Finite Group Databasebeta

← C2×#24920085 #36283150

Subgroups — C2×#24920085 #36283150

Order 21248.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128414C211yesmaximal, characteristic
2C2×#19128406C211yesmaximal, characteristic, complemented
3#24920085C2116yesmaximal, direct product factor
4C2×#19128105C211yesmaximal, characteristic, complemented
5C2×#19128045C211yesmaximal, characteristic, complemented
6C2×#19128042C211yesmaximal, characteristic, complemented
7C2×#19128016C211yesmaximal, characteristic, complemented
8C2×#19128014C211yesmaximal, characteristic, complemented
9C2×#19127995C211yesmaximal, characteristic, complemented
10C2×#19127990C211yesmaximal, characteristic, complemented
11C2×#19127948C211yesmaximal, characteristic, complemented
12C2×#19127947C211yesmaximal, characteristic, complemented
13C2×#19127788C211yesmaximal, characteristic, complemented
14C2×#19127777C211yesmaximal, characteristic, complemented
15C2×#19127740C211yesmaximal, characteristic, complemented
16C2×#428×C83C211yesmaximal, characteristic, complemented
17C22×#13050579C2211yescharacteristic
18C22×#13050573C2211yescharacteristic
19#19128414—24no—
20#19128414C2218yes—
21#19128406—24no—
22#19128406C2218yescomplemented
23C2×#14581791C2211yescharacteristic
24C2×#14581791C2211yescharacteristic
25C2×#14581782—21no—
26C2×#14581780—21no—
27C2×#14581778—21no—
28C2×#14581772C2211yescharacteristic
29C2×#14581771—21no—
30C2×#14581771C2211yescharacteristic
31C2×#14581770—21no—
32C2×#14581767C2211yescharacteristic
33C2×#14581766C2211yescharacteristic
34C2×#14581765—21no—
35C2×#14581757C2211yescharacteristic
36C2×#14581754C2211yescharacteristic
37C2×C4×C22⋊D83—21no—
38C2×C4×C22⋊D83C2211yescharacteristic
39C2×#14581750C2211yescharacteristic
40C2×#14581749—21no—
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128105C2218yescomplemented
43#19128045C2218yescomplemented
44#19128042C2218yescomplemented
45#19128016C2218yescomplemented
46#19128014C2218yescomplemented
47#19127995C2218yescomplemented
48#19127990C2218yescomplemented
49#19127948C2218yescomplemented
50#19127947C2218yescomplemented
51#19127788C2218yescomplemented
52#19127777C2218yescomplemented
53#19127740C2218yescomplemented
54C2×#14581726C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×#14581717C2211yescharacteristic
61C2×#14581715C2211yescharacteristic
62C2×#14581715C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C22×M16×C83C2211yescharacteristic
70C2×#117×C83C2211yescharacteristic
71C22×C4⋊C4×C83C2211yescharacteristic
72#428×C83C2218yescomplemented
73C2×#107×C83C2211yescharacteristic
74C2×#107×C83C2211yescharacteristic
75C2×#106×C83C2211yescharacteristic
76C2×#106×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166C2311yescharacteristic
80C22×D332—21no—
81C22×D332C2311yescharacteristic
82C22×C22⋊D83—21no—
83C22×C22⋊D83D411yescharacteristic
84C22×C4×D83—21no—
85C22×C4×D83—21no—
86C22×C4×D83C2311yescharacteristic
87C2×#13050579—24no—
88C2×#13050579C2314yes—
89C2×#13050573—24no—
90C2×#13050573C2314yes—
91C22×C83⋊C8C2311yescharacteristic
92C22×C83⋊C8C2311yescharacteristic
93#14581791—22no—
94#14581791—22no—
95#14581791C2314yes—
96#14581791C2314yes—
97#14581782—28no—
98#14581780—28no—
99#14581778—28no—
100#14581772—22no—
101#14581772C2314yes—
102#14581771—28no—
103#14581771—22no—
104#14581771C2314yes—
105#14581770—28no—
106#14581767—22no—
107#14581767C2314yes—
108#14581766—22no—
109#14581766C2314yes—
110#14581765—28no—
111#14581757—22no—
112#14581757C2314yes—
113#14581754—22no—
114#14581754C2314yes—
115C4×C22⋊D83—28no—
116C4×C22⋊D83D414yes—
117C4×C22⋊D83C2314yes—
118#14581750—22no—
119#14581750C2314yes—
120#14581749—28no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83C2311yescharacteristic
123C2×C4⋊Dic83C2311yescharacteristic
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4D411yescharacteristic
130C4⋊C4×D83—22no—
131C4⋊C4×D83C2314yes—
132C2×C22⋊Dic83—21no—
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)⋊C4D411yescharacteristic
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83C2311yescharacteristic
143#14581726C2314yes—
144#14581725C2314yes—
145#14581725C2314yes—
146#14581725C2314yes—
147#14581723C2314yes—
148Dic83⋊C8C2314yes—
149#14581717C2314yes—
150#14581715C2314yes—
151#14581715C2314yes—
152#14581714C2314yes—
153#14581712C2314yes—
154#14581712C2314yes—
155C22⋊(C83⋊C8)C2314yes—
156(C2×D83)⋊C8C2314yes—
157C8×Dic83C2314yes—
158C23×C4×C83—21no—
159C23×C4×C83C2311yescharacteristic
160C2×M16×C83—24no—
161C2×M16×C83C2314yes—
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164#117×C83—22no—
165#117×C83C2314yes—
166C2×C4⋊C4×C83—22no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2314yes—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C22⋊C4×C83—21no—
174C2×C42×C83—21no—
175#107×C83C2314yes—
176#107×C83C2314yes—
177#106×C83C2314yes—
178#106×C83C2314yes—
179C23×D83—21no—
180C23×D83C2×D411yescharacteristic
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—21no—
184C2×Dic166—24no—
185C2×Dic166—24no—
186C2×Dic166—82no—
187C2×Dic166—82no—
188C2×Dic166C2412yes—
189C2×D332—22no—
190C2×D332—22no—
191C2×D332—21no—
192C2×D332—24no—
193C2×D332—82no—
194C2×D332C2412yes—
195C2×C22⋊D83—24no—
196C2×C22⋊D83—24no—
197C2×C22⋊D83—82no—
198C2×C22⋊D83C2×D414yes—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83C2×D411yescharacteristic
203C22×Dic83C2×D411yescharacteristic
204C22×Dic83C2×D411yescharacteristic
205C2×C4×D83—22no—
206C2×C4×D83—22no—
207C2×C4×D83—24no—
208C2×C4×D83—24no—
209C2×C4×D83—44no—
210C2×C4×D83—82no—
211C2×C4×D83C2×D412yes—
212C2×C4×D83C2412yes—
213#13050579—28no—
214#13050573—28no—
215C2×C83⋊C8—22no—
216C2×C83⋊C8—22no—
217C2×C83⋊C8C2412yes—
218C2×C83⋊C8C2412yes—
219C4⋊Dic83—21no—
220C4⋊Dic83—21no—
221C4⋊Dic83—24no—
222C4⋊Dic83C2412yes—
223C4⋊Dic83C2412yes—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4C2×D414yes—
230C22⋊Dic83—24no—
231C22⋊Dic83C2×D414yes—
232(C2×D83)⋊C4—24no—
233(C2×D83)⋊C4—24no—
234(C2×D83)⋊C4—24no—
235(C2×D83)⋊C4—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4C2×D414yes—
238C4×Dic83—24no—
239C4×Dic83—24no—
240C4×Dic83C2×D412yes—
241C4×Dic83C2412yes—
242C24×C83C2×D411yescharacteristic
243C22×C4×C83—22no—
244C22×C4×C83—22no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—24no—
250C22×C4×C83—82no—
251C22×C4×C83C2×D412yes—
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2412yes—
254C22×C4×C83C2411yescharacteristic
255M16×C83—28no—
256C2×C8×C83—22no—
257C2×C8×C83#4114yes—
258C2×C8×C83C2412yes—
259C2×C8×C83C2412yes—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—21no—
264C4⋊C4×C83—21no—
265C4⋊C4×C83C2412yes—
266C4⋊C4×C83C2412yes—
267C4⋊C4×C83C2412yes—
268C4⋊C4×C83C2412yes—
269C22⋊C4×C83—24no—
270C42×C83—24no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83C22×D412yes—
275C23×C83C22×D411yescharacteristic
276C22×D83—22no—
277C22×D83—22no—
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—42no—
281C22×D83—42no—
282C22×D83—42no—
283C22×D83C22×D412yes—
284C2×C4×C83—22no—
285C2×C4×C83—24no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—42no—
293C2×C4×C83—42no—
294C2×C4×C83—42no—
295C2×C4×C83—42no—
296C2×C4×C83—84no—
297C2×C4×C83C22×D412yes—
298C2×C4×C83C22×D411yescharacteristic
299C2×C4×C83C2×#4112yes—
300C2×C4×C832−1+412yes—
301C2×C4×C83C2511yescharacteristic
302C22⋊D83—28no—
303C22⋊D83—84no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—42no—
310C2×Dic83—42no—
311C2×Dic83—42no—
312C2×Dic83#13714yes—
313C2×Dic83C22×D412yes—
314C2×Dic83C22×D412yes—
315C2×Dic83C22×D412yes—
316D332—22no—
317D332—22no—
318D332—42no—
319D332—84no—
320C4×D83—24no—
321C4×D83—22no—
322C4×D83—22no—
323C4×D83—48no—
324C4×D83—84no—
325Dic166—22no—
326Dic166—22no—
327Dic166—42no—
328Dic166—84no—
329Dic166—84no—
330C8×C83—22no—
331C8×C83C2×#4114yes—
332C83⋊C8—22no—
333C83⋊C8—22no—
334C22×C83—22no—
335C22×C83—22no—
336C22×C83—22no—
337C22×C83—44no—
338C22×C83#54712yes—
339C22×C83C2×#13712yes—
340C22×C83#57612yes—
341C22×C83C23×D411yescharacteristic
342C2×D83—22no—
343C2×D83—22no—
344C2×D83—22no—
345C2×D83—44no—
346C2×D83—42no—
347C2×D83—42no—
348C2×D83—42no—
349C2×D83—84no—
350C4×C83—22no—
351C4×C83—42no—
352C4×C83—42no—
353C4×C83—42no—
354C4×C83—42no—
355C4×C83#54712yes—
356C4×C83C22×#4111yescharacteristic
357C4×C83C2×2−1+411yescharacteristic
358Dic83—22no—
359Dic83—22no—
360Dic83—42no—
361Dic83—42no—
362Dic83—42no—
363Dic83C2×#13714yes—
364C2×#3357—831nomaximal, Sylow
365C2×C83—42no—
366C2×C83#335714yescomplemented
367C2×C83C2×#54711yescharacteristic
368C2×C83C22×#13711yescharacteristic
369C2×C83C2×#57611yescharacteristic
370D83—42no—
371D83—82no—
372C2×#555—831no—
373C2×#554—831no—
374#3357—8316no—
375C2×#500—831no—
376C2×#485—831no—
377C2×#485—831no—
378C2×#480—831no—
379C2×#480—831no—
380C2×#477—831no—
381C2×#476—831no—
382C2×#468—831no—
383C2×#468—831no—
384C2×C4×SD16—831no—
385C2×#436—831no—
386C2×#428—831no—
387C2×#428D8311yescharacteristic, complemented
388C83C2×#335711yescharacteristic, complemented, Sylow
389C22×SD16—831no—
390C22×M16—831no—
391C22×M16C2×D8311yescharacteristic
392#555—838no—
393#555—1664no—
394#554—838no—
395#554—1664no—
396C2×C4⋊Q8—831no—
397C2×C4⋊Q8—831no—
398C2×#125—1661no—
399C2×#124—1661no—
400C2×#124—1661no—
401C2×C22⋊Q8—831no—
402C2×C22⋊Q8—831no—
403C2×C22⋊Q8—1661no—
404C2×C22⋊Q8—1661no—
405C2×#121—831no—
406C2×#121—831no—
407C2×#121—1661no—
408C2×C4×Q8—831no—
409C2×C4×D4—831no—
410C2×C4×D4—831no—
411C2×C4×D4—1661no—
412C2×#117—831no—
413C2×#117—1661no—
414C2×#117C2×D8311yescharacteristic
415C22×C4⋊C4—831no—
416C22×C4⋊C4C2×D8311yescharacteristic
417#500—838no—
418#485—838no—
419#485—838no—
420#480—838no—
421#480—838no—
422#477—838no—
423#476—838no—
424#468—838no—
425#468—838no—
426C4×SD16—838no—
427#436—838no—
428#428—838no—
429#428C2×D8318yescomplemented
430C2×#107—831no—
431C2×#107—831no—
432C2×#107—831no—
433C2×#107—831no—
434C2×#107C2×D8311yescharacteristic
435C2×#107C2×D8311yescharacteristic
436C2×#106—831no—
437C2×#106C2×D8311yescharacteristic
438C2×#106C2×D8311yescharacteristic
439C2×C4⋊C8—831no—
440C2×#103—831no—
441C2×#103—831no—
442C2×#103—831no—
443C2×#102—831no—
444C2×#102—831no—
445C2×#102—831no—
446C2×C22⋊C8—831no—
447C2×C22⋊C8—831no—
448C2×C4×C8—831no—
449C22×Q8—831no—
450C22×Q8—1661no—
451C22×Q8—1661no—
452C22×D4—831no—
453C22×D4—831no—
454C22×D4—1661no—
455C22×D4—1661no—
456C23×C4—21no—
457C23×C4—831no—
458C23×C4—1661no—
459C23×C4—1661no—
460C23×C4C22×D8311yescharacteristic
461C2×SD16—834no—
462C2×SD16—1664no—
463C2×M16—24no—
464C2×M16—834no—
465C2×M16—1664no—
466C2×M16C22×D8314yes—
467C22×C8—831no—
468C22×C8—831no—
469C22×C8C22×D8311yescharacteristic
470C22×C8C22×D8311yescharacteristic
471C4⋊Q8—834no—
472C4⋊Q8—834no—
473C4⋊Q8—1662no—
474C4⋊Q8—1662no—
475#125—1668no—
476#124—1668no—
477#124—1668no—
478C22⋊Q8—834no—
479C22⋊Q8—834no—
480C22⋊Q8—1668no—
481C22⋊Q8—1668no—
482C22⋊Q8—1662no—
483C22⋊Q8—1662no—
484#121—834no—
485#121—834no—
486#121—1668no—
487#121—1662no—
488#121—1662no—
489C4×Q8—834no—
490C4×Q8—1662no—
491C4×D4—834no—
492C4×D4—834no—
493C4×D4—834no—
494C4×D4—1662no—
495C4×D4—1668no—
496#117—22no—
497#117—834no—
498#117—1668no—
499#117—1662no—
500#117C22×D8314yes—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—831no—
504C2×C4⋊C4—831no—
505C2×C4⋊C4—831no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—1662no—
508C2×C4⋊C4—1661no—
509C2×C4⋊C4—1661no—
510C2×C4⋊C4—1661no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4C22×D8311yescharacteristic
515C2×C4⋊C4C22×D8311yescharacteristic
516C2×C4⋊C4C22×D8314yes—
517C2×C4⋊C4C22×D8311yescharacteristic
518C2×C4⋊C4C22×D8311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—831no—
521C2×C22⋊C4—831no—
522C2×C22⋊C4—1661no—
523C2×C22⋊C4—1661no—
524C2×C22⋊C4—1661no—
525C2×C22⋊C4—1661no—
526C2×C22⋊C4—1661no—
527C2×C22⋊C4—1661no—
528C2×C42—21no—
529C2×C42—831no—
530C2×C42—1661no—
531C2×C42—1661no—
532#107—834no—
533#107—834no—
534#107—834no—
535#107—834no—
536#107C22×D8314yes—
537#107C22×D8314yes—
538#106—834no—
539#106C22×D8314yes—
540#106C22×D8314yes—
541C4⋊C8—834no—
542#103—834no—
543#103—834no—
544#103—834no—
545#102—834no—
546#102—834no—
547#102—834no—
548C22⋊C8—834no—
549C22⋊C8—834no—
550C4×C8—834no—
551C24—831no—
552C24—1661no—
553C24D4×D8311yescharacteristic
554C2×Q8—832no—
555C2×Q8—6642no—
556C2×Q8—6642no—
557C2×Q8—1664no—
558C2×Q8—1664no—
559C2×Q8—1662no—
560C2×Q8—1662no—
561C2×Q8—1661no—
562C2×D4—834no—
563C2×D4—832no—
564C2×D4—6642no—
565C2×D4—6642no—
566C2×D4—1664no—
567C2×D4—1664no—
568C2×D4—1664no—
569C2×D4—1661no—
570C2×D4—1662no—
571C2×D4—1662no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—3324no—
581C22×C4—831no—
582C22×C4—831no—
583C22×C4—831no—
584C22×C4—832no—
585C22×C4—832no—
586C22×C4—6642no—
587C22×C4—1664no—
588C22×C4—1664no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4D4×D8312yes—
595C22×C4D4×D8311yescharacteristic
596C22×C4C23×D8312yes—
597C22×C4C23×D8311yescharacteristic
598SD16—1668no—
599M16—28no—
600M16—1668no—
601C2×C8—22no—
602C2×C8—832no—
603C2×C8—832no—
604C2×C8—1662no—
605C2×C8—1662no—
606C2×C8#1305059014yes—
607C2×C8C23×D8312yes—
608C2×C8C23×D8312yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—834no—
615C4⋊C4—832no—
616C4⋊C4—832no—
617C4⋊C4—1664no—
618C4⋊C4—1664no—
619C4⋊C4—1664no—
620C4⋊C4—1664no—
621C4⋊C4—1664no—
622C4⋊C4—1661no—
623C4⋊C4—1661no—
624C4⋊C4—1664no—
625C4⋊C4C23×D8312yes—
626C4⋊C4C23×D8312yes—
627C4⋊C4C23×D8312yes—
628C4⋊C4C23×D8312yes—
629C22⋊C4—24no—
630C22⋊C4—834no—
631C22⋊C4—834no—
632C22⋊C4—1664no—
633C22⋊C4—1664no—
634C22⋊C4—1664no—
635C22⋊C4—1664no—
636C22⋊C4—1664no—
637C22⋊C4—1664no—
638C42—24no—
639C42—832no—
640C42—832no—
641C42—1664no—
642C42—1664no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—3322no—
647C23—3322no—
648C23—3322no—
649C23—832no—
650C23—1662no—
651C23—1662no—
652C23—1662no—
653C23—1662no—
654C23C2×D4×D8312yes—
655C23C2×D4×D8311yescharacteristic
656Q8—3322no—
657Q8—6644no—
658Q8—6644no—
659Q8—1662no—
660Q8—1662no—
661D4—3322no—
662D4—6644no—
663D4—6644no—
664D4—1668no—
665D4—1662no—
666D4—1662no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—3328no—
681C2×C4—3322no—
682C2×C4—3322no—
683C2×C4—3322no—
684C2×C4—834no—
685C2×C4—832no—
686C2×C4—832no—
687C2×C4—832no—
688C2×C4—6644no—
689C2×C4—1662no—
690C2×C4—1662no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1664no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4C2×D4×D8312yes—
698C2×C4C2×D4×D8311yescharacteristic
699C2×C4C2×#1305059012yes—
700C2×C4#1458184012yes—
701C2×C4C24×D8311yescharacteristic
702C8—22no—
703C8—1662no—
704C8—1662no—
705C8C2×#1305059014yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—3324no—
711C22—3322no—
712C22—3322no—
713C22—3322no—
714C22—6644no—
715C22—1662no—
716C22—1662no—
717C22—1662no—
718C22#1912835212yes—
719C22#137×D8312yes—
720C22#1912850512yes—
721C22C22×D4×D8311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—3322no—
728C4—3322no—
729C4—3322no—
730C4—834no—
731C4—1662no—
732C4—1662no—
733C4#1912835212yes—
734C4C22×#1305059011yescharacteristic
735C4C2×#1458184011yescharacteristic
736C2—42no—
737C2—3322no—
738C2—6642no—
739C2#2492008514yesdirect product factor
740C2C2×#1912835211yescharacteristic
741C2C2×#137×D8311yescharacteristic
742C2C2×#1912850511yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#428×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128414C2
hypercenterC2×#428D83
hypocenterC83C2×#3357
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#19128406C2semidirect
3. #24920085C2direct (N × H)
4. C2×#19128105C2semidirect
5. C2×#19128045C2semidirect
6. C2×#19128042C2semidirect
7. C2×#19128016C2semidirect
8. C2×#19128014C2semidirect
9. C2×#19127995C2semidirect
10. C2×#19127990C2semidirect
11. C2×#19127948C2semidirect
12. C2×#19127947C2semidirect
13. C2×#19127788C2semidirect
14. C2×#19127777C2semidirect
15. C2×#19127740C2semidirect
16. C2×#428×C83C2semidirect
22. #19128406C22semidirect
42. #19128105C22semidirect
43. #19128045C22semidirect
44. #19128042C22semidirect
45. #19128016C22semidirect
46. #19128014C22semidirect
47. #19127995C22semidirect
48. #19127990C22semidirect
49. #19127948C22semidirect
50. #19127947C22semidirect
51. #19127788C22semidirect
52. #19127777C22semidirect
53. #19127740C22semidirect
72. #428×C83C22semidirect
366. C2×C83#3357semidirect
387. C2×#428D83semidirect
388. C83C2×#3357semidirect
429. #428C2×D83semidirect
739. C2#24920085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284142
C2×#191284062
#249200852
C2×#191281052
C2×#191280452
C2×#191280422
C2×#191280162
C2×#191280142
C2×#191279952
C2×#191279902
C2×#191279482
C2×#191279472
C2×#191277882
C2×#191277772
C2×#191277402
C2×#428×C832
C2×#335783