Finite Group Databasebeta

← C2×#24919985 #36283022

Subgroups — C2×#24919985 #36283022

Order 21248.

1898 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×#19128417C211yesmaximal, characteristic
2C2×#19128392C211yesmaximal, characteristic, complemented
3#24919985C2116yesmaximal, direct product factor
4C2×#19128107C211yesmaximal, characteristic, complemented
5C2×#19128021C211yesmaximal, characteristic, complemented
6C2×#19128041C211yesmaximal, characteristic, complemented
7C2×#19128040C211yesmaximal, characteristic, complemented
8C2×#19128027C211yesmaximal, characteristic, complemented
9C2×#19128002C211yesmaximal, characteristic, complemented
10C2×#19127950C211yesmaximal, characteristic, complemented
11C2×#19127933C211yesmaximal, characteristic, complemented
12C2×#19127799C211yesmaximal, characteristic, complemented
13C2×#19127771C211yesmaximal, characteristic, complemented
14C2×#19127740C211yesmaximal, characteristic, complemented
15C2×#19127736C211yesmaximal, characteristic, complemented
16C2×#475×C83C211yesmaximal, characteristic, complemented
17C22×#13050577C2211yescharacteristic
18C22×#13050573C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20#19128417—24no—
21#19128417C2218yes—
22#19128392—24no—
23#19128392C2218yescomplemented
24C2×#14581786—21no—
25C2×#14581784C2211yescharacteristic
26C2×#14581782—21no—
27C2×#14581781—21no—
28C2×#14581781—21no—
29C2×#14581777—21no—
30C2×#14581768C2211yescharacteristic
31C2×#14581768C2211yescharacteristic
32C2×#14581767—21no—
33C2×#14581767C2211yescharacteristic
34C2×#14581767C2211yescharacteristic
35C2×C4×D332C2211yescharacteristic
36C2×C4×D332C2211yescharacteristic
37C2×#14581750—21no—
38C2×#14581750C2211yescharacteristic
39C2×#14581750C2211yescharacteristic
40C2×#14581750C2211yescharacteristic
41C2×#14581749—21no—
42C2×C4⋊C4×D83C2211yescharacteristic
43#19128107C2218yescomplemented
44#19128041C2218yescomplemented
45#19128040C2218yescomplemented
46#19128027C2218yescomplemented
47#19128021C2218yescomplemented
48#19128002C2218yescomplemented
49#19127950C2218yescomplemented
50#19127933C2218yescomplemented
51#19127799C2218yescomplemented
52#19127771C2218yescomplemented
53#19127740C2218yescomplemented
54#19127736C2218yescomplemented
55C2×#14581726C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58C2×#14581725C2211yescharacteristic
59C2×#14581724C2211yescharacteristic
60C2×#14581723C2211yescharacteristic
61C2×#14581723C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×(C2×D83)⋊C8C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×#14581703C2211yescharacteristic
69C2×C4⋊Q8×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71#475×C83C2218yescomplemented
72C2×#106×C83C2211yescharacteristic
73C2×#106×C83C2211yescharacteristic
74C2×C4⋊C8×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#103×C83C2211yescharacteristic
77C22×D332—21no—
78C22×D332—21no—
79C22×D332D411yescharacteristic
80C22×D332C2311yescharacteristic
81C22×C4×D83—21no—
82C22×C4×D83—21no—
83C22×C4×D83C2311yescharacteristic
84C22×C4×D83C2311yescharacteristic
85C2×#13050577—24no—
86C2×#13050577C2314yes—
87C2×#13050573—24no—
88C2×#13050573C2314yes—
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91C2×C8×D83—24no—
92C2×C8×D83C2314yes—
93#14581786—28no—
94#14581784—22no—
95#14581784C2314yes—
96#14581782—28no—
97#14581781—28no—
98#14581781—28no—
99#14581777—28no—
100#14581768—22no—
101#14581768—22no—
102#14581768C2314yes—
103#14581768C2314yes—
104#14581767—28no—
105#14581767—22no—
106#14581767—22no—
107#14581767C2314yes—
108#14581767C2314yes—
109C4×D332—22no—
110C4×D332D414yes—
111C4×D332C2314yes—
112C4×D332C2314yes—
113#14581750—22no—
114#14581750—22no—
115#14581750—22no—
116#14581750—28no—
117#14581750C2314yes—
118#14581750C2314yes—
119#14581750C2314yes—
120#14581749—28no—
121C2×C4⋊Dic83D411yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C4⋊C4×D83—22no—
131C4⋊C4×D83C2314yes—
132C2×(C2×D83)⋊C4—21no—
133C2×(C2×D83)⋊C4—21no—
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×(C2×D83)⋊C4D411yescharacteristic
142C2×C4×Dic83—21no—
143C2×C4×Dic83—21no—
144C2×C4×Dic83—21no—
145#14581726C2314yes—
146#14581725C2314yes—
147#14581725C2314yes—
148#14581725C2314yes—
149#14581724C2314yes—
150#14581723C2314yes—
151#14581723C2314yes—
152#14581716C2314yes—
153#14581714C2314yes—
154#14581714C2314yes—
155#14581712C2314yes—
156(C2×D83)⋊C8C2314yes—
157(C2×D83)⋊C8C2314yes—
158#14581703C2314yes—
159C22×Q8×C83—21no—
160C22×Q8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C4⋊Q8×C83—22no—
164C4⋊Q8×C83C2314yes—
165C4×Q8×C83—22no—
166C4×Q8×C83C2314yes—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C42×C83—21no—
173C2×C42×C83C2311yescharacteristic
174#106×C83C2314yes—
175#106×C83C2314yes—
176C4⋊C8×C83C2314yes—
177#103×C83C2314yes—
178#103×C83C2314yes—
179C23×D83—21no—
180C23×D83C2×D411yescharacteristic
181C23×D83C2×D411yescharacteristic
182C2×D332—22no—
183C2×D332—22no—
184C2×D332—21no—
185C2×D332—24no—
186C2×D332—24no—
187C2×D332—42no—
188C2×D332—82no—
189C2×D332—82no—
190C2×D332C2×D414yes—
191C2×D332C2412yes—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83C2×D411yescharacteristic
196C22×Dic83C2×D411yescharacteristic
197C2×C4×D83—22no—
198C2×C4×D83—22no—
199C2×C4×D83—22no—
200C2×C4×D83—22no—
201C2×C4×D83—24no—
202C2×C4×D83—24no—
203C2×C4×D83—44no—
204C2×C4×D83—44no—
205C2×C4×D83C2×D412yes—
206C2×C4×D83C2×D412yes—
207C2×C4×D83C2412yes—
208C2×C4×D83C2412yes—
209#13050577—28no—
210#13050573—28no—
211C2×C83⋊C8—22no—
212C2×C83⋊C8#4114yes—
213C2×C83⋊C8C2412yes—
214C2×C83⋊C8C2412yes—
215C8×D83—28no—
216C4⋊Dic83—21no—
217C4⋊Dic83—21no—
218C4⋊Dic83—21no—
219C4⋊Dic83C2×D414yes—
220C4⋊Dic83C2412yes—
221C4⋊Dic83C2412yes—
222C4⋊Dic83C2412yes—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊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)⋊C4—24no—
234(C2×D83)⋊C4—24no—
235(C2×D83)⋊C4—24no—
236(C2×D83)⋊C4C2×D414yes—
237(C2×D83)⋊C4C2×D414yes—
238C4×Dic83—24no—
239C4×Dic83—24no—
240C4×Dic83—24no—
241C2×Q8×C83—21no—
242C2×Q8×C83—24no—
243C2×Q8×C83—22no—
244C2×Q8×C83—22no—
245C2×Q8×C83—82no—
246C2×Q8×C83C2412yes—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2411yescharacteristic
254C2×C8×C83—22no—
255C2×C8×C83—22no—
256C2×C8×C83C2412yes—
257C2×C8×C83C2412yes—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83C2412yes—
264C4⋊C4×C83C2412yes—
265C4⋊C4×C83C2412yes—
266C42×C83—24no—
267C42×C83C2×D412yes—
268C42×C83C2412yes—
269C23×C83C22×D411yescharacteristic
270C22×D83—22no—
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—42no—
278C22×D83—42no—
279C22×D83—42no—
280C22×D83C22×D412yes—
281C22×D83C22×D412yes—
282Q8×C83—22no—
283Q8×C83—22no—
284Q8×C83—42no—
285Q8×C83—84no—
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×C83C22×D412yes—
297C2×C4×C83C22×D412yes—
298C2×C4×C83C22×D411yescharacteristic
299C2×C4×C83C2×#4112yes—
300C2×C4×C832−1+412yes—
301C2×C4×C83C2511yescharacteristic
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—42no—
308C2×Dic83—42no—
309C2×Dic83—42no—
310C2×Dic83C22×D412yes—
311C2×Dic83C22×D412yes—
312D332—22no—
313D332—22no—
314D332—44no—
315D332—42no—
316D332—84no—
317D332—84no—
318C4×D83—24no—
319C4×D83—24no—
320C4×D83—22no—
321C4×D83—22no—
322C4×D83—22no—
323C4×D83—22no—
324C4×D83—48no—
325C4×D83—48no—
326C8×C83—22no—
327C8×C83—22no—
328C83⋊C8—22no—
329C83⋊C8C2×#4114yes—
330C22×C83#54712yes—
331C22×C83#57512yes—
332C22×C83#57712yes—
333C22×C83C23×D411yescharacteristic
334C2×D83—22no—
335C2×D83—22no—
336C2×D83—22no—
337C2×D83—22no—
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—44no—
341C2×D83—44no—
342C2×D83—42no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—84no—
346C4×C83—22no—
347C4×C83—22no—
348C4×C83—42no—
349C4×C83—42no—
350C4×C83—42no—
351C4×C83—42no—
352C4×C83#54712yes—
353C4×C83C22×#4111yescharacteristic
354C4×C83C2×2−1+411yescharacteristic
355Dic83—22no—
356Dic83—22no—
357Dic83—42no—
358Dic83—42no—
359Dic83—42no—
360C2×#3348—831nomaximal, Sylow
361C2×C83#334814yescomplemented
362C2×C83C2×#54711yescharacteristic
363C2×C83C2×#57511yescharacteristic
364C2×C83C2×#57711yescharacteristic
365D83—42no—
366D83—42no—
367D83—82no—
368C2×#555—831no—
369C2×#552—831no—
370#3348—8316no—
371C2×#501—831no—
372C2×#481—831no—
373C2×#485—831no—
374C2×#485—831no—
375C2×#482—831no—
376C2×#475D8311yescharacteristic, complemented
377C2×#478—831no—
378C2×#468—831no—
379C2×#465—831no—
380C2×#440—831no—
381C2×#435—831no—
382C2×#428—831no—
383C2×#427—831no—
384C83C2×#334811yescharacteristic, complemented, Sylow
385C22×SD16—831no—
386C22×M16—831no—
387C23×C8—831no—
388#555—838no—
389#555—1664no—
390#552—838no—
391#552—1664no—
392C2×C4⋊Q8C2×D8311yescharacteristic
393C2×#126—1661no—
394C2×#125—831no—
395C2×#125—1661no—
396C2×#124—1661no—
397C2×#124—1661no—
398C2×#123—1661no—
399C2×C22⋊Q8—831no—
400C2×C22⋊Q8—831no—
401C2×#121—831no—
402C2×#121—831no—
403C2×#121—1661no—
404C2×C4×Q8C2×D8311yescharacteristic
405C2×C4×D4—831no—
406C2×C4×D4—831no—
407C2×#117—831no—
408C2×#117—831no—
409C2×#117—831no—
410C2×#117—1661no—
411C2×#117—1661no—
412C22×C4⋊C4—831no—
413#501—838no—
414#485—838no—
415#485—838no—
416#482—838no—
417#481—838no—
418#478—838no—
419#475C2×D8318yescomplemented
420#468—838no—
421#465—838no—
422#440—838no—
423#435—838no—
424#428—838no—
425#427—838no—
426C2×#107—831no—
427C2×#107—831no—
428C2×#107—831no—
429C2×#107—831no—
430C2×#106—831no—
431C2×#106—831no—
432C2×#106—831no—
433C2×#106C2×D8311yescharacteristic
434C2×#106C2×D8311yescharacteristic
435C2×C4⋊C8C2×D8311yescharacteristic
436C2×#103—831no—
437C2×#103C2×D8311yescharacteristic
438C2×#103C2×D8311yescharacteristic
439C2×#102—831no—
440C2×#102—831no—
441C2×#102—831no—
442C2×C22⋊C8—831no—
443C2×C22⋊C8—831no—
444C2×#97—831no—
445C22×Q8—21no—
446C22×Q8C22×D8311yescharacteristic
447C22×D4—831no—
448C22×D4—831no—
449C22×D4—1661no—
450C22×D4—1661no—
451C23×C4—831no—
452C23×C4—831no—
453C23×C4—1661no—
454C23×C4—1661no—
455C2×SD16—834no—
456C2×SD16—1664no—
457C2×M16—834no—
458C2×M16—1664no—
459C22×C8—831no—
460C22×C8—831no—
461C22×C8—834no—
462C22×C8—1664no—
463C22×C8C22×D8311yescharacteristic
464C22×C8C22×D8311yescharacteristic
465C4⋊Q8—22no—
466C4⋊Q8C22×D8314yes—
467#126—1668no—
468#125—834no—
469#125—1668no—
470#125—1662no—
471#124—1668no—
472#124—1668no—
473#123—1668no—
474C22⋊Q8—834no—
475C22⋊Q8—834no—
476C22⋊Q8—1662no—
477C22⋊Q8—1662no—
478#121—834no—
479#121—834no—
480#121—1662no—
481#121—1662no—
482#121—1668no—
483C4×Q8—22no—
484C4×Q8C22×D8314yes—
485C4×D4—834no—
486C4×D4—834no—
487C4×D4—834no—
488C4×D4—1662no—
489#117—834no—
490#117—834no—
491#117—834no—
492#117—1668no—
493#117—1668no—
494#117—1662no—
495#117—1662no—
496#117—1662no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—831no—
500C2×C4⋊C4—831no—
501C2×C4⋊C4—831no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—1662no—
505C2×C4⋊C4—1661no—
506C2×C4⋊C4—1661no—
507C2×C4⋊C4—1661no—
508C2×C4⋊C4—1661no—
509C2×C4⋊C4—1661no—
510C2×C4⋊C4C22×D8311yescharacteristic
511C2×C4⋊C4C22×D8311yescharacteristic
512C2×C4⋊C4C22×D8311yescharacteristic
513C2×C22⋊C4—831no—
514C2×C22⋊C4—831no—
515C2×C22⋊C4—1661no—
516C2×C22⋊C4—1661no—
517C2×C22⋊C4—1661no—
518C2×C22⋊C4—1661no—
519C2×C22⋊C4—1661no—
520C2×C22⋊C4—1661no—
521C2×C22⋊C4—1661no—
522C2×C22⋊C4—1661no—
523C2×C42—21no—
524C2×C42—1661no—
525C2×C42—1661no—
526C2×C42—1661no—
527C2×C42C22×D8311yescharacteristic
528#107—834no—
529#107—834no—
530#107—834no—
531#107—834no—
532#106—834no—
533#106—834no—
534#106—834no—
535#106C22×D8314yes—
536#106C22×D8314yes—
537C4⋊C8C22×D8314yes—
538#103—834no—
539#103C22×D8314yes—
540#103C22×D8314yes—
541#102—834no—
542#102—834no—
543#102—834no—
544C22⋊C8—834no—
545C22⋊C8—834no—
546#97—834no—
547C24—831no—
548C24—831no—
549C24—1661no—
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—82no—
555C2×Q8C23×D8312yes—
556C2×D4—3322no—
557C2×D4—834no—
558C2×D4—832no—
559C2×D4—6642no—
560C2×D4—6642no—
561C2×D4—1664no—
562C2×D4—1664no—
563C2×D4—1661no—
564C2×D4—1662no—
565C2×D4—1662no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—3324no—
571C22×C4—3324no—
572C22×C4—831no—
573C22×C4—831no—
574C22×C4—832no—
575C22×C4—832no—
576C22×C4—832no—
577C22×C4—832no—
578C22×C4—1664no—
579C22×C4—1661no—
580C22×C4—1661no—
581C22×C4—1661no—
582C22×C4—1664no—
583C22×C4—1662no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4—1662no—
587C22×C4D4×D8311yescharacteristic
588C22×C4D4×D8311yescharacteristic
589C22×C4C23×D8311yescharacteristic
590SD16—1668no—
591M16—1668no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—834no—
595C2×C8—832no—
596C2×C8—832no—
597C2×C8—1668no—
598C2×C8—1662no—
599C2×C8C23×D8312yes—
600C2×C8C23×D8312yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
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—1661no—
614C4⋊C4—1661no—
615C4⋊C4—1661no—
616C4⋊C4—1664no—
617C4⋊C4—1664no—
618C4⋊C4C23×D8312yes—
619C4⋊C4C23×D8312yes—
620C4⋊C4C23×D8312yes—
621C22⋊C4—834no—
622C22⋊C4—834no—
623C22⋊C4—1664no—
624C22⋊C4—1664no—
625C22⋊C4—1664no—
626C22⋊C4—1664no—
627C22⋊C4—1664no—
628C22⋊C4—1664no—
629C22⋊C4—1664no—
630C22⋊C4—1664no—
631C42—24no—
632C42—1664no—
633C42—1664no—
634C42—1664no—
635C42D4×D8312yes—
636C42C23×D8312yes—
637C23—3322no—
638C23—3322no—
639C23—3322no—
640C23—832no—
641C23—832no—
642C23—1662no—
643C23—1662no—
644C23—1662no—
645C23—1662no—
646C23—1662no—
647C23—1662no—
648C23—1662no—
649C23C2×D4×D8311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654D4—3324no—
655D4—3322no—
656D4—6644no—
657D4—6644no—
658D4—1662no—
659D4—1662no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—3328no—
671C2×C4—3328no—
672C2×C4—3322no—
673C2×C4—3322no—
674C2×C4—3322no—
675C2×C4—832no—
676C2×C4—832no—
677C2×C4—1662no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—1664no—
683C2×C4—1664no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4—1662no—
687C2×C4—1662no—
688C2×C4C2×D4×D8312yes—
689C2×C4C2×D4×D8312yes—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4#41×D8312yes—
692C2×C4#1458184012yes—
693C2×C4C24×D8311yescharacteristic
694C8—22no—
695C8—22no—
696C8—834no—
697C8—1662no—
698C22—3324no—
699C22—3324no—
700C22—3322no—
701C22—3322no—
702C22—3322no—
703C22—6644no—
704C22—1662no—
705C22—1662no—
706C22—1662no—
707C22—1662no—
708C22—1662no—
709C22—1662no—
710C22#1912835312yes—
711C22#1912850012yes—
712C22#1912850712yes—
713C22C22×D4×D8311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—3322no—
721C4—3322no—
722C4—3322no—
723C4—1662no—
724C4—1662no—
725C4#1912835312yes—
726C4C2×#41×D8311yescharacteristic
727C4C2×#1458184011yescharacteristic
728C2—3322no—
729C2—3322no—
730C2—6642no—
731C2#2491998514yesdirect product factor
732C2C2×#1912835311yescharacteristic
733C2C2×#1912850011yescharacteristic
734C2C2×#1912850711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#475×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128417C2
hypercenterC2×#475D83
hypocenterC83C2×#3348
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#19128392C2semidirect
3. #24919985C2direct (N × H)
4. C2×#19128107C2semidirect
5. C2×#19128021C2semidirect
6. C2×#19128041C2semidirect
7. C2×#19128040C2semidirect
8. C2×#19128027C2semidirect
9. C2×#19128002C2semidirect
10. C2×#19127950C2semidirect
11. C2×#19127933C2semidirect
12. C2×#19127799C2semidirect
13. C2×#19127771C2semidirect
14. C2×#19127740C2semidirect
15. C2×#19127736C2semidirect
16. C2×#475×C83C2semidirect
23. #19128392C22semidirect
43. #19128107C22semidirect
44. #19128041C22semidirect
45. #19128040C22semidirect
46. #19128027C22semidirect
47. #19128021C22semidirect
48. #19128002C22semidirect
49. #19127950C22semidirect
50. #19127933C22semidirect
51. #19127799C22semidirect
52. #19127771C22semidirect
53. #19127740C22semidirect
54. #19127736C22semidirect
71. #475×C83C22semidirect
361. C2×C83#3348semidirect
376. C2×#475D83semidirect
384. C83C2×#3348semidirect
419. #475C2×D83semidirect
731. C2#24919985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284172
C2×#191283922
#249199852
C2×#191281072
C2×#191280212
C2×#191280412
C2×#191280402
C2×#191280272
C2×#191280022
C2×#191279502
C2×#191279332
C2×#191277992
C2×#191277712
C2×#191277402
C2×#191277362
C2×#475×C832
C2×#334883