849C4#1912827012yes—
850C4C2×#1458183811yescharacteristic
851C4C2×#1458183811yescharacteristic
852C2—42no—
853C2—6642no—
854C2—6642no—
855C2—6642no—
856C2—6642no—
857C2#2491855914yesdirect product factor
858C2C2×#1912827011yescharacteristic
859C2C2×#1912850611yescharacteristic
860C2C2×#1912851311yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#433×C83C2
socleC23×C83C22×D4
hypercenterC2×#433D83
hypocenterC83C2×#3224
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#19128322C2semidirect
2. C2×#19128270C2semidirect
3. #24918559C2direct (N × H)
4. C2×#19128090C2semidirect
5. C2×#19128085C2semidirect
6. C2×#19128061C2semidirect
7. C2×#19128048C2semidirect
8. C2×#19127924C2semidirect
9. C2×#19127902C2semidirect
10. C2×#19127917C2semidirect
11. C2×#19127897C2semidirect
12. C2×#19127865C2semidirect
13. C2×#19127848C2semidirect
14. C2×#19127854C2semidirect
15. C2×#19127837C2semidirect
16. C2×#433×C83C2semidirect
19. C22×Dic332C22semidirect
22. C22×#13050579C22semidirect
23. C22×#13050579C22semidirect
26. C22×D664C22semidirect
28. #19128322C22semidirect
30. #19128270C22semidirect
31. C2×#14581792C22semidirect
37. C2×#14581780C22semidirect
47. C2×C4×Dic166C22semidirect
48. C2×C4×D332C22semidirect
49. #19128090C22semidirect
50. #19128085C22semidirect
51. #19128061C22semidirect
52. #19128048C22semidirect
53. #19127924C22semidirect
54. #19127917C22semidirect
55. #19127902C22semidirect
56. #19127897C22semidirect
57. #19127865C22semidirect
58. #19127854C22semidirect
59. #19127848C22semidirect
60. #19127837C22semidirect
61. C2×#14581717C22semidirect
62. C2×#14581717C22semidirect
67. C2×#14581714C22semidirect
68. C2×#14581714C22semidirect
70. #433×C83C22semidirect
71. C2×C4⋊C8×C83C22semidirect
72. C2×C4⋊C8×C83C22semidirect
75. C2×#97×C83C22semidirect
76. C2×C4×C8×C83C22semidirect
103. C2×Dic332C23semidirect
110. C2×#13050579C23semidirect
111. C2×#13050579C23semidirect
117. C2×D664C23semidirect
119. #14581792C23semidirect
130. #14581780C23semidirect
143. C4×Dic166C23semidirect
145. C4×D332C23semidirect
161. #14581717C23semidirect
162. #14581717C23semidirect
167. #14581714C23semidirect
168. #14581714C23semidirect
182. C4⋊C8×C83C23semidirect
183. C4⋊C8×C83C23semidirect
186. #97×C83C23semidirect
187. C4×C8×C83C23semidirect
423. C2×C83#3224semidirect
446. C2×#433D83semidirect
447. C83C2×#3224semidirect
493. #433C2×D83semidirect
494. C2×C4⋊C8C2×D83semidirect
495. C2×C4⋊C8C2×D83semidirect
506. C2×#97C2×D83semidirect
507. C2×C4×C8C2×D83semidirect
605. C4⋊C8C22×D83semidirect
606. C4⋊C8C22×D83semidirect
617. #97C22×D83semidirect
618. C4×C8C22×D83semidirect
857. C2#24918559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283222
C2×#191282702
#249185592
C2×#191280902
C2×#191280852
C2×#191280612
C2×#191280482
C2×#191279242
C2×#191279022
C2×#191279172
C2×#191278972
C2×#191278652
C2×#191278482
C2×#191278542
C2×#191278372
C2×#433×C832
C2×#322483