Finite Group Databasebeta

← C2×#24920218 #36284155

Subgroups — C2×#24920218 #36284155

Order 21248.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128436C211yesmaximal, characteristic, complemented
2C2×#19128411C211yesmaximal, characteristic, complemented
3#24920218C2116yesmaximal, direct product factor
4C2×#19128066C211yesmaximal, characteristic, complemented
5C2×#19128061C211yesmaximal, characteristic, complemented
6C2×#19128056C211yesmaximal, characteristic, complemented
7C2×#19128009C211yesmaximal, characteristic, complemented
8C2×#19128002C211yesmaximal, characteristic, complemented
9C2×#19127982C211yesmaximal, characteristic, complemented
10C2×#19127917C211yesmaximal, characteristic, complemented
11C2×#19127917C211yesmaximal, characteristic, complemented
12C2×#19127897C211yesmaximal, characteristic
13C2×#19127814C211yesmaximal, characteristic, complemented
14C2×#19127803C211yesmaximal, characteristic, complemented
15C2×C4×D664C211yesmaximal, characteristic, complemented
16C2×#446×C83C211yesmaximal, characteristic, complemented
17C22×#13050579C2211yescharacteristic
18C22×D664C2211yescharacteristic
19C22×D664C2211yescharacteristic
20#19128436—24no—
21#19128436C2218yescomplemented
22#19128411—24no—
23#19128411C2218yescomplemented
24C2×#14581792C2211yescharacteristic
25C2×#14581789C2211yescharacteristic
26C2×#14581784C2211yescharacteristic
27C2×#14581784C2211yescharacteristic
28C2×#14581781—21no—
29C2×#14581780C2211yescharacteristic
30C2×#14581780C2211yescharacteristic
31C2×#14581777—21no—
32C2×#14581777—21no—
33C2×#14581770—21no—
34C2×#14581770—21no—
35C2×#14581768—21no—
36C2×C4×Dic166C2211yescharacteristic
37C2×C4×D332C2211yescharacteristic
38C2×C4×D332C2211yescharacteristic
39C2×C4×D332C2211yescharacteristic
40C2×C4×D332C2211yescharacteristic
41C2×C4×D332C2211yescharacteristic
42C2×#14581754—21no—
43C2×C4⋊C4×D83—21no—
44#19128066C2218yescomplemented
45#19128061C2218yescomplemented
46#19128056C2218yescomplemented
47#19128009C2218yescomplemented
48#19128002C2218yescomplemented
49#19127982C2218yescomplemented
50#19127917C2218yescomplemented
51#19127917C2218yescomplemented
52#19127897C2218yes—
53#19127814C2218yescomplemented
54#19127803C2218yescomplemented
55C4×D664C2218yescomplemented
56C2×#14581726C2211yescharacteristic
57C2×#14581726C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581717C2211yescharacteristic
60C2×#14581717C2211yescharacteristic
61C2×#14581717C2211yescharacteristic
62C2×#14581714C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic
68C2×#14581714C2211yescharacteristic
69C2×C4×Q8×C83C2211yescharacteristic
70#446×C83C2218yescomplemented
71C2×C4⋊C8×C83C2211yescharacteristic
72C2×C4⋊C8×C83C2211yescharacteristic
73C2×C4⋊C8×C83C2211yescharacteristic
74C2×#97×C83C2211yescharacteristic
75C2×#97×C83C2211yescharacteristic
76C2×C4×C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×D332—21no—
80C22×D332—21no—
81C22×D332C2311yescharacteristic
82C22×D332C2311yescharacteristic
83C22×D332C2311yescharacteristic
84C22×C4×D83—21no—
85C22×C4×D83—21no—
86C22×C4×D83—21no—
87C22×C4×D83—21no—
88C22×C4×D83—21no—
89C2×#13050579—24no—
90C2×#13050579C2314yes—
91C2×D664—24no—
92C2×D664—24no—
93C2×D664C2314yes—
94C2×D664C2314yes—
95#14581792—22no—
96#14581792C2314yes—
97#14581789—22no—
98#14581789C2314yes—
99#14581784—22no—
100#14581784—22no—
101#14581784C2314yes—
102#14581784C2314yes—
103#14581781—28no—
104#14581780—22no—
105#14581780—22no—
106#14581780C2314yes—
107#14581780C2314yes—
108#14581777—28no—
109#14581777—28no—
110#14581770—28no—
111#14581770—28no—
112#14581768—28no—
113C4×Dic166—22no—
114C4×Dic166C2314yes—
115C4×D332—22no—
116C4×D332—22no—
117C4×D332—22no—
118C4×D332—22no—
119C4×D332—22no—
120C4×D332C2314yes—
121C4×D332C2314yes—
122C4×D332C2314yes—
123C4×D332C2314yes—
124C4×D332C2314yes—
125#14581754—28no—
126C2×C4⋊Dic83—21no—
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×C4⋊Dic83C2311yescharacteristic
130C2×C4⋊Dic83C2311yescharacteristic
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C4⋊C4×D83—28no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×C4×Dic83—21no—
147#14581726C2314yes—
148#14581726C2314yes—
149#14581724C2314yes—
150#14581717C2314yes—
151#14581717C2314yes—
152#14581717C2314yes—
153#14581714C2314yes—
154#14581714C2314yes—
155#14581714C2314yes—
156#14581714C2314yes—
157#14581714C2314yes—
158#14581714C2314yes—
159#14581714C2314yes—
160C22×Q8×C83D411yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164C22×C8×C83C2311yescharacteristic
165C4×Q8×C83D414yes—
166C4×Q8×C83C2314yes—
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83D411yescharacteristic
170C2×C42×C83C2311yescharacteristic
171C2×C42×C83C2311yescharacteristic
172C2×C42×C83C2311yescharacteristic
173C4⋊C8×C83C2314yes—
174C4⋊C8×C83C2314yes—
175C4⋊C8×C83C2314yes—
176#97×C83C2314yes—
177#97×C83C2314yes—
178C4×C8×C83C2314yes—
179C23×D83—21no—
180C23×D83—21no—
181C23×D83—21no—
182C2×Dic166—22no—
183C2×Dic166—22no—
184C2×Dic166—21no—
185C2×Dic166—24no—
186C2×Dic166—82no—
187C2×Dic166C2412yes—
188C2×D332—21no—
189C2×D332—22no—
190C2×D332—22no—
191C2×D332—22no—
192C2×D332—22no—
193C2×D332—22no—
194C2×D332—21no—
195C2×D332—21no—
196C2×D332—24no—
197C2×D332—24no—
198C2×D332—44no—
199C2×D332—82no—
200C2×D332#4114yes—
201C2×D332C2412yes—
202C2×D332C2412yes—
203C2×D332C2412yes—
204C22×Dic83—21no—
205C22×Dic83—21no—
206C22×Dic83—21no—
207C22×Dic83—21no—
208C22×Dic83—21no—
209C2×C4×D83—24no—
210C2×C4×D83—24no—
211C2×C4×D83—24no—
212C2×C4×D83—24no—
213C2×C4×D83—24no—
214C2×C4×D83—44no—
215C2×C4×D83—82no—
216C2×C4×D83—82no—
217C2×C4×D83—82no—
218C2×C4×D83—82no—
219#13050579—28no—
220D664—28no—
221D664—28no—
222C4⋊Dic83—24no—
223C4⋊Dic83—21no—
224C4⋊Dic83—21no—
225C4⋊Dic83—21no—
226C4⋊Dic83—21no—
227C4⋊Dic83C2412yes—
228C4⋊Dic83C2412yes—
229C4⋊Dic83C2412yes—
230C4⋊Dic83C2412yes—
231Dic83⋊C4—24no—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234Dic83⋊C4—24no—
235Dic83⋊C4—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4—24no—
238(C2×D83)⋊C4—24no—
239(C2×D83)⋊C4—24no—
240(C2×D83)⋊C4—24no—
241(C2×D83)⋊C4—24no—
242(C2×D83)⋊C4—24no—
243(C2×D83)⋊C4—24no—
244(C2×D83)⋊C4—24no—
245C4×Dic83—24no—
246C2×Q8×C83—42no—
247C2×Q8×C83C2×D414yes—
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2411yescharacteristic
255C2×C8×C83—22no—
256C2×C8×C83—22no—
257C2×C8×C83—22no—
258C2×C8×C83—22no—
259C2×C8×C83C2412yes—
260C2×C8×C83C2412yes—
261C2×C8×C83C2412yes—
262C2×C8×C83C2412yes—
263C4⋊C4×C83C2×D414yes—
264C4⋊C4×C83C2×D414yes—
265C4⋊C4×C83C2×D414yes—
266C42×C83C2×D412yes—
267C42×C83C2×D412yes—
268C42×C83C2×D412yes—
269C42×C83C2412yes—
270C42×C83C2412yes—
271C42×C83C2412yes—
272C23×C83C22×D411yescharacteristic
273C22×D83—24no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—42no—
278C22×D83—42no—
279C22×D83—42no—
280C22×D83—42no—
281C22×D83—42no—
282C22×D83—42no—
283C22×D83—42no—
284C22×D83—42no—
285Q8×C83—44no—
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×C83C22×D412yes—
293C2×C4×C83C22×D412yes—
294C2×C4×C83C22×D412yes—
295C2×C4×C83C22×D412yes—
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×Dic83—42no—
311C2×Dic83—42no—
312D332—24no—
313D332—22no—
314D332—22no—
315D332—22no—
316D332—22no—
317D332—22no—
318D332—48no—
319D332—42no—
320D332—42no—
321D332—84no—
322D332C2×#4114yes—
323C4×D83—48no—
324C4×D83—84no—
325C4×D83—84no—
326C4×D83—84no—
327C4×D83—84no—
328Dic166—22no—
329Dic166—22no—
330Dic166—42no—
331Dic166—84no—
332C8×C83—22no—
333C8×C83—22no—
334C8×C83—22no—
335C8×C83—22no—
336C22×C83#54812yes—
337C22×C83#57512yes—
338C22×C83#57612yes—
339C22×C83C23×D411yescharacteristic
340C2×D83—24no—
341C2×D83—48no—
342C2×D83—42no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—42no—
346C2×D83—42no—
347C2×D83—42no—
348C2×D83—42no—
349C2×D83—42no—
350C2×D83—84no—
351C2×D83—84no—
352C4×C83—22no—
353C4×C83—22no—
354C4×C83—22no—
355C4×C83—22no—
356C4×C83—22no—
357C4×C83—22no—
358C4×C83#54812yes—
359C4×C83C22×#4111yescharacteristic
360C4×C83C2×2−1+411yescharacteristic
361Dic83—42no—
362Dic83—42no—
363Dic83—42no—
364Dic83—42no—
365Dic83—42no—
366C2×#3370—831nomaximal, Sylow
367C2×C83#337014yescomplemented
368C2×C83C2×#54811yescharacteristic
369C2×C83C2×#57511yescharacteristic
370C2×C83C2×#57611yescharacteristic
371D83—44no—
372D83—82no—
373D83—82no—
374C2×#559—831no—
375C2×#554—831no—
376#3370—8316no—
377C2×#490—831no—
378C2×#489—831no—
379C2×#488—831no—
380C2×#479—831no—
381C2×#478—831no—
382C2×#474—831no—
383C2×#463—831no—
384C2×#463—831no—
385C2×#459—831no—
386C2×#446D8311yescharacteristic, complemented
387C2×#442—831no—
388C2×#440—831no—
389C2×C4×D8—831no—
390C83C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—831no—
392C22×D8—831no—
393C22×D8—831no—
394#559—838no—
395#559—1664no—
396#554—838no—
397#554—1664no—
398C2×C4⋊Q8—831no—
399C2×#127—831no—
400C2×#125—831no—
401C2×#125—831no—
402C2×#124—831no—
403C2×#124—831no—
404C2×#124—1661no—
405C2×#123—1661no—
406C2×#123—1661no—
407C2×C22⋊Q8—1661no—
408C2×C22⋊Q8—1661no—
409C2×C22⋊Q8—1661no—
410C2×C4×Q8—831no—
411C2×C4×Q8C2×D8311yescharacteristic
412C2×C4×D4—831no—
413C2×C4×D4—831no—
414C2×C4×D4—831no—
415C2×C4×D4—831no—
416C2×C4×D4—831no—
417C2×C4×D4—1661no—
418C22×C4⋊C4—1661no—
419#490—838no—
420#489—838no—
421#488—838no—
422#479—838no—
423#478—838no—
424#474—838no—
425#463—838no—
426#463—838no—
427#459—838no—
428#446C2×D8318yescomplemented
429#442—838no—
430#440—838no—
431C4×D8—838no—
432C2×#107—831no—
433C2×#107—831no—
434C2×#106—831no—
435C2×C4⋊C8C2×D8311yescharacteristic
436C2×C4⋊C8C2×D8311yescharacteristic
437C2×C4⋊C8C2×D8311yescharacteristic
438C2×#103—831no—
439C2×#103—831no—
440C2×#103—831no—
441C2×#102—831no—
442C2×#102—831no—
443C2×#102—831no—
444C2×#102—831no—
445C2×#102—831no—
446C2×#102—831no—
447C2×#102—831no—
448C2×#97C2×D8311yescharacteristic
449C2×#97C2×D8311yescharacteristic
450C2×C4×C8C2×D8311yescharacteristic
451C22×Q8—831no—
452C22×Q8—1661no—
453C22×Q8D33211yescharacteristic
454C22×D4—831no—
455C22×D4—831no—
456C22×D4—831no—
457C22×D4—1661no—
458C22×D4—1661no—
459C23×C4—1661no—
460C23×C4—1661no—
461C23×C4—1661no—
462C23×C4—1661no—
463C23×C4—1661no—
464C2×SD16—834no—
465C2×SD16—1664no—
466C2×D8—834no—
467C2×D8—834no—
468C2×D8—1664no—
469C2×D8—1664no—
470C22×C8C22×D8311yescharacteristic
471C22×C8C22×D8311yescharacteristic
472C22×C8C22×D8311yescharacteristic
473C22×C8C22×D8311yescharacteristic
474C4⋊Q8—834no—
475C4⋊Q8—1662no—
476#127—834no—
477#127—1662no—
478#125—834no—
479#125—834no—
480#125—1662no—
481#125—1662no—
482#124—834no—
483#124—834no—
484#124—1668no—
485#124—1662no—
486#124—1662no—
487#123—1668no—
488#123—1668no—
489C22⋊Q8—1668no—
490C22⋊Q8—1668no—
491C22⋊Q8—1668no—
492C4×Q8—834no—
493C4×Q8—1662no—
494C4×Q8D33214yes—
495C4×Q8C22×D8314yes—
496C4×D4—834no—
497C4×D4—834no—
498C4×D4—834no—
499C4×D4—834no—
500C4×D4—834no—
501C4×D4—1668no—
502C4×D4—1662no—
503C4×D4—1662no—
504C4×D4—1662no—
505C4×D4—1662no—
506C4×D4—1662no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—831no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1661no—
517C2×C4⋊C4—1668no—
518C2×C4⋊C4D33211yescharacteristic
519C2×C4⋊C4D33211yescharacteristic
520C2×C4⋊C4D33211yescharacteristic
521C2×C22⋊C4—1661no—
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×C22⋊C4—1661no—
529C2×C22⋊C4—1661no—
530C2×C42—1661no—
531C2×C42C22×D8311yescharacteristic
532C2×C42C22×D8311yescharacteristic
533C2×C42C22×D8311yescharacteristic
534#107—834no—
535#107—834no—
536#106—834no—
537C4⋊C8C22×D8314yes—
538C4⋊C8C22×D8314yes—
539C4⋊C8C22×D8314yes—
540#103—834no—
541#103—834no—
542#103—834no—
543#102—834no—
544#102—834no—
545#102—834no—
546#102—834no—
547#102—834no—
548#102—834no—
549#102—834no—
550#97C22×D8314yes—
551#97C22×D8314yes—
552C4×C8C22×D8314yes—
553C24—1661no—
554C24—1661no—
555C24—1661no—
556C2×Q8—42no—
557C2×Q8—832no—
558C2×Q8—6642no—
559C2×Q8—1662no—
560C2×Q8—1662no—
561C2×Q8—1661no—
562C2×Q8—1664no—
563C2×Q8C2×D33214yes—
564C2×D4—3324no—
565C2×D4—834no—
566C2×D4—832no—
567C2×D4—832no—
568C2×D4—832no—
569C2×D4—6642no—
570C2×D4—1664no—
571C2×D4—1661no—
572C2×D4—1661no—
573C2×D4—1664no—
574C2×D4—1661no—
575C2×D4—1662no—
576C2×D4—1662no—
577C2×D4—1662no—
578C2×D4—1662no—
579C2×D4—1662no—
580C22×C4—3324no—
581C22×C4—6642no—
582C22×C4—6642no—
583C22×C4—6642no—
584C22×C4—6642no—
585C22×C4—1661no—
586C22×C4—1661no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1664no—
591C22×C4—1664no—
592C22×C4—1664no—
593C22×C4—1664no—
594C22×C4—1664no—
595C22×C4C2×D33211yescharacteristic
596C22×C4C2×D33211yescharacteristic
597C22×C4C2×D33211yescharacteristic
598C22×C4C2×D33211yescharacteristic
599C22×C4C2×D33211yescharacteristic
600C22×C4C2×D33211yescharacteristic
601C22×C4C23×D8311yescharacteristic
602SD16—1668no—
603D8—1668no—
604D8—1668no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C23×D8312yes—
610C2×C8C23×D8312yes—
611C2×C8C23×D8312yes—
612C2×C8C23×D8312yes—
613C4⋊C4—832no—
614C4⋊C4—832no—
615C4⋊C4—832no—
616C4⋊C4—832no—
617C4⋊C4—1661no—
618C4⋊C4—1661no—
619C4⋊C4—1661no—
620C4⋊C4—1661no—
621C4⋊C4—1664no—
622C4⋊C4—1664no—
623C4⋊C4—1664no—
624C4⋊C4—1664no—
625C4⋊C4—1664no—
626C4⋊C4—1664no—
627C4⋊C4C2×D33214yes—
628C4⋊C4C2×D33214yes—
629C4⋊C4C2×D33214yes—
630C22⋊C4—1664no—
631C22⋊C4—1664no—
632C22⋊C4—1664no—
633C22⋊C4—1664no—
634C22⋊C4—1664no—
635C22⋊C4—1664no—
636C22⋊C4—1664no—
637C22⋊C4—1664no—
638C22⋊C4—1664no—
639C42—1664no—
640C42C2×D33212yes—
641C42C2×D33212yes—
642C42C2×D33212yes—
643C42C23×D8312yes—
644C42C23×D8312yes—
645C42C23×D8312yes—
646C23—3322no—
647C23—3322no—
648C23—3322no—
649C23—3322no—
650C23—3322no—
651C23—3322no—
652C23—3322no—
653C23—3322no—
654C23—1662no—
655C23—1662no—
656C23—1664no—
657C23—1662no—
658C23C22×D33211yescharacteristic
659Q8—44no—
660Q8—3322no—
661Q8—6644no—
662Q8—1662no—
663Q8—1662no—
664D4—3328no—
665D4—3322no—
666D4—3322no—
667D4—834no—
668D4—6644no—
669D4—1664no—
670D4—1662no—
671D4—1662no—
672D4—1662no—
673D4—1662no—
674D4—1662no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—3328no—
682C2×C4—3322no—
683C2×C4—3322no—
684C2×C4—3322no—
685C2×C4—3322no—
686C2×C4—3322no—
687C2×C4—6644no—
688C2×C4—6644no—
689C2×C4—6644no—
690C2×C4—6644no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4C22×D33212yes—
697C2×C4C22×D33212yes—
698C2×C4C22×D33212yes—
699C2×C4C22×D33212yes—
700C2×C4C22×D33212yes—
701C2×C4C22×D33212yes—
702C2×C4C22×D33211yescharacteristic
703C2×C4#41×D8312yes—
704C2×C4#1458184012yes—
705C2×C4C24×D8311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—3322no—
711C22—3322no—
712C22—3328no—
713C22—3322no—
714C22—3322no—
715C22—3322no—
716C22—3322no—
717C22—3322no—
718C22—3322no—
719C22—6644no—
720C22—6644no—
721C22—1664no—
722C22#1912836312yes—
723C22#1912850112yes—
724C22#1912850612yes—
725C22C23×D33211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—3322no—
733C4—3322no—
734C4—3322no—
735C4—3322no—
736C4—3322no—
737C4#1912836312yes—
738C4C2×#41×D8311yescharacteristic
739C4C2×#1458184011yescharacteristic
740C2—3324no—
741C2—6642no—
742C2—6642no—
743C2#2492021814yesdirect product factor
744C2C2×#1912836311yescharacteristic
745C2C2×#1912850111yescharacteristic
746C2C2×#1912850611yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#446×C83C2
socleC23×C83C22×D4
prime radicalC2×#19127897C2
hypercenterC2×#446D83
hypocenterC83C2×#3370
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#19128436C2semidirect
2. C2×#19128411C2semidirect
3. #24920218C2direct (N × H)
4. C2×#19128066C2semidirect
5. C2×#19128061C2semidirect
6. C2×#19128056C2semidirect
7. C2×#19128009C2semidirect
8. C2×#19128002C2semidirect
9. C2×#19127982C2semidirect
10. C2×#19127917C2semidirect
11. C2×#19127917C2semidirect
13. C2×#19127814C2semidirect
14. C2×#19127803C2semidirect
15. C2×C4×D664C2semidirect
16. C2×#446×C83C2semidirect
21. #19128436C22semidirect
23. #19128411C22semidirect
44. #19128066C22semidirect
45. #19128061C22semidirect
46. #19128056C22semidirect
47. #19128009C22semidirect
48. #19128002C22semidirect
49. #19127982C22semidirect
50. #19127917C22semidirect
51. #19127917C22semidirect
53. #19127814C22semidirect
54. #19127803C22semidirect
55. C4×D664C22semidirect
70. #446×C83C22semidirect
367. C2×C83#3370semidirect
386. C2×#446D83semidirect
390. C83C2×#3370semidirect
428. #446C2×D83semidirect
743. C2#24920218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284362
C2×#191284112
#249202182
C2×#191280662
C2×#191280612
C2×#191280562
C2×#191280092
C2×#191280022
C2×#191279822
C2×#191279172
C2×#191278972
C2×#191278142
C2×#191278032
C2×C4×D6642
C2×#446×C832
C2×#337083