Finite Group Databasebeta

← C2×#24919933 #36282967

Subgroups — C2×#24919933 #36282967

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
2#24919933C2116yesmaximal, direct product factor
3C2×#19128107C211yesmaximal, characteristic, complemented
4C2×#19128019C211yesmaximal, characteristic, complemented
5C2×#19128017C211yesmaximal, characteristic, complemented
6C2×#19128022C211yesmaximal, characteristic, complemented
7C2×#19128014C211yesmaximal, characteristic, complemented
8C2×#19128001C211yesmaximal, characteristic, complemented
9C2×#19127988C211yesmaximal, characteristic, complemented
10C2×#19127952C211yesmaximal, characteristic, complemented
11C2×#19127935C211yesmaximal, characteristic, complemented
12C2×#19127811C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic, complemented
14C2×#19127741C211yesmaximal, characteristic, complemented
15C22×#14581723C211yesmaximal, characteristic, complemented
16C2×#547×C83C211yesmaximal, characteristic, complemented
17C22×#13050575C2211yescharacteristic
18C22×#13050574C2211yescharacteristic
19C23×C83⋊C8C2211yescharacteristic
20#19128397—24no—
21#19128397C2218yescomplemented
22C2×#14581787—21no—
23C2×#14581784C2211yescharacteristic
24C2×#14581774—21no—
25C2×#14581766C2211yescharacteristic
26C2×#14581766C2211yescharacteristic
27C2×#14581764—21no—
28C2×C4×D332C2211yescharacteristic
29C2×(C22⋊D83)⋊C4—21no—
30C2×#14581751C2211yescharacteristic
31C22×C4⋊Dic83C2211yescharacteristic
32#19128107C2218yescomplemented
33#19128022C2218yescomplemented
34#19128019C2218yescomplemented
35#19128017C2218yescomplemented
36#19128014C2218yescomplemented
37#19128001C2218yescomplemented
38#19127988C2218yescomplemented
39#19127952C2218yescomplemented
40#19127935C2218yescomplemented
41#19127811C2218yescomplemented
42#19127773C2218yescomplemented
43#19127741C2218yescomplemented
44C2×#14581725C2211yescharacteristic
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×#14581723C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581723C2211yescharacteristic
52C2×#14581723C2211yescharacteristic
53C2×#14581723C2218yescomplemented
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581713C2211yescharacteristic
56C2×#14581713C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64C22×#41×C83—21no—
65#547×C83—24no—
66#547×C83C2218yescomplemented
67C2×C4⋊Q8×C83C2211yescharacteristic
68C2×#123×C83—21no—
69C2×#123×C83—21no—
70C2×C22⋊Q8×C83—21no—
71C2×#121×C83C2211yescharacteristic
72C2×#121×C83C2211yescharacteristic
73C2×C4×D4×C83C2211yescharacteristic
74C2×C4×D4×C83C2211yescharacteristic
75C22×C4⋊C4×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C22×D332C2311yescharacteristic
78C22×C22⋊D83—21no—
79C22×C22⋊D83—21no—
80C23×Dic83—21no—
81C22×C4×D83—21no—
82C2×#13050575—24no—
83C2×#13050575C2314yes—
84C2×#13050574—24no—
85C2×#13050574C2314yes—
86C22×C83⋊C8—24no—
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2314yes—
91C22×C83⋊C8C2311yescharacteristic
92#14581787—28no—
93#14581784—22no—
94#14581784C2314yes—
95#14581774—28no—
96#14581766—22no—
97#14581766—22no—
98#14581766C2314yes—
99#14581766C2314yes—
100#14581764—28no—
101C4×D332—22no—
102C4×D332C2314yes—
103(C22⋊D83)⋊C4—28no—
104#14581751—22no—
105#14581751C2314yes—
106C2×C4⋊Dic83—22no—
107C2×C4⋊Dic83—21no—
108C2×C4⋊Dic83C2314yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×Dic83⋊C4—21no—
113C2×Dic83⋊C4—21no—
114C2×C22⋊Dic83—21no—
115C2×(C2×D83)⋊C4—21no—
116C2×(C2×D83)⋊C4—21no—
117C2×(C2×D83)⋊C4—21no—
118C2×C4×Dic83—21no—
119#14581725C2314yes—
120#14581725C2314yes—
121#14581725C2314yes—
122#14581723C2314yes—
123#14581723C2314yes—
124#14581723C2314yes—
125#14581723C2314yes—
126#14581723C2314yes—
127#14581723C2314yes—
128C4⋊(C83⋊C8)C2314yes—
129#14581713C2314yes—
130#14581713C2314yes—
131#14581713C2314yes—
132#14581712C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
135C22⋊(C83⋊C8)C2314yes—
136C22⋊(C83⋊C8)C2314yes—
137#14581703C2314yes—
138C2×#41×C83—28no—
139C2×#41×C83—48no—
140C22×Q8×C83—21no—
141C22×D4×C83—21no—
142C22×D4×C83—21no—
143C22×D4×C83D411yescharacteristic
144C22×D4×C83C2311yescharacteristic
145C23×C4×C83—21no—
146C23×C4×C83—21no—
147C23×C4×C83—21no—
148C23×C4×C83C2311yescharacteristic
149C23×C4×C83C2311yescharacteristic
150C4⋊Q8×C83—22no—
151C4⋊Q8×C83C2314yes—
152#123×C83—28no—
153#123×C83—28no—
154C22⋊Q8×C83—28no—
155#121×C83—22no—
156#121×C83—22no—
157#121×C83C2314yes—
158#121×C83C2314yes—
159C4×D4×C83—22no—
160C4×D4×C83D414yes—
161C4×D4×C83C2314yes—
162C4×D4×C83C2314yes—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—22no—
166C2×C4⋊C4×C83—22no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2314yes—
173C2×C4⋊C4×C83C2314yes—
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177C2×C22⋊C4×C83D411yescharacteristic
178C2×C22⋊C4×C83D411yescharacteristic
179C2×C42×C83C2311yescharacteristic
180C23×D83—21no—
181C2×D332—22no—
182C2×D332—22no—
183C2×D332—21no—
184C2×D332C2412yes—
185C2×C22⋊D83—24no—
186C2×C22⋊D83—24no—
187C2×C22⋊D83—44no—
188C2×C22⋊D83—82no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—24no—
193C22×Dic83—82no—
194C2×C4×D83—24no—
195C2×C4×D83—82no—
196#13050575—28no—
197#13050574—28no—
198C2×C83⋊C8—22no—
199C2×C83⋊C8—22no—
200C2×C83⋊C8—22no—
201C2×C83⋊C8—28no—
202C2×C83⋊C8#4114yescomplemented
203C2×C83⋊C8C2412yes—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C2×C83⋊C8C2412yes—
207C4⋊Dic83—21no—
208C4⋊Dic83—21no—
209C4⋊Dic83—24no—
210C4⋊Dic83—21no—
211C4⋊Dic83C2412yes—
212C4⋊Dic83C2412yes—
213C4⋊Dic83C2412yes—
214Dic83⋊C4—24no—
215Dic83⋊C4—24no—
216C22⋊Dic83—24no—
217(C2×D83)⋊C4—24no—
218(C2×D83)⋊C4—24no—
219(C2×D83)⋊C4—24no—
220C4×Dic83—24no—
221C24×C83—21no—
222C24×C83C2×D411yescharacteristic
223C24×C83C2×D411yescharacteristic
224#41×C83—432no—
225C2×Q8×C83—24no—
226C2×Q8×C83—44no—
227C2×D4×C83—24no—
228C2×D4×C83—24no—
229C2×D4×C83—24no—
230C2×D4×C83—21no—
231C2×D4×C83—22no—
232C2×D4×C83—22no—
233C2×D4×C83—44no—
234C2×D4×C83—44no—
235C2×D4×C83C2×D414yes—
236C2×D4×C83C2412yes—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—24no—
245C22×C4×C83—24no—
246C22×C4×C83—24no—
247C22×C4×C83—44no—
248C22×C4×C83—44no—
249C22×C4×C83—44no—
250C22×C4×C83C2×D412yes—
251C22×C4×C83C2×D412yes—
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2412yes—
257C22×C4×C83C2412yes—
258C22×C4×C83C2411yescharacteristic
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83—24no—
263C4⋊C4×C83—24no—
264C4⋊C4×C83—24no—
265C4⋊C4×C83C2×D414yes—
266C4⋊C4×C83C2412yes—
267C4⋊C4×C83C2412yes—
268C4⋊C4×C83C2412yes—
269C22⋊C4×C83—24no—
270C22⋊C4×C83—24no—
271C22⋊C4×C83—24no—
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×C83—22no—
282C23×C83—42no—
283C23×C83—42no—
284C23×C83—42no—
285C23×C83AGL(1,ℤ/8)14yes—
286C23×C83C22×D412yes—
287C23×C83C22×D412yes—
288C23×C83C22×D411yescharacteristic
289C22×D83—22no—
290C22×D83—42no—
291C22×D83—42no—
292C22×D83—42no—
293Q8×C83—48no—
294D4×C83—28no—
295D4×C83—22no—
296D4×C83—22no—
297D4×C83—48no—
298D4×C83—48no—
299D4×C83—42no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—24no—
305C2×C4×C83—24no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—48no—
314C2×C4×C83—48no—
315C2×C4×C83—42no—
316C2×C4×C83—42no—
317C2×C4×C83—42no—
318C2×C4×C83—48no—
319C2×C4×C83C22×D412yes—
320C2×C4×C83C22×D412yes—
321C2×C4×C83C22×D412yes—
322C2×C4×C83C22×D412yes—
323C2×C4×C83C22×D411yescharacteristic
324C2×C4×C83C2×#4112yes—
325C2×C4×C832−1+412yes—
326C2×C4×C83C2511yescharacteristic
327C22⋊D83—48no—
328C22⋊D83—84no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—42no—
333C2×Dic83—42no—
334C2×Dic83—42no—
335C2×Dic83—84no—
336D332—22no—
337D332—22no—
338D332—42no—
339C4×D83—84no—
340C83⋊C8—22no—
341C83⋊C8—22no—
342C83⋊C8—22no—
343C83⋊C8C2×#4114yescomplemented
344C22×C83—28no—
345C22×C83—22no—
346C22×C83—22no—
347C22×C83—22no—
348C22×C83—22no—
349C22×C83—22no—
350C22×C83—44no—
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—42no—
354C22×C83—84no—
355C22×C83#54712yes—
356C22×C83C2×AGL(1,ℤ/8)14yes—
357C22×C83C2×AGL(1,ℤ/8)12yes—
358C22×C83#57712yes—
359C22×C83C23×D411yescharacteristic
360C2×D83—42no—
361C2×D83—42no—
362C2×D83—42no—
363C2×D83—84no—
364C4×C83—22no—
365C4×C83—22no—
366C4×C83—22no—
367C4×C83—22no—
368C4×C83—42no—
369C4×C83—42no—
370C4×C83—42no—
371C4×C83#54712yes—
372C4×C83C22×#4111yescharacteristic
373C4×C83C2×2−1+411yescharacteristic
374Dic83—42no—
375Dic83—42no—
376Dic83—42no—
377C2×#3345—831nomaximal, Sylow
378C2×C83—24no—
379C2×C83—42no—
380C2×C83—82no—
381C2×C83#334514yescomplemented
382C2×C83C2×#54711yescharacteristic
383C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
384C2×C83C2×#57711yescharacteristic
385D83—82no—
386C2×#553—831no—
387C2×#547D8311yescharacteristic, complemented
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×#435—831no—
400C2×#428—831no—
401C22×#106—831no—
402C83C2×#334511yescharacteristic, complemented, Sylow
403C22×#41—21no—
404C22×D8—831no—
405C22×M16—831no—
406C23×C8—831no—
407#553—838no—
408#553—1664no—
409#547—24no—
410#547C2×D8318yescomplemented
411C2×C4⋊Q8C2×D8311yescharacteristic
412C2×#126—1661no—
413C2×#125—831no—
414C2×#123—21no—
415C2×#123—21no—
416C2×#123—1661no—
417C2×C22⋊Q8—21no—
418C2×#121—831no—
419C2×#121—831no—
420C2×#121—1661no—
421C2×#121C2×D8311yescharacteristic
422C2×#121C2×D8311yescharacteristic
423C2×C4×D4—831no—
424C2×C4×D4—1661no—
425C2×C4×D4C2×D8311yescharacteristic
426C2×C4×D4C2×D8311yescharacteristic
427C2×#117—831no—
428C22×C4⋊C4—831no—
429C22×C4⋊C4C2×D8311yescharacteristic
430C22×C4⋊C4C2×D8311yescharacteristic
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#435—838no—
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⋊C8—831no—
454C2×#102—831no—
455C2×#102—831no—
456C2×#102—831no—
457C2×#102—831no—
458C2×#102—831no—
459C2×#102—831no—
460C2×C22⋊C8—831no—
461C2×C22⋊C8—831no—
462C2×#97—831no—
463C2×#41—28no—
464C2×#41—48no—
465C22×Q8—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—831no—
469C22×D4—1661no—
470C22×D4—1661no—
471C22×D4C22⋊D8311yescharacteristic
472C22×D4C22×D8311yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—1661no—
477C23×C4—1661no—
478C23×C4C22×D8311yescharacteristic
479C23×C4C22×D8311yescharacteristic
480C2×D8—834no—
481C2×D8—1664no—
482C2×M16—834no—
483C2×M16—1664no—
484C22×C8—831no—
485C22×C8—831no—
486C22×C8—834no—
487C22×C8—831no—
488C22×C8—831no—
489C22×C8—1664no—
490C4⋊Q8—22no—
491C4⋊Q8C22×D8314yes—
492#126—1668no—
493#125—834no—
494#125—1662no—
495#123—28no—
496#123—28no—
497#123—1668no—
498C22⋊Q8—28no—
499#121—22no—
500#121—22no—
501#121—834no—
502#121—834no—
503#121—1668no—
504#121—1662no—
505#121—1662no—
506#121C22×D8314yes—
507#121C22×D8314yes—
508C4×D4—22no—
509C4×D4—834no—
510C4×D4—1668no—
511C4×D4—1662no—
512C4×D4C22⋊D8314yes—
513C4×D4C22×D8314yes—
514C4×D4C22×D8314yes—
515#117—834no—
516#117—1662no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—831no—
523C2×C4⋊C4—831no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—831no—
526C2×C4⋊C4—1661no—
527C2×C4⋊C4—1662no—
528C2×C4⋊C4—1661no—
529C2×C4⋊C4—1661no—
530C2×C4⋊C4C22⋊D8311yescharacteristic
531C2×C4⋊C4C22×D8311yescharacteristic
532C2×C4⋊C4C22×D8311yescharacteristic
533C2×C4⋊C4C22×D8311yescharacteristic
534C2×C4⋊C4C22×D8314yes—
535C2×C4⋊C4C22×D8314yes—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—1661no—
540C2×C22⋊C4—1661no—
541C2×C22⋊C4—1661no—
542C2×C22⋊C4—1661no—
543C2×C22⋊C4C22⋊D8311yescharacteristic
544C2×C22⋊C4C22⋊D8311yescharacteristic
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⋊C8—834no—
557#102—834no—
558#102—834no—
559#102—834no—
560#102—834no—
561#102—834no—
562#102—834no—
563C22⋊C8—834no—
564C22⋊C8—834no—
565#97—834no—
566C24—21no—
567C24—1661no—
568C24C2×C22⋊D8311yescharacteristic
569C24C2×C22⋊D8311yescharacteristic
570#41—432no—
571C2×Q8—24no—
572C2×Q8—44no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—3324no—
582C2×D4—832no—
583C2×D4—6642no—
584C2×D4—1664no—
585C2×D4—1664no—
586C2×D4—1661no—
587C2×D4—1662no—
588C2×D4—1662no—
589C2×D4C2×C22⋊D8314yes—
590C2×D4C23×D8312yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—6642no—
605C22×C4—6642no—
606C22×C4—1661no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1664no—
610C22×C4—1664no—
611C22×C4C2×C22⋊D8312yes—
612C22×C4C2×C22⋊D8312yes—
613C22×C4C2×C22⋊D8311yescharacteristic
614C22×C4C2×C22⋊D8311yescharacteristic
615C22×C4C2×C22⋊D8311yescharacteristic
616C22×C4C2×C22⋊D8311yescharacteristic
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C22×C4C23×D8311yescharacteristic
620D8—1668no—
621M16—1668no—
622C2×C8—834no—
623C2×C8—832no—
624C2×C8—832no—
625C2×C8—832no—
626C2×C8—832no—
627C2×C8—1668no—
628C2×C8—1662no—
629C2×C8—1662no—
630C2×C8—1662no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—832no—
638C4⋊C4—832no—
639C4⋊C4—832no—
640C4⋊C4—1661no—
641C4⋊C4—1661no—
642C4⋊C4—1664no—
643C4⋊C4—1661no—
644C4⋊C4—1664no—
645C4⋊C4—1664no—
646C4⋊C4C2×C22⋊D8314yes—
647C4⋊C4C23×D8312yes—
648C4⋊C4C23×D8312yes—
649C4⋊C4C23×D8312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—1664no—
654C22⋊C4—1664no—
655C22⋊C4—1664no—
656C22⋊C4—1664no—
657C22⋊C4C2×C22⋊D8314yes—
658C22⋊C4C2×C22⋊D8314yes—
659C42—1664no—
660C42C2×C22⋊D8312yes—
661C42C23×D8312yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—3322no—
672C23—3322no—
673C23—3322no—
674C23—1662no—
675C23#1458181814yes—
676C23C22×C22⋊D8312yes—
677C23C22×C22⋊D8312yes—
678C23C22×C22⋊D8311yescharacteristic
679Q8—48no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—42no—
686D4—3328no—
687D4—3322no—
688D4—6644no—
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—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—48no—
710C2×C4—3322no—
711C2×C4—3322no—
712C2×C4—3322no—
713C2×C4—6644no—
714C2×C4—6644no—
715C2×C4—1662no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4C22×C22⋊D8312yes—
719C2×C4C22×C22⋊D8312yes—
720C2×C4C22×C22⋊D8312yes—
721C2×C4C22×C22⋊D8312yes—
722C2×C4C22×C22⋊D8311yescharacteristic
723C2×C4#41×D8312yes—
724C2×C4#1458183912yes—
725C2×C4C24×D8311yescharacteristic
726C8—834no—
727C8—1662no—
728C8—1662no—
729C8—1662no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—3322no—
742C22—3322no—
743C22—3322no—
744C22—6644no—
745C22#1912835012yes—
746C22C2×#1458181814yes—
747C22C2×#1458181812yes—
748C22#1912850912yes—
749C22C23×C22⋊D8311yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—3322no—
758C4—3322no—
759C4—3322no—
760C4#1912835012yes—
761C4C2×#41×D8311yescharacteristic
762C4C2×#1458183911yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—6642no—
767C2#2491993314yesdirect product factor
768C2C2×#1912835011yescharacteristic
769C2C22×#1458181811yescharacteristic
770C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#547×C83C2
socleC23×C83C22×D4
hypercenterC2×#547D83
hypocenterC83C2×#3345
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#19128397C2semidirect
2. #24919933C2direct (N × H)
3. C2×#19128107C2semidirect
4. C2×#19128019C2semidirect
5. C2×#19128017C2semidirect
6. C2×#19128022C2semidirect
7. C2×#19128014C2semidirect
8. C2×#19128001C2semidirect
9. C2×#19127988C2semidirect
10. C2×#19127952C2semidirect
11. C2×#19127935C2semidirect
12. C2×#19127811C2semidirect
13. C2×#19127773C2semidirect
14. C2×#19127741C2semidirect
15. C22×#14581723C2semidirect
16. C2×#547×C83C2semidirect
21. #19128397C22semidirect
32. #19128107C22semidirect
33. #19128022C22semidirect
34. #19128019C22semidirect
35. #19128017C22semidirect
36. #19128014C22semidirect
37. #19128001C22semidirect
38. #19127988C22semidirect
39. #19127952C22semidirect
40. #19127935C22semidirect
41. #19127811C22semidirect
42. #19127773C22semidirect
43. #19127741C22semidirect
53. C2×#14581723C22semidirect
66. #547×C83C22semidirect
202. C2×C83⋊C8#41semidirect
343. C83⋊C8C2×#41semidirect
381. C2×C83#3345semidirect
387. C2×#547D83semidirect
402. C83C2×#3345semidirect
410. #547C2×D83semidirect
767. C2#24919933direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283972
#249199332
C2×#191281072
C2×#191280192
C2×#191280172
C2×#191280222
C2×#191280142
C2×#191280012
C2×#191279882
C2×#191279522
C2×#191279352
C2×#191278112
C2×#191277732
C2×#191277412
C22×#145817232
C2×#547×C832
C2×#334583