Finite Group Databasebeta

← C2×#24916341 #36268562

Subgroups — C2×#24916341 #36268562

Order 21248.

2806 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581813C211yesmaximal, characteristic
2C2×#19128183C211yesmaximal, characteristic, complemented
3C2×#19128180C211yesmaximal, characteristic, complemented
4#24916341C2116yesmaximal, direct product factor
5C2×#19127811C211yesmaximal, characteristic, complemented
6C2×#19127810C211yesmaximal, characteristic, complemented
7C2×#19127806C211yesmaximal, characteristic, complemented
8C2×#19127805C211yesmaximal, characteristic, complemented
9C2×C4×#13050579C211yesmaximal, characteristic, complemented
10C2×SD16×Dic83C211yesmaximal, characteristic, complemented
11C2×#19127788C211yesmaximal, characteristic, complemented
12C2×#106×D83C211yesmaximal, characteristic, complemented
13C2×#19127701C211yesmaximal, characteristic, complemented
14C2×#19127699C211yesmaximal, characteristic, complemented
15C2×#19127655C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×#13050589C2211yescharacteristic
19C2×#14581813C4116yescomplemented
20C2×#14581813C2218yes—
21C22×#13050580C2211yescharacteristic
22C22×#13050579C2211yescharacteristic
23C22×#13050575C2211yescharacteristic
24C22×#13050573C2211yescharacteristic
25C22×C8×D83C2211yescharacteristic
26#19128183—24no—
27#19128183C2218yescomplemented
28#19128180—24no—
29#19128180C2218yescomplemented
30C2×Q8×Dic83C2211yescharacteristic
31C2×C4×Dic166C2211yescharacteristic
32C2×#14581757C2211yescharacteristic
33C2×C4×D332—21no—
34C2×C4×D332C2211yescharacteristic
35C2×D4×Dic83C2211yescharacteristic
36C2×#14581754—21no—
37C2×#14581754C2211yescharacteristic
38C2×C4×C22⋊D83—21no—
39C2×(C22⋊D83)⋊C4—21no—
40C2×#14581749—21no—
41C2×#14581749C2211yescharacteristic
42C2×#14581748—21no—
43C22×Dic83⋊C4—21no—
44C2×C4⋊C4×D83—21no—
45C2×C4⋊C4×D83C2211yescharacteristic
46C2×C4⋊C4×D83C2211yescharacteristic
47#19127811C2218yescomplemented
48#19127810C2218yescomplemented
49#19127806C2218yescomplemented
50#19127805C2218yescomplemented
51C4×#13050579C2218yescomplemented
52SD16×Dic83C2218yescomplemented
53#19127788C2218yescomplemented
54C2×#14581724C2211yescharacteristic
55C2×#14581723C2211yescharacteristic
56C2×#14581723C2211yescharacteristic
57#106×D83C2218yescomplemented
58#19127701C2218yescomplemented
59#19127699C2218yescomplemented
60C2×#14581717C2211yescharacteristic
61C2×#14581716C2211yescharacteristic
62C2×#14581715C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66#19127655C2218yescomplemented
67C2×#14581703C2211yescharacteristic
68C2×#14581702C2211yescharacteristic
69C2×C8×Dic83C2211yescharacteristic
70C22×SD16×C83C2211yescharacteristic
71C2×C4×Q8×C83C2211yescharacteristic
72C2×C4×D4×C83C2211yescharacteristic
73C4×SD16×C83C2218yescomplemented
74C2×#106×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C2×C4×C8×C83C2211yescharacteristic
78C2×#13050591—22no—
79C2×#13050591—24no—
80C2×#13050591C2×C418yescomplemented
81C2×#13050591C2314yes—
82C2×#13050589—22no—
83C2×#13050589—24no—
84C2×#13050589C2×C418yescomplemented
85C2×#13050589C2314yes—
86C22×Dic166C2311yescharacteristic
87C22×D332—21no—
88C22×D332C2311yescharacteristic
89C22×C22⋊D83—21no—
90C23×Dic83—21no—
91C23×Dic83—21no—
92C22×C4×D83—21no—
93C22×C4×D83—21no—
94C22×C4×D83—21no—
95C22×C4×D83—21no—
96C22×C4×D83—21no—
97C22×C4×D83C2311yescharacteristic
98#14581813C2×C4164yescomplemented
99C2×#13050580C2×C418yescomplemented
100C2×#13050580C2314yes—
101C2×#13050579C2×C418yescomplemented
102C2×#13050579C2314yes—
103C2×#13050575C2×C418yescomplemented
104C2×#13050575C2314yes—
105C2×#13050573—24no—
106C2×#13050573C2314yes—
107C22×C83⋊C8C2311yescharacteristic
108C22×C83⋊C8C2311yescharacteristic
109C2×C8×D83C2×C418yescomplemented
110C2×C8×D83C2314yes—
111Q8×Dic83—22no—
112Q8×Dic83C2314yes—
113C4×Dic166—22no—
114C4×Dic166C2314yes—
115#14581757—22no—
116#14581757C2314yes—
117C4×D332—28no—
118C4×D332—22no—
119C4×D332C2314yes—
120D4×Dic83—22no—
121D4×Dic83C2314yes—
122#14581754—28no—
123#14581754—22no—
124#14581754C2314yes—
125C4×C22⋊D83—28no—
126(C22⋊D83)⋊C4—28no—
127#14581749—28no—
128#14581749D414yes—
129#14581749C2314yes—
130#14581748—28no—
131C2×C4⋊Dic83—21no—
132C2×C4⋊Dic83C2311yescharacteristic
133C2×C4⋊Dic83C2311yescharacteristic
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4—21no—
137C2×Dic83⋊C4—28no—
138C2×Dic83⋊C4—21no—
139C2×Dic83⋊C4D411yescharacteristic
140C2×Dic83⋊C4D411yescharacteristic
141C4⋊C4×D83—22no—
142C4⋊C4×D83—22no—
143C4⋊C4×D83—28no—
144C4⋊C4×D83C2314yes—
145C4⋊C4×D83C2314yes—
146C2×C22⋊Dic83—21no—
147C2×(C2×D83)⋊C4—21no—
148C2×(C2×D83)⋊C4—21no—
149C2×(C2×D83)⋊C4D411yescharacteristic
150C2×(C2×D83)⋊C4D411yescharacteristic
151C2×C4×Dic83—21no—
152C2×C4×Dic83—21no—
153C2×C4×Dic83—21no—
154C2×C4×Dic83C2311yescharacteristic
155#14581724C2314yes—
156#14581723C2314yes—
157#14581723C2314yes—
158#14581717C2314yes—
159#14581716C2314yes—
160#14581715C2314yes—
161#14581714C2314yes—
162#14581713C2314yes—
163#14581712C2314yes—
164#14581703C2314yes—
165#14581702C2314yes—
166C8×Dic83C2314yes—
167C22×Q8×C83C2311yescharacteristic
168C22×D4×C83C2311yescharacteristic
169C23×C4×C83—21no—
170C2×SD16×C83C2×C418yescomplemented
171C2×SD16×C83C2314yes—
172C22×C8×C83C2311yescharacteristic
173C22×C8×C83C2311yescharacteristic
174C4×Q8×C83—22no—
175C4×Q8×C83C2314yes—
176C4×D4×C83—22no—
177C4×D4×C83C2314yes—
178C2×C4⋊C4×C83—21no—
179C2×C4⋊C4×C83C2311yescharacteristic
180C2×C4⋊C4×C83C2311yescharacteristic
181C2×C22⋊C4×C83—21no—
182C2×C42×C83—21no—
183C2×C42×C83C2311yescharacteristic
184#106×C83C2314yes—
185#103×C83C2314yes—
186#102×C83C2314yes—
187C4×C8×C83C2314yes—
188C23×D83—21no—
189C23×D83C2×D411yescharacteristic
190#13050591—216no—
191#13050591—28no—
192#13050591C22×C4116yescomplemented
193#13050589—216no—
194#13050589—28no—
195#13050589C22×C4116yescomplemented
196C2×Dic166—21no—
197C2×Dic166—22no—
198C2×Dic166C22×C414yes—
199C2×Dic166C2412yes—
200C2×D332—28no—
201C2×D332—24no—
202C2×D332—21no—
203C2×D332—22no—
204C2×D332C22×C414yes—
205C2×D332C2412yes—
206C2×C22⋊D83—28no—
207C2×C22⋊D83—24no—
208C22×Dic83—21no—
209C22×Dic83—28no—
210C22×Dic83—24no—
211C22×Dic83—21no—
212C22×Dic83—21no—
213C22×Dic83—24no—
214C22×Dic83—82no—
215C22×Dic83C2×D411yescharacteristic
216C22×Dic83C2×D411yescharacteristic
217C22×Dic83C2×D411yescharacteristic
218C2×C4×D83—28no—
219C2×C4×D83—24no—
220C2×C4×D83—24no—
221C2×C4×D83—24no—
222C2×C4×D83—24no—
223C2×C4×D83—24no—
224C2×C4×D83—82no—
225C2×C4×D83—82no—
226C2×C4×D83—82no—
227C2×C4×D83—82no—
228C2×C4×D83C22×C414yes—
229C2×C4×D83C2×D412yes—
230C2×C4×D83#4114yes—
231C2×C4×D83C2412yes—
232#13050580C22×C4116yescomplemented
233#13050579C22×C4116yescomplemented
234#13050575C22×C4116yescomplemented
235#13050573—28no—
236C2×C83⋊C8—22no—
237C2×C83⋊C8C22×C414yes—
238C2×C83⋊C8C2412yes—
239C2×C83⋊C8C2412yes—
240C8×D83C22×C4116yescomplemented
241C4⋊Dic83—21no—
242C4⋊Dic83—21no—
243C4⋊Dic83—24no—
244C4⋊Dic83C2412yes—
245C4⋊Dic83C2412yes—
246Dic83⋊C4—24no—
247Dic83⋊C4—24no—
248Dic83⋊C4—24no—
249Dic83⋊C4—24no—
250Dic83⋊C4C2×D414yes—
251Dic83⋊C4C2×D414yes—
252C22⋊Dic83—24no—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4C2×D414yes—
256(C2×D83)⋊C4C2×D414yes—
257C4×Dic83—24no—
258C4×Dic83—24no—
259C4×Dic83—24no—
260C4×Dic83C2×D412yes—
261C4×Dic83C2412yes—
262C24×C83—21no—
263C2×Q8×C83—21no—
264C2×Q8×C83—22no—
265C2×Q8×C83C22×C414yes—
266C2×Q8×C83C2412yes—
267C2×D4×C83—21no—
268C2×D4×C83—22no—
269C2×D4×C83C22×C414yes—
270C2×D4×C83C2412yes—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—24no—
275C22×C4×C83—82no—
276C22×C4×C83C2×D411yescharacteristic
277C22×C4×C83C2×D411yescharacteristic
278C22×C4×C83C2411yescharacteristic
279SD16×C83C22×C4116yescomplemented
280C2×C8×C83—22no—
281C2×C8×C83C22×C414yes—
282C2×C8×C83C2412yes—
283C2×C8×C83C2412yes—
284C4⋊C4×C83—24no—
285C4⋊C4×C83—21no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83C2412yes—
288C4⋊C4×C83C2412yes—
289C22⋊C4×C83—24no—
290C42×C83—24no—
291C42×C83C2×D412yes—
292C42×C83C2412yes—
293C23×C83—24no—
294C23×C83—22no—
295C23×C83—42no—
296C23×C83—42no—
297C23×C83C22×D411yescharacteristic
298C22×D83—22no—
299C22×D83—22no—
300C22×D83—24no—
301C22×D83—22no—
302C22×D83—42no—
303C22×D83—42no—
304C22×D83C4×D414yes—
305C22×D83C22×D412yes—
306Q8×C83—24no—
307Q8×C83—22no—
308Q8×C83C23×C414yes—
309D4×C83—24no—
310D4×C83—22no—
311D4×C83C23×C414yes—
312C2×C4×C83—24no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—42no—
319C2×C4×C83—42no—
320C2×C4×C83—84no—
321C2×C4×C83C23×C412yes—
322C2×C4×C83C22×D412yes—
323C2×C4×C83C22×D412yes—
324C2×C4×C83C22×D411yescharacteristic
325C2×C4×C83C2×#4112yes—
326C2×C4×C83C2511yescharacteristic
327C22⋊D83—216no—
328C2×Dic83—24no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—216no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—42no—
336C2×Dic83—42no—
337C2×Dic83—84no—
338C2×Dic83C4×D414yes—
339C2×Dic83C22×D412yes—
340C2×Dic83C22×D412yes—
341C2×Dic83C22×D412yes—
342D332—216no—
343D332—24no—
344D332—22no—
345D332C23×C414yes—
346C4×D83—216no—
347C4×D83—84no—
348C4×D83—84no—
349C4×D83—84no—
350C4×D83—84no—
351C4×D83C4×D418yes—
352C4×D83C23×C414yes—
353C4×D83C2×#4114yes—
354Dic166—24no—
355Dic166—22no—
356Dic166C23×C414yes—
357C8×C83—22no—
358C8×C83C23×C414yes—
359C83⋊C8—22no—
360C83⋊C8C23×C414yes—
361C22×C83—24no—
362C22×C83—48no—
363C22×C83—42no—
364C22×C83—42no—
365C22×C83C2×C4×D412yes—
366C22×C83#57712yes—
367C22×C83#57712yes—
368C22×C83C23×D411yescharacteristic
369C2×D83—28no—
370C2×D83—22no—
371C2×D83—22no—
372C2×D83—24no—
373C2×D83—48no—
374C2×D83—42no—
375C2×D83—42no—
376C2×D83C2×C4×D414yes—
377C4×C83—24no—
378C4×C83—22no—
379C4×C83—22no—
380C4×C83—42no—
381C4×C83—42no—
382C4×C83C2×C4×D412yes—
383C4×C83C24×C411yescharacteristic
384C4×C83C22×#4111yescharacteristic
385Dic83—24no—
386Dic83—22no—
387Dic83—22no—
388Dic83—42no—
389Dic83—42no—
390Dic83C2×C4×D414yes—
391C2×#2952—831nomaximal, Sylow
392C2×C83—44no—
393C2×C83#295214yescomplemented
394C2×C83C22×C4×D411yescharacteristic
395C2×C83C2×#57711yescharacteristic
396C2×C83C2×#57711yescharacteristic
397D83—24no—
398D83—44no—
399C22×#135—831no—
400C2×#520—831no—
401C2×#520—831no—
402#2952—8316no—
403C2×#442—831no—
404C2×#442—831no—
405C2×#441—831no—
406C2×#441—831no—
407C2×C4×SD16—831no—
408C2×C4×SD16—831no—
409C2×C4×SD16—831no—
410C2×C4×SD16D8311yescharacteristic, complemented
411C22×#106—831no—
412C2×#417—831no—
413C2×#417—831no—
414C2×#405—831no—
415C83C2×#295211yescharacteristic, complemented, Sylow
416C22×#41—831no—
417C22×#41—831no—
418C2×#135—8316no—
419C2×#135—838no—
420C22×Q16—831no—
421C22×SD16—831no—
422C22×SD16C2×D8311yescharacteristic
423C22×D8—831no—
424C22×M16—831no—
425C23×C8—831no—
426#520—838no—
427#520—838no—
428#520—1664no—
429#520—1664no—
430C2×C4×Q8—831no—
431C2×C4×Q8—831no—
432C2×C4×Q8—831no—
433C2×C4×Q8C2×D8311yescharacteristic
434C2×C4×D4—831no—
435C2×C4×D4—831no—
436C2×C4×D4—831no—
437C2×C4×D4—1661no—
438C2×C4×D4—1661no—
439C2×C4×D4—1661no—
440C2×C4×D4—1661no—
441C2×C4×D4C2×D8311yescharacteristic
442C2×#117—831no—
443C2×#117—1661no—
444C2×#117—1661no—
445C22×C4⋊C4—831no—
446C22×C4⋊C4—831no—
447C22×C4⋊C4—1661no—
448C22×C4⋊C4—1661no—
449#442—838no—
450#442—838no—
451#441—838no—
452#441—838no—
453C4×SD16—838no—
454C4×SD16—838no—
455C4×SD16—838no—
456C4×SD16C2×D8318yescomplemented
457C2×#106—831no—
458C2×#106—831no—
459C2×#106—831no—
460C2×#106—838no—
461C2×#106C2×D8311yescharacteristic
462#417—838no—
463#417—838no—
464C2×#103—831no—
465C2×#103—831no—
466C2×#103—831no—
467C2×#103C2×D8311yescharacteristic
468C2×#102—831no—
469C2×#102—831no—
470C2×#102—831no—
471C2×#102C2×D8311yescharacteristic
472#405—838no—
473C2×#97—831no—
474C2×#97—831no—
475C2×C4×C8—831no—
476C2×C4×C8C2×D8311yescharacteristic
477C2×#41—838no—
478C2×#41—834no—
479C2×#41—838no—
480C2×#41—834no—
481C2×#41—1662no—
482C2×#41—1664no—
483C2×#41—1662no—
484C2×#41—1664no—
485C22×Q8—831no—
486C22×Q8C22×D8311yescharacteristic
487C22×D4—831no—
488C22×D4—1661no—
489C22×D4—1661no—
490C22×D4C22×D8311yescharacteristic
491C23×C4—21no—
492C23×C4—831no—
493C23×C4—1661no—
494C23×C4—1661no—
495C23×C4—1661no—
496C23×C4—1661no—
497C23×C4—1661no—
498C23×C4—1661no—
499C23×C4—1661no—
500#135—8364no—
501C2×Q16—838no—
502C2×Q16—834no—
503C2×SD16—838no—
504C2×SD16—834no—
505C2×SD16C4×D8318yescomplemented
506C2×SD16C22×D8314yes—
507C2×D8—838no—
508C2×D8—834no—
509C2×M16—834no—
510C2×M16—1664no—
511C22×C8—831no—
512C22×C8—838no—
513C22×C8—834no—
514C22×C8—831no—
515C22×C8C22×D8311yescharacteristic
516C22×C8C22×D8311yescharacteristic
517C4×Q8—22no—
518C4×Q8—834no—
519C4×Q8—834no—
520C4×Q8—834no—
521C4×Q8—1662no—
522C4×Q8—1662no—
523C4×Q8—1662no—
524C4×Q8C22×D8314yes—
525C4×D4—22no—
526C4×D4—834no—
527C4×D4—834no—
528C4×D4—834no—
529C4×D4—1668no—
530C4×D4—1662no—
531C4×D4—1662no—
532C4×D4—1668no—
533C4×D4—1668no—
534C4×D4—1668no—
535C4×D4—1662no—
536C4×D4C22×D8314yes—
537#117—834no—
538#117—834no—
539#117—1668no—
540#117—1668no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—831no—
543C2×C4⋊C4—831no—
544C2×C4⋊C4—831no—
545C2×C4⋊C4—831no—
546C2×C4⋊C4—834no—
547C2×C4⋊C4—834no—
548C2×C4⋊C4—1668no—
549C2×C4⋊C4—1662no—
550C2×C4⋊C4—1662no—
551C2×C4⋊C4—1668no—
552C2×C4⋊C4—1661no—
553C2×C4⋊C4—1661no—
554C2×C4⋊C4—1661no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1661no—
557C2×C4⋊C4C22×D8311yescharacteristic
558C2×C4⋊C4C22×D8311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—831no—
561C2×C22⋊C4—831no—
562C2×C22⋊C4—1661no—
563C2×C22⋊C4—1661no—
564C2×C22⋊C4—1661no—
565C2×C42—21no—
566C2×C42—831no—
567C2×C42—1661no—
568C2×C42—1661no—
569C2×C42—1661no—
570C2×C42C22×D8311yescharacteristic
571#106—834no—
572#106—834no—
573#106—834no—
574#106C22×D8314yes—
575#103—834no—
576#103—834no—
577#103—834no—
578#103C22×D8314yes—
579#102—834no—
580#102—834no—
581#102—834no—
582#102C22×D8314yes—
583#97—834no—
584#97—834no—
585C4×C8—834no—
586C4×C8C22×D8314yes—
587C24—21no—
588C24—831no—
589C24—1661no—
590#41—8316no—
591#41—8316no—
592#41—16616no—
593#41—1668no—
594#41—16616no—
595#41—1668no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—834no—
599C2×Q8—832no—
600C2×Q8—1661no—
601C2×Q8—1662no—
602C2×Q8C2×C4×D8314yes—
603C2×Q8C23×D8312yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—834no—
607C2×D4—832no—
608C2×D4—1664no—
609C2×D4—1668no—
610C2×D4—1664no—
611C2×D4—1668no—
612C2×D4—1661no—
613C2×D4—1662no—
614C2×D4C2×C4×D8314yes—
615C2×D4C23×D8312yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—831no—
622C22×C4—834no—
623C22×C4—832no—
624C22×C4—834no—
625C22×C4—832no—
626C22×C4—831no—
627C22×C4—831no—
628C22×C4—6642no—
629C22×C4—6642no—
630C22×C4—6642no—
631C22×C4—6642no—
632C22×C4—6642no—
633C22×C4—1664no—
634C22×C4—1664no—
635C22×C4—1668no—
636C22×C4—1664no—
637C22×C4—1664no—
638C22×C4—1661no—
639C22×C4—1661no—
640C22×C4—1664no—
641C22×C4—1664no—
642C22×C4—1668no—
643C22×C4—1664no—
644C22×C4—1661no—
645C22×C4D4×D8311yescharacteristic
646C22×C4D4×D8311yescharacteristic
647C22×C4C23×D8311yescharacteristic
648Q16—8316no—
649SD16—8316no—
650SD16C2×C4×D83116yescomplemented
651D8—8316no—
652M16—1668no—
653C2×C8—22no—
654C2×C8—834no—
655C2×C8—832no—
656C2×C8—8316no—
657C2×C8—832no—
658C2×C8—1662no—
659C2×C8C2×C4×D8314yes—
660C2×C8C23×D8312yes—
661C2×C8C23×D8312yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—834no—
666C4⋊C4—834no—
667C4⋊C4—832no—
668C4⋊C4—832no—
669C4⋊C4—1664no—
670C4⋊C4—1664no—
671C4⋊C4—1664no—
672C4⋊C4—1664no—
673C4⋊C4—1661no—
674C4⋊C4—1661no—
675C4⋊C4—1664no—
676C4⋊C4C23×D8312yes—
677C4⋊C4C23×D8312yes—
678C22⋊C4—24no—
679C22⋊C4—834no—
680C22⋊C4—834no—
681C22⋊C4—1664no—
682C22⋊C4—1664no—
683C22⋊C4—1664no—
684C42—24no—
685C42—832no—
686C42—832no—
687C42—1664no—
688C42—1664no—
689C42—1664no—
690C42D4×D8312yes—
691C42C23×D8312yes—
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—3322no—
697C23—3322no—
698C23—834no—
699C23—832no—
700C23—1664no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23C2×D4×D8311yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—834no—
708Q8—1664no—
709Q8—1662no—
710Q8C22×C4×D8314yes—
711D4—24no—
712D4—22no—
713D4—834no—
714D4—16616no—
715D4—16616no—
716D4—1664no—
717D4—1662no—
718D4C22×C4×D8314yes—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—3322no—
729C2×C4—3322no—
730C2×C4—834no—
731C2×C4—832no—
732C2×C4—838no—
733C2×C4—834no—
734C2×C4—834no—
735C2×C4—832no—
736C2×C4—832no—
737C2×C4—6644no—
738C2×C4—6644no—
739C2×C4—6644no—
740C2×C4—6644no—
741C2×C4—6644no—
742C2×C4—16616no—
743C2×C4—1662no—
744C2×C4—1662no—
745C2×C4—16616no—
746C2×C4—1664no—
747C2×C4—1662no—
748C2×C4—1662no—
749C2×C4—1662no—
750C2×C4C22×C4×D8312yes—
751C2×C4C2×D4×D8312yes—
752C2×C4C2×D4×D8312yes—
753C2×C4C2×D4×D8311yescharacteristic
754C2×C4#41×D8312yes—
755C2×C4C24×D8311yescharacteristic
756C8—22no—
757C8—834no—
758C8—1662no—
759C8C22×C4×D8314yes—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—48no—
764C22—3322no—
765C22—3322no—
766C22—3328no—
767C22—834no—
768C22—1664no—
769C22—1662no—
770C22—1662no—
771C22—1668no—
772C22C4×D4×D8312yes—
773C22#1912850712yes—
774C22#1912850812yes—
775C22C22×D4×D8311yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—3322no—
782C4—3322no—
783C4—834no—
784C4—1664no—
785C4—1662no—
786C4—1662no—
787C4C4×D4×D8312yes—
788C4C23×C4×D8311yescharacteristic
789C4C2×#41×D8311yescharacteristic
790C2—44no—
791C2—3324no—
792C2—1664no—
793C2#2491634114yesdirect product factor
794C2C2×C4×D4×D8311yescharacteristic
795C2C2×#1912850711yescharacteristic
796C2C2×#1912850811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC4×C83C24×C4
FrattiniC2×C4C24×D83
FittingC2×C4×SD16×C83C2
socleC23×C83C22×D4
prime radicalC22×#14581813C2
cosocleC2×C4×C83C25
hypercenterC2×C4×SD16D83
hypocenterC83C2×#2952
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#19128183C2semidirect
3. C2×#19128180C2semidirect
4. #24916341C2direct (N × H)
5. C2×#19127811C2semidirect
6. C2×#19127810C2semidirect
7. C2×#19127806C2semidirect
8. C2×#19127805C2semidirect
9. C2×C4×#13050579C2semidirect
10. C2×SD16×Dic83C2semidirect
11. C2×#19127788C2semidirect
12. C2×#106×D83C2semidirect
13. C2×#19127701C2semidirect
14. C2×#19127699C2semidirect
15. C2×#19127655C2semidirect
16. C2×C4×SD16×C83C2semidirect
19. C2×#14581813C4semidirect
27. #19128183C22semidirect
29. #19128180C22semidirect
47. #19127811C22semidirect
48. #19127810C22semidirect
49. #19127806C22semidirect
50. #19127805C22semidirect
51. C4×#13050579C22semidirect
52. SD16×Dic83C22semidirect
53. #19127788C22semidirect
57. #106×D83C22semidirect
58. #19127701C22semidirect
59. #19127699C22semidirect
66. #19127655C22semidirect
73. C4×SD16×C83C22semidirect
80. C2×#13050591C2×C4semidirect
84. C2×#13050589C2×C4semidirect
98. #14581813C2×C4semidirect
99. C2×#13050580C2×C4semidirect
101. C2×#13050579C2×C4semidirect
103. C2×#13050575C2×C4semidirect
109. C2×C8×D83C2×C4semidirect
170. C2×SD16×C83C2×C4semidirect
192. #13050591C22×C4semidirect
195. #13050589C22×C4semidirect
232. #13050580C22×C4semidirect
233. #13050579C22×C4semidirect
234. #13050575C22×C4semidirect
240. C8×D83C22×C4semidirect
279. SD16×C83C22×C4semidirect
393. C2×C83#2952semidirect
410. C2×C4×SD16D83semidirect
415. C83C2×#2952semidirect
456. C4×SD16C2×D83semidirect
505. C2×SD16C4×D83semidirect
650. SD16C2×C4×D83semidirect
793. C2#24916341direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145818132
C2×#191281832
C2×#191281802
#249163412
C2×#191278112
C2×#191278102
C2×#191278062
C2×#191278052
C2×C4×#130505792
C2×SD16×Dic832
C2×#191277882
C2×#106×D832
C2×#191277012
C2×#191276992
C2×#191276552
C2×C4×SD16×C832
C2×#295283