Finite Group Databasebeta

← C2×#24920387 #36284908

Subgroups — C2×#24920387 #36284908

Order 21248.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128427C211yesmaximal, characteristic, complemented
2C2×#19128366C211yesmaximal, characteristic
3#24920387C2116yesmaximal, direct product factor
4C2×#19128109C211yesmaximal, characteristic, complemented
5C2×#19128107C211yesmaximal, characteristic, complemented
6C2×#19128105C211yesmaximal, characteristic, complemented
7C2×#19127994C211yesmaximal, characteristic, complemented
8C2×#19127984C211yesmaximal, characteristic, complemented
9C2×#19128004C211yesmaximal, characteristic
10C2×#19128002C211yesmaximal, characteristic
11C2×#19127980C211yesmaximal, characteristic
12C2×#19127830C211yesmaximal, characteristic, complemented
13C2×#19127804C211yesmaximal, characteristic
14C2×#19127799C211yesmaximal, characteristic
15C2×#19127786C211yesmaximal, characteristic
16C2×#477×C83C211yesmaximal, characteristic, complemented
17C22×Q8×D83—21no—
18C22×#13050577C2211yescharacteristic
19#19128427—24no—
20#19128427C2218yescomplemented
21#19128366—24no—
22#19128366C2218yes—
23C2×#14581791—21no—
24C2×#14581791C2211yescharacteristic
25C2×#14581791C2211yescharacteristic
26C2×#14581791C2211yescharacteristic
27C2×#14581784—21no—
28C2×#14581784C2211yescharacteristic
29C2×#14581783—21no—
30C2×#14581783C2211yescharacteristic
31C2×#14581770—21no—
32C2×#14581770—21no—
33C2×#14581768—21no—
34C2×Q8×Dic83C2211yescharacteristic
35C2×Q8×Dic83C2211yescharacteristic
36C2×C4×Dic166—21no—
37C2×C4×Dic166C2211yescharacteristic
38C2×C4×D332C2211yescharacteristic
39C2×#14581754C2211yescharacteristic
40C2×#14581754C2211yescharacteristic
41#19128109C2218yescomplemented
42#19128107C2218yescomplemented
43#19128105C2218yescomplemented
44#19128004C2218yes—
45#19128002C2218yes—
46#19127994C2218yescomplemented
47#19127984C2218yescomplemented
48#19127980C2218yes—
49#19127830C2218yescomplemented
50#19127804C2218yes—
51#19127799C2218yes—
52#19127786C2218yes—
53C2×#14581726C2211yescharacteristic
54C2×#14581725C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581724C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×#14581723C2211yescharacteristic
60C2×Dic83⋊C8C2211yescharacteristic
61C2×Dic83⋊C8C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×#14581703C2211yescharacteristic
67C2×#14581702C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×C4⋊Q8×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71#477×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#107×C83C2211yescharacteristic
74C2×C4⋊C8×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#103×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166—21no—
80C22×Dic166D411yescharacteristic
81C2×Q8×D83—28no—
82C2×Q8×D83—48no—
83C22×D332C2311yescharacteristic
84C22×C4×D83—21no—
85C22×C4×D83—21no—
86C22×C4×D83—21no—
87C2×#13050577Q818yescomplemented
88C2×#13050577C2314yes—
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91#14581791—28no—
92#14581791—22no—
93#14581791—22no—
94#14581791—22no—
95#14581791C2314yes—
96#14581791C2314yes—
97#14581791C2314yes—
98#14581784—28no—
99#14581784—22no—
100#14581784C2314yes—
101#14581783—28no—
102#14581783—22no—
103#14581783C2314yes—
104#14581770—28no—
105#14581770—28no—
106#14581768—28no—
107Q8×Dic83—22no—
108Q8×Dic83—22no—
109Q8×Dic83C2314yes—
110Q8×Dic83C2314yes—
111C4×Dic166—28no—
112C4×Dic166D414yes—
113C4×Dic166C2314yes—
114C4×D332—22no—
115C4×D332C2314yes—
116#14581754—22no—
117#14581754—22no—
118#14581754C2314yes—
119#14581754C2314yes—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83D411yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×C4⋊Dic83C2311yescharacteristic
126C2×C4⋊Dic83C2311yescharacteristic
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4D411yescharacteristic
134C2×Dic83⋊C4D411yescharacteristic
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×C4×Dic83—21no—
139C2×C4×Dic83—21no—
140C2×C4×Dic83C2311yescharacteristic
141C2×C4×Dic83C2311yescharacteristic
142#14581726C2314yes—
143#14581725C2314yes—
144#14581725C2314yes—
145#14581725C2314yes—
146#14581724C2314yes—
147#14581723C2314yes—
148#14581723C2314yes—
149Dic83⋊C8C2314yes—
150Dic83⋊C8C2314yes—
151#14581716C2314yes—
152#14581714C2314yes—
153#14581714C2314yes—
154#14581712C2314yes—
155#14581703C2314yes—
156#14581702C2314yes—
157C8×Dic83C2314yes—
158C22×Q8×C83—21no—
159C22×Q8×C83C2311yescharacteristic
160C22×C8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C4⋊Q8×C83—22no—
163C4⋊Q8×C83C2314yes—
164C4×Q8×C83—22no—
165C4×Q8×C83C2314yes—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C42×C83—21no—
172C2×C42×C83C2311yescharacteristic
173#107×C83C2314yes—
174#107×C83C2314yes—
175C4⋊C8×C83C2314yes—
176#103×C83C2314yes—
177#103×C83C2314yes—
178C23×D83—21no—
179C2×Dic166—24no—
180C2×Dic166—24no—
181C2×Dic166—24no—
182C2×Dic166—24no—
183C2×Dic166—44no—
184C2×Dic166—44no—
185C2×Dic166—44no—
186C2×Dic166C2×D414yes—
187Q8×D83—432no—
188C2×D332—21no—
189C2×D332—22no—
190C2×D332C2×Q814yes—
191C2×D332C2412yes—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83C2×D411yescharacteristic
196C22×Dic83C2×D411yescharacteristic
197C22×Dic83C2×D411yescharacteristic
198C22×Dic83C2×D411yescharacteristic
199C2×C4×D83—24no—
200C2×C4×D83—24no—
201C2×C4×D83—24no—
202C2×C4×D83—44no—
203C2×C4×D83—44no—
204C2×C4×D83—44no—
205#13050577C2×Q8116yescomplemented
206C2×C83⋊C8—22no—
207C2×C83⋊C8C2×Q814yescomplemented
208C2×C83⋊C8C2412yes—
209C2×C83⋊C8C2412yes—
210C4⋊Dic83—21no—
211C4⋊Dic83—21no—
212C4⋊Dic83—21no—
213C4⋊Dic83—24no—
214C4⋊Dic83—24no—
215C4⋊Dic83—24no—
216C4⋊Dic83C2×D414yes—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4C2×D414yes—
227Dic83⋊C4C2×D414yes—
228(C2×D83)⋊C4—24no—
229(C2×D83)⋊C4—24no—
230(C2×D83)⋊C4—24no—
231C4×Dic83—24no—
232C4×Dic83—24no—
233C4×Dic83C2×D412yes—
234C4×Dic83C2×D412yes—
235C4×Dic83C2412yes—
236C4×Dic83C2412yes—
237C2×Q8×C83—21no—
238C2×Q8×C83—24no—
239C2×Q8×C83—22no—
240C2×Q8×C83—44no—
241C2×Q8×C83C2×Q814yescomplemented
242C2×Q8×C83C2412yes—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2411yescharacteristic
250C2×C8×C83—22no—
251C2×C8×C83—22no—
252C2×C8×C83C2412yes—
253C2×C8×C83C2412yes—
254C4⋊C4×C83—24no—
255C4⋊C4×C83—24no—
256C4⋊C4×C83—21no—
257C4⋊C4×C83—21no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83C2412yes—
260C4⋊C4×C83C2412yes—
261C4⋊C4×C83C2412yes—
262C42×C83—24no—
263C42×C83C2×D412yes—
264C42×C83C2412yes—
265C23×C83C22×D411yescharacteristic
266C22×D83—24no—
267C22×D83—22no—
268C22×D83—42no—
269C22×D83—42no—
270Q8×C83—24no—
271Q8×C83—22no—
272Q8×C83—48no—
273Q8×C83C22×Q814yescomplemented
274C2×C4×C83—24no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—42no—
282C2×C4×C83—42no—
283C2×C4×C83—42no—
284C2×C4×C83C22×D412yes—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D411yescharacteristic
287C2×C4×C83C22×Q812yes—
288C2×C4×C832−1+412yes—
289C2×C4×C83C2511yescharacteristic
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—42no—
297C2×Dic83—42no—
298C2×Dic83—42no—
299C2×Dic83AGL(1,ℤ/8)14yes—
300C2×Dic83C22×D412yes—
301C2×Dic83C22×D412yes—
302C2×Dic83C22×D412yes—
303C2×Dic83C22×D412yes—
304D332—24no—
305D332—22no—
306D332C22×Q814yes—
307C4×D83—48no—
308C4×D83—48no—
309C4×D83—48no—
310Dic166—28no—
311Dic166—48no—
312Dic166—48no—
313Dic166—48no—
314C8×C83—22no—
315C8×C83—22no—
316C83⋊C8—22no—
317C83⋊C8C22×Q814yescomplemented
318C22×C83D4×Q812yes—
319C22×C83C2×AGL(1,ℤ/8)12yes—
320C22×C83#57812yes—
321C22×C83C23×D411yescharacteristic
322C2×D83—24no—
323C2×D83—48no—
324C2×D83—42no—
325C2×D83—42no—
326C4×C83—24no—
327C4×C83—22no—
328C4×C83—22no—
329C4×C83—42no—
330C4×C83—42no—
331C4×C83—42no—
332C4×C83D4×Q812yes—
333C4×C83C23×Q811yescharacteristic
334C4×C83C2×2−1+411yescharacteristic
335Dic83—22no—
336Dic83—22no—
337Dic83—22no—
338Dic83—42no—
339Dic83—42no—
340Dic83—42no—
341Dic83C2×AGL(1,ℤ/8)14yes—
342C2×#3386—831nomaximal, Sylow
343C2×C83#338614yescomplemented
344C2×C83C2×D4×Q811yescharacteristic
345C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
346C2×C83C2×#57811yescharacteristic
347D83—44no—
348C2×#557—831no—
349C2×D4×Q8—831no—
350#3386—8316no—
351C2×#501—831no—
352C2×#501—831no—
353C2×#500—831no—
354C2×#477—831no—
355C2×#477D8311yescharacteristic, complemented
356C2×#475—831no—
357C2×#478—831no—
358C2×#478—831no—
359C2×#474—831no—
360C2×#446—831no—
361C2×#440—831no—
362C2×#440—831no—
363C2×C4×SD16—831no—
364C83C2×#338611yescharacteristic, complemented, Sylow
365C23×Q8—1661no—
366C22×SD16—831no—
367#557—838no—
368#557—1664no—
369D4×Q8—838no—
370D4×Q8—1664no—
371C2×C4⋊Q8—831no—
372C2×C4⋊Q8—831no—
373C2×C4⋊Q8—831no—
374C2×C4⋊Q8—1661no—
375C2×C4⋊Q8C2×D8311yescharacteristic
376C2×#125—831no—
377C2×#125—831no—
378C2×#125—1661no—
379C2×#125—1661no—
380C2×C22⋊Q8—1661no—
381C2×C22⋊Q8—1661no—
382C2×C22⋊Q8—1661no—
383C2×C4×Q8—831no—
384C2×C4×Q8—831no—
385C2×C4×Q8—831no—
386C2×C4×Q8—1661no—
387C2×C4×Q8C2×D8311yescharacteristic
388C2×C4×D4—831no—
389C2×C4×D4—831no—
390C2×C4×D4—831no—
391#501—838no—
392#501—838no—
393#500—838no—
394#478—838no—
395#478—838no—
396#477—838no—
397#477C2×D8318yescomplemented
398#475—838no—
399#474—838no—
400#446—838no—
401#440—838no—
402#440—838no—
403C4×SD16—838no—
404C2×#107—831no—
405C2×#107—831no—
406C2×#107—831no—
407C2×#107—831no—
408C2×#107C2×D8311yescharacteristic
409C2×#107C2×D8311yescharacteristic
410C2×#106—831no—
411C2×#106—831no—
412C2×#106—831no—
413C2×C4⋊C8—831no—
414C2×C4⋊C8—831no—
415C2×C4⋊C8C2×D8311yescharacteristic
416C2×#103—831no—
417C2×#103C2×D8311yescharacteristic
418C2×#103C2×D8311yescharacteristic
419C2×#102—831no—
420C2×#102—831no—
421C2×#102—831no—
422C2×#97—831no—
423C2×#97—831no—
424C2×C4×C8—831no—
425C22×Q8—21no—
426C22×Q8—3328no—
427C22×Q8—831no—
428C22×Q8—1661no—
429C22×Q8—1661no—
430C22×Q8—1661no—
431C22×Q8—1668no—
432C22×Q8C22×D8311yescharacteristic
433C22×D4—831no—
434C23×C4—1661no—
435C23×C4—1661no—
436C23×C4—1661no—
437C2×SD16—838no—
438C2×SD16—834no—
439C22×C8—831no—
440C22×C8—831no—
441C22×C8C22×D8311yescharacteristic
442C22×C8C22×D8311yescharacteristic
443C4⋊Q8—22no—
444C4⋊Q8—834no—
445C4⋊Q8—834no—
446C4⋊Q8—834no—
447C4⋊Q8—1662no—
448C4⋊Q8—1662no—
449C4⋊Q8—1662no—
450C4⋊Q8—1668no—
451C4⋊Q8C22×D8314yes—
452#125—834no—
453#125—834no—
454#125—1668no—
455#125—1662no—
456#125—1668no—
457#125—1662no—
458C22⋊Q8—1668no—
459C22⋊Q8—1668no—
460C22⋊Q8—1668no—
461C4×Q8—22no—
462C4×Q8—834no—
463C4×Q8—834no—
464C4×Q8—834no—
465C4×Q8—834no—
466C4×Q8—1668no—
467C4×Q8—1662no—
468C4×Q8—1662no—
469C4×Q8C22×D8314yes—
470C4×D4—834no—
471C4×D4—834no—
472C4×D4—834no—
473C4×D4—1662no—
474C4×D4—1662no—
475C4×D4—1662no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—831no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—1661no—
485C2×C4⋊C4—1661no—
486C2×C4⋊C4—1661no—
487C2×C4⋊C4—1661no—
488C2×C4⋊C4—1661no—
489C2×C4⋊C4—1661no—
490C2×C4⋊C4—1661no—
491C2×C4⋊C4—1661no—
492C2×C4⋊C4—1661no—
493C2×C4⋊C4C22×D8311yescharacteristic
494C2×C4⋊C4C22×D8311yescharacteristic
495C2×C4⋊C4C22×D8311yescharacteristic
496C2×C22⋊C4—1661no—
497C2×C22⋊C4—1661no—
498C2×C22⋊C4—1661no—
499C2×C42—21no—
500C2×C42—831no—
501C2×C42—831no—
502C2×C42—1661no—
503C2×C42—1661no—
504C2×C42C22×D8311yescharacteristic
505#107—834no—
506#107—834no—
507#107—834no—
508#107—834no—
509#107C22×D8314yes—
510#107C22×D8314yes—
511#106—834no—
512#106—834no—
513#106—834no—
514C4⋊C8—834no—
515C4⋊C8—834no—
516C4⋊C8C22×D8314yes—
517#103—834no—
518#103C22×D8314yes—
519#103C22×D8314yes—
520#102—834no—
521#102—834no—
522#102—834no—
523#97—834no—
524#97—834no—
525C4×C8—834no—
526C24—1661no—
527C2×Q8—21no—
528C2×Q8—24no—
529C2×Q8—22no—
530C2×Q8—44no—
531C2×Q8—3324no—
532C2×Q8—3324no—
533C2×Q8—3324no—
534C2×Q8—33232no—
535C2×Q8—834no—
536C2×Q8—1664no—
537C2×Q8—1664no—
538C2×Q8—1664no—
539C2×Q8—1664no—
540C2×Q8Q8×D8314yescomplemented
541C2×Q8C23×D8312yes—
542C2×D4—834no—
543C2×D4—832no—
544C2×D4—1661no—
545C2×D4—1662no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—3324no—
551C22×C4—3324no—
552C22×C4—3324no—
553C22×C4—831no—
554C22×C4—831no—
555C22×C4—831no—
556C22×C4—831no—
557C22×C4—1664no—
558C22×C4—1664no—
559C22×C4—1661no—
560C22×C4—1661no—
561C22×C4—1661no—
562C22×C4—1664no—
563C22×C4D4×D8311yescharacteristic
564C22×C4D4×D8311yescharacteristic
565C22×C4C23×D8311yescharacteristic
566SD16—8316no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—834no—
570C2×C8—832no—
571C2×C8—832no—
572C2×C8—1662no—
573C2×C8C23×D8312yes—
574C2×C8C23×D8312yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—834no—
581C4⋊C4—834no—
582C4⋊C4—834no—
583C4⋊C4—832no—
584C4⋊C4—832no—
585C4⋊C4—832no—
586C4⋊C4—1664no—
587C4⋊C4—1664no—
588C4⋊C4—1664no—
589C4⋊C4—1664no—
590C4⋊C4—1664no—
591C4⋊C4—1664no—
592C4⋊C4—1664no—
593C4⋊C4—1661no—
594C4⋊C4—1661no—
595C4⋊C4—1661no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4C23×D8312yes—
599C4⋊C4C23×D8312yes—
600C4⋊C4C23×D8312yes—
601C22⋊C4—1664no—
602C22⋊C4—1664no—
603C22⋊C4—1664no—
604C42—24no—
605C42—832no—
606C42—832no—
607C42—832no—
608C42—832no—
609C42—1664no—
610C42—1664no—
611C42D4×D8312yes—
612C42C23×D8312yes—
613C23—3322no—
614C23—3322no—
615C23—1664no—
616C23—1662no—
617C23C2×D4×D8311yescharacteristic
618Q8—24no—
619Q8—22no—
620Q8—48no—
621Q8—3328no—
622Q8—3328no—
623Q8—3328no—
624Q8—1668no—
625Q8C2×Q8×D8314yescomplemented
626D4—834no—
627D4—1664no—
628D4—1662no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—3328no—
640C2×C4—3328no—
641C2×C4—3328no—
642C2×C4—3322no—
643C2×C4—3322no—
644C2×C4—3322no—
645C2×C4—834no—
646C2×C4—832no—
647C2×C4—832no—
648C2×C4—832no—
649C2×C4—832no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4C2×D4×D8312yes—
657C2×C4C2×D4×D8312yes—
658C2×C4C2×D4×D8311yescharacteristic
659C2×C4C2×Q8×D8312yes—
660C2×C4#1458183912yes—
661C2×C4C24×D8311yescharacteristic
662C8—22no—
663C8—22no—
664C8—834no—
665C8—1662no—
666C22—3328no—
667C22—3322no—
668C22—3322no—
669C22—1664no—
670C22#1912836412yes—
671C22AGL(1,ℤ/8)×D8312yes—
672C22#1912851412yes—
673C22C22×D4×D8311yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—3322no—
681C4—3322no—
682C4—3322no—
683C4—834no—
684C4—1662no—
685C4—1662no—
686C4—1662no—
687C4#1912836412yes—
688C4C22×Q8×D8311yescharacteristic
689C4C2×#1458183911yescharacteristic
690C2—3324no—
691C2#2492038714yesdirect product factor
692C2C2×#1912836411yescharacteristic
693C2C2×AGL(1,ℤ/8)×D8311yescharacteristic
694C2C2×#1912851411yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#477×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenterC2×#477D83
hypocenterC83C2×#3386
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#19128427C2semidirect
3. #24920387C2direct (N × H)
4. C2×#19128109C2semidirect
5. C2×#19128107C2semidirect
6. C2×#19128105C2semidirect
7. C2×#19127994C2semidirect
8. C2×#19127984C2semidirect
12. C2×#19127830C2semidirect
16. C2×#477×C83C2semidirect
20. #19128427C22semidirect
41. #19128109C22semidirect
42. #19128107C22semidirect
43. #19128105C22semidirect
46. #19127994C22semidirect
47. #19127984C22semidirect
49. #19127830C22semidirect
71. #477×C83C22semidirect
87. C2×#13050577Q8semidirect
205. #13050577C2×Q8semidirect
207. C2×C83⋊C8C2×Q8semidirect
241. C2×Q8×C83C2×Q8semidirect
273. Q8×C83C22×Q8semidirect
317. C83⋊C8C22×Q8semidirect
343. C2×C83#3386semidirect
355. C2×#477D83semidirect
364. C83C2×#3386semidirect
397. #477C2×D83semidirect
540. C2×Q8Q8×D83semidirect
625. Q8C2×Q8×D83semidirect
691. C2#24920387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284272
C2×#191283662
#249203872
C2×#191281092
C2×#191281072
C2×#191281052
C2×#191279942
C2×#191279842
C2×#191280042
C2×#191280022
C2×#191279802
C2×#191278302
C2×#191278042
C2×#191277992
C2×#191277862
C2×#477×C832
C2×#338683