Finite Group Databasebeta

← C2×#24918309 #36275051

Subgroups — C2×#24918309 #36275051

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×#19128265C211yesmaximal, characteristic, complemented
2#24918309C2116yesmaximal, direct product factor
3C2×#19128019C211yesmaximal, characteristic, complemented
4C2×#19128039C211yesmaximal, characteristic, complemented
5C2×#19128022C211yesmaximal, characteristic, complemented
6C2×#19128014C211yesmaximal, characteristic, complemented
7C2×#19127952C211yesmaximal, characteristic, complemented
8C2×#19127949C211yesmaximal, characteristic, complemented
9C2×#19127935C211yesmaximal, characteristic, complemented
10C2×#19127932C211yesmaximal, characteristic, complemented
11C2×#19127846C211yesmaximal, characteristic, complemented
12C2×#19127846C211yesmaximal, characteristic, complemented
13C2×#19127851C211yesmaximal, characteristic, complemented
14C2×#19127834C211yesmaximal, characteristic, complemented
15C2×#19127668C211yesmaximal, characteristic, complemented
16C2×#537×C83C211yesmaximal, characteristic, complemented
17C23×D332C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20C22×#13050575C2211yescharacteristic
21C22×#13050575C2211yescharacteristic
22C22×#13050574C2211yescharacteristic, complemented
23C23×C83⋊C8C2211yescharacteristic, complemented
24#19128265—24no—
25#19128265C2218yescomplemented
26C2×#14581788—21no—
27C2×#14581781—21no—
28C2×#14581766C2211yescharacteristic
29C2×#14581766C2211yescharacteristic
30C2×#14581766C2211yescharacteristic
31C2×#14581766C2211yescharacteristic
32C2×#14581760—21no—
33C2×#14581760—21no—
34C2×#14581751C2211yescharacteristic
35#19128039C2218yescomplemented
36#19128022C2218yescomplemented
37#19128019C2218yescomplemented
38#19128014C2218yescomplemented
39#19127952C2218yescomplemented
40#19127949C2218yescomplemented
41#19127935C2218yescomplemented
42#19127932C2218yescomplemented
43#19127851C2218yescomplemented
44#19127846C2218yescomplemented
45#19127846C2218yescomplemented
46#19127834C2218yescomplemented
47C2×#14581725C2211yescharacteristic, complemented
48C2×#14581725C2211yescharacteristic, complemented
49C2×#14581723C2211yescharacteristic, complemented
50C2×#14581723C2211yescharacteristic, complemented
51C2×#14581716C2211yescharacteristic, complemented
52C2×#14581716C2211yescharacteristic, complemented
53C2×#14581713C2211yescharacteristic, complemented
54C2×#14581713C2211yescharacteristic, complemented
55C2×#14581712C2211yescharacteristic
56C2×#14581712C2211yescharacteristic
57C2×#14581712C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
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
65C22×#41×C83C2211yescharacteristic, complemented
66#537×C83—24no—
67#537×C83C2218yescomplemented
68C2×C22⋊Q8×C83—21no—
69C2×C22⋊Q8×C83C2211yescharacteristic
70C2×C22⋊Q8×C83C2211yescharacteristic, complemented
71C2×#121×C83—21no—
72C2×#121×C83—21no—
73C2×#121×C83—21no—
74C2×#121×C83C2211yescharacteristic
75C2×#121×C83C2211yescharacteristic, complemented
76C22×C4⋊C4×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C22×D332—21no—
79C22×D332—22no—
80C22×D332—42no—
81C22×D332—42no—
82C22×D332C2311yescharacteristic
83C22×D332C2311yescharacteristic
84C22×D332C2314yes—
85C22×C22⋊D83—21no—
86C22×C22⋊D83—21no—
87C22×C22⋊D83—21no—
88C22×C22⋊D83—21no—
89C2×#13050577—42no—
90C2×#13050577—42no—
91C2×#13050577C2314yes—
92C2×#13050577C2314yes—
93C2×#13050575—42no—
94C2×#13050575—42no—
95C2×#13050575C2314yes—
96C2×#13050575C2314yes—
97C2×#13050574—42no—
98C2×#13050574C2314yescomplemented
99C22×C83⋊C8—42no—
100C22×C83⋊C8C2311yescharacteristic
101C22×C83⋊C8C2311yescharacteristic
102C22×C83⋊C8C2311yescharacteristic
103C22×C83⋊C8C2311yescharacteristic
104C22×C83⋊C8C2314yescomplemented
105#14581788—28no—
106#14581781—28no—
107#14581766—22no—
108#14581766—22no—
109#14581766—22no—
110#14581766—22no—
111#14581766C2314yes—
112#14581766C2314yes—
113#14581766C2314yes—
114#14581766C2314yes—
115#14581760—28no—
116#14581760—28no—
117#14581751—22no—
118#14581751C2314yes—
119C2×C4⋊Dic83C2311yescharacteristic
120C2×C4⋊Dic83C2311yescharacteristic
121C2×C22⋊Dic83—21no—
122C2×(C2×D83)⋊C4—21no—
123C2×(C2×D83)⋊C4—21no—
124C2×(C2×D83)⋊C4—21no—
125C2×(C2×D83)⋊C4—21no—
126C2×C4×Dic83—21no—
127#14581725C2314yescomplemented
128#14581725C2314yescomplemented
129#14581723C2314yescomplemented
130#14581723C2314yescomplemented
131#14581716C2314yescomplemented
132#14581716C2314yescomplemented
133#14581713C2314yescomplemented
134#14581713C2314yescomplemented
135#14581712C2314yes—
136#14581712C2314yes—
137#14581712C2314yes—
138#14581712C2314yes—
139C22⋊(C83⋊C8)C2314yes—
140C22⋊(C83⋊C8)C2314yes—
141C22⋊(C83⋊C8)C2314yescomplemented
142C22⋊(C83⋊C8)C2314yescomplemented
143C2×#41×C83—22no—
144C2×#41×C83—42no—
145C2×#41×C83—42no—
146C2×#41×C83—42no—
147C2×#41×C83—42no—
148C2×#41×C83D414yes—
149C2×#41×C83C2314yes—
150C2×#41×C83C2314yescomplemented
151C22×Q8×C83D411yescharacteristic
152C22×Q8×C83C2311yescharacteristic
153C22×D4×C83—21no—
154C22×D4×C83—21no—
155C22×D4×C83—21no—
156C22×D4×C83D411yescharacteristic
157C22×D4×C83D411yescharacteristic
158C22×D4×C83D411yescharacteristic
159C22×D4×C83C2311yescharacteristic
160C23×C4×C83—21no—
161C23×C4×C83—21no—
162C23×C4×C83C2311yescharacteristic
163C23×C4×C83C2311yescharacteristic
164C23×C4×C83C2311yescharacteristic
165C22⋊Q8×C83—28no—
166C22⋊Q8×C83—22no—
167C22⋊Q8×C83—22no—
168C22⋊Q8×C83C2314yes—
169C22⋊Q8×C83C2314yescomplemented
170#121×C83—28no—
171#121×C83—28no—
172#121×C83—28no—
173#121×C83—22no—
174#121×C83—22no—
175#121×C83C2314yes—
176#121×C83C2314yescomplemented
177C2×C4⋊C4×C83—21no—
178C2×C4⋊C4×C83—22no—
179C2×C4⋊C4×C83—21no—
180C2×C4⋊C4×C83—21no—
181C2×C4⋊C4×C83C2311yescharacteristic
182C2×C4⋊C4×C83C2311yescharacteristic
183C2×C4⋊C4×C83C2314yescomplemented
184C2×C22⋊C4×C83—21no—
185C2×C22⋊C4×C83—21no—
186C2×C22⋊C4×C83—21no—
187C2×C22⋊C4×C83—21no—
188C23×D83—21no—
189C23×D83—21no—
190C23×D83—24no—
191C23×D83—44no—
192C23×D83—82no—
193C23×D83—82no—
194C2×D332—22no—
195C2×D332—22no—
196C2×D332—22no—
197C2×D332—22no—
198C2×D332—21no—
199C2×D332—21no—
200C2×D332—24no—
201C2×D332—44no—
202C2×D332—44no—
203C2×D332—44no—
204C2×D332—48no—
205C2×D332C2412yes—
206C2×D332C2412yes—
207C2×C22⋊D83—24no—
208C2×C22⋊D83—24no—
209C2×C22⋊D83—24no—
210C2×C22⋊D83—24no—
211C2×C22⋊D83—82no—
212C2×C22⋊D83—82no—
213C2×C22⋊D83—82no—
214C2×C22⋊D83—82no—
215C22×Dic83—21no—
216C22×Dic83—21no—
217#13050577—44no—
218#13050577—44no—
219#13050575—44no—
220#13050575—44no—
221#13050574—44no—
222C2×C83⋊C8—22no—
223C2×C83⋊C8—22no—
224C2×C83⋊C8—22no—
225C2×C83⋊C8—22no—
226C2×C83⋊C8—44no—
227C2×C83⋊C8C2412yes—
228C2×C83⋊C8C2412yes—
229C2×C83⋊C8C2412yes—
230C2×C83⋊C8C2412yes—
231C4⋊Dic83—21no—
232C4⋊Dic83—21no—
233C4⋊Dic83C2412yes—
234C4⋊Dic83C2412yes—
235C22⋊Dic83—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4—24no—
238(C2×D83)⋊C4—24no—
239(C2×D83)⋊C4—24no—
240C4×Dic83—24no—
241C24×C83—21no—
242C24×C83C2×D411yescharacteristic
243C24×C83C2×D411yescharacteristic
244C24×C83C2×D411yescharacteristic
245#41×C83—48no—
246#41×C83—44no—
247#41×C83—44no—
248#41×C83—44no—
249#41×C83—44no—
250#41×C83—48no—
251C2×Q8×C83—21no—
252C2×Q8×C83—22no—
253C2×Q8×C83—22no—
254C2×Q8×C83—42no—
255C2×Q8×C83C2×D414yes—
256C2×Q8×C83C2412yes—
257C2×D4×C83—24no—
258C2×D4×C83—24no—
259C2×D4×C83—24no—
260C2×D4×C83—21no—
261C2×D4×C83—22no—
262C2×D4×C83—22no—
263C2×D4×C83—42no—
264C2×D4×C83—42no—
265C2×D4×C83—42no—
266C2×D4×C83—44no—
267C2×D4×C83—82no—
268C2×D4×C83—82no—
269C2×D4×C83C2×D414yes—
270C2×D4×C83C2×D414yes—
271C2×D4×C83C2×D414yes—
272C2×D4×C83C2412yes—
273C22×C4×C83—22no—
274C22×C4×C83—22no—
275C22×C4×C83—22no—
276C22×C4×C83—22no—
277C22×C4×C83—22no—
278C22×C4×C83—22no—
279C22×C4×C83—21no—
280C22×C4×C83—21no—
281C22×C4×C83—21no—
282C22×C4×C83—24no—
283C22×C4×C83—24no—
284C22×C4×C83—44no—
285C22×C4×C83—82no—
286C22×C4×C83C2×D412yes—
287C22×C4×C83C2×D412yes—
288C22×C4×C83C2×D411yescharacteristic
289C22×C4×C83C2×D412yes—
290C22×C4×C83C2×D411yescharacteristic
291C22×C4×C83C2×D411yescharacteristic
292C22×C4×C83C2412yes—
293C22×C4×C83C2412yes—
294C22×C4×C83C2412yes—
295C22×C4×C83C2411yescharacteristic
296C4⋊C4×C83—21no—
297C4⋊C4×C83—21no—
298C4⋊C4×C83—24no—
299C4⋊C4×C83—24no—
300C4⋊C4×C83—24no—
301C4⋊C4×C83C2412yes—
302C4⋊C4×C83C2412yes—
303C22⋊C4×C83—24no—
304C22⋊C4×C83—24no—
305C22⋊C4×C83—24no—
306C22⋊C4×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—42no—
318C23×C83—42no—
319C23×C83—42no—
320C23×C83C22×D412yes—
321C23×C83C22×D412yes—
322C23×C83C22×D412yes—
323C23×C83C22×D411yescharacteristic
324C22×D83—22no—
325C22×D83—22no—
326C22×D83—48no—
327C22×D83—42no—
328C22×D83—42no—
329C22×D83—42no—
330C22×D83—42no—
331C22×D83—42no—
332C22×D83—42no—
333C22×D83—84no—
334C22×D83—84no—
335C22×D83—816no—
336Q8×C83—22no—
337Q8×C83—22no—
338Q8×C83—44no—
339Q8×C83—42no—
340D4×C83—22no—
341D4×C83—22no—
342D4×C83—44no—
343D4×C83—44no—
344D4×C83—44no—
345D4×C83—48no—
346D4×C83—42no—
347D4×C83—84no—
348D4×C83—84no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—24no—
353C2×C4×C83—24no—
354C2×C4×C83—24no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
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—48no—
365C2×C4×C83—42no—
366C2×C4×C83—42no—
367C2×C4×C83—42no—
368C2×C4×C83—84no—
369C2×C4×C83C22×D412yes—
370C2×C4×C83C22×D412yes—
371C2×C4×C83C22×D412yes—
372C2×C4×C83C22×D411yescharacteristic
373C2×C4×C83H(5,𝔽2)12yes—
374C2×C4×C83H(5,𝔽2)12yes—
375C2×C4×C83C2511yescharacteristic
376C22⋊D83—84no—
377C22⋊D83—84no—
378C22⋊D83—84no—
379C22⋊D83—84no—
380C2×Dic83—22no—
381C2×Dic83—22no—
382C2×Dic83—42no—
383C2×Dic83—42no—
384D332—22no—
385D332—22no—
386D332—22no—
387D332—22no—
388D332—48no—
389D332—42no—
390D332—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—84no—
411C22×C83#53412yes—
412C22×C83#57612yes—
413C22×C83#57712yes—
414C22×C83C23×D411yescharacteristic
415C2×D83—42no—
416C2×D83—42no—
417C2×D83—42no—
418C2×D83—42no—
419C2×D83—42no—
420C2×D83—42no—
421C2×D83—816no—
422C2×D83—84no—
423C2×D83—84no—
424C4×C83—22no—
425C4×C83—22no—
426C4×C83—22no—
427C4×C83—42no—
428C4×C83—42no—
429C4×C83—42no—
430C4×C83#53412yes—
431C4×C83C2×H(5,𝔽2)11yescharacteristic
432C4×C83C2×H(5,𝔽2)11yescharacteristic
433Dic83—42no—
434Dic83—42no—
435C2×#3198—831nomaximal, Sylow
436C2×C83—42no—
437C2×C83—42no—
438C2×C83—42no—
439C2×C83—82no—
440C2×C83#319814yescomplemented
441C2×C83C2×#53411yescharacteristic
442C2×C83C2×#57611yescharacteristic
443C2×C83C2×#57711yescharacteristic
444D83—82no—
445D83—82no—
446C2×#537D8311yescharacteristic, complemented
447C2×#535—831no—
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×#41C2×D8311yescharacteristic
464C22×#41C2×D8311yescharacteristic, complemented
465C23×D4—831no—
466C22×SD16—831no—
467C22×SD16—831no—
468C22×D8—831no—
469C22×D8—831no—
470C22×M16—831no—
471C23×C8—831no—
472#537—24no—
473#537C2×D8318yescomplemented
474#535—838no—
475#535—1664no—
476C2×#127—1661no—
477C2×#124—1661no—
478C2×C22⋊Q8—21no—
479C2×C22⋊Q8C2×D8311yescharacteristic
480C2×C22⋊Q8C2×D8311yescharacteristic, complemented
481C2×#121—21no—
482C2×#121—21no—
483C2×#121—21no—
484C2×#121—831no—
485C2×#121—831no—
486C2×#121—831no—
487C2×#121—831no—
488C2×#121C2×D8311yescharacteristic
489C2×#121C2×D8311yescharacteristic, complemented
490C2×#120—1661no—
491C2×#120—1661no—
492C2×#117—831no—
493C22×C4⋊C4C2×D8311yescharacteristic, complemented
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—1661no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41C22⋊D8314yes—
530C2×#41C22×D8314yes—
531C2×#41C22×D8314yescomplemented
532C22×Q8C22⋊D8311yescharacteristic
533C22×Q8C22×D8311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—3322no—
538C22×D4—3322no—
539C22×D4—834no—
540C22×D4—831no—
541C22×D4—831no—
542C22×D4—1661no—
543C22×D4—1661no—
544C22×D4—1661no—
545C22×D4—1661no—
546C22×D4—1661no—
547C22×D4—1662no—
548C22×D4C22⋊D8311yescharacteristic
549C22×D4C22⋊D8311yescharacteristic
550C22×D4C22⋊D8311yescharacteristic
551C22×D4C22×D8311yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
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—1668no—
574#124—1668no—
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8C22×D8314yes—
579C22⋊Q8C22×D8314yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—834no—
586#121—834no—
587#121—834no—
588#121—834no—
589#121—1662no—
590#121—1662no—
591#121—1662no—
592#121—1662no—
593#121C22×D8314yes—
594#121C22×D8314yescomplemented
595#120—1668no—
596#120—1668no—
597#117—834no—
598#117—1662no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—831no—
604C2×C4⋊C4—831no—
605C2×C4⋊C4C22×D8311yescharacteristic
606C2×C4⋊C4C22×D8311yescharacteristic
607C2×C4⋊C4C22×D8314yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1661no—
613C2×C22⋊C4—1661no—
614C2×C22⋊C4—1661no—
615C2×C22⋊C4—1661no—
616C2×C22⋊C4—1661no—
617C2×C42—1661no—
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—3324no—
636C24—6642no—
637C24—6642no—
638C24—1661no—
639C24—1661no—
640C24—1664no—
641C24C2×C22⋊D8311yescharacteristic
642C24C2×C22⋊D8311yescharacteristic
643C24C2×C22⋊D8311yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—44no—
649#41—48no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—42no—
654C2×Q8C2×C22⋊D8314yes—
655C2×Q8C23×D8312yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—3324no—
669C2×D4—3328no—
670C2×D4—3324no—
671C2×D4—3324no—
672C2×D4—832no—
673C2×D4—832no—
674C2×D4—6642no—
675C2×D4—6642no—
676C2×D4—6642no—
677C2×D4—6642no—
678C2×D4—1664no—
679C2×D4—1664no—
680C2×D4—1664no—
681C2×D4—1664no—
682C2×D4—1661no—
683C2×D4—1661no—
684C2×D4—1664no—
685C2×D4—1662no—
686C2×D4—1662no—
687C2×D4—1662no—
688C2×D4—1662no—
689C2×D4C2×C22⋊D8314yes—
690C2×D4C2×C22⋊D8314yes—
691C2×D4C2×C22⋊D8314yes—
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—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—82no—
706C22×C4—1661no—
707C22×C4—1661no—
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—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—832no—
738C4⋊C4—832no—
739C4⋊C4—1661no—
740C4⋊C4—1661no—
741C4⋊C4C23×D8312yes—
742C4⋊C4C23×D8312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—1664no—
748C22⋊C4—1664no—
749C22⋊C4—1664no—
750C22⋊C4—1664no—
751C22⋊C4—1664no—
752C42—1664no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—3328no—
767C23—3322no—
768C23—3322no—
769C23—3322no—
770C23—3322no—
771C23—3322no—
772C23—3322no—
773C23—6644no—
774C23—6644no—
775C23—66416no—
776C23—1662no—
777C23—1662no—
778C23C22×C22⋊D8312yes—
779C23C22×C22⋊D8312yes—
780C23C22×C22⋊D8312yes—
781C23C22×C22⋊D8311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—44no—
790D4—44no—
791D4—48no—
792D4—42no—
793D4—84no—
794D4—84no—
795D4—3328no—
796D4—3322no—
797D4—3322no—
798D4—6644no—
799D4—6644no—
800D4—6644no—
801D4—6644no—
802D4—1662no—
803D4—1662no—
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—22no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—3322no—
827C2×C4—3322no—
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—84no—
857C22—3322no—
858C22—3322no—
859C22—3322no—
860C22—3322no—
861C22—3322no—
862C22—3322no—
863C22—66416no—
864C22—6644no—
865C22—6644no—
866C22#1912826012yes—
867C22#1912850412yes—
868C22#1912850912yes—
869C22C23×C22⋊D8311yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—3322no—
877C4—3322no—
878C4#1912826012yes—
879C4C2×#1458183711yescharacteristic
880C4C2×#1458183711yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—6642no—
886C2—6642no—
887C2#2491830914yesdirect product factor
888C2C2×#1912826011yescharacteristic
889C2C2×#1912850411yescharacteristic
890C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#537×C83C2
socleC23×C83C22×D4
hypercenterC2×#537D83
hypocenterC83C2×#3198
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#19128265C2semidirect
2. #24918309C2direct (N × H)
3. C2×#19128019C2semidirect
4. C2×#19128039C2semidirect
5. C2×#19128022C2semidirect
6. C2×#19128014C2semidirect
7. C2×#19127952C2semidirect
8. C2×#19127949C2semidirect
9. C2×#19127935C2semidirect
10. C2×#19127932C2semidirect
11. C2×#19127846C2semidirect
12. C2×#19127846C2semidirect
13. C2×#19127851C2semidirect
14. C2×#19127834C2semidirect
15. C2×#19127668C2semidirect
16. C2×#537×C83C2semidirect
22. C22×#13050574C22semidirect
23. C23×C83⋊C8C22semidirect
25. #19128265C22semidirect
35. #19128039C22semidirect
36. #19128022C22semidirect
37. #19128019C22semidirect
38. #19128014C22semidirect
39. #19127952C22semidirect
40. #19127949C22semidirect
41. #19127935C22semidirect
42. #19127932C22semidirect
43. #19127851C22semidirect
44. #19127846C22semidirect
45. #19127846C22semidirect
46. #19127834C22semidirect
47. C2×#14581725C22semidirect
48. C2×#14581725C22semidirect
49. C2×#14581723C22semidirect
50. C2×#14581723C22semidirect
51. C2×#14581716C22semidirect
52. C2×#14581716C22semidirect
53. C2×#14581713C22semidirect
54. C2×#14581713C22semidirect
59. #19127668C22semidirect
62. C2×C22⋊(C83⋊C8)C22semidirect
63. C2×C22⋊(C83⋊C8)C22semidirect
65. C22×#41×C83C22semidirect
67. #537×C83C22semidirect
70. C2×C22⋊Q8×C83C22semidirect
75. C2×#121×C83C22semidirect
76. C22×C4⋊C4×C83C22semidirect
98. C2×#13050574C23semidirect
104. C22×C83⋊C8C23semidirect
127. #14581725C23semidirect
128. #14581725C23semidirect
129. #14581723C23semidirect
130. #14581723C23semidirect
131. #14581716C23semidirect
132. #14581716C23semidirect
133. #14581713C23semidirect
134. #14581713C23semidirect
141. C22⋊(C83⋊C8)C23semidirect
142. C22⋊(C83⋊C8)C23semidirect
150. C2×#41×C83C23semidirect
169. C22⋊Q8×C83C23semidirect
176. #121×C83C23semidirect
183. C2×C4⋊C4×C83C23semidirect
440. C2×C83#3198semidirect
446. C2×#537D83semidirect
462. C83C2×#3198semidirect
464. C22×#41C2×D83semidirect
473. #537C2×D83semidirect
480. C2×C22⋊Q8C2×D83semidirect
489. C2×#121C2×D83semidirect
493. C22×C4⋊C4C2×D83semidirect
531. C2×#41C22×D83semidirect
579. C22⋊Q8C22×D83semidirect
594. #121C22×D83semidirect
607. C2×C4⋊C4C22×D83semidirect
887. C2#24918309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282652
#249183092
C2×#191280192
C2×#191280392
C2×#191280222
C2×#191280142
C2×#191279522
C2×#191279492
C2×#191279352
C2×#191279322
C2×#191278462
C2×#191278512
C2×#191278342
C2×#191276682
C2×#537×C832
C2×#319883