Finite Group Databasebeta

← C2×#24918019 #36274115

Subgroups — C2×#24918019 #36274115

Order 21248.

2286 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128255C211yesmaximal, characteristic, complemented
2C2×#19128248C211yesmaximal, characteristic
3#24918019C2116yesmaximal, direct product factor
4C2×#19128098C211yesmaximal, characteristic, complemented
5C2×#19128072C211yesmaximal, characteristic, complemented
6C2×#19128050C211yesmaximal, characteristic, complemented
7C2×#19128046C211yesmaximal, characteristic, complemented
8C2×#19127933C211yesmaximal, characteristic, complemented
9C2×#19127931C211yesmaximal, characteristic, complemented
10C2×#19127929C211yesmaximal, characteristic, complemented
11C2×#19127927C211yesmaximal, characteristic, complemented
12C2×C4×#13050579C211yesmaximal, characteristic, complemented
13C2×C4×#13050577C211yesmaximal, characteristic, complemented
14C2×C4×#13050578C211yesmaximal, characteristic, complemented
15C2×C4×C8×D83C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C83C211yesmaximal, characteristic, complemented
17C22×#13050590—21no—
18C22×#13050579C2211yescharacteristic
19C22×#13050578C2211yescharacteristic
20C22×#13050577C2211yescharacteristic
21C22×C8×D83C2211yescharacteristic
22C22×C8×D83C2211yescharacteristic
23#19128255—24no—
24#19128255C2218yescomplemented
25#19128248—24no—
26#19128248C2218yes—
27C2×#14581791C2211yescharacteristic
28C2×#14581791C2211yescharacteristic
29C2×#14581790C2211yescharacteristic
30C2×#14581788C2211yescharacteristic
31C2×#14581782—21no—
32C2×#14581778—21no—
33C2×#14581772C2211yescharacteristic
34C2×#14581770—21no—
35C2×#14581768C2211yescharacteristic
36C2×#14581767C2211yescharacteristic
37C2×#14581765—21no—
38C2×#14581763C2211yescharacteristic
39C2×C4×Dic166—21no—
40C2×C4×Dic166C2211yescharacteristic
41C2×C4×D332C2211yescharacteristic
42C2×C4×C22⋊D83—21no—
43C2×#14581749—21no—
44C2×C42×D83C2211yescharacteristic
45#19128098C2218yescomplemented
46#19128072C2218yescomplemented
47#19128050C2218yescomplemented
48#19128046C2218yescomplemented
49#19127933C2218yescomplemented
50#19127931C2218yescomplemented
51#19127929C2218yescomplemented
52#19127927C2218yescomplemented
53C4×#13050579C2218yescomplemented
54C4×#13050577C2218yescomplemented
55C4×#13050578C2218yescomplemented
56C2×#14581724C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×#14581717C2211yescharacteristic
60C2×#14581716C2211yescharacteristic
61C2×#14581715C2211yescharacteristic
62C2×#14581714C2211yescharacteristic
63C2×#14581713C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×C4×C83⋊C8C2211yescharacteristic
66C2×C8×Dic83C2211yescharacteristic
67C2×C8×Dic83C2211yescharacteristic
68C4×C8×D83C2218yescomplemented
69C22×SD16×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71C2×C4×D4×C83C2211yescharacteristic
72C4×SD16×C83C2218yescomplemented
73C2×#106×C83C2211yescharacteristic
74C2×#103×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×C4×C8×C83C2211yescharacteristic
77C2×#13050590—28no—
78C2×#13050590—48no—
79C22×Dic166—21no—
80C22×Dic166—21no—
81C22×Dic166C2311yescharacteristic
82C22×D332—21no—
83C22×D332C2311yescharacteristic
84C22×C22⋊D83—21no—
85C22×C22⋊D83—21no—
86C22×C22⋊D83—21no—
87C22×C4×D83—21no—
88C22×C4×D83D411yescharacteristic
89C22×C4×D83D411yescharacteristic
90C22×C4×D83C2311yescharacteristic
91C2×#13050579—24no—
92C2×#13050579C2314yes—
93C2×#13050578—24no—
94C2×#13050578C2314yes—
95C2×#13050577—24no—
96C2×#13050577C2314yes—
97C22×C83⋊C8C2311yescharacteristic
98C22×C83⋊C8C2311yescharacteristic
99C2×C8×D83—24no—
100C2×C8×D83—24no—
101C2×C8×D83C2314yes—
102C2×C8×D83C2314yes—
103#14581791—22no—
104#14581791—22no—
105#14581791C2314yes—
106#14581791C2314yes—
107#14581790—22no—
108#14581790C2314yes—
109#14581788—22no—
110#14581788C2314yes—
111#14581782—28no—
112#14581778—28no—
113#14581772—22no—
114#14581772C2314yes—
115#14581770—28no—
116#14581768—22no—
117#14581768C2314yes—
118#14581767—22no—
119#14581767C2314yes—
120#14581765—28no—
121#14581763—22no—
122#14581763C2314yes—
123C4×Dic166—28no—
124C4×Dic166—22no—
125C4×Dic166C2314yes—
126C4×D332—22no—
127C4×D332C2314yes—
128C4×C22⋊D83—28no—
129#14581749—28no—
130C2×C4⋊Dic83—21no—
131C2×C4⋊Dic83C2311yescharacteristic
132C2×C4⋊Dic83C2311yescharacteristic
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4—21no—
137C2×Dic83⋊C4—21no—
138C2×Dic83⋊C4—21no—
139C2×C22⋊Dic83—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×C4×Dic83—21no—
145C2×C4×Dic83D411yescharacteristic
146C2×C4×Dic83D411yescharacteristic
147C2×C4×Dic83C2311yescharacteristic
148C42×D83D414yes—
149C42×D83C2314yes—
150#14581724C2314yes—
151#14581723C2314yes—
152#14581723C2314yes—
153#14581717C2314yes—
154#14581716C2314yes—
155#14581715C2314yes—
156#14581714C2314yes—
157#14581713C2314yes—
158#14581712C2314yes—
159C4×C83⋊C8C2314yes—
160C8×Dic83C2314yes—
161C8×Dic83C2314yes—
162C22×Q8×C83C2311yescharacteristic
163C22×D4×C83C2311yescharacteristic
164C23×C4×C83—21no—
165C2×SD16×C83—24no—
166C2×SD16×C83C2314yes—
167C22×C8×C83C2311yescharacteristic
168C22×C8×C83C2311yescharacteristic
169C4×Q8×C83—22no—
170C4×Q8×C83C2314yes—
171C4×D4×C83—22no—
172C4×D4×C83C2314yes—
173C2×C4⋊C4×C83—21no—
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C4⋊C4×C83C2311yescharacteristic
176C2×C22⋊C4×C83—21no—
177C2×C42×C83—21no—
178C2×C42×C83C2311yescharacteristic
179#106×C83C2314yes—
180#103×C83C2314yes—
181#102×C83C2314yes—
182C4×C8×C83C2314yes—
183C23×D83—21no—
184C23×D83C2×D411yescharacteristic
185#13050590—432no—
186C2×Dic166—22no—
187C2×Dic166—22no—
188C2×Dic166—21no—
189C2×Dic166—24no—
190C2×Dic166—24no—
191C2×Dic166—44no—
192C2×Dic166—44no—
193C2×Dic166C2412yes—
194C2×D332—22no—
195C2×D332—22no—
196C2×D332—24no—
197C2×D332—21no—
198C2×D332—44no—
199C2×D332C2412yes—
200C2×C22⋊D83—24no—
201C2×C22⋊D83—24no—
202C2×C22⋊D83—24no—
203C2×C22⋊D83—44no—
204C2×C22⋊D83—44no—
205C2×C22⋊D83—44no—
206C22×Dic83—21no—
207C22×Dic83—21no—
208C22×Dic83—21no—
209C22×Dic83C2×D411yescharacteristic
210C22×Dic83C2×D411yescharacteristic
211C22×Dic83C2×D411yescharacteristic
212C2×C4×D83—22no—
213C2×C4×D83—22no—
214C2×C4×D83—24no—
215C2×C4×D83—24no—
216C2×C4×D83—44no—
217C2×C4×D83SD1618yescomplemented
218C2×C4×D83C2×D412yes—
219C2×C4×D83C2×D414yes—
220C2×C4×D83C2×D414yes—
221C2×C4×D83C2412yes—
222#13050579—28no—
223#13050578—28no—
224#13050577—28no—
225C2×C83⋊C8—22no—
226C2×C83⋊C8#4114yescomplemented
227C2×C83⋊C8C2412yes—
228C2×C83⋊C8C2412yes—
229C8×D83—28no—
230C8×D83—28no—
231C4⋊Dic83—21no—
232C4⋊Dic83—21no—
233C4⋊Dic83—24no—
234C4⋊Dic83C2412yes—
235C4⋊Dic83C2412yes—
236Dic83⋊C4—24no—
237Dic83⋊C4—24no—
238Dic83⋊C4—24no—
239Dic83⋊C4—24no—
240Dic83⋊C4—24no—
241Dic83⋊C4—24no—
242C22⋊Dic83—24no—
243(C2×D83)⋊C4—24no—
244(C2×D83)⋊C4—24no—
245(C2×D83)⋊C4—24no—
246(C2×D83)⋊C4—24no—
247C4×Dic83—24no—
248C4×Dic83C2×D414yes—
249C4×Dic83C2×D412yes—
250C4×Dic83C2×D414yes—
251C4×Dic83C2412yes—
252C24×C83—21no—
253C2×Q8×C83—21no—
254C2×Q8×C83—22no—
255C2×Q8×C83—22no—
256C2×Q8×C83C2412yes—
257C2×D4×C83—21no—
258C2×D4×C83—22no—
259C2×D4×C83—22no—
260C2×D4×C83C2412yes—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83—24no—
265C22×C4×C83—44no—
266C22×C4×C83C2×D411yescharacteristic
267C22×C4×C83C2×D411yescharacteristic
268C22×C4×C83C2411yescharacteristic
269SD16×C83—28no—
270C2×C8×C83—22no—
271C2×C8×C83#4114yescomplemented
272C2×C8×C83C2412yes—
273C2×C8×C83C2412yes—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—24no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83C2412yes—
278C4⋊C4×C83C2412yes—
279C22⋊C4×C83—24no—
280C42×C83—24no—
281C42×C83C2×D412yes—
282C42×C83C2412yes—
283C23×C83—22no—
284C23×C83—42no—
285C23×C83—42no—
286C23×C83—42no—
287C23×C83C22×D411yescharacteristic
288C22×D83—22no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—42no—
292C22×D83—42no—
293C22×D83—42no—
294C22×D83C2×SD1614yes—
295C22×D83C22×D412yes—
296Q8×C83—22no—
297Q8×C83—22no—
298Q8×C83—42no—
299D4×C83—22no—
300D4×C83—22no—
301D4×C83—42no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—42no—
307C2×C4×C83—42no—
308C2×C4×C83—42no—
309C2×C4×C83—48no—
310C2×C4×C83C2×SD1614yes—
311C2×C4×C83C22×D412yes—
312C2×C4×C83C22×D411yescharacteristic
313C2×C4×C83C22×D412yes—
314C2×C4×C83C2×#4112yes—
315C2×C4×C83C2×#4112yes—
316C2×C4×C83C2511yescharacteristic
317C22⋊D83—48no—
318C22⋊D83—48no—
319C22⋊D83—48no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—42no—
325C2×Dic83—42no—
326C2×Dic83—42no—
327C2×Dic83C2×SD1614yes—
328C2×Dic83#13514yes—
329C2×Dic83C22×D412yes—
330C2×Dic83C22×D412yes—
331C2×Dic83C22×D412yes—
332D332—22no—
333D332—22no—
334D332—48no—
335D332—42no—
336C4×D83—24no—
337C4×D83—22no—
338C4×D83—22no—
339C4×D83—28no—
340C4×D83—48no—
341C4×D83C2×SD16116yescomplemented
342Dic166—22no—
343Dic166—22no—
344Dic166—42no—
345Dic166—48no—
346Dic166—48no—
347C8×C83—22no—
348C8×C83C2×#4114yescomplemented
349C83⋊C8—22no—
350C83⋊C8C2×#4114yescomplemented
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—42no—
354C22×C83—84no—
355C22×C83#53212yes—
356C22×C83C22×SD1612yes—
357C22×C83C2×#13512yes—
358C22×C83C23×D411yescharacteristic
359C2×D83—28no—
360C2×D83—22no—
361C2×D83—22no—
362C2×D83—42no—
363C2×D83—42no—
364C2×D83—42no—
365C2×D83—84no—
366C2×D83C22×SD1614yes—
367C4×C83—22no—
368C4×C83—42no—
369C4×C83—42no—
370C4×C83—42no—
371C4×C83#53212yes—
372C4×C83C22×SD1614yes—
373C4×C83C22×#4111yescharacteristic
374C4×C83C22×#4111yescharacteristic
375Dic83—22no—
376Dic83—42no—
377Dic83—42no—
378Dic83—42no—
379Dic83C22×SD1614yes—
380Dic83C2×#13514yes—
381C2×#3167—831nomaximal, Sylow
382C2×C83—82no—
383C2×C83#316714yescomplemented
384C2×C83C2×#53211yescharacteristic
385C2×C83C23×SD1611yescharacteristic
386C2×C83C22×#13511yescharacteristic
387D83—24no—
388D83—82no—
389C2×#533—831no—
390C2×#532—831no—
391#3167—8316no—
392C2×#498—831no—
393C2×#492—831no—
394C2×#487—831no—
395C2×#486—831no—
396C2×#465—831no—
397C2×#465—831no—
398C2×#465—831no—
399C2×#465—831no—
400C2×C4×SD16—831no—
401C2×C4×SD16—831no—
402C2×C4×SD16—831no—
403C2×C4×SD16D8311yescharacteristic, complemented
404C22×C4×C8—831no—
405C83C2×#316711yescharacteristic, complemented, Sylow
406C22×#41—1661no—
407C22×SD16—831no—
408C22×SD16—831no—
409C22×SD16—831no—
410C22×SD16C2×D8311yescharacteristic
411C23×C8—831no—
412C23×C8—831no—
413#533—838no—
414#533—1664no—
415#532—838no—
416#532—1664no—
417C2×C4⋊Q8—831no—
418C2×C4⋊Q8—831no—
419C2×C4⋊Q8—831no—
420C2×#127—831no—
421C2×#125—1661no—
422C2×#124—1661no—
423C2×C22⋊Q8—831no—
424C2×C22⋊Q8—831no—
425C2×C22⋊Q8—1661no—
426C2×#121—831no—
427C2×#121—831no—
428C2×#121—1661no—
429C2×C4×Q8—831no—
430C2×C4×Q8—1661no—
431C2×C4×Q8C2×D8311yescharacteristic
432C2×C4×D4—831no—
433C2×C4×D4—1661no—
434C2×C4×D4C2×D8311yescharacteristic
435C2×#117—1661no—
436C22×C42—831no—
437#498—838no—
438#492—838no—
439#487—838no—
440#486—838no—
441#465—838no—
442#465—838no—
443#465—838no—
444#465—838no—
445C4×SD16—838no—
446C4×SD16—838no—
447C4×SD16—838no—
448C4×SD16C2×D8318yescomplemented
449C2×#106—831no—
450C2×#106—831no—
451C2×#106—831no—
452C2×#106C2×D8311yescharacteristic
453C2×#103—831no—
454C2×#103—831no—
455C2×#103—831no—
456C2×#103C2×D8311yescharacteristic
457C2×#102—831no—
458C2×#102—831no—
459C2×#102—831no—
460C2×#102C2×D8311yescharacteristic
461C2×C4×C8—831no—
462C2×C4×C8—831no—
463C2×C4×C8—831no—
464C2×C4×C8—838no—
465C2×C4×C8C2×D8311yescharacteristic
466C2×#41—3328no—
467C2×#41—1668no—
468C22×Q8—831no—
469C22×Q8—1661no—
470C22×Q8—1661no—
471C22×Q8C22×D8311yescharacteristic
472C22×D4—831no—
473C22×D4—1661no—
474C22×D4—1661no—
475C22×D4—1661no—
476C22×D4—1661no—
477C22×D4C22×D8311yescharacteristic
478C23×C4—21no—
479C23×C4—831no—
480C23×C4—831no—
481C23×C4—831no—
482C23×C4—1661no—
483C2×SD16—24no—
484C2×SD16—834no—
485C2×SD16—834no—
486C2×SD16—834no—
487C2×SD16—1664no—
488C2×SD16—1664no—
489C2×SD16—1664no—
490C2×SD16C22×D8314yes—
491C22×C8—831no—
492C22×C8—831no—
493C22×C8—834no—
494C22×C8—834no—
495C22×C8—1664no—
496C22×C8—1664no—
497C22×C8C22×D8311yescharacteristic
498C22×C8C22×D8311yescharacteristic
499C4⋊Q8—834no—
500C4⋊Q8—834no—
501C4⋊Q8—834no—
502C4⋊Q8—1662no—
503C4⋊Q8—1662no—
504C4⋊Q8—1662no—
505#127—834no—
506#127—1662no—
507#125—1668no—
508#124—1668no—
509C22⋊Q8—834no—
510C22⋊Q8—834no—
511C22⋊Q8—1668no—
512C22⋊Q8—1662no—
513C22⋊Q8—1662no—
514#121—834no—
515#121—834no—
516#121—1668no—
517#121—1662no—
518#121—1662no—
519C4×Q8—22no—
520C4×Q8—834no—
521C4×Q8—1668no—
522C4×Q8—1662no—
523C4×Q8C22×D8314yes—
524C4×D4—22no—
525C4×D4—834no—
526C4×D4—1668no—
527C4×D4—1662no—
528C4×D4C22×D8314yes—
529#117—1668no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—831no—
532C2×C4⋊C4—831no—
533C2×C4⋊C4—1661no—
534C2×C4⋊C4—1661no—
535C2×C4⋊C4—1661no—
536C2×C4⋊C4—1661no—
537C2×C4⋊C4—1661no—
538C2×C4⋊C4—1661no—
539C2×C4⋊C4—1661no—
540C2×C4⋊C4C22×D8311yescharacteristic
541C2×C4⋊C4C22×D8311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1661no—
544C2×C22⋊C4—1661no—
545C2×C22⋊C4—1661no—
546C2×C22⋊C4—1661no—
547C2×C22⋊C4—1661no—
548C2×C42—21no—
549C2×C42—831no—
550C2×C42—831no—
551C2×C42—831no—
552C2×C42—834no—
553C2×C42—834no—
554C2×C42—1661no—
555C2×C42C22×D8311yescharacteristic
556#106—834no—
557#106—834no—
558#106—834no—
559#106C22×D8314yes—
560#103—834no—
561#103—834no—
562#103—834no—
563#103C22×D8314yes—
564#102—834no—
565#102—834no—
566#102—834no—
567#102C22×D8314yes—
568C4×C8—834no—
569C4×C8—834no—
570C4×C8—834no—
571C4×C8C22×D8314yes—
572C24—21no—
573C24—831no—
574C24—1661no—
575#41—33232no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—3324no—
580C2×Q8—3324no—
581C2×Q8—832no—
582C2×Q8—1664no—
583C2×Q8—1664no—
584C2×Q8—1662no—
585C2×Q8—1662no—
586C2×Q8—1661no—
587C2×Q8C23×D8312yes—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—3324no—
592C2×D4—3324no—
593C2×D4—3324no—
594C2×D4—3324no—
595C2×D4—832no—
596C2×D4—1664no—
597C2×D4—1664no—
598C2×D4—1664no—
599C2×D4—1664no—
600C2×D4—1661no—
601C2×D4—1662no—
602C2×D4—1662no—
603C2×D4C23×D8312yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—44no—
609C22×C4—3324no—
610C22×C4—831no—
611C22×C4—831no—
612C22×C4—838no—
613C22×C4—834no—
614C22×C4—831no—
615C22×C4—834no—
616C22×C4—832no—
617C22×C4—832no—
618C22×C4—1664no—
619C22×C4—1661no—
620C22×C4—1661no—
621C22×C4—1661no—
622C22×C4—1664no—
623C22×C4—1662no—
624C22×C4—1662no—
625C22×C4D4×D8311yescharacteristic
626C22×C4D4×D8311yescharacteristic
627C22×C4C23×D8311yescharacteristic
628SD16—28no—
629SD16—1668no—
630SD16—1668no—
631SD16—1668no—
632C2×C8—22no—
633C2×C8—834no—
634C2×C8—832no—
635C2×C8—832no—
636C2×C8—1668no—
637C2×C8—1662no—
638C2×C8—1668no—
639C2×C8#1305059014yescomplemented
640C2×C8C23×D8312yes—
641C2×C8C23×D8312yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—832no—
646C4⋊C4—832no—
647C4⋊C4—1664no—
648C4⋊C4—1664no—
649C4⋊C4—1664no—
650C4⋊C4—1664no—
651C4⋊C4—1664no—
652C4⋊C4—1664no—
653C4⋊C4—1661no—
654C4⋊C4—1661no—
655C4⋊C4—1664no—
656C4⋊C4C23×D8312yes—
657C4⋊C4C23×D8312yes—
658C22⋊C4—24no—
659C22⋊C4—1664no—
660C22⋊C4—1664no—
661C22⋊C4—1664no—
662C22⋊C4—1664no—
663C22⋊C4—1664no—
664C42—24no—
665C42—834no—
666C42—834no—
667C42—832no—
668C42—832no—
669C42—1664no—
670C42D4×D8312yes—
671C42C23×D8312yes—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—3322no—
677C23—3322no—
678C23—3322no—
679C23—834no—
680C23—832no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23C2×D4×D8311yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—3328no—
689Q8—3328no—
690Q8—3322no—
691Q8—1662no—
692Q8—1662no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—3328no—
697D4—3328no—
698D4—3328no—
699D4—3328no—
700D4—3322no—
701D4—1662no—
702D4—1662no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—48no—
711C2×C4—3322no—
712C2×C4—3322no—
713C2×C4—3322no—
714C2×C4—3328no—
715C2×C4—834no—
716C2×C4—834no—
717C2×C4—832no—
718C2×C4—832no—
719C2×C4—8316no—
720C2×C4—832no—
721C2×C4—1668no—
722C2×C4—1662no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1664no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4SD16×D8314yes—
730C2×C4C2×D4×D8312yes—
731C2×C4C2×D4×D8312yes—
732C2×C4C2×D4×D8311yescharacteristic
733C2×C4#41×D8312yes—
734C2×C4C2×#1305059012yes—
735C2×C4C24×D8311yescharacteristic
736C8—22no—
737C8—834no—
738C8—1662no—
739C8C2×#1305059014yescomplemented
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—3322no—
745C22—3322no—
746C22—3322no—
747C22—834no—
748C22—6644no—
749C22—1668no—
750C22—1662no—
751C22—1662no—
752C22#1912824812yes—
753C22C2×SD16×D8312yes—
754C22#135×D8312yes—
755C22C22×D4×D8311yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—3322no—
761C4—3322no—
762C4—3322no—
763C4—834no—
764C4—834no—
765C4—1662no—
766C4#1912824812yes—
767C4C2×SD16×D8314yes—
768C4C2×#41×D8311yescharacteristic
769C4C22×#1305059011yescharacteristic
770C2—82no—
771C2—6642no—
772C2—1664no—
773C2#2491801914yesdirect product factor
774C2C2×#1912824811yescharacteristic
775C2C22×SD16×D8311yescharacteristic
776C2C2×#135×D8311yescharacteristic
subgroupG/H
centerC22×C4D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×C4×SD16×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128248C2
hypercenterC2×C4×SD16D83
hypocenterC83C2×#3167
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#19128255C2semidirect
3. #24918019C2direct (N × H)
4. C2×#19128098C2semidirect
5. C2×#19128072C2semidirect
6. C2×#19128050C2semidirect
7. C2×#19128046C2semidirect
8. C2×#19127933C2semidirect
9. C2×#19127931C2semidirect
10. C2×#19127929C2semidirect
11. C2×#19127927C2semidirect
12. C2×C4×#13050579C2semidirect
13. C2×C4×#13050577C2semidirect
14. C2×C4×#13050578C2semidirect
15. C2×C4×C8×D83C2semidirect
16. C2×C4×SD16×C83C2semidirect
24. #19128255C22semidirect
45. #19128098C22semidirect
46. #19128072C22semidirect
47. #19128050C22semidirect
48. #19128046C22semidirect
49. #19127933C22semidirect
50. #19127931C22semidirect
51. #19127929C22semidirect
52. #19127927C22semidirect
53. C4×#13050579C22semidirect
54. C4×#13050577C22semidirect
55. C4×#13050578C22semidirect
68. C4×C8×D83C22semidirect
72. C4×SD16×C83C22semidirect
217. C2×C4×D83SD16semidirect
226. C2×C83⋊C8#41semidirect
271. C2×C8×C83#41semidirect
341. C4×D83C2×SD16semidirect
348. C8×C83C2×#41semidirect
350. C83⋊C8C2×#41semidirect
383. C2×C83#3167semidirect
403. C2×C4×SD16D83semidirect
405. C83C2×#3167semidirect
448. C4×SD16C2×D83semidirect
639. C2×C8#13050590semidirect
739. C8C2×#13050590semidirect
773. C2#24918019direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282552
C2×#191282482
#249180192
C2×#191280982
C2×#191280722
C2×#191280502
C2×#191280462
C2×#191279332
C2×#191279312
C2×#191279292
C2×#191279272
C2×C4×#130505792
C2×C4×#130505772
C2×C4×#130505782
C2×C4×C8×D832
C2×C4×SD16×C832
C2×#316783