Finite Group Databasebeta

← C2×#24918315 #36275057

Subgroups — C2×#24918315 #36275057

Order 21248.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128279C211yesmaximal, characteristic, complemented
2#24918315C2116yesmaximal, direct product factor
3C2×#19128017C211yesmaximal, characteristic, complemented
4C2×#19128042C211yesmaximal, characteristic, complemented
5C2×#19128025C211yesmaximal, characteristic, complemented
6C2×#19128012C211yesmaximal, characteristic, complemented
7C2×#19127952C211yesmaximal, characteristic, complemented
8C2×#19127945C211yesmaximal, characteristic, complemented
9C2×#19127935C211yesmaximal, characteristic, complemented
10C2×#19127928C211yesmaximal, characteristic, complemented
11C2×#19127844C211yesmaximal, characteristic, complemented
12C2×#19127844C211yesmaximal, characteristic, complemented
13C2×#19127852C211yesmaximal, characteristic, complemented
14C2×#19127835C211yesmaximal, characteristic, complemented
15C2×#19127668C211yesmaximal, characteristic, complemented
16C2×#535×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic, complemented
18C22×#13050578C2211yescharacteristic
19C22×#13050578C2211yescharacteristic
20C22×#13050575C2211yescharacteristic
21C22×#13050575C2211yescharacteristic
22C22×#13050574C2211yescharacteristic, complemented
23C23×C83⋊C8C2211yescharacteristic, complemented
24#19128279—24no—
25#19128279C2218yescomplemented
26C2×#14581771C2211yescharacteristic
27C2×#14581771C2211yescharacteristic, complemented
28C2×#14581768—21no—
29C2×#14581766C2211yescharacteristic
30C2×#14581766C2211yescharacteristic, complemented
31C2×#14581764—21no—
32C2×#14581764—21no—
33C2×#14581763—21no—
34C22×C4⋊Dic83C2211yescharacteristic, complemented
35#19128042C2218yescomplemented
36#19128025C2218yescomplemented
37#19128017C2218yescomplemented
38#19128012C2218yescomplemented
39#19127952C2218yescomplemented
40#19127945C2218yescomplemented
41#19127935C2218yescomplemented
42#19127928C2218yescomplemented
43#19127852C2218yescomplemented
44#19127844C2218yescomplemented
45#19127844C2218yescomplemented
46#19127835C2218yescomplemented
47C2×#14581725C2211yescharacteristic, complemented
48C2×#14581725C2211yescharacteristic, complemented
49C2×#14581723C2211yescharacteristic, complemented
50C2×#14581723C2211yescharacteristic, complemented
51C2×#14581715C2211yescharacteristic, complemented
52C2×#14581715C2211yescharacteristic, complemented
53C2×#14581713C2211yescharacteristic
54C2×#14581713C2211yescharacteristic
55C2×#14581713C2211yescharacteristic
56C2×#14581713C2211yescharacteristic
57C2×#14581712C2211yescharacteristic, complemented
58C2×#14581712C2211yescharacteristic, complemented
59#19127668C2218yescomplemented
60C2×C22⋊(C83⋊C8)C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C83⋊C8)C2211yescharacteristic, complemented
64C22×#41×C83C2211yescharacteristic
65C23×D4×C83C2211yescharacteristic
66#535×C83—24no—
67#535×C83C2218yescomplemented
68C2×#127×C83—21no—
69C2×#124×C83—21no—
70C2×#121×C83C2211yescharacteristic
71C2×#121×C83C2211yescharacteristic
72C2×#121×C83C2211yescharacteristic
73C2×#121×C83C2211yescharacteristic
74C2×#120×C83—21no—
75C2×#120×C83—21no—
76C2×#117×C83C2211yescharacteristic
77C2×#13050590—22no—
78C2×#13050590—42no—
79C2×#13050590—42no—
80C2×#13050590C2314yescomplemented
81C22×Dic166C2311yescharacteristic
82C22×D332C2311yescharacteristic
83C22×C22⋊D83—21no—
84C22×C22⋊D83—21no—
85C22×C22⋊D83—21no—
86C23×Dic83—21no—
87C22×C4×D83—21no—
88C2×#13050578—42no—
89C2×#13050578—42no—
90C2×#13050578C2314yes—
91C2×#13050578C2314yes—
92C2×#13050575—42no—
93C2×#13050575—42no—
94C2×#13050575C2314yes—
95C2×#13050575C2314yes—
96C2×#13050574—42no—
97C2×#13050574C2314yescomplemented
98C22×C83⋊C8—42no—
99C22×C83⋊C8C2311yescharacteristic
100C22×C83⋊C8C2311yescharacteristic
101C22×C83⋊C8C2311yescharacteristic
102C22×C83⋊C8C2311yescharacteristic
103C22×C83⋊C8C2314yescomplemented
104#14581771—22no—
105#14581771—22no—
106#14581771C2314yes—
107#14581771C2314yescomplemented
108#14581768—28no—
109#14581766—22no—
110#14581766—22no—
111#14581766C2314yes—
112#14581766C2314yescomplemented
113#14581764—28no—
114#14581764—28no—
115#14581763—28no—
116C2×C4⋊Dic83—21no—
117C2×C4⋊Dic83—22no—
118C2×C4⋊Dic83C2311yescharacteristic
119C2×C4⋊Dic83C2311yescharacteristic
120C2×C4⋊Dic83C2314yescomplemented
121C2×Dic83⋊C4—21no—
122C2×Dic83⋊C4—21no—
123C2×C22⋊Dic83—21no—
124C2×C22⋊Dic83—21no—
125C2×(C2×D83)⋊C4—21no—
126C2×(C2×D83)⋊C4—21no—
127#14581725C2314yescomplemented
128#14581725C2314yescomplemented
129#14581723C2314yescomplemented
130#14581723C2314yescomplemented
131#14581715C2314yescomplemented
132#14581715C2314yescomplemented
133#14581713C2314yes—
134#14581713C2314yes—
135#14581713C2314yes—
136#14581713C2314yes—
137#14581712C2314yescomplemented
138#14581712C2314yescomplemented
139C22⋊(C83⋊C8)C2314yes—
140C22⋊(C83⋊C8)C2314yes—
141C22⋊(C83⋊C8)C2314yescomplemented
142C22⋊(C83⋊C8)C2314yescomplemented
143C25×C83—21no—
144C2×#41×C83—42no—
145C2×#41×C83—42no—
146C2×#41×C83D414yes—
147C2×#41×C83C2314yes—
148C22×Q8×C83D411yescharacteristic
149C22×D4×C83—21no—
150C22×D4×C83—21no—
151C22×D4×C83—21no—
152C22×D4×C83—21no—
153C22×D4×C83—21no—
154C22×D4×C83—22no—
155C22×D4×C83—42no—
156C22×D4×C83—42no—
157C22×D4×C83D411yescharacteristic
158C22×D4×C83D411yescharacteristic
159C22×D4×C83D411yescharacteristic
160C22×D4×C83C2311yescharacteristic
161C22×D4×C83C2311yescharacteristic
162C22×D4×C83C2314yes—
163C23×C4×C83C2311yescharacteristic
164C23×C4×C83C2311yescharacteristic
165C23×C4×C83C2311yescharacteristic
166#127×C83—28no—
167#124×C83—28no—
168#121×C83—22no—
169#121×C83—22no—
170#121×C83—22no—
171#121×C83—22no—
172#121×C83C2314yes—
173#121×C83C2314yes—
174#121×C83C2314yes—
175#121×C83C2314yes—
176#120×C83—28no—
177#120×C83—28no—
178#117×C83—22no—
179#117×C83C2314yes—
180C2×C4⋊C4×C83C2311yescharacteristic
181C2×C4⋊C4×C83C2311yescharacteristic
182C2×C22⋊C4×C83—21no—
183C2×C22⋊C4×C83—21no—
184C2×C22⋊C4×C83—21no—
185C2×C22⋊C4×C83—21no—
186C2×C22⋊C4×C83—21no—
187C2×C42×C83—21no—
188C23×D83—21no—
189#13050590—44no—
190#13050590—44no—
191#13050590—48no—
192C2×Dic166—22no—
193C2×Dic166—22no—
194C2×Dic166—21no—
195C2×Dic166C2412yes—
196C2×D332—22no—
197C2×D332—22no—
198C2×D332—21no—
199C2×D332C2412yes—
200C2×C22⋊D83—24no—
201C2×C22⋊D83—24no—
202C2×C22⋊D83—24no—
203C2×C22⋊D83—44no—
204C2×C22⋊D83—82no—
205C2×C22⋊D83—82no—
206C22×Dic83—21no—
207C22×Dic83—21no—
208C22×Dic83—21no—
209C22×Dic83—24no—
210C22×Dic83—82no—
211C2×C4×D83—24no—
212C2×C4×D83—44no—
213#13050578—44no—
214#13050578—44no—
215#13050575—44no—
216#13050575—44no—
217#13050574—44no—
218C2×C83⋊C8—22no—
219C2×C83⋊C8—22no—
220C2×C83⋊C8—22no—
221C2×C83⋊C8—22no—
222C2×C83⋊C8—44no—
223C2×C83⋊C8C2412yes—
224C2×C83⋊C8C2412yes—
225C2×C83⋊C8C2412yes—
226C2×C83⋊C8C2412yes—
227C4⋊Dic83—24no—
228C4⋊Dic83—21no—
229C4⋊Dic83—21no—
230C4⋊Dic83C2412yes—
231C4⋊Dic83C2412yes—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234C22⋊Dic83—24no—
235C22⋊Dic83—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4—24no—
238C24×C83—21no—
239C24×C83—21no—
240C24×C83—24no—
241C24×C83—44no—
242C24×C83—82no—
243C24×C83—82no—
244C24×C83C2×D411yescharacteristic
245C24×C83C2×D411yescharacteristic
246C24×C83C2×D411yescharacteristic
247#41×C83—48no—
248#41×C83—44no—
249#41×C83—44no—
250C2×Q8×C83—42no—
251C2×Q8×C83C2×D414yes—
252C2×D4×C83—24no—
253C2×D4×C83—24no—
254C2×D4×C83—24no—
255C2×D4×C83—24no—
256C2×D4×C83—21no—
257C2×D4×C83—21no—
258C2×D4×C83—24no—
259C2×D4×C83—22no—
260C2×D4×C83—22no—
261C2×D4×C83—22no—
262C2×D4×C83—22no—
263C2×D4×C83—44no—
264C2×D4×C83—44no—
265C2×D4×C83—42no—
266C2×D4×C83—42no—
267C2×D4×C83—42no—
268C2×D4×C83—44no—
269C2×D4×C83—48no—
270C2×D4×C83—82no—
271C2×D4×C83—82no—
272C2×D4×C83—82no—
273C2×D4×C83—82no—
274C2×D4×C83C2×D414yes—
275C2×D4×C83C2×D414yes—
276C2×D4×C83C2×D414yes—
277C2×D4×C83C2412yes—
278C2×D4×C83C2412yes—
279C22×C4×C83—22no—
280C22×C4×C83—22no—
281C22×C4×C83—22no—
282C22×C4×C83—22no—
283C22×C4×C83—22no—
284C22×C4×C83—22no—
285C22×C4×C83—21no—
286C22×C4×C83—21no—
287C22×C4×C83C2×D412yes—
288C22×C4×C83C2×D412yes—
289C22×C4×C83C2×D411yescharacteristic
290C22×C4×C83C2×D412yes—
291C22×C4×C83C2×D411yescharacteristic
292C22×C4×C83C2×D411yescharacteristic
293C22×C4×C83C2412yes—
294C22×C4×C83C2412yes—
295C22×C4×C83C2412yes—
296C22×C4×C83C2411yescharacteristic
297C4⋊C4×C83—21no—
298C4⋊C4×C83—21no—
299C4⋊C4×C83C2412yes—
300C4⋊C4×C83C2412yes—
301C22⋊C4×C83—24no—
302C22⋊C4×C83—24no—
303C22⋊C4×C83—24no—
304C22⋊C4×C83—24no—
305C22⋊C4×C83—24no—
306C42×C83—24no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83—22no—
311C23×C83—22no—
312C23×C83—22no—
313C23×C83—22no—
314C23×C83—22no—
315C23×C83—22no—
316C23×C83—22no—
317C23×C83—22no—
318C23×C83—48no—
319C23×C83—42no—
320C23×C83—42no—
321C23×C83—42no—
322C23×C83—42no—
323C23×C83—42no—
324C23×C83—42no—
325C23×C83—84no—
326C23×C83—84no—
327C23×C83—816no—
328C23×C83C22×D412yes—
329C23×C83C22×D412yes—
330C23×C83C22×D412yes—
331C23×C83C22×D411yescharacteristic
332C22×D83—22no—
333C22×D83—42no—
334C22×D83—42no—
335C22×D83—42no—
336Q8×C83—44no—
337D4×C83—22no—
338D4×C83—22no—
339D4×C83—22no—
340D4×C83—22no—
341D4×C83—44no—
342D4×C83—44no—
343D4×C83—44no—
344D4×C83—48no—
345D4×C83—42no—
346D4×C83—42no—
347D4×C83—84no—
348D4×C83—84no—
349D4×C83—84no—
350D4×C83—84no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—24no—
355C2×C4×C83—24no—
356C2×C4×C83—24no—
357C2×C4×C83—22no—
358C2×C4×C83—22no—
359C2×C4×C83—22no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—42no—
366C2×C4×C83—42no—
367C2×C4×C83C22×D412yes—
368C2×C4×C83C22×D412yes—
369C2×C4×C83C22×D412yes—
370C2×C4×C83C22×D411yescharacteristic
371C2×C4×C83H(5,𝔽2)12yes—
372C2×C4×C83H(5,𝔽2)12yes—
373C2×C4×C83C2511yescharacteristic
374C22⋊D83—48no—
375C22⋊D83—84no—
376C22⋊D83—84no—
377C2×Dic83—22no—
378C2×Dic83—22no—
379C2×Dic83—22no—
380C2×Dic83—42no—
381C2×Dic83—42no—
382C2×Dic83—42no—
383C2×Dic83—84no—
384D332—22no—
385D332—22no—
386D332—42no—
387C4×D83—48no—
388Dic166—22no—
389Dic166—22no—
390Dic166—42no—
391C83⋊C8—22no—
392C83⋊C8—22no—
393C83⋊C8—22no—
394C83⋊C8—22no—
395C22×C83—22no—
396C22×C83—22no—
397C22×C83—22no—
398C22×C83—22no—
399C22×C83—22no—
400C22×C83—22no—
401C22×C83—22no—
402C22×C83—22no—
403C22×C83—22no—
404C22×C83—44no—
405C22×C83—44no—
406C22×C83—44no—
407C22×C83—42no—
408C22×C83—42no—
409C22×C83—42no—
410C22×C83—42no—
411C22×C83—42no—
412C22×C83—42no—
413C22×C83—816no—
414C22×C83—84no—
415C22×C83—84no—
416C22×C83#53412yes—
417C22×C83#57612yes—
418C22×C83#57712yes—
419C22×C83C23×D411yescharacteristic
420C2×D83—42no—
421C2×D83—42no—
422C2×D83—42no—
423C2×D83—84no—
424C4×C83—22no—
425C4×C83—22no—
426C4×C83—22no—
427C4×C83—42no—
428C4×C83—42no—
429C4×C83#53412yes—
430C4×C83C2×H(5,𝔽2)11yescharacteristic
431C4×C83C2×H(5,𝔽2)11yescharacteristic
432Dic83—42no—
433Dic83—42no—
434Dic83—42no—
435C2×#3198—831nomaximal, Sylow
436C2×C83—42no—
437C2×C83—42no—
438C2×C83—42no—
439C2×C83—82no—
440C2×C83—82no—
441C2×C83#319814yescomplemented
442C2×C83C2×#53411yescharacteristic
443C2×C83C2×#57611yescharacteristic
444C2×C83C2×#57711yescharacteristic
445D83—82no—
446C2×#537—831no—
447C2×#535D8311yescharacteristic, complemented
448#3198—8316no—
449C2×#481—831no—
450C2×#485—831no—
451C2×#482—831no—
452C2×#480—831no—
453C2×#469—831no—
454C2×#468—831no—
455C2×#466—831no—
456C2×#465—831no—
457C2×#449—831no—
458C2×#449—831no—
459C2×#450—831no—
460C2×#447—831no—
461C2×#408—831no—
462C83C2×#319811yescharacteristic, complemented, Sylow
463C22×#41—831no—
464C22×#41C2×D8311yescharacteristic
465C23×D4C2×D8311yescharacteristic
466C22×SD16—831no—
467C22×SD16—831no—
468C22×D8—831no—
469C22×D8—831no—
470C22×M16—831no—
471C23×C8—831no—
472#537—838no—
473#537—1664no—
474#535—24no—
475#535C2×D8318yescomplemented
476C2×#127—21no—
477C2×#124—21no—
478C2×C22⋊Q8—831no—
479C2×C22⋊Q8—831no—
480C2×C22⋊Q8—1661no—
481C2×#121—831no—
482C2×#121—831no—
483C2×#121—1661no—
484C2×#121—1661no—
485C2×#121—1661no—
486C2×#121C2×D8311yescharacteristic
487C2×#121C2×D8311yescharacteristic
488C2×#121C2×D8311yescharacteristic
489C2×#121C2×D8311yescharacteristic
490C2×#120—21no—
491C2×#120—21no—
492C2×#117C2×D8311yescharacteristic
493C22×C4⋊C4—831no—
494#485—838no—
495#482—838no—
496#481—838no—
497#480—838no—
498#469—838no—
499#468—838no—
500#466—838no—
501#465—838no—
502#450—838no—
503#449—838no—
504#449—838no—
505#447—838no—
506C2×#107—831no—
507C2×#107—831no—
508C2×#106—831no—
509C2×#106—831no—
510C2×#103—831no—
511C2×#103—831no—
512C2×#102—831no—
513C2×#102—831no—
514C2×#102—831no—
515C2×#102—831no—
516C2×#102—831no—
517C2×#102—831no—
518#408—838no—
519C2×C22⋊C8—831no—
520C2×C22⋊C8—831no—
521C2×C22⋊C8—831no—
522C2×C22⋊C8—831no—
523C25—21no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—3322no—
527C2×#41—3322no—
528C2×#41—834no—
529C2×#41—1662no—
530C2×#41C22⋊D8314yes—
531C2×#41C22×D8314yes—
532C22×Q8—831no—
533C22×Q8C22⋊D8311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—831no—
543C22×D4—1661no—
544C22×D4—1661no—
545C22×D4—1661no—
546C22×D4C22⋊D8311yescharacteristic
547C22×D4C22⋊D8311yescharacteristic
548C22×D4C22⋊D8311yescharacteristic
549C22×D4C22×D8311yescharacteristic
550C22×D4C22×D8311yescharacteristic
551C22×D4C22×D8314yes—
552C23×C4—1661no—
553C23×C4—1661no—
554C23×C4C22×D8311yescharacteristic
555C23×C4C22×D8311yescharacteristic
556C23×C4C22×D8311yescharacteristic
557C2×SD16—3322no—
558C2×SD16—3322no—
559C2×SD16—834no—
560C2×SD16—834no—
561C2×D8—3322no—
562C2×D8—3322no—
563C2×D8—834no—
564C2×D8—834no—
565C2×M16—3322no—
566C2×M16—834no—
567C22×C8—3322no—
568C22×C8—834no—
569C22×C8—831no—
570C22×C8—831no—
571C22×C8—831no—
572C22×C8—831no—
573#127—28no—
574#124—28no—
575C22⋊Q8—834no—
576C22⋊Q8—834no—
577C22⋊Q8—1668no—
578C22⋊Q8—1662no—
579C22⋊Q8—1662no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—834no—
585#121—834no—
586#121—1668no—
587#121—1668no—
588#121—1668no—
589#121—1662no—
590#121—1662no—
591#121C22×D8314yes—
592#121C22×D8314yes—
593#121C22×D8314yes—
594#121C22×D8314yes—
595#120—28no—
596#120—28no—
597#117—22no—
598#117C22×D8314yes—
599C2×C4⋊C4—831no—
600C2×C4⋊C4—831no—
601C2×C4⋊C4—834no—
602C2×C4⋊C4—1661no—
603C2×C4⋊C4—1662no—
604C2×C4⋊C4—1661no—
605C2×C4⋊C4—1661no—
606C2×C4⋊C4C22×D8311yescharacteristic
607C2×C4⋊C4C22×D8311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—1661no—
614C2×C22⋊C4—1661no—
615C2×C22⋊C4—1661no—
616C2×C22⋊C4—1661no—
617C2×C42—21no—
618#107—834no—
619#107—834no—
620#106—834no—
621#106—834no—
622#103—834no—
623#103—834no—
624#102—834no—
625#102—834no—
626#102—834no—
627#102—834no—
628#102—834no—
629#102—834no—
630C22⋊C8—834no—
631C22⋊C8—834no—
632C22⋊C8—834no—
633C22⋊C8—834no—
634C24—21no—
635C24—21no—
636C24—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24—1661no—
641C24C2×C22⋊D8311yescharacteristic
642C24C2×C22⋊D8311yescharacteristic
643C24C2×C22⋊D8311yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—3328no—
648#41—3324no—
649#41—3324no—
650C2×Q8—42no—
651C2×Q8—832no—
652C2×Q8—1662no—
653C2×Q8—1662no—
654C2×Q8—1661no—
655C2×Q8C2×C22⋊D8314yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—24no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—44no—
673C2×D4—48no—
674C2×D4—82no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4—82no—
678C2×D4—3324no—
679C2×D4—832no—
680C2×D4—6642no—
681C2×D4—6642no—
682C2×D4—1664no—
683C2×D4—1664no—
684C2×D4—1664no—
685C2×D4—1661no—
686C2×D4—1662no—
687C2×D4—1662no—
688C2×D4C2×C22⋊D8314yes—
689C2×D4C2×C22⋊D8314yes—
690C2×D4C2×C22⋊D8314yes—
691C2×D4C23×D8312yes—
692C2×D4C23×D8312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—3324no—
702C22×C4—6642no—
703C22×C4—1661no—
704C22×C4—1661no—
705C22×C4—1661no—
706C22×C4—1664no—
707C22×C4—1664no—
708C22×C4C2×C22⋊D8312yes—
709C22×C4C2×C22⋊D8312yes—
710C22×C4C2×C22⋊D8312yes—
711C22×C4C2×C22⋊D8311yescharacteristic
712C22×C4C2×C22⋊D8311yescharacteristic
713C22×C4C2×C22⋊D8311yescharacteristic
714C22×C4C23×D8312yes—
715C22×C4C23×D8312yes—
716C22×C4C23×D8312yes—
717C22×C4C23×D8311yescharacteristic
718SD16—3324no—
719SD16—3324no—
720D8—3324no—
721D8—3324no—
722M16—3324no—
723C2×C8—3324no—
724C2×C8—832no—
725C2×C8—832no—
726C2×C8—832no—
727C2×C8—832no—
728C2×C8—1662no—
729C2×C8—1662no—
730C2×C8—1662no—
731C2×C8—1662no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—832no—
735C4⋊C4—832no—
736C4⋊C4—1664no—
737C4⋊C4—1661no—
738C4⋊C4—1661no—
739C4⋊C4—1664no—
740C4⋊C4—1664no—
741C4⋊C4C23×D8312yes—
742C4⋊C4C23×D8312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—1664no—
749C22⋊C4—1664no—
750C22⋊C4—1664no—
751C22⋊C4—1664no—
752C42—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—48no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—84no—
772C23—84no—
773C23—816no—
774C23—3322no—
775C23—3322no—
776C23—3322no—
777C23—1662no—
778C23C22×C22⋊D8312yes—
779C23C22×C22⋊D8312yes—
780C23C22×C22⋊D8312yes—
781C23C22×C22⋊D8311yescharacteristic
782Q8—44no—
783Q8—3322no—
784Q8—1662no—
785Q8—1662no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—48no—
794D4—42no—
795D4—42no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800D4—3328no—
801D4—3322no—
802D4—6644no—
803D4—6644no—
804D4—1662no—
805D4—1662no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—3328no—
823C2×C4—3322no—
824C2×C4—3322no—
825C2×C4—3322no—
826C2×C4—6644no—
827C2×C4—1662no—
828C2×C4—1662no—
829C2×C4—1662no—
830C2×C4C22×C22⋊D8312yes—
831C2×C4C22×C22⋊D8312yes—
832C2×C4C22×C22⋊D8312yes—
833C2×C4C22×C22⋊D8311yescharacteristic
834C2×C4#1458183712yes—
835C2×C4#1458183712yes—
836C2×C4C24×D8311yescharacteristic
837C8—1662no—
838C8—1662no—
839C8—1662no—
840C8—1662no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—816no—
860C22—84no—
861C22—84no—
862C22—3322no—
863C22—3322no—
864C22—3322no—
865C22—6644no—
866C22#1912826012yes—
867C22#1912850412yes—
868C22#1912851212yes—
869C22C23×C22⋊D8311yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—3322no—
876C4—3322no—
877C4—3322no—
878C4#1912826012yes—
879C4C2×#1458183711yescharacteristic
880C4C2×#1458183711yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—82no—
886C2—6642no—
887C2#2491831514yesdirect product factor
888C2C2×#1912826011yescharacteristic
889C2C2×#1912850411yescharacteristic
890C2C2×#1912851211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#535×C83C2
socleC23×C83C22×D4
hypercenterC2×#535D83
hypocenterC83C2×#3198
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#19128279C2semidirect
2. #24918315C2direct (N × H)
3. C2×#19128017C2semidirect
4. C2×#19128042C2semidirect
5. C2×#19128025C2semidirect
6. C2×#19128012C2semidirect
7. C2×#19127952C2semidirect
8. C2×#19127945C2semidirect
9. C2×#19127935C2semidirect
10. C2×#19127928C2semidirect
11. C2×#19127844C2semidirect
12. C2×#19127844C2semidirect
13. C2×#19127852C2semidirect
14. C2×#19127835C2semidirect
15. C2×#19127668C2semidirect
16. C2×#535×C83C2semidirect
17. C22×#13050590C22semidirect
22. C22×#13050574C22semidirect
23. C23×C83⋊C8C22semidirect
25. #19128279C22semidirect
27. C2×#14581771C22semidirect
30. C2×#14581766C22semidirect
34. C22×C4⋊Dic83C22semidirect
35. #19128042C22semidirect
36. #19128025C22semidirect
37. #19128017C22semidirect
38. #19128012C22semidirect
39. #19127952C22semidirect
40. #19127945C22semidirect
41. #19127935C22semidirect
42. #19127928C22semidirect
43. #19127852C22semidirect
44. #19127844C22semidirect
45. #19127844C22semidirect
46. #19127835C22semidirect
47. C2×#14581725C22semidirect
48. C2×#14581725C22semidirect
49. C2×#14581723C22semidirect
50. C2×#14581723C22semidirect
51. C2×#14581715C22semidirect
52. C2×#14581715C22semidirect
57. C2×#14581712C22semidirect
58. C2×#14581712C22semidirect
59. #19127668C22semidirect
62. C2×C22⋊(C83⋊C8)C22semidirect
63. C2×C22⋊(C83⋊C8)C22semidirect
67. #535×C83C22semidirect
80. C2×#13050590C23semidirect
97. C2×#13050574C23semidirect
103. C22×C83⋊C8C23semidirect
107. #14581771C23semidirect
112. #14581766C23semidirect
120. C2×C4⋊Dic83C23semidirect
127. #14581725C23semidirect
128. #14581725C23semidirect
129. #14581723C23semidirect
130. #14581723C23semidirect
131. #14581715C23semidirect
132. #14581715C23semidirect
137. #14581712C23semidirect
138. #14581712C23semidirect
141. C22⋊(C83⋊C8)C23semidirect
142. C22⋊(C83⋊C8)C23semidirect
441. C2×C83#3198semidirect
447. C2×#535D83semidirect
462. C83C2×#3198semidirect
475. #535C2×D83semidirect
887. C2#24918315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282792
#249183152
C2×#191280172
C2×#191280422
C2×#191280252
C2×#191280122
C2×#191279522
C2×#191279452
C2×#191279352
C2×#191279282
C2×#191278442
C2×#191278522
C2×#191278352
C2×#191276682
C2×#535×C832
C2×#319883