Finite Group Databasebeta

← C2×#24919840 #36282849

Subgroups — C2×#24919840 #36282849

Order 21248.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128399C211yesmaximal, characteristic
2C2×#19128393C211yesmaximal, characteristic, complemented
3#24919840C2116yesmaximal, direct product factor
4C2×#19128102C211yesmaximal, characteristic, complemented
5C2×#19128041C211yesmaximal, characteristic, complemented
6C2×#19128028C211yesmaximal, characteristic, complemented
7C2×#19128015C211yesmaximal, characteristic, complemented
8C2×#19128010C211yesmaximal, characteristic, complemented
9C2×#19128004C211yesmaximal, characteristic, complemented
10C2×#19127933C211yesmaximal, characteristic, complemented
11C2×#19127932C211yesmaximal, characteristic, complemented
12C2×#19127786C211yesmaximal, characteristic, complemented
13C2×(C22⋊D83)⋊C8C211yesmaximal, characteristic, complemented
14C2×#19127738C211yesmaximal, characteristic, complemented
15C22×#14581723C211yesmaximal, characteristic, complemented
16C2×#484×C83C211yesmaximal, characteristic, complemented
17C22×#13050577C2211yescharacteristic
18C23×C83⋊C8C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20#19128399—24no—
21#19128399C2218yes—
22#19128393—24no—
23#19128393C2218yescomplemented
24C2×#14581787—21no—
25C2×#14581787—21no—
26C2×#14581783—21no—
27C2×#14581783C2211yescharacteristic
28C2×#14581783C2211yescharacteristic
29C2×#14581777—21no—
30C2×#14581776—21no—
31C2×#14581768C2211yescharacteristic
32C2×#14581767C2211yescharacteristic
33C2×#14581766—21no—
34C2×#14581766C2211yescharacteristic
35C2×Q8×Dic83C2211yescharacteristic
36C2×#14581754C2211yescharacteristic
37C2×C4×C22⋊D83—21no—
38C2×C4×C22⋊D83C2211yescharacteristic
39C2×#14581750C2211yescharacteristic
40C2×#14581750C2211yescharacteristic
41C2×#14581748—21no—
42C22×C4⋊Dic83C2211yescharacteristic
43#19128102C2218yescomplemented
44#19128041C2218yescomplemented
45#19128028C2218yescomplemented
46#19128015C2218yescomplemented
47#19128010C2218yescomplemented
48#19128004C2218yescomplemented
49#19127933C2218yescomplemented
50#19127932C2218yescomplemented
51#19127786C2218yescomplemented
52(C22⋊D83)⋊C8C2218yescomplemented
53#19127738C2218yescomplemented
54C2×#14581726C2211yescharacteristic
55C2×#14581726C2211yescharacteristic
56C2×#14581723C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×#14581723C2211yescharacteristic
60C2×#14581723C2211yescharacteristic
61C2×#14581723C2218yescomplemented
62C2×Dic83⋊C8C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581712C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×C22⋊Q8×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2211yescharacteristic
71#484×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#107×C83C2211yescharacteristic
74C2×#103×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic
77C22×D332—21no—
78C22×D332C2311yescharacteristic
79C22×C22⋊D83—21no—
80C22×C22⋊D83D411yescharacteristic
81C23×Dic83—21no—
82C22×C4×D83—21no—
83C22×C4×D83C2311yescharacteristic
84C2×#13050577—24no—
85C2×#13050577C2314yes—
86C22×C83⋊C8—24no—
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2314yes—
89C22×C83⋊C8C2311yescharacteristic
90C2×C8×D83—24no—
91C2×C8×D83C2314yes—
92#14581787—28no—
93#14581787—28no—
94#14581783—28no—
95#14581783—22no—
96#14581783—22no—
97#14581783C2314yes—
98#14581783C2314yes—
99#14581777—28no—
100#14581776—28no—
101#14581768—22no—
102#14581768C2314yes—
103#14581767—22no—
104#14581767C2314yes—
105#14581766—28no—
106#14581766—22no—
107#14581766C2314yes—
108Q8×Dic83—22no—
109Q8×Dic83C2314yes—
110#14581754—22no—
111#14581754C2314yes—
112C4×C22⋊D83—28no—
113C4×C22⋊D83D414yes—
114C4×C22⋊D83C2314yes—
115#14581750—22no—
116#14581750—22no—
117#14581750C2314yes—
118#14581750C2314yes—
119#14581748—28no—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83—22no—
124C2×C4⋊Dic83—21no—
125C2×C4⋊Dic83C2314yes—
126C2×C4⋊Dic83C2311yescharacteristic
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4D411yescharacteristic
133C2×C22⋊Dic83D411yescharacteristic
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4D411yescharacteristic
141C2×C4×Dic83—21no—
142C2×C4×Dic83—21no—
143C2×C4×Dic83—21no—
144C2×C4×Dic83C2311yescharacteristic
145#14581726C2314yes—
146#14581726C2314yes—
147#14581723C2314yes—
148#14581723C2314yes—
149#14581723C2314yes—
150#14581723C2314yes—
151#14581723C2314yes—
152Dic83⋊C8C2314yes—
153#14581716C2314yes—
154#14581714C2314yes—
155#14581714C2314yes—
156#14581712C2314yes—
157(C2×D83)⋊C8C2314yes—
158C8×Dic83C2314yes—
159C22×Q8×C83C2311yescharacteristic
160C23×C4×C83—21no—
161C23×C4×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164C22⋊Q8×C83—22no—
165C22⋊Q8×C83C2314yes—
166C2×C4⋊C4×C83—22no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83C2314yes—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C22⋊C4×C83—21no—
174#107×C83C2314yes—
175#107×C83C2314yes—
176#103×C83C2314yes—
177#103×C83C2314yes—
178C22⋊C8×C83C2314yes—
179C23×D83—21no—
180C23×D83C2×D411yescharacteristic
181C2×D332—22no—
182C2×D332—22no—
183C2×D332—21no—
184C2×D332—24no—
185C2×D332—82no—
186C2×D332C2412yes—
187C2×C22⋊D83—24no—
188C2×C22⋊D83—24no—
189C2×C22⋊D83—44no—
190C2×C22⋊D83C2×D414yes—
191C22×Dic83—24no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—44no—
196C22×Dic83C2×D411yescharacteristic
197C22×Dic83C2×D411yescharacteristic
198C22×Dic83C2×D411yescharacteristic
199C2×C4×D83—22no—
200C2×C4×D83—22no—
201C2×C4×D83—24no—
202C2×C4×D83—82no—
203C2×C4×D83C2×D412yes—
204C2×C4×D83C2412yes—
205#13050577—28no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—28no—
208C2×C83⋊C8#4114yes—
209C2×C83⋊C8C2412yes—
210C2×C83⋊C8C2412yes—
211C8×D83—28no—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83—24no—
215C4⋊Dic83—21no—
216C4⋊Dic83—24no—
217C4⋊Dic83—24no—
218C4⋊Dic83—24no—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221C4⋊Dic83C2412yes—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4C2×D414yes—
226C22⋊Dic83C2×D414yes—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—24no—
229(C2×D83)⋊C4—24no—
230(C2×D83)⋊C4—24no—
231(C2×D83)⋊C4—24no—
232(C2×D83)⋊C4—24no—
233(C2×D83)⋊C4C2×D414yes—
234C4×Dic83—24no—
235C4×Dic83—24no—
236C4×Dic83—24no—
237C4×Dic83C2×D412yes—
238C4×Dic83C2412yes—
239C24×C83C2×D411yescharacteristic
240C2×Q8×C83—21no—
241C2×Q8×C83—22no—
242C2×Q8×C83—22no—
243C2×Q8×C83C2412yes—
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—24no—
251C22×C4×C83—82no—
252C22×C4×C83C2×D412yes—
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2412yes—
255C22×C4×C83C2411yescharacteristic
256C2×C8×C83—22no—
257C2×C8×C83—22no—
258C2×C8×C83C2412yes—
259C2×C8×C83C2412yes—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—24no—
263C4⋊C4×C83—21no—
264C4⋊C4×C83—21no—
265C4⋊C4×C83C2412yes—
266C4⋊C4×C83C2412yes—
267C4⋊C4×C83C2412yes—
268C22⋊C4×C83—24no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83#13514yes—
272C23×C83C22×D412yes—
273C23×C83C22×D411yescharacteristic
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—22no—
278C22×D83—42no—
279C22×D83—42no—
280C22×D83—42no—
281C22×D83C22×D412yes—
282Q8×C83—22no—
283Q8×C83—22no—
284Q8×C83—42no—
285C2×C4×C83—22no—
286C2×C4×C83—24no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—42no—
294C2×C4×C83—42no—
295C2×C4×C83—42no—
296C2×C4×C83—42no—
297C2×C4×C83—84no—
298C2×C4×C83C22×D412yes—
299C2×C4×C83C22×D411yescharacteristic
300C2×C4×C83C2×#4112yes—
301C2×C4×C832−1+412yes—
302C2×C4×C83C2511yescharacteristic
303C22⋊D83—28no—
304C22⋊D83—48no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—48no—
312C2×Dic83—42no—
313C2×Dic83—42no—
314C2×Dic83—42no—
315C2×Dic83C22×D412yes—
316C2×Dic83C22×D412yes—
317C2×Dic83C22×D412yes—
318D332—22no—
319D332—22no—
320D332—42no—
321D332—84no—
322C4×D83—24no—
323C4×D83—22no—
324C4×D83—22no—
325C4×D83—84no—
326C8×C83—22no—
327C8×C83—22no—
328C83⋊C8—22no—
329C83⋊C8C2×#4114yes—
330C22×C83—28no—
331C22×C83—22no—
332C22×C83—22no—
333C22×C83#54712yes—
334C22×C83C2×#13514yes—
335C22×C83C2×#13512yes—
336C22×C83#57712yes—
337C22×C83C23×D411yescharacteristic
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—22no—
341C2×D83—44no—
342C2×D83—42no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—84no—
346C4×C83—22no—
347C4×C83—42no—
348C4×C83—42no—
349C4×C83—42no—
350C4×C83—42no—
351C4×C83#54712yes—
352C4×C83C22×#4111yescharacteristic
353C4×C83C2×2−1+411yescharacteristic
354Dic83—22no—
355Dic83—22no—
356Dic83—22no—
357Dic83—42no—
358Dic83—42no—
359Dic83—42no—
360C2×#3337—831nomaximal, Sylow
361C2×C83—24no—
362C2×C83#333714yescomplemented
363C2×C83C2×#54711yescharacteristic
364C2×C83C22×#13511yescharacteristic
365C2×C83C2×#57711yescharacteristic
366D83—42no—
367D83—82no—
368C2×#553—831no—
369C2×#552—831no—
370#3337—8316no—
371C2×#499—831no—
372C2×#484D8311yescharacteristic, complemented
373C2×#485—831no—
374C2×#482—831no—
375C2×#480—831no—
376C2×#479—831no—
377C2×#478—831no—
378C2×#465—831no—
379C2×#465—831no—
380C2×C4×SD16—831no—
381C2×C8×D4—831no—
382C2×#427—831no—
383C22×#106—831no—
384C83C2×#333711yescharacteristic, complemented, Sylow
385C22×SD16—831no—
386C23×C8—831no—
387C23×C8—831no—
388#553—838no—
389#553—1664no—
390#552—838no—
391#552—1664no—
392C2×#126—1661no—
393C2×#126—1661no—
394C2×#125—831no—
395C2×#125—831no—
396C2×#125—1661no—
397C2×#123—1661no—
398C2×#123—1661no—
399C2×C22⋊Q8—831no—
400C2×C22⋊Q8C2×D8311yescharacteristic
401C2×#121—831no—
402C2×#121—831no—
403C2×#121—1661no—
404C2×C4×Q8—831no—
405C2×C4×D4—831no—
406C2×C4×D4—831no—
407C2×C4×D4—1661no—
408C2×#117—831no—
409C2×#117—831no—
410C2×#117—1661no—
411C22×C4⋊C4—831no—
412C22×C4⋊C4C2×D8311yescharacteristic
413#499—838no—
414#485—838no—
415#484C2×D8318yescomplemented
416#482—838no—
417#480—838no—
418#479—838no—
419#478—838no—
420#465—838no—
421#465—838no—
422C4×SD16—838no—
423C8×D4—838no—
424#427—838no—
425C2×#107—831no—
426C2×#107—831no—
427C2×#107C2×D8311yescharacteristic
428C2×#107C2×D8311yescharacteristic
429C2×#106—831no—
430C2×#106—831no—
431C2×#106—838no—
432C2×#106—831no—
433C2×#106—831no—
434C2×#106—831no—
435C2×C4⋊C8—831no—
436C2×#103—831no—
437C2×#103C2×D8311yescharacteristic
438C2×#103C2×D8311yescharacteristic
439C2×#102—831no—
440C2×#102—831no—
441C2×#102—831no—
442C2×C22⋊C8—831no—
443C2×C22⋊C8C2×D8311yescharacteristic
444C2×C4×C8—831no—
445C22×Q8C22×D8311yescharacteristic
446C22×D4—831no—
447C22×D4—831no—
448C22×D4—1661no—
449C22×D4—1661no—
450C23×C4—21no—
451C23×C4—831no—
452C23×C4—1661no—
453C23×C4—1661no—
454C23×C4C22×D8311yescharacteristic
455C2×SD16—834no—
456C2×SD16—1664no—
457C22×C8—831no—
458C22×C8—831no—
459C22×C8—834no—
460C22×C8—834no—
461C22×C8—1664no—
462C22×C8—1664no—
463C22×C8C22×D8311yescharacteristic
464C22×C8C22×D8311yescharacteristic
465#126—1668no—
466#126—1668no—
467#125—834no—
468#125—834no—
469#125—1662no—
470#125—1662no—
471#125—1668no—
472#123—1668no—
473#123—1668no—
474C22⋊Q8—22no—
475C22⋊Q8—834no—
476C22⋊Q8—1662no—
477C22⋊Q8C22×D8314yes—
478#121—834no—
479#121—834no—
480#121—1662no—
481#121—1668no—
482#121—1662no—
483C4×Q8—834no—
484C4×Q8—1662no—
485C4×D4—834no—
486C4×D4—834no—
487C4×D4—834no—
488C4×D4—1662no—
489C4×D4—1668no—
490#117—834no—
491#117—834no—
492#117—1668no—
493#117—1662no—
494#117—1662no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—831no—
499C2×C4⋊C4—831no—
500C2×C4⋊C4—831no—
501C2×C4⋊C4—834no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—1661no—
504C2×C4⋊C4—1661no—
505C2×C4⋊C4—1661no—
506C2×C4⋊C4—1661no—
507C2×C4⋊C4—1661no—
508C2×C4⋊C4—1661no—
509C2×C4⋊C4—1661no—
510C2×C4⋊C4—1662no—
511C2×C4⋊C4C22×D8311yescharacteristic
512C2×C4⋊C4C22×D8311yescharacteristic
513C2×C4⋊C4C22×D8314yes—
514C2×C4⋊C4C22×D8311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—831no—
517C2×C22⋊C4—831no—
518C2×C22⋊C4—1661no—
519C2×C22⋊C4—1661no—
520C2×C22⋊C4—1661no—
521C2×C22⋊C4—1661no—
522C2×C22⋊C4—1661no—
523C2×C22⋊C4—1661no—
524C2×C42—831no—
525C2×C42—1661no—
526C2×C42—1661no—
527C2×C42—1661no—
528#107—834no—
529#107—834no—
530#107C22×D8314yes—
531#107C22×D8314yes—
532#106—834no—
533#106—834no—
534#106—834no—
535#106—834no—
536#106—834no—
537C4⋊C8—834no—
538#103—834no—
539#103C22×D8314yes—
540#103C22×D8314yes—
541#102—834no—
542#102—834no—
543#102—834no—
544C22⋊C8—834no—
545C22⋊C8C22×D8314yes—
546C4×C8—834no—
547C24—831no—
548C24—1661no—
549C24D4×D8311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D8312yes—
554C2×D4—3324no—
555C2×D4—834no—
556C2×D4—832no—
557C2×D4—6642no—
558C2×D4—1664no—
559C2×D4—1664no—
560C2×D4—1664no—
561C2×D4—1661no—
562C2×D4—1662no—
563C2×D4—1662no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—3324no—
573C22×C4—831no—
574C22×C4—831no—
575C22×C4—831no—
576C22×C4—832no—
577C22×C4—832no—
578C22×C4—6642no—
579C22×C4—1664no—
580C22×C4—1664no—
581C22×C4—1661no—
582C22×C4—1661no—
583C22×C4—1661no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4D4×D8312yes—
587C22×C4D4×D8311yescharacteristic
588C22×C4C23×D8312yes—
589C22×C4C23×D8311yescharacteristic
590SD16—1668no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—834no—
594C2×C8—832no—
595C2×C8—832no—
596C2×C8—1668no—
597C2×C8—1668no—
598C2×C8—1662no—
599C2×C8C23×D8312yes—
600C2×C8C23×D8312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—834no—
607C4⋊C4—832no—
608C4⋊C4—832no—
609C4⋊C4—832no—
610C4⋊C4—1664no—
611C4⋊C4—1664no—
612C4⋊C4—1664no—
613C4⋊C4—1664no—
614C4⋊C4—1664no—
615C4⋊C4—1664no—
616C4⋊C4—1661no—
617C4⋊C4—1661no—
618C4⋊C4—1664no—
619C4⋊C4—1661no—
620C4⋊C4C23×D8312yes—
621C4⋊C4C23×D8312yes—
622C4⋊C4C23×D8312yes—
623C22⋊C4—24no—
624C22⋊C4—834no—
625C22⋊C4—834no—
626C22⋊C4—1664no—
627C22⋊C4—1664no—
628C22⋊C4—1664no—
629C22⋊C4—1664no—
630C22⋊C4—1664no—
631C22⋊C4—1664no—
632C42—832no—
633C42—832no—
634C42—1664no—
635C42—1664no—
636C42—1664no—
637C23—22no—
638C23—22no—
639C23—3322no—
640C23—3322no—
641C23—3322no—
642C23—832no—
643C23—1662no—
644C23—1662no—
645C23—1662no—
646C23—1662no—
647C23#1458181514yes—
648C23C2×D4×D8312yes—
649C23C2×D4×D8311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—3328no—
654D4—3322no—
655D4—6644no—
656D4—1668no—
657D4—1662no—
658D4—1662no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—84no—
672C2×C4—3328no—
673C2×C4—3322no—
674C2×C4—3322no—
675C2×C4—3322no—
676C2×C4—832no—
677C2×C4—832no—
678C2×C4—832no—
679C2×C4—6644no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—1662no—
683C2×C4—1662no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4—1664no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4C2×D4×D8312yes—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4#41×D8312yes—
692C2×C4#1458183912yes—
693C2×C4C24×D8311yescharacteristic
694C8—22no—
695C8—22no—
696C8—834no—
697C8—1662no—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—3324no—
702C22—3322no—
703C22—3322no—
704C22—3322no—
705C22—6644no—
706C22—1662no—
707C22—1662no—
708C22—1662no—
709C22#1912834912yes—
710C22C2×#1458181514yes—
711C22C2×#1458181512yes—
712C22#1912851112yes—
713C22C22×D4×D8311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—3322no—
720C4—3322no—
721C4—3322no—
722C4—1662no—
723C4—1662no—
724C4—1662no—
725C4#1912834912yes—
726C4C2×#41×D8311yescharacteristic
727C4C2×#1458183911yescharacteristic
728C2—24no—
729C2—3322no—
730C2—6642no—
731C2#2491984014yesdirect product factor
732C2C2×#1912834911yescharacteristic
733C2C22×#1458181511yescharacteristic
734C2C2×#1912851111yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#484×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128399C2
hypercenterC2×#484D83
hypocenterC83C2×#3337
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C2×#19128393C2semidirect
3. #24919840C2direct (N × H)
4. C2×#19128102C2semidirect
5. C2×#19128041C2semidirect
6. C2×#19128028C2semidirect
7. C2×#19128015C2semidirect
8. C2×#19128010C2semidirect
9. C2×#19128004C2semidirect
10. C2×#19127933C2semidirect
11. C2×#19127932C2semidirect
12. C2×#19127786C2semidirect
13. C2×(C22⋊D83)⋊C8C2semidirect
14. C2×#19127738C2semidirect
15. C22×#14581723C2semidirect
16. C2×#484×C83C2semidirect
23. #19128393C22semidirect
43. #19128102C22semidirect
44. #19128041C22semidirect
45. #19128028C22semidirect
46. #19128015C22semidirect
47. #19128010C22semidirect
48. #19128004C22semidirect
49. #19127933C22semidirect
50. #19127932C22semidirect
51. #19127786C22semidirect
52. (C22⋊D83)⋊C8C22semidirect
53. #19127738C22semidirect
61. C2×#14581723C22semidirect
71. #484×C83C22semidirect
362. C2×C83#3337semidirect
372. C2×#484D83semidirect
384. C83C2×#3337semidirect
415. #484C2×D83semidirect
731. C2#24919840direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283992
C2×#191283932
#249198402
C2×#191281022
C2×#191280412
C2×#191280282
C2×#191280152
C2×#191280102
C2×#191280042
C2×#191279332
C2×#191279322
C2×#191277862
C2×(C22⋊D83)⋊C82
C2×#191277382
C22×#145817232
C2×#484×C832
C2×#333783