Finite Group Databasebeta

← C2×#24919545 #36280931

Subgroups — C2×#24919545 #36280931

Order 21248.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128406C211yesmaximal, characteristic, complemented
2C2×#19128339C211yesmaximal, characteristic
3#24919545C2116yesmaximal, direct product factor
4C2×#19128062C211yesmaximal, characteristic, complemented
5C2×#19128035C211yesmaximal, characteristic, complemented
6C2×#19128014C211yesmaximal, characteristic, complemented
7C2×#19127979C211yesmaximal, characteristic, complemented
8C2×#19127947C211yesmaximal, characteristic, complemented
9C2×#19127941C211yesmaximal, characteristic, complemented
10C2×#19127926C211yesmaximal, characteristic, complemented
11C2×#19127863C211yesmaximal, characteristic, complemented
12C2×#19127853C211yesmaximal, characteristic, complemented
13C2×#19127798C211yesmaximal, characteristic, complemented
14C2×#19127770C211yesmaximal, characteristic, complemented
15C2×#102×D83C211yesmaximal, characteristic, complemented
16C2×#417×C83C211yesmaximal, characteristic, complemented
17C22×D4×D83C2211yescharacteristic
18C22×#13050580C2211yescharacteristic, complemented
19C22×#13050579C2211yescharacteristic
20C22×#13050578C2211yescharacteristic
21C22×C8×D83C2211yescharacteristic
22#19128406—24no—
23#19128406C2218yescomplemented
24#19128339—24no—
25#19128339C2218yes—
26C2×#14581791C2211yescharacteristic, complemented
27C2×#14581782—21no—
28C2×#14581781C2211yescharacteristic
29C2×#14581775—21no—
30C2×#14581772C2211yescharacteristic
31C2×#14581771—21no—
32C2×#14581771C2211yescharacteristic, complemented
33C2×#14581770—21no—
34C2×#14581768C2211yescharacteristic
35C2×#14581766C2211yescharacteristic
36C2×#14581764—21no—
37C2×#14581760—21no—
38C2×#14581757C2211yescharacteristic, complemented
39C2×D4×Dic83C2211yescharacteristic
40C2×C4×C22⋊D83—21no—
41C2×C4×C22⋊D83C2211yescharacteristic
42C2×C4⋊C4×D83C2211yescharacteristic
43C22×(C2×D83)⋊C4—21no—
44#19128062C2218yescomplemented
45#19128035C2218yescomplemented
46#19128014C2218yescomplemented
47#19127979C2218yescomplemented
48#19127947C2218yescomplemented
49#19127941C2218yescomplemented
50#19127926C2218yescomplemented
51#19127863C2218yescomplemented
52#19127853C2218yescomplemented
53#19127798C2218yescomplemented
54#19127770C2218yescomplemented
55C2×#14581726C2211yescharacteristic, complemented
56C2×#14581725C2211yescharacteristic, complemented
57C2×#14581725C2211yescharacteristic, complemented
58C2×Dic83⋊C8C2211yescharacteristic, complemented
59C2×#14581717C2211yescharacteristic, complemented
60C2×#14581716C2211yescharacteristic, complemented
61C2×#14581714C2211yescharacteristic
62C2×#14581713C2211yescharacteristic
63C2×#14581712C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65#102×D83C2218yescomplemented
66C2×C22⋊(C83⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×#14581702C2211yescharacteristic, complemented
69C22×#41×C83C2211yescharacteristic
70C22×M16×C83C2211yescharacteristic, complemented
71C22×C4⋊C4×C83C2211yescharacteristic, complemented
72#417×C83C2218yescomplemented
73C2×#103×C83C2211yescharacteristic, complemented
74C2×#103×C83C2211yescharacteristic, complemented
75C2×#102×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C24×D83—21no—
78C22×Dic166—21no—
79C22×Dic166C2311yescharacteristic
80C22×D332C2311yescharacteristic
81C22×C22⋊D83—21no—
82C22×C22⋊D83—21no—
83C22×C22⋊D83D411yescharacteristic
84C2×D4×D83—22no—
85C2×D4×D83—24no—
86C2×D4×D83—42no—
87C2×D4×D83C2314yes—
88C23×Dic83—21no—
89C22×C4×D83—21no—
90C22×C4×D83C2311yescharacteristic
91C2×#13050580—42no—
92C2×#13050580C2314yescomplemented
93C2×#13050579—42no—
94C2×#13050579C2314yes—
95C2×#13050578—24no—
96C2×#13050578C2314yes—
97C22×C83⋊C8C2311yescharacteristic
98C22×C83⋊C8C2311yescharacteristic
99C2×C8×D83—42no—
100C2×C8×D83C2314yes—
101#14581791—22no—
102#14581791C2314yescomplemented
103#14581782—28no—
104#14581781—22no—
105#14581781C2314yes—
106#14581775—28no—
107#14581772—22no—
108#14581772C2314yes—
109#14581771—28no—
110#14581771—22no—
111#14581771C2314yescomplemented
112#14581770—28no—
113#14581768—22no—
114#14581768C2314yes—
115#14581766—22no—
116#14581766C2314yes—
117#14581764—28no—
118#14581760—28no—
119#14581757—22no—
120#14581757C2314yescomplemented
121D4×Dic83—22no—
122D4×Dic83C2314yes—
123C4×C22⋊D83—28no—
124C4×C22⋊D83D414yes—
125C4×C22⋊D83C2314yes—
126C2×C4⋊Dic83—21no—
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
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⋊Dic83—21no—
139C2×C22⋊Dic83D411yescharacteristic
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)⋊C4D411yescharacteristic
147C2×C4×Dic83—21no—
148C2×C4×Dic83C2311yescharacteristic
149#14581726C2314yescomplemented
150#14581725C2314yescomplemented
151#14581725C2314yescomplemented
152Dic83⋊C8C2314yescomplemented
153#14581717C2314yescomplemented
154#14581716C2314yescomplemented
155#14581714C2314yes—
156#14581713C2314yes—
157#14581712C2314yes—
158#14581712C2314yes—
159C22⋊(C83⋊C8)C2314yescomplemented
160(C2×D83)⋊C8C2314yes—
161#14581702C2314yescomplemented
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×C83—21no—
171C23×C4×C83C2311yescharacteristic
172C2×M16×C83—42no—
173C2×M16×C83C2314yescomplemented
174C22×C8×C83C2311yescharacteristic
175C22×C8×C83C2311yescharacteristic
176C2×C4⋊C4×C83—22no—
177C2×C4⋊C4×C83—21no—
178C2×C4⋊C4×C83C2311yescharacteristic
179C2×C4⋊C4×C83C2311yescharacteristic
180C2×C4⋊C4×C83C2314yescomplemented
181#103×C83C2314yescomplemented
182#103×C83C2314yescomplemented
183#102×C83C2314yes—
184#102×C83C2314yes—
185C23×D83—21no—
186C23×D83—24no—
187C23×D83—44no—
188C23×D83—44no—
189C23×D83—82no—
190C23×D83C2×D411yescharacteristic
191C2×Dic166—22no—
192C2×Dic166—22no—
193C2×Dic166—21no—
194C2×Dic166—24no—
195C2×Dic166—82no—
196C2×Dic166C2412yes—
197C2×D332—22no—
198C2×D332—22no—
199C2×D332—21no—
200C2×D332C2412yes—
201C2×C22⋊D83—24no—
202C2×C22⋊D83—24no—
203C2×C22⋊D83—24no—
204C2×C22⋊D83—44no—
205C2×C22⋊D83—82no—
206C2×C22⋊D83C2×D414yes—
207D4×D83—28no—
208D4×D83—44no—
209D4×D83—48no—
210C22×Dic83—21no—
211C22×Dic83—21no—
212C22×Dic83—21no—
213C22×Dic83—24no—
214C22×Dic83—82no—
215C22×Dic83C2×D411yescharacteristic
216C22×Dic83C2×D411yescharacteristic
217C22×Dic83C2×D411yescharacteristic
218C2×C4×D83—22no—
219C2×C4×D83—22no—
220C2×C4×D83—24no—
221C2×C4×D83—82no—
222C2×C4×D83C2×D412yes—
223C2×C4×D83C2412yes—
224#13050580—44no—
225#13050579—44no—
226#13050578—28no—
227C2×C83⋊C8—22no—
228C2×C83⋊C8—22no—
229C2×C83⋊C8C2412yes—
230C2×C83⋊C8C2412yes—
231C8×D83—44no—
232C4⋊Dic83—21no—
233C4⋊Dic83—21no—
234C4⋊Dic83—24no—
235C4⋊Dic83C2412yes—
236C4⋊Dic83C2412yes—
237Dic83⋊C4—24no—
238Dic83⋊C4—24no—
239Dic83⋊C4—24no—
240Dic83⋊C4—24no—
241Dic83⋊C4—24no—
242Dic83⋊C4C2×D414yes—
243C22⋊Dic83—24no—
244C22⋊Dic83—24no—
245C22⋊Dic83C2×D414yes—
246(C2×D83)⋊C4—24no—
247(C2×D83)⋊C4—24no—
248(C2×D83)⋊C4—24no—
249(C2×D83)⋊C4—24no—
250(C2×D83)⋊C4—24no—
251(C2×D83)⋊C4C2×D414yes—
252C4×Dic83—24no—
253C4×Dic83C2×D412yes—
254C4×Dic83C2412yes—
255C24×C83—21no—
256C24×C83C2×D411yescharacteristic
257#41×C83—28no—
258#41×C83—44no—
259#41×C83—48no—
260C2×Q8×C83—21no—
261C2×Q8×C83—22no—
262C2×Q8×C83—22no—
263C2×Q8×C83C2412yes—
264C2×D4×C83—24no—
265C2×D4×C83—21no—
266C2×D4×C83—22no—
267C2×D4×C83—44no—
268C2×D4×C83#4114yes—
269C2×D4×C83C2412yes—
270C22×C4×C83—22no—
271C22×C4×C83—22no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83—24no—
276C22×C4×C83—24no—
277C22×C4×C83—44no—
278C22×C4×C83—82no—
279C22×C4×C83C2×D412yes—
280C22×C4×C83C2×D411yescharacteristic
281C22×C4×C83C2412yes—
282C22×C4×C83C2411yescharacteristic
283M16×C83—44no—
284C2×C8×C83—22no—
285C2×C8×C83—22no—
286C2×C8×C83C2412yes—
287C2×C8×C83C2412yes—
288C4⋊C4×C83—24no—
289C4⋊C4×C83—21no—
290C4⋊C4×C83—21no—
291C4⋊C4×C83C2412yes—
292C4⋊C4×C83C2412yes—
293C23×C83—22no—
294C23×C83—24no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—42no—
299C23×C83—42no—
300C23×C83C22×D412yes—
301C23×C83C22×D411yescharacteristic
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—48no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—42no—
309C22×D83—48no—
310C22×D83—84no—
311C22×D83—816no—
312C22×D83#13714yes—
313C22×D83C22×D412yes—
314Q8×C83—22no—
315Q8×C83—22no—
316Q8×C83—42no—
317D4×C83—24no—
318D4×C83—22no—
319D4×C83—48no—
320D4×C83C2×#4114yes—
321C2×C4×C83—22no—
322C2×C4×C83—24no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—48no—
329C2×C4×C83—42no—
330C2×C4×C83—42no—
331C2×C4×C83—42no—
332C2×C4×C83—84no—
333C2×C4×C83C22×D412yes—
334C2×C4×C83C22×D411yescharacteristic
335C2×C4×C83C2×#4112yes—
336C2×C4×C83H(5,𝔽2)12yes—
337C2×C4×C83C2511yescharacteristic
338C22⋊D83—28no—
339C22⋊D83—48no—
340C22⋊D83—84no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—42no—
348C2×Dic83—42no—
349C2×Dic83—42no—
350C2×Dic83—84no—
351C2×Dic83C22×D412yes—
352C2×Dic83C22×D412yes—
353C2×Dic83C22×D412yes—
354D332—22no—
355D332—22no—
356D332—42no—
357C4×D83—24no—
358C4×D83—22no—
359C4×D83—22no—
360C4×D83—84no—
361Dic166—22no—
362Dic166—22no—
363Dic166—42no—
364Dic166—84no—
365C8×C83—22no—
366C8×C83—22no—
367C83⋊C8—22no—
368C83⋊C8—22no—
369C22×C83—24no—
370C22×C83—22no—
371C22×C83—22no—
372C22×C83—22no—
373C22×C83—48no—
374C22×C83—44no—
375C22×C83—42no—
376C22×C83—42no—
377C22×C83#54612yes—
378C22×C83C2×#13712yes—
379C22×C83#57612yes—
380C22×C83C23×D411yescharacteristic
381C2×D83—22no—
382C2×D83—28no—
383C2×D83—22no—
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—816no—
388C2×D83—84no—
389C2×D83C2×#13714yes—
390C4×C83—22no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83#54612yes—
395C4×C83C22×#4111yescharacteristic
396C4×C83C2×H(5,𝔽2)11yescharacteristic
397Dic83—22no—
398Dic83—22no—
399Dic83—22no—
400Dic83—42no—
401Dic83—42no—
402Dic83—42no—
403C2×#3314—831nomaximal, Sylow
404C2×C83—44no—
405C2×C83—42no—
406C2×C83#331414yescomplemented
407C2×C83C2×#54611yescharacteristic
408C2×C83C22×#13711yescharacteristic
409C2×C83C2×#57611yescharacteristic
410D83—24no—
411D83—82no—
412C2×#554—831no—
413C2×#546—831no—
414#3314—8316no—
415C2×#489—831no—
416C2×#484—831no—
417C2×#480—831no—
418C2×#474—831no—
419C2×#468—831no—
420C2×#467—831no—
421C2×#464—831no—
422C2×#452—831no—
423C2×#450—831no—
424C2×#440—831no—
425C2×#435—831no—
426C2×#417D8311yescharacteristic, complemented
427C22×#102—831no—
428C83C2×#331411yescharacteristic, complemented, Sylow
429C22×#41C2×D8311yescharacteristic
430C23×D4—831no—
431C22×Q16—831no—
432C22×SD16—831no—
433C22×SD16—831no—
434C22×M16C2×D8311yescharacteristic, complemented
435C23×C8—831no—
436#554—838no—
437#554—1664no—
438#546—838no—
439#546—1664no—
440C2×C4⋊Q8—831no—
441C2×#125—1661no—
442C2×#124—831no—
443C2×#123—1661no—
444C2×C22⋊Q8—831no—
445C2×C22⋊Q8—831no—
446C2×C22⋊Q8—831no—
447C2×C22⋊Q8—1661no—
448C2×C22⋊Q8—1661no—
449C2×#121—831no—
450C2×#121—1661no—
451C2×#120—1661no—
452C2×C4×Q8—831no—
453C2×C4×D4—831no—
454C2×C4×D4—831no—
455C2×C4×D4—1661no—
456C22×C4⋊C4—831no—
457C22×C4⋊C4C2×D8311yescharacteristic, complemented
458C22×C22⋊C4—1661no—
459#489—838no—
460#484—838no—
461#480—838no—
462#474—838no—
463#468—838no—
464#467—838no—
465#464—838no—
466#452—838no—
467#450—838no—
468#440—838no—
469#435—838no—
470C2×#107—831no—
471C2×#107—831no—
472C2×#107—831no—
473C2×C4⋊C8—831no—
474#417C2×D8318yescomplemented
475C2×#103—831no—
476C2×#103—831no—
477C2×#103C2×D8311yescharacteristic, complemented
478C2×#103C2×D8311yescharacteristic, complemented
479C2×#102—831no—
480C2×#102—831no—
481C2×#102—831no—
482C2×#102—831no—
483C2×#102—838no—
484C2×#102C2×D8311yescharacteristic
485C2×#102C2×D8311yescharacteristic
486C2×C22⋊C8—831no—
487C2×C22⋊C8—831no—
488C2×#97—831no—
489C25—1661no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41C22×D8314yes—
494C22×Q8—831no—
495C22×Q8—1661no—
496C22×Q8C22×D8311yescharacteristic
497C22×D4—21no—
498C22×D4—3322no—
499C22×D4—834no—
500C22×D4—831no—
501C22×D4—831no—
502C22×D4—1662no—
503C22×D4—1661no—
504C22×D4—1664no—
505C22×D4—1661no—
506C22×D4C22×D8311yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—831no—
510C23×C4—1661no—
511C23×C4—1661no—
512C23×C4C22×D8311yescharacteristic
513C2×Q16—3322no—
514C2×Q16—834no—
515C2×SD16—3322no—
516C2×SD16—834no—
517C2×SD16—834no—
518C2×SD16—1664no—
519C2×M16—42no—
520C2×M16C22×D8314yescomplemented
521C22×C8—3322no—
522C22×C8—834no—
523C22×C8—831no—
524C22×C8—831no—
525C22×C8C22×D8311yescharacteristic
526C22×C8C22×D8311yescharacteristic
527C4⋊Q8—834no—
528C4⋊Q8—1662no—
529#125—1668no—
530#124—834no—
531#124—1662no—
532#123—1668no—
533C22⋊Q8—834no—
534C22⋊Q8—834no—
535C22⋊Q8—834no—
536C22⋊Q8—1668no—
537C22⋊Q8—1668no—
538C22⋊Q8—1662no—
539C22⋊Q8—1662no—
540C22⋊Q8—1662no—
541#121—834no—
542#121—1668no—
543#121—1662no—
544#120—1668no—
545C4×Q8—834no—
546C4×Q8—1662no—
547C4×D4—834no—
548C4×D4—834no—
549C4×D4—834no—
550C4×D4—1662no—
551C4×D4—1668no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—831no—
555C2×C4⋊C4—831no—
556C2×C4⋊C4—831no—
557C2×C4⋊C4—834no—
558C2×C4⋊C4—1662no—
559C2×C4⋊C4—1661no—
560C2×C4⋊C4—1661no—
561C2×C4⋊C4—1661no—
562C2×C4⋊C4—1661no—
563C2×C4⋊C4—1661no—
564C2×C4⋊C4—1661no—
565C2×C4⋊C4C22×D8311yescharacteristic
566C2×C4⋊C4C22×D8311yescharacteristic
567C2×C4⋊C4C22×D8314yescomplemented
568C2×C22⋊C4—831no—
569C2×C22⋊C4—831no—
570C2×C22⋊C4—1668no—
571C2×C22⋊C4—1661no—
572C2×C22⋊C4—1661no—
573C2×C22⋊C4—1661no—
574C2×C22⋊C4—1661no—
575C2×C22⋊C4—1661no—
576C2×C22⋊C4—1661no—
577C2×C22⋊C4—1661no—
578C2×C42—831no—
579C2×C42—1661no—
580#107—834no—
581#107—834no—
582#107—834no—
583C4⋊C8—834no—
584#103—834no—
585#103—834no—
586#103C22×D8314yescomplemented
587#103C22×D8314yescomplemented
588#102—834no—
589#102—834no—
590#102—834no—
591#102—834no—
592#102C22×D8314yes—
593#102C22×D8314yes—
594C22⋊C8—834no—
595C22⋊C8—834no—
596#97—834no—
597C24—21no—
598C24—3324no—
599C24—3324no—
600C24—831no—
601C24—6642no—
602C24—1664no—
603C24—1661no—
604C24D4×D8311yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—832no—
612C2×Q8—6642no—
613C2×Q8—1664no—
614C2×Q8—1662no—
615C2×Q8—1662no—
616C2×Q8—1661no—
617C2×Q8C23×D8312yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—3328no—
623C2×D4—3324no—
624C2×D4—3324no—
625C2×D4—834no—
626C2×D4—832no—
627C2×D4—6642no—
628C2×D4—1664no—
629C2×D4—1668no—
630C2×D4—1664no—
631C2×D4—1664no—
632C2×D4—1661no—
633C2×D4—1662no—
634C2×D4—1662no—
635C2×D4#1305059014yes—
636C2×D4C23×D8312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—831no—
647C22×C4—831no—
648C22×C4—831no—
649C22×C4—832no—
650C22×C4—832no—
651C22×C4—6642no—
652C22×C4—6642no—
653C22×C4—1664no—
654C22×C4—1661no—
655C22×C4—1661no—
656C22×C4—1661no—
657C22×C4—1664no—
658C22×C4—1662no—
659C22×C4—1662no—
660C22×C4D4×D8312yes—
661C22×C4D4×D8311yescharacteristic
662C22×C4C23×D8312yes—
663C22×C4C23×D8311yescharacteristic
664Q16—3324no—
665SD16—3324no—
666SD16—1668no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—3324no—
671C2×C8—832no—
672C2×C8—832no—
673C2×C8—1662no—
674C2×C8—1662no—
675C2×C8C23×D8312yes—
676C2×C8C23×D8312yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—834no—
681C4⋊C4—832no—
682C4⋊C4—832no—
683C4⋊C4—1664no—
684C4⋊C4—1664no—
685C4⋊C4—1664no—
686C4⋊C4—1664no—
687C4⋊C4—1664no—
688C4⋊C4—1661no—
689C4⋊C4—1661no—
690C4⋊C4—1664no—
691C4⋊C4C23×D8312yes—
692C4⋊C4C23×D8312yes—
693C22⋊C4—834no—
694C22⋊C4—834no—
695C22⋊C4—1664no—
696C22⋊C4—1664no—
697C22⋊C4—1664no—
698C22⋊C4—1664no—
699C22⋊C4—1664no—
700C22⋊C4—1664no—
701C22⋊C4—1664no—
702C42—832no—
703C42—832no—
704C42—1664no—
705C23—22no—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—3328no—
713C23—3328no—
714C23—3322no—
715C23—3322no—
716C23—3322no—
717C23—834no—
718C23—832no—
719C23—6644no—
720C23—66416no—
721C23—1662no—
722C23—1662no—
723C23—1662no—
724C23C2×D4×D8312yes—
725C23C2×D4×D8311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—3322no—
730Q8—6644no—
731Q8—1662no—
732Q8—1662no—
733D4—24no—
734D4—22no—
735D4—48no—
736D4—3328no—
737D4—3322no—
738D4—6644no—
739D4—1668no—
740D4—1662no—
741D4—1662no—
742D4C2×#1305059014yes—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—84no—
755C2×C4—3322no—
756C2×C4—3322no—
757C2×C4—3322no—
758C2×C4—832no—
759C2×C4—832no—
760C2×C4—832no—
761C2×C4—6644no—
762C2×C4—6644no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1664no—
770C2×C4—1662no—
771C2×C4—1662no—
772C2×C4C2×D4×D8312yes—
773C2×C4C2×D4×D8311yescharacteristic
774C2×C4C2×#1305059012yes—
775C2×C4#1458183712yes—
776C2×C4C24×D8311yescharacteristic
777C8—22no—
778C8—22no—
779C8—1662no—
780C8—1662no—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—22no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—48no—
789C22—3322no—
790C22—3322no—
791C22—3322no—
792C22—834no—
793C22—66416no—
794C22—6644no—
795C22—1662no—
796C22—1662no—
797C22—1668no—
798C22#1912834112yes—
799C22#137×D8312yes—
800C22#1912850512yes—
801C22C22×D4×D8311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—3322no—
807C4—3322no—
808C4—3322no—
809C4—1662no—
810C4—1662no—
811C4—1662no—
812C4#1912834112yes—
813C4C22×#1305059011yescharacteristic
814C4C2×#1458183711yescharacteristic
815C2—42no—
816C2—44no—
817C2—6642no—
818C2—1664no—
819C2#2491954514yesdirect product factor
820C2C2×#1912834111yescharacteristic
821C2C2×#137×D8311yescharacteristic
822C2C2×#1912850511yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#417×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128339C2
hypercenterC2×#417D83
hypocenterC83C2×#3314
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#19128406C2semidirect
3. #24919545C2direct (N × H)
4. C2×#19128062C2semidirect
5. C2×#19128035C2semidirect
6. C2×#19128014C2semidirect
7. C2×#19127979C2semidirect
8. C2×#19127947C2semidirect
9. C2×#19127941C2semidirect
10. C2×#19127926C2semidirect
11. C2×#19127863C2semidirect
12. C2×#19127853C2semidirect
13. C2×#19127798C2semidirect
14. C2×#19127770C2semidirect
15. C2×#102×D83C2semidirect
16. C2×#417×C83C2semidirect
18. C22×#13050580C22semidirect
23. #19128406C22semidirect
26. C2×#14581791C22semidirect
32. C2×#14581771C22semidirect
38. C2×#14581757C22semidirect
44. #19128062C22semidirect
45. #19128035C22semidirect
46. #19128014C22semidirect
47. #19127979C22semidirect
48. #19127947C22semidirect
49. #19127941C22semidirect
50. #19127926C22semidirect
51. #19127863C22semidirect
52. #19127853C22semidirect
53. #19127798C22semidirect
54. #19127770C22semidirect
55. C2×#14581726C22semidirect
56. C2×#14581725C22semidirect
57. C2×#14581725C22semidirect
58. C2×Dic83⋊C8C22semidirect
59. C2×#14581717C22semidirect
60. C2×#14581716C22semidirect
65. #102×D83C22semidirect
66. C2×C22⋊(C83⋊C8)C22semidirect
68. C2×#14581702C22semidirect
70. C22×M16×C83C22semidirect
71. C22×C4⋊C4×C83C22semidirect
72. #417×C83C22semidirect
73. C2×#103×C83C22semidirect
74. C2×#103×C83C22semidirect
92. C2×#13050580C23semidirect
102. #14581791C23semidirect
111. #14581771C23semidirect
120. #14581757C23semidirect
149. #14581726C23semidirect
150. #14581725C23semidirect
151. #14581725C23semidirect
152. Dic83⋊C8C23semidirect
153. #14581717C23semidirect
154. #14581716C23semidirect
159. C22⋊(C83⋊C8)C23semidirect
161. #14581702C23semidirect
173. C2×M16×C83C23semidirect
180. C2×C4⋊C4×C83C23semidirect
181. #103×C83C23semidirect
182. #103×C83C23semidirect
406. C2×C83#3314semidirect
426. C2×#417D83semidirect
428. C83C2×#3314semidirect
434. C22×M16C2×D83semidirect
457. C22×C4⋊C4C2×D83semidirect
474. #417C2×D83semidirect
477. C2×#103C2×D83semidirect
478. C2×#103C2×D83semidirect
520. C2×M16C22×D83semidirect
567. C2×C4⋊C4C22×D83semidirect
586. #103C22×D83semidirect
587. #103C22×D83semidirect
819. C2#24919545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284062
C2×#191283392
#249195452
C2×#191280622
C2×#191280352
C2×#191280142
C2×#191279792
C2×#191279472
C2×#191279412
C2×#191279262
C2×#191278632
C2×#191278532
C2×#191277982
C2×#191277702
C2×#102×D832
C2×#417×C832
C2×#331483