Finite Group Databasebeta

← C2×#24919314 #36280772

Subgroups — C2×#24919314 #36280772

Order 21248.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128395C211yesmaximal, characteristic, complemented
2C2×#19128339C211yesmaximal, characteristic, complemented
3#24919314C2116yesmaximal, direct product factor
4C2×#19128057C211yesmaximal, characteristic, complemented
5C2×#19128035C211yesmaximal, characteristic, complemented
6C2×#19128025C211yesmaximal, characteristic, complemented
7C2×#19127999C211yesmaximal, characteristic, complemented
8C2×#19127937C211yesmaximal, characteristic, complemented
9C2×#19127933C211yesmaximal, characteristic, complemented
10C2×#19127919C211yesmaximal, characteristic, complemented
11C2×#19127846C211yesmaximal, characteristic, complemented
12C2×#19127836C211yesmaximal, characteristic, complemented
13C2×#19127781C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D83C211yesmaximal, characteristic, complemented
15C2×#102×D83C211yesmaximal, characteristic, complemented
16C2×#416×C83C211yesmaximal, characteristic, complemented
17C22×D4×D83C2211yescharacteristic
18C22×#13050577C2211yescharacteristic, complemented
19C22×D664C2211yescharacteristic
20C22×#13050575C2211yescharacteristic
21C22×C8×D83C2211yescharacteristic
22#19128395—24no—
23#19128395C2218yescomplemented
24#19128339—24no—
25#19128339C2218yescomplemented
26C2×#14581786—21no—
27C2×#14581783C2211yescharacteristic, complemented
28C2×#14581781C2211yescharacteristic
29C2×#14581775—21no—
30C2×#14581774—21no—
31C2×#14581768C2211yescharacteristic
32C2×#14581767C2211yescharacteristic
33C2×#14581766C2211yescharacteristic
34C2×#14581766C2211yescharacteristic, complemented
35C2×#14581765—21no—
36C2×#14581764—21no—
37C2×#14581760—21no—
38C2×C4×D332—21no—
39C2×D4×Dic83C2211yescharacteristic
40C2×#14581754C2211yescharacteristic, complemented
41C2×C4×C22⋊D83C2211yescharacteristic
42C2×C4⋊C4×D83C2211yescharacteristic
43C22×(C2×D83)⋊C4—21no—
44#19128057C2218yescomplemented
45#19128035C2218yescomplemented
46#19128025C2218yescomplemented
47#19127999C2218yescomplemented
48#19127937C2218yescomplemented
49#19127933C2218yescomplemented
50#19127919C2218yescomplemented
51#19127846C2218yescomplemented
52#19127836C2218yescomplemented
53#19127781C2218yescomplemented
54C8×C22⋊D83C2218yescomplemented
55C2×#14581726C2211yescharacteristic, complemented
56C2×#14581725C2211yescharacteristic, complemented
57C2×#14581723C2211yescharacteristic, complemented
58C2×Dic83⋊C8C2211yescharacteristic, complemented
59C2×#14581716C2211yescharacteristic, complemented
60C2×#14581714C2211yescharacteristic
61C2×#14581714C2211yescharacteristic, complemented
62C2×#14581713C2211yescharacteristic
63C2×#14581712C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65#102×D83C2218yescomplemented
66C2×C22⋊(C83⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic, complemented
69C22×#41×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic, complemented
71C2×#117×C83C2211yescharacteristic, complemented
72#416×C83C2218yescomplemented
73C2×#103×C83C2211yescharacteristic, complemented
74C2×#103×C83C2211yescharacteristic, complemented
75C2×#102×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C24×D83—21no—
78C22×D332—21no—
79C22×D332C2311yescharacteristic
80C22×D332C2311yescharacteristic
81C22×C22⋊D83—21no—
82C22×C22⋊D83—21no—
83C22×C22⋊D83—21no—
84C22×C22⋊D83D411yescharacteristic
85C2×D4×D83—22no—
86C2×D4×D83—24no—
87C2×D4×D83—42no—
88C2×D4×D83C2314yes—
89C23×Dic83—21no—
90C22×C4×D83—21no—
91C22×C4×D83—21no—
92C22×C4×D83C2311yescharacteristic
93C2×#13050577—42no—
94C2×#13050577C2314yescomplemented
95C2×D664—42no—
96C2×D664C2314yes—
97C2×#13050575—24no—
98C2×#13050575C2314yes—
99C22×C83⋊C8C2311yescharacteristic
100C22×C83⋊C8C2311yescharacteristic
101C2×C8×D83—42no—
102C2×C8×D83C2314yes—
103#14581786—28no—
104#14581783—22no—
105#14581783C2314yescomplemented
106#14581781—22no—
107#14581781C2314yes—
108#14581775—28no—
109#14581774—28no—
110#14581768—22no—
111#14581768C2314yes—
112#14581767—22no—
113#14581767C2314yes—
114#14581766—22no—
115#14581766—22no—
116#14581766C2314yes—
117#14581766C2314yescomplemented
118#14581765—28no—
119#14581764—28no—
120#14581760—28no—
121C4×D332—28no—
122D4×Dic83—22no—
123D4×Dic83C2314yes—
124#14581754—22no—
125#14581754C2314yescomplemented
126C4×C22⋊D83D414yes—
127C4×C22⋊D83C2314yes—
128C2×C4⋊Dic83—21no—
129C2×C4⋊Dic83C2311yescharacteristic
130C2×C4⋊Dic83C2311yescharacteristic
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4D411yescharacteristic
135C4⋊C4×D83—22no—
136C4⋊C4×D83C2314yes—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83D411yescharacteristic
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—28no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C2×(C2×D83)⋊C4D411yescharacteristic
148C2×C4×Dic83C2311yescharacteristic
149#14581726C2314yescomplemented
150#14581725C2314yescomplemented
151#14581723C2314yescomplemented
152Dic83⋊C8C2314yescomplemented
153#14581716C2314yescomplemented
154#14581714C2314yes—
155#14581714C2314yescomplemented
156#14581713C2314yes—
157#14581712C2314yes—
158#14581712C2314yes—
159C22⋊(C83⋊C8)C2314yescomplemented
160(C2×D83)⋊C8C2314yes—
161C8×Dic83C2314yescomplemented
162C2×#41×C83—22no—
163C2×#41×C83—24no—
164C2×#41×C83—42no—
165C2×#41×C83C2314yes—
166C22×Q8×C83C2311yescharacteristic
167C22×D4×C83—21no—
168C22×D4×C83C2311yescharacteristic
169C23×C4×C83—21no—
170C23×C4×C83C2311yescharacteristic
171C22×C8×C83—42no—
172C22×C8×C83C2311yescharacteristic
173C22×C8×C83C2311yescharacteristic
174C22×C8×C83C2314yescomplemented
175#117×C83—22no—
176#117×C83C2314yescomplemented
177C2×C4⋊C4×C83C2311yescharacteristic
178C2×C4⋊C4×C83C2311yescharacteristic
179C2×C22⋊C4×C83—21no—
180C2×C42×C83—21no—
181#103×C83C2314yescomplemented
182#103×C83C2314yescomplemented
183#102×C83C2314yes—
184#102×C83C2314yes—
185C23×D83—21no—
186C23×D83—21no—
187C23×D83—24no—
188C23×D83—44no—
189C23×D83—44no—
190C23×D83—82no—
191C23×D83C2×D411yescharacteristic
192C2×D332—22no—
193C2×D332—22no—
194C2×D332—22no—
195C2×D332—22no—
196C2×D332—24no—
197C2×D332—21no—
198C2×D332—21no—
199C2×D332—44no—
200C2×D332C2412yes—
201C2×D332C2412yes—
202C2×C22⋊D83—24no—
203C2×C22⋊D83—24no—
204C2×C22⋊D83—24no—
205C2×C22⋊D83—24no—
206C2×C22⋊D83—44no—
207C2×C22⋊D83—82no—
208C2×C22⋊D83—82no—
209C2×C22⋊D83C2×D414yes—
210D4×D83—28no—
211D4×D83—44no—
212D4×D83—48no—
213C22×Dic83—21no—
214C22×Dic83—21no—
215C22×Dic83—24no—
216C22×Dic83—82no—
217C22×Dic83C2×D411yescharacteristic
218C22×Dic83C2×D411yescharacteristic
219C22×Dic83C2×D411yescharacteristic
220C2×C4×D83—22no—
221C2×C4×D83—22no—
222C2×C4×D83—24no—
223C2×C4×D83—24no—
224C2×C4×D83—82no—
225C2×C4×D83—82no—
226C2×C4×D83C2×D412yes—
227C2×C4×D83C2412yes—
228#13050577—44no—
229D664—44no—
230#13050575—28no—
231C2×C83⋊C8—22no—
232C2×C83⋊C8—22no—
233C2×C83⋊C8C2412yes—
234C2×C83⋊C8C2412yes—
235C8×D83—44no—
236C4⋊Dic83—21no—
237C4⋊Dic83—21no—
238C4⋊Dic83—24no—
239C4⋊Dic83C2412yes—
240C4⋊Dic83C2412yes—
241Dic83⋊C4—24no—
242Dic83⋊C4—24no—
243Dic83⋊C4—24no—
244Dic83⋊C4C2×D414yes—
245C22⋊Dic83—24no—
246C22⋊Dic83C2×D414yes—
247(C2×D83)⋊C4—24no—
248(C2×D83)⋊C4—24no—
249(C2×D83)⋊C4—24no—
250(C2×D83)⋊C4—24no—
251(C2×D83)⋊C4—24no—
252(C2×D83)⋊C4—24no—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4C2×D414yes—
255C4×Dic83C2×D412yes—
256C4×Dic83C2412yes—
257C24×C83—21no—
258C24×C83C2×D411yescharacteristic
259#41×C83—28no—
260#41×C83—44no—
261#41×C83—48no—
262C2×Q8×C83—21no—
263C2×Q8×C83—22no—
264C2×Q8×C83—22no—
265C2×Q8×C83C2412yes—
266C2×D4×C83—24no—
267C2×D4×C83—21no—
268C2×D4×C83—22no—
269C2×D4×C83—44no—
270C2×D4×C83#4114yes—
271C2×D4×C83C2412yes—
272C22×C4×C83—22no—
273C22×C4×C83—22no—
274C22×C4×C83—21no—
275C22×C4×C83—21no—
276C22×C4×C83—21no—
277C22×C4×C83—24no—
278C22×C4×C83—44no—
279C22×C4×C83C2×D412yes—
280C22×C4×C83C2×D411yescharacteristic
281C22×C4×C83C2412yes—
282C22×C4×C83C2411yescharacteristic
283C2×C8×C83—22no—
284C2×C8×C83—22no—
285C2×C8×C83—44no—
286C2×C8×C83C2412yes—
287C2×C8×C83C2412yes—
288C4⋊C4×C83—21no—
289C4⋊C4×C83—21no—
290C4⋊C4×C83C2412yes—
291C4⋊C4×C83C2412yes—
292C22⋊C4×C83—24no—
293C42×C83—24no—
294C23×C83—22no—
295C23×C83—24no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—22no—
299C23×C83—42no—
300C23×C83—42no—
301C23×C83C22×D412yes—
302C23×C83C22×D411yescharacteristic
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—22no—
306C22×D83—22no—
307C22×D83—48no—
308C22×D83—42no—
309C22×D83—42no—
310C22×D83—42no—
311C22×D83—42no—
312C22×D83—42no—
313C22×D83—42no—
314C22×D83—48no—
315C22×D83—84no—
316C22×D83—816no—
317C22×D83#13514yes—
318C22×D83C22×D412yes—
319Q8×C83—22no—
320Q8×C83—22no—
321Q8×C83—42no—
322D4×C83—24no—
323D4×C83—22no—
324D4×C83—48no—
325D4×C83C2×#4114yes—
326C2×C4×C83—22no—
327C2×C4×C83—24no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—48no—
334C2×C4×C83—42no—
335C2×C4×C83—42no—
336C2×C4×C83—42no—
337C2×C4×C83C22×D412yes—
338C2×C4×C83C22×D411yescharacteristic
339C2×C4×C83C2×#4112yes—
340C2×C4×C83H(5,𝔽2)12yes—
341C2×C4×C83C2511yescharacteristic
342C22⋊D83—28no—
343C22⋊D83—48no—
344C22⋊D83—84no—
345C22⋊D83—84no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—42no—
352C2×Dic83—42no—
353C2×Dic83—84no—
354C2×Dic83C22×D412yes—
355C2×Dic83C22×D412yes—
356C2×Dic83C22×D412yes—
357D332—22no—
358D332—22no—
359D332—22no—
360D332—22no—
361D332—48no—
362D332—42no—
363D332—42no—
364C4×D83—24no—
365C4×D83—22no—
366C4×D83—22no—
367C4×D83—84no—
368C4×D83—84no—
369C8×C83—22no—
370C8×C83—22no—
371C83⋊C8—22no—
372C83⋊C8—22no—
373C22×C83—24no—
374C22×C83—22no—
375C22×C83—22no—
376C22×C83—22no—
377C22×C83—48no—
378C22×C83—44no—
379C22×C83—42no—
380C22×C83—42no—
381C22×C83#54612yes—
382C22×C83C2×#13512yes—
383C22×C83#57612yes—
384C22×C83C23×D411yescharacteristic
385C2×D83—22no—
386C2×D83—28no—
387C2×D83—22no—
388C2×D83—42no—
389C2×D83—42no—
390C2×D83—42no—
391C2×D83—42no—
392C2×D83—42no—
393C2×D83—42no—
394C2×D83—816no—
395C2×D83—84no—
396C2×D83—84no—
397C2×D83C2×#13514yes—
398C4×C83—22no—
399C4×C83—42no—
400C4×C83—42no—
401C4×C83—42no—
402C4×C83#54612yes—
403C4×C83C22×#4111yescharacteristic
404C4×C83C2×H(5,𝔽2)11yescharacteristic
405Dic83—22no—
406Dic83—22no—
407Dic83—22no—
408Dic83—42no—
409Dic83—42no—
410C2×#3297—831nomaximal, Sylow
411C2×C83—44no—
412C2×C83—42no—
413C2×C83#329714yescomplemented
414C2×C83C2×#54611yescharacteristic
415C2×C83C22×#13511yescharacteristic
416C2×C83C2×#57611yescharacteristic
417D83—24no—
418D83—82no—
419D83—82no—
420C2×#553—831no—
421C2×#546—831no—
422#3297—8316no—
423C2×#488—831no—
424C2×#484—831no—
425C2×#482—831no—
426C2×#478—831no—
427C2×#466—831no—
428C2×#465—831no—
429C2×#463—831no—
430C2×#449—831no—
431C2×#447—831no—
432C2×C4×D8—831no—
433C2×C8×D4—831no—
434C2×#416D8311yescharacteristic, complemented
435C22×#102—831no—
436C83C2×#329711yescharacteristic, complemented, Sylow
437C22×#41C2×D8311yescharacteristic
438C23×D4—831no—
439C22×SD16—831no—
440C22×D8—831no—
441C22×D8—831no—
442C23×C8—831no—
443C23×C8C2×D8311yescharacteristic, complemented
444#553—838no—
445#553—1664no—
446#546—838no—
447#546—1664no—
448C2×#126—1661no—
449C2×#125—831no—
450C2×#124—831no—
451C2×#123—1661no—
452C2×#123—1661no—
453C2×C22⋊Q8—831no—
454C2×#121—831no—
455C2×#121—831no—
456C2×#121—831no—
457C2×#121—1661no—
458C2×#121—1661no—
459C2×#120—1661no—
460C2×C4×D4—831no—
461C2×C4×D4—831no—
462C2×C4×D4—831no—
463C2×C4×D4—1661no—
464C2×#117C2×D8311yescharacteristic, complemented
465C22×C4⋊C4—831no—
466C22×C22⋊C4—1661no—
467#488—838no—
468#484—838no—
469#482—838no—
470#478—838no—
471#466—838no—
472#465—838no—
473#463—838no—
474#449—838no—
475#447—838no—
476C4×D8—838no—
477C8×D4—838no—
478C2×#107—831no—
479C2×#107—831no—
480C2×#106—831no—
481C2×C4⋊C8—831no—
482#416C2×D8318yescomplemented
483C2×#103—831no—
484C2×#103C2×D8311yescharacteristic, complemented
485C2×#103C2×D8311yescharacteristic, complemented
486C2×#102—831no—
487C2×#102—831no—
488C2×#102—831no—
489C2×#102—831no—
490C2×#102—831no—
491C2×#102—838no—
492C2×#102C2×D8311yescharacteristic
493C2×#102C2×D8311yescharacteristic
494C2×C22⋊C8—831no—
495C2×C22⋊C8—831no—
496C2×C4×C8—831no—
497C25—1661no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D8314yes—
502C22×Q8C22×D8311yescharacteristic
503C22×D4—21no—
504C22×D4—3322no—
505C22×D4—834no—
506C22×D4—831no—
507C22×D4—831no—
508C22×D4—831no—
509C22×D4—1661no—
510C22×D4—1662no—
511C22×D4—1661no—
512C22×D4—1664no—
513C22×D4—1661no—
514C22×D4—1661no—
515C22×D4C22×D8311yescharacteristic
516C23×C4—21no—
517C23×C4—831no—
518C23×C4—1661no—
519C23×C4—1661no—
520C23×C4—1661no—
521C23×C4C22×D8311yescharacteristic
522C2×SD16—3322no—
523C2×SD16—834no—
524C2×D8—3322no—
525C2×D8—834no—
526C2×D8—834no—
527C2×D8—1664no—
528C22×C8—42no—
529C22×C8—3322no—
530C22×C8—834no—
531C22×C8—831no—
532C22×C8—831no—
533C22×C8C22×D8311yescharacteristic
534C22×C8C22×D8311yescharacteristic
535C22×C8C22×D8314yescomplemented
536#126—1668no—
537#125—834no—
538#125—1662no—
539#124—834no—
540#124—1662no—
541#123—1668no—
542#123—1668no—
543C22⋊Q8—834no—
544C22⋊Q8—1662no—
545#121—834no—
546#121—834no—
547#121—834no—
548#121—1668no—
549#121—1668no—
550#121—1662no—
551#121—1662no—
552#121—1662no—
553#120—1668no—
554C4×D4—834no—
555C4×D4—834no—
556C4×D4—834no—
557C4×D4—834no—
558C4×D4—1668no—
559C4×D4—1662no—
560C4×D4—1662no—
561#117—22no—
562#117C22×D8314yescomplemented
563C2×C4⋊C4—831no—
564C2×C4⋊C4—831no—
565C2×C4⋊C4—831no—
566C2×C4⋊C4—834no—
567C2×C4⋊C4—1662no—
568C2×C4⋊C4—1661no—
569C2×C4⋊C4—1661no—
570C2×C4⋊C4—1661no—
571C2×C4⋊C4—1661no—
572C2×C4⋊C4C22×D8311yescharacteristic
573C2×C4⋊C4C22×D8311yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—831no—
576C2×C22⋊C4—831no—
577C2×C22⋊C4—1668no—
578C2×C22⋊C4—1661no—
579C2×C22⋊C4—1661no—
580C2×C22⋊C4—1661no—
581C2×C22⋊C4—1661no—
582C2×C22⋊C4—1661no—
583C2×C22⋊C4—1661no—
584C2×C22⋊C4—1661no—
585C2×C22⋊C4—1661no—
586C2×C42—21no—
587C2×C42—831no—
588#107—834no—
589#107—834no—
590#106—834no—
591C4⋊C8—834no—
592#103—834no—
593#103C22×D8314yescomplemented
594#103C22×D8314yescomplemented
595#102—834no—
596#102—834no—
597#102—834no—
598#102—834no—
599#102—834no—
600#102C22×D8314yes—
601#102C22×D8314yes—
602C22⋊C8—834no—
603C22⋊C8—834no—
604C4×C8—834no—
605C24—21no—
606C24—3324no—
607C24—3324no—
608C24—831no—
609C24—6642no—
610C24—1664no—
611C24—1661no—
612C24—1661no—
613C24D4×D8311yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D8312yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—3324no—
626C2×D4—3328no—
627C2×D4—3324no—
628C2×D4—3324no—
629C2×D4—834no—
630C2×D4—832no—
631C2×D4—832no—
632C2×D4—6642no—
633C2×D4—6642no—
634C2×D4—1664no—
635C2×D4—1664no—
636C2×D4—1668no—
637C2×D4—1664no—
638C2×D4—1664no—
639C2×D4—1664no—
640C2×D4—1661no—
641C2×D4—1661no—
642C2×D4—1662no—
643C2×D4—1662no—
644C2×D4—1662no—
645C2×D4—1662no—
646C2×D4#1305059014yes—
647C2×D4C23×D8312yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—831no—
656C22×C4—831no—
657C22×C4—831no—
658C22×C4—832no—
659C22×C4—832no—
660C22×C4—6642no—
661C22×C4—6642no—
662C22×C4—6642no—
663C22×C4—1664no—
664C22×C4—1664no—
665C22×C4—1661no—
666C22×C4—1661no—
667C22×C4—1664no—
668C22×C4—1662no—
669C22×C4—1662no—
670C22×C4D4×D8312yes—
671C22×C4D4×D8311yescharacteristic
672C22×C4C23×D8312yes—
673C22×C4C23×D8311yescharacteristic
674SD16—3324no—
675D8—3324no—
676D8—1668no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—44no—
680C2×C8—3324no—
681C2×C8—832no—
682C2×C8—832no—
683C2×C8—1662no—
684C2×C8—1662no—
685C2×C8C23×D8312yes—
686C2×C8C23×D8312yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—834no—
690C4⋊C4—832no—
691C4⋊C4—832no—
692C4⋊C4—1664no—
693C4⋊C4—1664no—
694C4⋊C4—1664no—
695C4⋊C4—1664no—
696C4⋊C4—1661no—
697C4⋊C4—1661no—
698C4⋊C4C23×D8312yes—
699C4⋊C4C23×D8312yes—
700C22⋊C4—24no—
701C22⋊C4—834no—
702C22⋊C4—834no—
703C22⋊C4—1664no—
704C22⋊C4—1664no—
705C22⋊C4—1664no—
706C22⋊C4—1664no—
707C22⋊C4—1664no—
708C22⋊C4—1664no—
709C22⋊C4—1664no—
710C22⋊C4—1664no—
711C42—24no—
712C42—832no—
713C42—832no—
714C23—22no—
715C23—24no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—3328no—
722C23—3328no—
723C23—3322no—
724C23—3322no—
725C23—3322no—
726C23—3322no—
727C23—3322no—
728C23—3322no—
729C23—834no—
730C23—832no—
731C23—6644no—
732C23—66416no—
733C23—1662no—
734C23—1662no—
735C23—1662no—
736C23—1662no—
737C23C2×D4×D8312yes—
738C23C2×D4×D8311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—24no—
743D4—22no—
744D4—48no—
745D4—3328no—
746D4—3328no—
747D4—3322no—
748D4—3322no—
749D4—6644no—
750D4—6644no—
751D4—1668no—
752D4—1662no—
753D4—1662no—
754D4—1662no—
755D4—1662no—
756D4C2×#1305059014yes—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—3322no—
769C2×C4—3322no—
770C2×C4—832no—
771C2×C4—832no—
772C2×C4—832no—
773C2×C4—6644no—
774C2×C4—6644no—
775C2×C4—6644no—
776C2×C4—1662no—
777C2×C4—1662no—
778C2×C4—1662no—
779C2×C4—1662no—
780C2×C4—1662no—
781C2×C4—1664no—
782C2×C4—1662no—
783C2×C4—1662no—
784C2×C4C2×D4×D8312yes—
785C2×C4C2×D4×D8311yescharacteristic
786C2×C4C2×#1305059012yes—
787C2×C4#1458183712yes—
788C2×C4C24×D8311yescharacteristic
789C8—22no—
790C8—22no—
791C8—1662no—
792C8—1662no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—44no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—3322no—
802C22—3322no—
803C22—3322no—
804C22—3322no—
805C22—3322no—
806C22—3322no—
807C22—834no—
808C22—66416no—
809C22—6644no—
810C22—6644no—
811C22—1668no—
812C22—1662no—
813C22—1662no—
814C22#1912834112yes—
815C22#135×D8312yes—
816C22#1912850312yes—
817C22C22×D4×D8311yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—3322no—
823C4—3322no—
824C4—1662no—
825C4—1662no—
826C4—1662no—
827C4#1912834112yes—
828C4C22×#1305059011yescharacteristic
829C4C2×#1458183711yescharacteristic
830C2—42no—
831C2—44no—
832C2—6642no—
833C2—6642no—
834C2—1664no—
835C2#2491931414yesdirect product factor
836C2C2×#1912834111yescharacteristic
837C2C2×#135×D8311yescharacteristic
838C2C2×#1912850311yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#416×C83C2
socleC23×C83C22×D4
hypercenterC2×#416D83
hypocenterC83C2×#3297
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#19128395C2semidirect
2. C2×#19128339C2semidirect
3. #24919314C2direct (N × H)
4. C2×#19128057C2semidirect
5. C2×#19128035C2semidirect
6. C2×#19128025C2semidirect
7. C2×#19127999C2semidirect
8. C2×#19127937C2semidirect
9. C2×#19127933C2semidirect
10. C2×#19127919C2semidirect
11. C2×#19127846C2semidirect
12. C2×#19127836C2semidirect
13. C2×#19127781C2semidirect
14. C2×C8×C22⋊D83C2semidirect
15. C2×#102×D83C2semidirect
16. C2×#416×C83C2semidirect
18. C22×#13050577C22semidirect
23. #19128395C22semidirect
25. #19128339C22semidirect
27. C2×#14581783C22semidirect
34. C2×#14581766C22semidirect
40. C2×#14581754C22semidirect
44. #19128057C22semidirect
45. #19128035C22semidirect
46. #19128025C22semidirect
47. #19127999C22semidirect
48. #19127937C22semidirect
49. #19127933C22semidirect
50. #19127919C22semidirect
51. #19127846C22semidirect
52. #19127836C22semidirect
53. #19127781C22semidirect
54. C8×C22⋊D83C22semidirect
55. C2×#14581726C22semidirect
56. C2×#14581725C22semidirect
57. C2×#14581723C22semidirect
58. C2×Dic83⋊C8C22semidirect
59. C2×#14581716C22semidirect
61. C2×#14581714C22semidirect
65. #102×D83C22semidirect
66. C2×C22⋊(C83⋊C8)C22semidirect
68. C2×C8×Dic83C22semidirect
70. C23×C8×C83C22semidirect
71. C2×#117×C83C22semidirect
72. #416×C83C22semidirect
73. C2×#103×C83C22semidirect
74. C2×#103×C83C22semidirect
94. C2×#13050577C23semidirect
105. #14581783C23semidirect
117. #14581766C23semidirect
125. #14581754C23semidirect
149. #14581726C23semidirect
150. #14581725C23semidirect
151. #14581723C23semidirect
152. Dic83⋊C8C23semidirect
153. #14581716C23semidirect
155. #14581714C23semidirect
159. C22⋊(C83⋊C8)C23semidirect
161. C8×Dic83C23semidirect
174. C22×C8×C83C23semidirect
176. #117×C83C23semidirect
181. #103×C83C23semidirect
182. #103×C83C23semidirect
413. C2×C83#3297semidirect
434. C2×#416D83semidirect
436. C83C2×#3297semidirect
443. C23×C8C2×D83semidirect
464. C2×#117C2×D83semidirect
482. #416C2×D83semidirect
484. C2×#103C2×D83semidirect
485. C2×#103C2×D83semidirect
535. C22×C8C22×D83semidirect
562. #117C22×D83semidirect
593. #103C22×D83semidirect
594. #103C22×D83semidirect
835. C2#24919314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283952
C2×#191283392
#249193142
C2×#191280572
C2×#191280352
C2×#191280252
C2×#191279992
C2×#191279372
C2×#191279332
C2×#191279192
C2×#191278462
C2×#191278362
C2×#191277812
C2×C8×C22⋊D832
C2×#102×D832
C2×#416×C832
C2×#329783