Finite Group Databasebeta

← C2×#24919935 #36282969

Subgroups — C2×#24919935 #36282969

Order 21248.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128397C211yesmaximal, characteristic, complemented
2C2×#19128355C211yesmaximal, characteristic, complemented
3#24919935C2116yesmaximal, direct product factor
4C2×#19128110C211yesmaximal, characteristic, complemented
5C2×#19128020C211yesmaximal, characteristic, complemented
6C2×#19128020C211yesmaximal, characteristic, complemented
7C2×#19128026C211yesmaximal, characteristic, complemented
8C2×#19128015C211yesmaximal, characteristic, complemented
9C2×#19128002C211yesmaximal, characteristic, complemented
10C2×#19127992C211yesmaximal, characteristic, complemented
11C2×#19127954C211yesmaximal, characteristic, complemented
12C2×#19127937C211yesmaximal, characteristic, complemented
13C2×#19127814C211yesmaximal, characteristic, complemented
14C2×#19127743C211yesmaximal, characteristic, complemented
15C22×#14581724C211yesmaximal, characteristic, complemented
16C2×#435×C83C211yesmaximal, characteristic, complemented
17C22×#13050589—21no—
18C22×D664C2211yescharacteristic
19#19128397—24no—
20#19128397C2218yescomplemented
21#19128355—24no—
22#19128355C2218yescomplemented
23C2×#14581792C2211yescharacteristic
24C2×#14581787—21no—
25C2×#14581784C2211yescharacteristic
26C2×#14581776—21no—
27C2×#14581776—21no—
28C2×#14581774—21no—
29C2×#14581772—21no—
30C2×#14581766C2211yescharacteristic
31C2×#14581766C2211yescharacteristic
32C2×#14581766C2211yescharacteristic
33C2×#14581766C2211yescharacteristic
34C2×#14581764—21no—
35C2×C4×D332C2211yescharacteristic
36C2×C4×D332C2211yescharacteristic
37C2×(C22⋊D83)⋊C4—21no—
38C2×#14581751C2211yescharacteristic
39C22×C4⋊Dic83C2211yescharacteristic
40C22×C4⋊Dic83C2211yescharacteristic
41C22×C4⋊Dic83C2211yescharacteristic
42#19128110C2218yescomplemented
43#19128026C2218yescomplemented
44#19128020C2218yescomplemented
45#19128020C2218yescomplemented
46#19128015C2218yescomplemented
47#19128002C2218yescomplemented
48#19127992C2218yescomplemented
49#19127954C2218yescomplemented
50#19127937C2218yescomplemented
51#19127814C2218yescomplemented
52#19127743C2218yescomplemented
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581726C2211yescharacteristic
56C2×#14581724C2211yescharacteristic
57C2×#14581724C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581724C2211yescharacteristic
60C2×#14581724C2211yescharacteristic
61C2×#14581724C2211yescharacteristic
62C2×#14581724C2218yescomplemented
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic
68C2×#14581714C2211yescharacteristic
69C22×M16×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic
71C2×C4×D4×C83C2211yescharacteristic
72#435×C83C2218yescomplemented
73C2×C4⋊C8×C83C2211yescharacteristic
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic
77C2×#13050589—28no—
78C2×#13050589—48no—
79C22×Dic166—21no—
80C22×D332C2311yescharacteristic
81C22×D332C2311yescharacteristic
82C22×C22⋊D83—21no—
83C22×C22⋊D83—21no—
84C22×C22⋊D83—21no—
85C22×C22⋊D83—21no—
86C23×Dic83—21no—
87C23×Dic83—21no—
88C23×Dic83—21no—
89C22×C4×D83—21no—
90C22×C4×D83—21no—
91C2×D664—24no—
92C2×D664C2314yes—
93#14581792—22no—
94#14581792C2314yes—
95#14581787—28no—
96#14581784—22no—
97#14581784C2314yes—
98#14581776—28no—
99#14581776—28no—
100#14581774—28no—
101#14581772—28no—
102#14581766—22no—
103#14581766—22no—
104#14581766—22no—
105#14581766—22no—
106#14581766C2314yes—
107#14581766C2314yes—
108#14581766C2314yes—
109#14581766C2314yes—
110#14581764—28no—
111C4×D332—22no—
112C4×D332—22no—
113C4×D332C2314yes—
114C4×D332C2314yes—
115(C22⋊D83)⋊C4—28no—
116#14581751—22no—
117#14581751C2314yes—
118C2×C4⋊Dic83—22no—
119C2×C4⋊Dic83—22no—
120C2×C4⋊Dic83—22no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83—21no—
124C2×C4⋊Dic83—21no—
125C2×C4⋊Dic83C2314yes—
126C2×C4⋊Dic83C2314yes—
127C2×C4⋊Dic83C2314yes—
128C2×C4⋊Dic83C2311yescharacteristic
129C2×C4⋊Dic83C2311yescharacteristic
130C2×C4⋊Dic83C2311yescharacteristic
131C2×C4⋊Dic83C2311yescharacteristic
132C2×C4⋊Dic83C2311yescharacteristic
133C2×C4⋊Dic83C2311yescharacteristic
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×C22⋊Dic83—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×C4×Dic83—21no—
144#14581726C2314yes—
145#14581726C2314yes—
146#14581726C2314yes—
147#14581724C2314yes—
148#14581724C2314yes—
149#14581724C2314yes—
150#14581724C2314yes—
151#14581724C2314yes—
152#14581724C2314yes—
153#14581714C2314yes—
154#14581714C2314yes—
155#14581714C2314yes—
156#14581714C2314yes—
157#14581714C2314yes—
158#14581714C2314yes—
159C22×D4×C83D411yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C23×C4×C83C2311yescharacteristic
162C2×M16×C83—24no—
163C2×M16×C83C2314yes—
164C22×C8×C83—24no—
165C22×C8×C83C2314yes—
166C22×C8×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168C22×C8×C83C2311yescharacteristic
169C22×C8×C83C2311yescharacteristic
170C4×D4×C83D414yes—
171C4×D4×C83C2314yes—
172C2×C4⋊C4×C83D411yescharacteristic
173C2×C22⋊C4×C83D411yescharacteristic
174C2×C22⋊C4×C83D411yescharacteristic
175C2×C42×C83C2311yescharacteristic
176C4⋊C8×C83C2314yes—
177C22⋊C8×C83C2314yes—
178C22⋊C8×C83C2314yes—
179#97×C83C2314yes—
180C23×D83—21no—
181C23×D83—21no—
182#13050589—432no—
183C2×Dic166—24no—
184C2×Dic166—44no—
185C2×D332—22no—
186C2×D332—22no—
187C2×D332—22no—
188C2×D332—22no—
189C2×D332—21no—
190C2×D332—21no—
191C2×D332C2412yes—
192C2×D332C2412yes—
193C2×C22⋊D83—24no—
194C2×C22⋊D83—24no—
195C2×C22⋊D83—24no—
196C2×C22⋊D83—24no—
197C2×C22⋊D83—44no—
198C2×C22⋊D83—44no—
199C2×C22⋊D83—44no—
200C2×C22⋊D83—82no—
201C22×Dic83—24no—
202C22×Dic83—24no—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C22×Dic83—21no—
206C22×Dic83—21no—
207C22×Dic83—21no—
208C22×Dic83—21no—
209C22×Dic83—24no—
210C22×Dic83—44no—
211C22×Dic83—44no—
212C22×Dic83—82no—
213C2×C4×D83—24no—
214C2×C4×D83—24no—
215C2×C4×D83—44no—
216C2×C4×D83—82no—
217D664—28no—
218C4⋊Dic83—21no—
219C4⋊Dic83—21no—
220C4⋊Dic83—21no—
221C4⋊Dic83—21no—
222C4⋊Dic83—24no—
223C4⋊Dic83—24no—
224C4⋊Dic83—24no—
225C4⋊Dic83—24no—
226C4⋊Dic83—21no—
227C4⋊Dic83—21no—
228C4⋊Dic83C2412yes—
229C4⋊Dic83C2412yes—
230C4⋊Dic83C2412yes—
231C4⋊Dic83C2412yes—
232C4⋊Dic83C2412yes—
233C4⋊Dic83C2412yes—
234Dic83⋊C4—24no—
235Dic83⋊C4—24no—
236C22⋊Dic83—24no—
237(C2×D83)⋊C4—24no—
238(C2×D83)⋊C4—24no—
239(C2×D83)⋊C4—24no—
240(C2×D83)⋊C4—24no—
241(C2×D83)⋊C4—24no—
242(C2×D83)⋊C4—24no—
243C4×Dic83—24no—
244C24×C83C2×D411yescharacteristic
245C24×C83C2×D411yescharacteristic
246C2×D4×C83—24no—
247C2×D4×C83C2×D414yes—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83C2×D412yes—
253C22×C4×C83C2×D412yes—
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2×D411yescharacteristic
258C22×C4×C83C2412yes—
259C22×C4×C83C2412yes—
260C22×C4×C83C2411yescharacteristic
261M16×C83—28no—
262C2×C8×C83—22no—
263C2×C8×C83—22no—
264C2×C8×C83—22no—
265C2×C8×C83—28no—
266C2×C8×C83#4114yescomplemented
267C2×C8×C83C2412yes—
268C2×C8×C83C2412yes—
269C2×C8×C83C2412yes—
270C2×C8×C83C2412yes—
271C4⋊C4×C83C2×D414yes—
272C22⋊C4×C83C2×D414yes—
273C22⋊C4×C83C2×D414yes—
274C42×C83C2×D412yes—
275C42×C83C2412yes—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—22no—
279C23×C83—22no—
280C23×C83—22no—
281C23×C83AGL(1,ℤ/8)14yes—
282C23×C83C22×D412yes—
283C23×C83C22×D412yes—
284C23×C83C22×D411yescharacteristic
285C22×D83—22no—
286C22×D83—22no—
287C22×D83—42no—
288C22×D83—42no—
289C22×D83—42no—
290C22×D83—42no—
291C22×D83—42no—
292C22×D83—42no—
293D4×C83—28no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—24no—
299C2×C4×C83—24no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83C22×D412yes—
305C2×C4×C83C22×D412yes—
306C2×C4×C83C22×D412yes—
307C2×C4×C83C22×D412yes—
308C2×C4×C83C22×D411yescharacteristic
309C2×C4×C83C2×#4112yes—
310C2×C4×C832−1+412yes—
311C2×C4×C83C2511yescharacteristic
312C22⋊D83—48no—
313C22⋊D83—48no—
314C22⋊D83—48no—
315C22⋊D83—84no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—48no—
323C2×Dic83—42no—
324C2×Dic83—42no—
325C2×Dic83—42no—
326C2×Dic83—48no—
327C2×Dic83—42no—
328C2×Dic83—42no—
329C2×Dic83—42no—
330C2×Dic83—84no—
331D332—22no—
332D332—22no—
333D332—22no—
334D332—22no—
335D332—42no—
336D332—42no—
337C4×D83—48no—
338C4×D83—84no—
339Dic166—48no—
340C8×C83—22no—
341C8×C83—22no—
342C8×C83—22no—
343C8×C83C2×#4114yescomplemented
344C22×C83—28no—
345C22×C83—22no—
346C22×C83—22no—
347C22×C83—22no—
348C22×C83—22no—
349C22×C83—22no—
350C22×C83—44no—
351C22×C83#54712yes—
352C22×C83C2×AGL(1,ℤ/8)14yes—
353C22×C83C2×AGL(1,ℤ/8)12yes—
354C22×C83#57712yes—
355C22×C83C23×D411yescharacteristic
356C2×D83—42no—
357C2×D83—42no—
358C2×D83—42no—
359C2×D83—42no—
360C2×D83—42no—
361C2×D83—42no—
362C2×D83—84no—
363C2×D83—84no—
364C4×C83—22no—
365C4×C83—22no—
366C4×C83—22no—
367C4×C83—22no—
368C4×C83#54712yes—
369C4×C83C22×#4111yescharacteristic
370C4×C83C2×2−1+411yescharacteristic
371Dic83—42no—
372Dic83—42no—
373Dic83—42no—
374Dic83—42no—
375Dic83—42no—
376Dic83—42no—
377C2×#3345—831nomaximal, Sylow
378C2×C83—24no—
379C2×C83—42no—
380C2×C83#334514yescomplemented
381C2×C83C2×#54711yescharacteristic
382C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C83C2×#57711yescharacteristic
384D83—82no—
385D83—82no—
386C2×#553—831no—
387C2×#547—831no—
388#3345—8316no—
389C2×#501—831no—
390C2×#481—831no—
391C2×#481—831no—
392C2×#482—831no—
393C2×#480—831no—
394C2×#478—831no—
395C2×#476—831no—
396C2×#469—831no—
397C2×#466—831no—
398C2×#442—831no—
399C2×#435D8311yescharacteristic, complemented
400C2×#428—831no—
401C22×#106—831no—
402C83C2×#334511yescharacteristic, complemented, Sylow
403C22×#41—1661no—
404C22×D8—831no—
405C22×M16C2×D8311yescharacteristic
406C23×C8C2×D8311yescharacteristic
407#553—838no—
408#553—1664no—
409#547—838no—
410#547—1664no—
411C2×C4⋊Q8—831no—
412C2×#126—1661no—
413C2×#125—831no—
414C2×#123—1661no—
415C2×#123—1661no—
416C2×#123—1661no—
417C2×C22⋊Q8—1661no—
418C2×#121—831no—
419C2×#121—831no—
420C2×#121—831no—
421C2×#121—831no—
422C2×#121—1661no—
423C2×C4×D4—831no—
424C2×C4×D4—831no—
425C2×C4×D4—1661no—
426C2×C4×D4C2×D8311yescharacteristic
427C2×#117—831no—
428C22×C4⋊C4—831no—
429C22×C4⋊C4—831no—
430C22×C4⋊C4—831no—
431#501—838no—
432#482—838no—
433#481—838no—
434#481—838no—
435#480—838no—
436#478—838no—
437#476—838no—
438#469—838no—
439#466—838no—
440#442—838no—
441#435C2×D8318yescomplemented
442#428—838no—
443C2×#107—831no—
444C2×#107—831no—
445C2×#107—831no—
446C2×#106—831no—
447C2×#106—831no—
448C2×#106—831no—
449C2×#106—831no—
450C2×#106—838no—
451C2×#106—831no—
452C2×#106—831no—
453C2×C4⋊C8C2×D8311yescharacteristic
454C2×#102—831no—
455C2×#102—831no—
456C2×#102—831no—
457C2×#102—831no—
458C2×#102—831no—
459C2×#102—831no—
460C2×C22⋊C8C2×D8311yescharacteristic
461C2×C22⋊C8C2×D8311yescharacteristic
462C2×#97C2×D8311yescharacteristic
463C2×#41—3328no—
464C2×#41—1668no—
465C22×Q8—1661no—
466C22×D4—831no—
467C22×D4—831no—
468C22×D4—1661no—
469C22×D4—1661no—
470C22×D4—1661no—
471C22×D4—1661no—
472C22×D4D33211yescharacteristic
473C23×C4—1661no—
474C23×C4—1661no—
475C23×C4—1661no—
476C23×C4—1661no—
477C23×C4—1661no—
478C23×C4C22×D8311yescharacteristic
479C23×C4C22×D8311yescharacteristic
480C2×D8—834no—
481C2×D8—1664no—
482C2×M16—24no—
483C2×M16C22×D8314yes—
484C22×C8—24no—
485C22×C8C22×D8311yescharacteristic
486C22×C8C22×D8314yes—
487C22×C8C22×D8311yescharacteristic
488C22×C8C22×D8311yescharacteristic
489C22×C8C22×D8311yescharacteristic
490C4⋊Q8—834no—
491C4⋊Q8—1662no—
492#126—1668no—
493#125—834no—
494#125—1662no—
495#123—1668no—
496#123—1668no—
497#123—1668no—
498C22⋊Q8—1668no—
499#121—834no—
500#121—834no—
501#121—834no—
502#121—834no—
503#121—1668no—
504#121—1662no—
505#121—1662no—
506#121—1662no—
507#121—1662no—
508C4×D4—834no—
509C4×D4—834no—
510C4×D4—1668no—
511C4×D4—1662no—
512C4×D4—1662no—
513C4×D4D33214yes—
514C4×D4C22×D8314yes—
515#117—834no—
516#117—1662no—
517C2×C4⋊C4—831no—
518C2×C4⋊C4—831no—
519C2×C4⋊C4—831no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—831no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—831no—
526C2×C4⋊C4—1661no—
527C2×C4⋊C4—1661no—
528C2×C4⋊C4—1661no—
529C2×C4⋊C4—1662no—
530C2×C4⋊C4—1662no—
531C2×C4⋊C4—1662no—
532C2×C4⋊C4—1661no—
533C2×C4⋊C4—1661no—
534C2×C4⋊C4—1661no—
535C2×C4⋊C4D33211yescharacteristic
536C2×C22⋊C4—1661no—
537C2×C22⋊C4—1661no—
538C2×C22⋊C4—1661no—
539C2×C22⋊C4—1661no—
540C2×C22⋊C4—1661no—
541C2×C22⋊C4—1661no—
542C2×C22⋊C4—1661no—
543C2×C22⋊C4D33211yescharacteristic
544C2×C22⋊C4D33211yescharacteristic
545C2×C42—1661no—
546C2×C42C22×D8311yescharacteristic
547#107—834no—
548#107—834no—
549#107—834no—
550#106—834no—
551#106—834no—
552#106—834no—
553#106—834no—
554#106—834no—
555#106—834no—
556C4⋊C8C22×D8314yes—
557#102—834no—
558#102—834no—
559#102—834no—
560#102—834no—
561#102—834no—
562#102—834no—
563C22⋊C8C22×D8314yes—
564C22⋊C8C22×D8314yes—
565#97C22×D8314yes—
566C24—1661no—
567C24—1661no—
568C24C2×D33211yescharacteristic
569C24C2×D33211yescharacteristic
570#41—33232no—
571C2×Q8—3324no—
572C2×Q8—1664no—
573C2×D4—24no—
574C2×D4—3324no—
575C2×D4—3324no—
576C2×D4—3324no—
577C2×D4—832no—
578C2×D4—832no—
579C2×D4—6642no—
580C2×D4—1664no—
581C2×D4—1664no—
582C2×D4—1664no—
583C2×D4—1664no—
584C2×D4—1661no—
585C2×D4—1661no—
586C2×D4—1662no—
587C2×D4—1662no—
588C2×D4—1662no—
589C2×D4—1662no—
590C2×D4C2×D33214yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—3324no—
596C22×C4—3324no—
597C22×C4—3324no—
598C22×C4—6642no—
599C22×C4—6642no—
600C22×C4—1664no—
601C22×C4—1664no—
602C22×C4—1661no—
603C22×C4—1661no—
604C22×C4—1661no—
605C22×C4—1661no—
606C22×C4—1661no—
607C22×C4—1661no—
608C22×C4—1664no—
609C22×C4—1664no—
610C22×C4—1664no—
611C22×C4C2×D33212yes—
612C22×C4C2×D33212yes—
613C22×C4C2×D33211yescharacteristic
614C22×C4C2×D33211yescharacteristic
615C22×C4C2×D33211yescharacteristic
616C22×C4C2×D33211yescharacteristic
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C22×C4C23×D8311yescharacteristic
620D8—1668no—
621M16—28no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—28no—
626C2×C8#1305058914yescomplemented
627C2×C8C23×D8312yes—
628C2×C8C23×D8312yes—
629C2×C8C23×D8312yes—
630C2×C8C23×D8312yes—
631C4⋊C4—832no—
632C4⋊C4—832no—
633C4⋊C4—832no—
634C4⋊C4—832no—
635C4⋊C4—832no—
636C4⋊C4—832no—
637C4⋊C4—1661no—
638C4⋊C4—1661no—
639C4⋊C4—1661no—
640C4⋊C4—1661no—
641C4⋊C4—1661no—
642C4⋊C4—1664no—
643C4⋊C4—1664no—
644C4⋊C4—1664no—
645C4⋊C4—1661no—
646C4⋊C4—1664no—
647C4⋊C4—1664no—
648C4⋊C4—1664no—
649C4⋊C4C2×D33214yes—
650C22⋊C4—1664no—
651C22⋊C4—1664no—
652C22⋊C4—1664no—
653C22⋊C4—1664no—
654C22⋊C4—1664no—
655C22⋊C4—1664no—
656C22⋊C4—1664no—
657C22⋊C4C2×D33214yes—
658C22⋊C4C2×D33214yes—
659C42—1664no—
660C42C2×D33212yes—
661C42C23×D8312yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—3322no—
668C23—3322no—
669C23—3322no—
670C23—3322no—
671C23—3322no—
672C23—3322no—
673C23—1662no—
674C23—1662no—
675C23#1458182014yes—
676C23C22×D33212yes—
677C23C22×D33212yes—
678C23C22×D33211yescharacteristic
679Q8—3328no—
680D4—28no—
681D4—3328no—
682D4—3328no—
683D4—3328no—
684D4—3322no—
685D4—3322no—
686D4—6644no—
687D4—1662no—
688D4—1662no—
689D4—1662no—
690D4—1662no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—3328no—
702C2×C4—3328no—
703C2×C4—3322no—
704C2×C4—3322no—
705C2×C4—3322no—
706C2×C4—3328no—
707C2×C4—3322no—
708C2×C4—3322no—
709C2×C4—3322no—
710C2×C4—6644no—
711C2×C4—6644no—
712C2×C4—1662no—
713C2×C4—1662no—
714C2×C4—1662no—
715C2×C4—1662no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4C22×D33212yes—
719C2×C4C22×D33212yes—
720C2×C4C22×D33212yes—
721C2×C4C22×D33212yes—
722C2×C4C22×D33211yescharacteristic
723C2×C4C2×#1305058912yes—
724C2×C4#1458183912yes—
725C2×C4C24×D8311yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8C2×#1305058914yescomplemented
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—3322no—
738C22—3322no—
739C22—3322no—
740C22—3322no—
741C22—3322no—
742C22—3322no—
743C22—6644no—
744C22—6644no—
745C22#1912835512yes—
746C22C2×#1458182014yes—
747C22C2×#1458182012yes—
748C22#1912851312yes—
749C22C23×D33211yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—3322no—
755C4—3322no—
756C4—3322no—
757C4—3322no—
758C4—3322no—
759C4—3322no—
760C4#1912835512yes—
761C4C22×#1305058911yescharacteristic
762C4C2×#1458183911yescharacteristic
763C2—24no—
764C2—42no—
765C2—6642no—
766C2—6642no—
767C2#2491993514yesdirect product factor
768C2C2×#1912835511yescharacteristic
769C2C22×#1458182011yescharacteristic
770C2C2×#1912851311yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#435×C83C2
socleC23×C83C22×D4
hypercenterC2×#435D83
hypocenterC83C2×#3345
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#19128397C2semidirect
2. C2×#19128355C2semidirect
3. #24919935C2direct (N × H)
4. C2×#19128110C2semidirect
5. C2×#19128020C2semidirect
6. C2×#19128020C2semidirect
7. C2×#19128026C2semidirect
8. C2×#19128015C2semidirect
9. C2×#19128002C2semidirect
10. C2×#19127992C2semidirect
11. C2×#19127954C2semidirect
12. C2×#19127937C2semidirect
13. C2×#19127814C2semidirect
14. C2×#19127743C2semidirect
15. C22×#14581724C2semidirect
16. C2×#435×C83C2semidirect
20. #19128397C22semidirect
22. #19128355C22semidirect
42. #19128110C22semidirect
43. #19128026C22semidirect
44. #19128020C22semidirect
45. #19128020C22semidirect
46. #19128015C22semidirect
47. #19128002C22semidirect
48. #19127992C22semidirect
49. #19127954C22semidirect
50. #19127937C22semidirect
51. #19127814C22semidirect
52. #19127743C22semidirect
62. C2×#14581724C22semidirect
72. #435×C83C22semidirect
266. C2×C8×C83#41semidirect
343. C8×C83C2×#41semidirect
380. C2×C83#3345semidirect
399. C2×#435D83semidirect
402. C83C2×#3345semidirect
441. #435C2×D83semidirect
626. C2×C8#13050589semidirect
729. C8C2×#13050589semidirect
767. C2#24919935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283972
C2×#191283552
#249199352
C2×#191281102
C2×#191280202
C2×#191280262
C2×#191280152
C2×#191280022
C2×#191279922
C2×#191279542
C2×#191279372
C2×#191278142
C2×#191277432
C22×#145817242
C2×#435×C832
C2×#334583