Finite Group Databasebeta

← C2×#24919546 #36280932

Subgroups — C2×#24919546 #36280932

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×#19128408C211yesmaximal, characteristic, complemented
2C2×#19128347C211yesmaximal, characteristic
3#24919546C2116yesmaximal, direct product factor
4C2×#19128061C211yesmaximal, characteristic, complemented
5C2×#19128037C211yesmaximal, characteristic, complemented
6C2×#19128015C211yesmaximal, characteristic, complemented
7C2×#19127982C211yesmaximal, characteristic, complemented
8C2×#19127947C211yesmaximal, characteristic, complemented
9C2×#19127942C211yesmaximal, characteristic, complemented
10C2×#19127924C211yesmaximal, characteristic, complemented
11C2×#19127865C211yesmaximal, characteristic, complemented
12C2×#19127854C211yesmaximal, characteristic, complemented
13C2×#19127803C211yesmaximal, characteristic, complemented
14C2×#19127703C211yesmaximal, characteristic, complemented
15C22×#14581714C211yesmaximal, characteristic, complemented
16C2×#435×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C22×Dic332C2211yescharacteristic, complemented
20C22×#13050579C2211yescharacteristic
21C22×#13050579C2211yescharacteristic
22#19128408—24no—
23#19128408C2218yescomplemented
24#19128347—24no—
25#19128347C2218yes—
26C2×#14581792C2211yescharacteristic, complemented
27C2×#14581783—21no—
28C2×#14581780C2211yescharacteristic
29C2×#14581777—21no—
30C2×#14581771C2211yescharacteristic
31C2×#14581771C2211yescharacteristic
32C2×#14581771C2211yescharacteristic, complemented
33C2×#14581769—21no—
34C2×#14581769—21no—
35C2×#14581766C2211yescharacteristic
36C2×#14581765—21no—
37C2×#14581760—21no—
38C2×C4×Dic166C2211yescharacteristic, complemented
39C2×C4×D332C2211yescharacteristic
40C2×D4×Dic83—21no—
41C22×C4⋊Dic83C2211yescharacteristic
42C22×C4⋊Dic83C2211yescharacteristic, complemented
43C2×C22⋊C4×D83—21no—
44#19128061C2218yescomplemented
45#19128037C2218yescomplemented
46#19128015C2218yescomplemented
47#19127982C2218yescomplemented
48#19127947C2218yescomplemented
49#19127942C2218yescomplemented
50#19127924C2218yescomplemented
51#19127865C2218yescomplemented
52#19127854C2218yescomplemented
53#19127803C2218yescomplemented
54C2×#14581726C2211yescharacteristic, complemented
55C2×#14581726C2211yescharacteristic, complemented
56C2×#14581726C2211yescharacteristic, complemented
57#19127703C2218yescomplemented
58C2×#14581717C2211yescharacteristic, complemented
59C2×#14581717C2211yescharacteristic, complemented
60C2×#14581717C2211yescharacteristic, complemented
61C2×#14581717C2211yescharacteristic, complemented
62C2×#14581714C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic
68C2×#14581714C2218yescomplemented
69C22×M16×C83C2211yescharacteristic, complemented
70C23×C8×C83C2211yescharacteristic
71C2×C4×D4×C83C2211yescharacteristic
72#435×C83C2218yescomplemented
73C2×C4⋊C8×C83C2211yescharacteristic, complemented
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic, complemented
76C2×#97×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050590—24no—
79C2×#13050590—22no—
80C2×#13050590—42no—
81C2×#13050590C2314yes—
82C22×Dic166—21no—
83C22×Dic166C2311yescharacteristic
84C22×Dic166C2311yescharacteristic
85C22×D332—24no—
86C22×D332—22no—
87C22×D332—21no—
88C22×D332—42no—
89C22×D332C2311yescharacteristic
90C22×D332C2314yes—
91C22×D332C2311yescharacteristic
92C22×C22⋊D83—21no—
93C22×C22⋊D83—21no—
94C23×Dic83—21no—
95C23×Dic83—21no—
96C22×C4×D83—21no—
97C22×C4×D83—21no—
98C2×Dic332—42no—
99C2×Dic332C2314yescomplemented
100C2×#13050579—24no—
101C2×#13050579—42no—
102C2×#13050579C2314yes—
103C2×#13050579C2314yes—
104#14581792—22no—
105#14581792C2314yescomplemented
106#14581783—28no—
107#14581780—22no—
108#14581780C2314yes—
109#14581777—28no—
110#14581771—22no—
111#14581771—22no—
112#14581771—22no—
113#14581771C2314yes—
114#14581771C2314yes—
115#14581771C2314yescomplemented
116#14581769—28no—
117#14581769—28no—
118#14581766—22no—
119#14581766C2314yes—
120#14581765—28no—
121#14581760—28no—
122C4×Dic166—22no—
123C4×Dic166C2314yescomplemented
124C4×D332—22no—
125C4×D332C2314yes—
126D4×Dic83—28no—
127C2×C4⋊Dic83—22no—
128C2×C4⋊Dic83—21no—
129C2×C4⋊Dic83—22no—
130C2×C4⋊Dic83—21no—
131C2×C4⋊Dic83—21no—
132C2×C4⋊Dic83C2311yescharacteristic
133C2×C4⋊Dic83C2314yes—
134C2×C4⋊Dic83C2311yescharacteristic
135C2×C4⋊Dic83C2311yescharacteristic
136C2×C4⋊Dic83C2311yescharacteristic
137C2×C4⋊Dic83C2314yescomplemented
138C2×Dic83⋊C4—21no—
139C2×Dic83⋊C4—21no—
140C2×Dic83⋊C4—21no—
141C2×Dic83⋊C4—21no—
142C2×C22⋊Dic83—21no—
143C2×C22⋊Dic83—21no—
144C2×C22⋊Dic83—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C2×(C2×D83)⋊C4—21no—
148C2×(C2×D83)⋊C4—21no—
149C22⋊C4×D83—28no—
150C2×C4×Dic83—21no—
151#14581726C2314yescomplemented
152#14581726C2314yescomplemented
153#14581726C2314yescomplemented
154#14581717C2314yescomplemented
155#14581717C2314yescomplemented
156#14581717C2314yescomplemented
157#14581717C2314yescomplemented
158#14581714C2314yes—
159#14581714C2314yes—
160#14581714C2314yes—
161#14581714C2314yes—
162#14581714C2314yes—
163#14581714C2314yes—
164C22×D4×C83D411yescharacteristic
165C23×C4×C83C2311yescharacteristic
166C23×C4×C83C2311yescharacteristic
167C2×M16×C83—42no—
168C2×M16×C83C2314yescomplemented
169C22×C8×C83—42no—
170C22×C8×C83C2311yescharacteristic
171C22×C8×C83C2311yescharacteristic
172C22×C8×C83C2311yescharacteristic
173C22×C8×C83C2311yescharacteristic
174C22×C8×C83C2314yes—
175C4×D4×C83D414yes—
176C4×D4×C83C2314yes—
177C2×C4⋊C4×C83D411yescharacteristic
178C2×C22⋊C4×C83D411yescharacteristic
179C2×C22⋊C4×C83D411yescharacteristic
180C2×C42×C83C2311yescharacteristic
181C4⋊C8×C83C2314yescomplemented
182C22⋊C8×C83C2314yes—
183C22⋊C8×C83C2314yescomplemented
184#97×C83C2314yescomplemented
185C23×D83—21no—
186C23×D83—21no—
187C23×D83—24no—
188C23×D83—44no—
189C23×D83—44no—
190C23×D83—82no—
191#13050590—28no—
192#13050590—44no—
193#13050590—48no—
194C2×Dic166—22no—
195C2×Dic166—22no—
196C2×Dic166—22no—
197C2×Dic166—22no—
198C2×Dic166—21no—
199C2×Dic166—21no—
200C2×Dic166—24no—
201C2×Dic166—82no—
202C2×Dic166C2412yes—
203C2×Dic166C2412yes—
204C2×D332—21no—
205C2×D332—22no—
206C2×D332—22no—
207C2×D332—22no—
208C2×D332—28no—
209C2×D332—24no—
210C2×D332—21no—
211C2×D332—44no—
212C2×D332—48no—
213C2×D332—44no—
214C2×D332#4114yes—
215C2×D332C2412yes—
216C2×D332C2412yes—
217C2×C22⋊D83—24no—
218C2×C22⋊D83—24no—
219C2×C22⋊D83—44no—
220C2×C22⋊D83—82no—
221C22×Dic83—21no—
222C22×Dic83—21no—
223C22×Dic83—21no—
224C22×Dic83—21no—
225C22×Dic83—21no—
226C22×Dic83—21no—
227C22×Dic83—24no—
228C22×Dic83—24no—
229C22×Dic83—82no—
230C22×Dic83—82no—
231C2×C4×D83—24no—
232C2×C4×D83—24no—
233C2×C4×D83—44no—
234C2×C4×D83—82no—
235Dic332—44no—
236#13050579—28no—
237#13050579—44no—
238C4⋊Dic83—21no—
239C4⋊Dic83—24no—
240C4⋊Dic83—24no—
241C4⋊Dic83—21no—
242C4⋊Dic83—21no—
243C4⋊Dic83—24no—
244C4⋊Dic83—21no—
245C4⋊Dic83C2412yes—
246C4⋊Dic83C2412yes—
247C4⋊Dic83C2412yes—
248C4⋊Dic83C2412yes—
249Dic83⋊C4—24no—
250Dic83⋊C4—24no—
251Dic83⋊C4—24no—
252Dic83⋊C4—24no—
253C22⋊Dic83—24no—
254C22⋊Dic83—24no—
255C22⋊Dic83—24no—
256(C2×D83)⋊C4—24no—
257(C2×D83)⋊C4—24no—
258(C2×D83)⋊C4—24no—
259(C2×D83)⋊C4—24no—
260C4×Dic83—24no—
261C24×C83C2×D411yescharacteristic
262C24×C83C2×D411yescharacteristic
263C2×D4×C83—24no—
264C2×D4×C83C2×D414yes—
265C22×C4×C83—22no—
266C22×C4×C83—22no—
267C22×C4×C83—22no—
268C22×C4×C83—22no—
269C22×C4×C83C2×D412yes—
270C22×C4×C83C2×D412yes—
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2×D411yescharacteristic
273C22×C4×C83C2×D411yescharacteristic
274C22×C4×C83C2×D411yescharacteristic
275C22×C4×C83C2412yes—
276C22×C4×C83C2412yes—
277C22×C4×C83C2411yescharacteristic
278M16×C83—44no—
279C2×C8×C83—22no—
280C2×C8×C83—22no—
281C2×C8×C83—22no—
282C2×C8×C83—22no—
283C2×C8×C83—44no—
284C2×C8×C83C2412yes—
285C2×C8×C83C2412yes—
286C2×C8×C83C2412yes—
287C2×C8×C83C2412yes—
288C4⋊C4×C83C2×D414yes—
289C22⋊C4×C83C2×D414yes—
290C22⋊C4×C83C2×D414yes—
291C42×C83C2×D412yes—
292C42×C83C2412yes—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83#13714yes—
299C23×C83C22×D412yes—
300C23×C83C22×D412yes—
301C23×C83C22×D411yescharacteristic
302C22×D83—24no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—48no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—42no—
309C22×D83—48no—
310C22×D83—42no—
311C22×D83—42no—
312C22×D83—84no—
313C22×D83—816no—
314D4×C83—28no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—24no—
320C2×C4×C83—24no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83C22×D412yes—
326C2×C4×C83C22×D412yes—
327C2×C4×C83C22×D412yes—
328C2×C4×C83C22×D412yes—
329C2×C4×C83C22×D411yescharacteristic
330C2×C4×C83C2×#4112yes—
331C2×C4×C83H(5,𝔽2)12yes—
332C2×C4×C83C2511yescharacteristic
333C22⋊D83—48no—
334C22⋊D83—84no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—42no—
342C2×Dic83—42no—
343C2×Dic83—42no—
344C2×Dic83—42no—
345C2×Dic83—42no—
346C2×Dic83—42no—
347C2×Dic83—84no—
348C2×Dic83—84no—
349D332—24no—
350D332—22no—
351D332—22no—
352D332—22no—
353D332—48no—
354D332—42no—
355D332C2×#4114yes—
356C4×D83—48no—
357C4×D83—84no—
358Dic166—22no—
359Dic166—22no—
360Dic166—22no—
361Dic166—22no—
362Dic166—42no—
363Dic166—42no—
364Dic166—84no—
365C8×C83—22no—
366C8×C83—22no—
367C8×C83—22no—
368C8×C83—22no—
369C22×C83—22no—
370C22×C83—28no—
371C22×C83—22no—
372C22×C83—22no—
373C22×C83—22no—
374C22×C83—22no—
375C22×C83—44no—
376C22×C83#54612yes—
377C22×C83C2×#13714yes—
378C22×C83C2×#13712yes—
379C22×C83#57612yes—
380C22×C83C23×D411yescharacteristic
381C2×D83—24no—
382C2×D83—48no—
383C2×D83—42no—
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—42no—
388C2×D83—816no—
389C2×D83—84no—
390C4×C83—22no—
391C4×C83—22no—
392C4×C83—22no—
393C4×C83—22no—
394C4×C83#54612yes—
395C4×C83C22×#4111yescharacteristic
396C4×C83C2×H(5,𝔽2)11yescharacteristic
397Dic83—42no—
398Dic83—42no—
399Dic83—42no—
400Dic83—42no—
401Dic83—42no—
402Dic83—42no—
403C2×#3314—831nomaximal, Sylow
404C2×C83—24no—
405C2×C83—42no—
406C2×C83#331414yescomplemented
407C2×C83C2×#54611yescharacteristic
408C2×C83C22×#13711yescharacteristic
409C2×C83C2×#57611yescharacteristic
410D83—44no—
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×#435D8311yescharacteristic, complemented
426C2×#417—831no—
427C22×#102—831no—
428C83C2×#331411yescharacteristic, complemented, Sylow
429C22×#41—831no—
430C23×D4—831no—
431C22×Q16—831no—
432C22×SD16—831no—
433C22×SD16—831no—
434C22×M16C2×D8311yescharacteristic, complemented
435C23×C8C2×D8311yescharacteristic
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—1661no—
455C2×C4×D4C2×D8311yescharacteristic
456C22×C4⋊C4—831no—
457C22×C4⋊C4—831no—
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#435C2×D8318yescomplemented
470C2×#107—831no—
471C2×#107—831no—
472C2×#107—831no—
473C2×C4⋊C8C2×D8311yescharacteristic, complemented
474#417—838no—
475C2×#103—831no—
476C2×#103—831no—
477C2×#103—831no—
478C2×#103—831no—
479C2×#102—831no—
480C2×#102—831no—
481C2×#102—831no—
482C2×#102—831no—
483C2×#102—831no—
484C2×#102—838no—
485C2×#102—831no—
486C2×C22⋊C8C2×D8311yescharacteristic
487C2×C22⋊C8C2×D8311yescharacteristic, complemented
488C2×#97C2×D8311yescharacteristic, complemented
489C25—1661no—
490C2×#41—3322no—
491C2×#41—834no—
492C2×#41—1664no—
493C2×#41—1662no—
494C22×Q8—831no—
495C22×Q8—831no—
496C22×Q8—1661no—
497C22×D4—3322no—
498C22×D4—834no—
499C22×D4—831no—
500C22×D4—831no—
501C22×D4—1664no—
502C22×D4—1661no—
503C22×D4—1661no—
504C22×D4—1661no—
505C22×D4—1662no—
506C22×D4D33211yescharacteristic
507C23×C4—1661no—
508C23×C4—1661no—
509C23×C4—1661no—
510C23×C4—1661no—
511C23×C4C22×D8311yescharacteristic
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—42no—
522C22×C8C22×D8311yescharacteristic
523C22×C8C22×D8311yescharacteristic
524C22×C8C22×D8311yescharacteristic
525C22×C8C22×D8311yescharacteristic
526C22×C8C22×D8314yes—
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—1662no—
537C22⋊Q8—1662no—
538C22⋊Q8—1662no—
539C22⋊Q8—1668no—
540C22⋊Q8—1668no—
541#121—834no—
542#121—1662no—
543#121—1668no—
544#120—1668no—
545C4×Q8—834no—
546C4×Q8—1662no—
547C4×D4—834no—
548C4×D4—1668no—
549C4×D4—1662no—
550C4×D4D33214yes—
551C4×D4C22×D8314yes—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—831no—
554C2×C4⋊C4—831no—
555C2×C4⋊C4—834no—
556C2×C4⋊C4—834no—
557C2×C4⋊C4—831no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4—1661no—
560C2×C4⋊C4—1662no—
561C2×C4⋊C4—1662no—
562C2×C4⋊C4—1661no—
563C2×C4⋊C4—1661no—
564C2×C4⋊C4—1661no—
565C2×C4⋊C4—1661no—
566C2×C4⋊C4—1661no—
567C2×C4⋊C4D33211yescharacteristic
568C2×C22⋊C4—1661no—
569C2×C22⋊C4—1661no—
570C2×C22⋊C4—1661no—
571C2×C22⋊C4—1661no—
572C2×C22⋊C4—1661no—
573C2×C22⋊C4—1661no—
574C2×C22⋊C4—1661no—
575C2×C22⋊C4—1668no—
576C2×C22⋊C4D33211yescharacteristic
577C2×C22⋊C4D33211yescharacteristic
578C2×C42—1661no—
579C2×C42C22×D8311yescharacteristic
580#107—834no—
581#107—834no—
582#107—834no—
583C4⋊C8C22×D8314yescomplemented
584#103—834no—
585#103—834no—
586#103—834no—
587#103—834no—
588#102—834no—
589#102—834no—
590#102—834no—
591#102—834no—
592#102—834no—
593#102—834no—
594C22⋊C8C22×D8314yes—
595C22⋊C8C22×D8314yescomplemented
596#97C22×D8314yescomplemented
597C24—3324no—
598C24—3324no—
599C24—6642no—
600C24—1661no—
601C24—1664no—
602C24—1661no—
603C24C2×D33211yescharacteristic
604C24C2×D33211yescharacteristic
605#41—3328no—
606#41—3324no—
607#41—1668no—
608C2×Q8—832no—
609C2×Q8—832no—
610C2×Q8—6642no—
611C2×Q8—1662no—
612C2×Q8—1662no—
613C2×Q8—1662no—
614C2×Q8—1662no—
615C2×Q8—1661no—
616C2×Q8—1661no—
617C2×Q8—1664no—
618C2×D4—24no—
619C2×D4—3324no—
620C2×D4—3328no—
621C2×D4—3324no—
622C2×D4—3324no—
623C2×D4—834no—
624C2×D4—832no—
625C2×D4—832no—
626C2×D4—6642no—
627C2×D4—1668no—
628C2×D4—1664no—
629C2×D4—1664no—
630C2×D4—1664no—
631C2×D4—1661no—
632C2×D4—1661no—
633C2×D4—1662no—
634C2×D4—1662no—
635C2×D4—1662no—
636C2×D4C2×D33214yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—3324no—
642C22×C4—6642no—
643C22×C4—6642no—
644C22×C4—6642no—
645C22×C4—1661no—
646C22×C4—1661no—
647C22×C4—1661no—
648C22×C4—1661no—
649C22×C4—1661no—
650C22×C4—1661no—
651C22×C4—1664no—
652C22×C4—1664no—
653C22×C4—1664no—
654C22×C4—1664no—
655C22×C4C2×D33212yes—
656C22×C4C2×D33212yes—
657C22×C4C2×D33211yescharacteristic
658C22×C4C2×D33211yescharacteristic
659C22×C4C2×D33211yescharacteristic
660C22×C4C2×D33211yescharacteristic
661C22×C4C23×D8312yes—
662C22×C4C23×D8312yes—
663C22×C4C23×D8311yescharacteristic
664Q16—3324no—
665SD16—3324no—
666SD16—1668no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—44no—
673C2×C8C23×D8312yes—
674C2×C8C23×D8312yes—
675C2×C8C23×D8312yes—
676C2×C8C23×D8312yes—
677C4⋊C4—832no—
678C4⋊C4—832no—
679C4⋊C4—832no—
680C4⋊C4—832no—
681C4⋊C4—1661no—
682C4⋊C4—1664no—
683C4⋊C4—1664no—
684C4⋊C4—1661no—
685C4⋊C4—1661no—
686C4⋊C4—1661no—
687C4⋊C4—1664no—
688C4⋊C4—1664no—
689C4⋊C4—1664no—
690C4⋊C4—1664no—
691C4⋊C4—1664no—
692C4⋊C4C2×D33214yes—
693C22⋊C4—1664no—
694C22⋊C4—1664no—
695C22⋊C4—1664no—
696C22⋊C4—1664no—
697C22⋊C4—1664no—
698C22⋊C4—1664no—
699C22⋊C4—1664no—
700C22⋊C4C2×D33214yes—
701C22⋊C4C2×D33214yes—
702C42—1664no—
703C42C2×D33212yes—
704C42C23×D8312yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—3328no—
711C23—3322no—
712C23—3322no—
713C23—3322no—
714C23—3328no—
715C23—3322no—
716C23—3322no—
717C23—6644no—
718C23—66416no—
719C23—1662no—
720C23—1664no—
721C23—1662no—
722C23#1458182514yes—
723C23C22×D33212yes—
724C23C22×D33212yes—
725C23C22×D33211yescharacteristic
726Q8—3322no—
727Q8—3322no—
728Q8—6644no—
729Q8—1662no—
730Q8—1662no—
731Q8—1662no—
732Q8—1662no—
733D4—28no—
734D4—3328no—
735D4—3328no—
736D4—3322no—
737D4—834no—
738D4—6644no—
739D4—1664no—
740D4—1662no—
741D4—1662no—
742D4—1662no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—3328no—
754C2×C4—3322no—
755C2×C4—3322no—
756C2×C4—3322no—
757C2×C4—3322no—
758C2×C4—3322no—
759C2×C4—3322no—
760C2×C4—6644no—
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×C4C22×D33212yes—
770C2×C4C22×D33212yes—
771C2×C4C22×D33212yes—
772C2×C4C22×D33212yes—
773C2×C4C22×D33211yescharacteristic
774C2×C4#41×D8312yes—
775C2×C4#1458183712yes—
776C2×C4C24×D8311yescharacteristic
777C8—22no—
778C8—22no—
779C8—22no—
780C8—22no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—3322no—
789C22—3322no—
790C22—3328no—
791C22—3322no—
792C22—3322no—
793C22—3322no—
794C22—66416no—
795C22—6644no—
796C22—1664no—
797C22#1912834612yes—
798C22C2×#1458182514yes—
799C22C2×#1458182512yes—
800C22#1912850612yes—
801C22C23×D33211yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—3322no—
807C4—3322no—
808C4—3322no—
809C4—3322no—
810C4—3322no—
811C4—3322no—
812C4#1912834612yes—
813C4C2×#41×D8311yescharacteristic
814C4C2×#1458183711yescharacteristic
815C2—24no—
816C2—42no—
817C2—3324no—
818C2—6642no—
819C2#2491954614yesdirect product factor
820C2C2×#1912834611yescharacteristic
821C2C22×#1458182511yescharacteristic
822C2C2×#1912850611yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#435×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128347C2
hypercenterC2×#435D83
hypocenterC83C2×#3314
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×#19128408C2semidirect
3. #24919546C2direct (N × H)
4. C2×#19128061C2semidirect
5. C2×#19128037C2semidirect
6. C2×#19128015C2semidirect
7. C2×#19127982C2semidirect
8. C2×#19127947C2semidirect
9. C2×#19127942C2semidirect
10. C2×#19127924C2semidirect
11. C2×#19127865C2semidirect
12. C2×#19127854C2semidirect
13. C2×#19127803C2semidirect
14. C2×#19127703C2semidirect
15. C22×#14581714C2semidirect
16. C2×#435×C83C2semidirect
19. C22×Dic332C22semidirect
23. #19128408C22semidirect
26. C2×#14581792C22semidirect
32. C2×#14581771C22semidirect
38. C2×C4×Dic166C22semidirect
42. C22×C4⋊Dic83C22semidirect
44. #19128061C22semidirect
45. #19128037C22semidirect
46. #19128015C22semidirect
47. #19127982C22semidirect
48. #19127947C22semidirect
49. #19127942C22semidirect
50. #19127924C22semidirect
51. #19127865C22semidirect
52. #19127854C22semidirect
53. #19127803C22semidirect
54. C2×#14581726C22semidirect
55. C2×#14581726C22semidirect
56. C2×#14581726C22semidirect
57. #19127703C22semidirect
58. C2×#14581717C22semidirect
59. C2×#14581717C22semidirect
60. C2×#14581717C22semidirect
61. C2×#14581717C22semidirect
68. C2×#14581714C22semidirect
69. C22×M16×C83C22semidirect
72. #435×C83C22semidirect
73. C2×C4⋊C8×C83C22semidirect
75. C2×C22⋊C8×C83C22semidirect
76. C2×#97×C83C22semidirect
99. C2×Dic332C23semidirect
105. #14581792C23semidirect
115. #14581771C23semidirect
123. C4×Dic166C23semidirect
137. C2×C4⋊Dic83C23semidirect
151. #14581726C23semidirect
152. #14581726C23semidirect
153. #14581726C23semidirect
154. #14581717C23semidirect
155. #14581717C23semidirect
156. #14581717C23semidirect
157. #14581717C23semidirect
168. C2×M16×C83C23semidirect
181. C4⋊C8×C83C23semidirect
183. C22⋊C8×C83C23semidirect
184. #97×C83C23semidirect
406. C2×C83#3314semidirect
425. C2×#435D83semidirect
428. C83C2×#3314semidirect
434. C22×M16C2×D83semidirect
469. #435C2×D83semidirect
473. C2×C4⋊C8C2×D83semidirect
487. C2×C22⋊C8C2×D83semidirect
488. C2×#97C2×D83semidirect
520. C2×M16C22×D83semidirect
583. C4⋊C8C22×D83semidirect
595. C22⋊C8C22×D83semidirect
596. #97C22×D83semidirect
819. C2#24919546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284082
C2×#191283472
#249195462
C2×#191280612
C2×#191280372
C2×#191280152
C2×#191279822
C2×#191279472
C2×#191279422
C2×#191279242
C2×#191278652
C2×#191278542
C2×#191278032
C2×#191277032
C22×#145817142
C2×#435×C832
C2×#331483