Finite Group Databasebeta

← C2×#24920204 #36284128

Subgroups — C2×#24920204 #36284128

Order 21248.

1842 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic166C211yesmaximal, characteristic, complemented
2C2×#19128423C211yesmaximal, characteristic
3#24920204C2116yesmaximal, direct product factor
4C2×#19128062C211yesmaximal, characteristic
5C2×#19128061C211yesmaximal, characteristic
6C2×#19128050C211yesmaximal, characteristic, complemented
7C2×#19127986C211yesmaximal, characteristic, complemented
8C2×#19127985C211yesmaximal, characteristic, complemented
9C2×#19127990C211yesmaximal, characteristic
10C2×#19127925C211yesmaximal, characteristic
11C2×#19127923C211yesmaximal, characteristic
12C2×#19127909C211yesmaximal, characteristic, complemented
13C2×#19127829C211yesmaximal, characteristic, complemented
14C2×#19127805C211yesmaximal, characteristic, complemented
15C2×#19127786C211yesmaximal, characteristic
16C2×#441×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19Q8×Dic166—24no—
20Q8×Dic166C2218yescomplemented
21#19128423—24no—
22#19128423C2218yes—
23C2×#14581792—21no—
24C2×#14581792C2211yescharacteristic
25C2×#14581791—21no—
26C2×#14581791—21no—
27C2×#14581791C2211yescharacteristic
28C2×#14581791C2211yescharacteristic
29C2×#14581790C2211yescharacteristic
30C2×#14581787—21no—
31C2×#14581786—21no—
32C2×#14581781C2211yescharacteristic
33C2×#14581780C2211yescharacteristic
34C2×#14581770—21no—
35C2×Q8×Dic83C2211yescharacteristic
36C2×Q8×Dic83C2211yescharacteristic
37C2×C4×Dic166—21no—
38C2×C4×Dic166C2211yescharacteristic
39C2×#14581757C2211yescharacteristic
40C2×#14581754C2211yescharacteristic
41C2×#14581749—21no—
42#19128062C2218yes—
43#19128061C2218yes—
44#19128050C2218yescomplemented
45#19127990C2218yes—
46#19127986C2218yescomplemented
47#19127985C2218yescomplemented
48#19127925C2218yes—
49#19127923C2218yes—
50#19127909C2218yescomplemented
51#19127829C2218yescomplemented
52#19127805C2218yescomplemented
53#19127786C2218yes—
54C2×#14581723C2211yescharacteristic
55C2×#14581723C2211yescharacteristic
56C2×C4⋊(C83⋊C8)C2211yescharacteristic
57C2×Dic83⋊C8C2211yescharacteristic
58C2×Dic83⋊C8C2211yescharacteristic
59C2×#14581717C2211yescharacteristic
60C2×#14581717C2211yescharacteristic
61C2×#14581716C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581715C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581712C2211yescharacteristic
67C2×#14581702C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C22×Q16×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71C2×C4×Q8×C83C2211yescharacteristic
72#441×C83C2218yescomplemented
73C2×#106×C83C2211yescharacteristic
74C2×#103×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166—21no—
80C22×Dic166D411yescharacteristic
81C22×Dic166C2311yescharacteristic
82C22×D332C2311yescharacteristic
83C22×C4×D83—21no—
84C2×#13050580—24no—
85C2×#13050580C2314yes—
86C2×#13050577—24no—
87C2×#13050577C2314yes—
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90#14581792—28no—
91#14581792—22no—
92#14581792C2314yes—
93#14581791—28no—
94#14581791—28no—
95#14581791—22no—
96#14581791—22no—
97#14581791C2314yes—
98#14581791C2314yes—
99#14581790—22no—
100#14581790C2314yes—
101#14581787—28no—
102#14581786—28no—
103#14581781—22no—
104#14581781C2314yes—
105#14581780—22no—
106#14581780C2314yes—
107#14581770—28no—
108Q8×Dic83—22no—
109Q8×Dic83—22no—
110Q8×Dic83C2314yes—
111Q8×Dic83C2314yes—
112C4×Dic166—28no—
113C4×Dic166D414yes—
114C4×Dic166C2314yes—
115#14581757—22no—
116#14581757C2314yes—
117#14581754—22no—
118#14581754C2314yes—
119#14581749—28no—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83D411yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×C4⋊Dic83C2311yescharacteristic
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4D411yescharacteristic
132C2×Dic83⋊C4D411yescharacteristic
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×C4×Dic83—21no—
139C2×C4×Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83C2311yescharacteristic
142C2×C4×Dic83C2311yescharacteristic
143#14581723C2314yes—
144#14581723C2314yes—
145C4⋊(C83⋊C8)C2314yes—
146Dic83⋊C8C2314yes—
147Dic83⋊C8C2314yes—
148#14581717C2314yes—
149#14581717C2314yes—
150#14581716C2314yes—
151#14581716C2314yes—
152#14581715C2314yes—
153#14581714C2314yes—
154#14581714C2314yes—
155#14581712C2314yes—
156#14581702C2314yes—
157C8×Dic83C2314yes—
158C22×Q8×C83C2311yescharacteristic
159C22×Q8×C83C2311yescharacteristic
160C2×Q16×C83—24no—
161C2×Q16×C83C2314yes—
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164C4×Q8×C83—22no—
165C4×Q8×C83—22no—
166C4×Q8×C83C2314yes—
167C4×Q8×C83C2314yes—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C42×C83—21no—
173C2×C42×C83—21no—
174C2×C42×C83C2311yescharacteristic
175#106×C83C2314yes—
176#103×C83C2314yes—
177#103×C83C2314yes—
178#97×C83C2314yes—
179C23×D83—21no—
180C2×Dic166—24no—
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—21no—
184C2×Dic166—24no—
185C2×Dic166—24no—
186C2×Dic166—24no—
187C2×Dic166—82no—
188C2×Dic166—82no—
189C2×Dic166—82no—
190C2×Dic166C2×D414yes—
191C2×Dic166C2412yes—
192C2×D332—22no—
193C2×D332—22no—
194C2×D332—21no—
195C2×D332C2412yes—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83—21no—
199C22×Dic83C2×D411yescharacteristic
200C22×Dic83C2×D411yescharacteristic
201C22×Dic83C2×D411yescharacteristic
202C22×Dic83C2×D411yescharacteristic
203C2×C4×D83—24no—
204C2×C4×D83—44no—
205#13050580—28no—
206#13050577—28no—
207C2×C83⋊C8—22no—
208C2×C83⋊C8—22no—
209C2×C83⋊C8C2412yes—
210C2×C83⋊C8C2412yes—
211C4⋊Dic83—21no—
212C4⋊Dic83—21no—
213C4⋊Dic83—24no—
214C4⋊Dic83—24no—
215C4⋊Dic83—24no—
216C4⋊Dic83C2×D414yes—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4C2×D414yes—
225Dic83⋊C4C2×D414yes—
226(C2×D83)⋊C4—24no—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—24no—
229(C2×D83)⋊C4—24no—
230(C2×D83)⋊C4—24no—
231C4×Dic83—24no—
232C4×Dic83—24no—
233C4×Dic83—24no—
234C4×Dic83C2×D412yes—
235C4×Dic83C2×D412yes—
236C4×Dic83C2412yes—
237C4×Dic83C2412yes—
238C2×Q8×C83—21no—
239C2×Q8×C83—21no—
240C2×Q8×C83—22no—
241C2×Q8×C83—22no—
242C2×Q8×C83—22no—
243C2×Q8×C83#4114yes—
244C2×Q8×C83C2412yes—
245C2×Q8×C83C2412yes—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2411yescharacteristic
253Q16×C83—28no—
254C2×C8×C83—22no—
255C2×C8×C83—22no—
256C2×C8×C83C2412yes—
257C2×C8×C83C2412yes—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—24no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83C2412yes—
263C4⋊C4×C83C2412yes—
264C42×C83—24no—
265C42×C83—24no—
266C42×C83C2×D412yes—
267C42×C83C2412yes—
268C23×C83C22×D411yescharacteristic
269C22×D83—22no—
270C22×D83—42no—
271C22×D83—42no—
272C22×D83—42no—
273Q8×C83—24no—
274Q8×C83—22no—
275Q8×C83—22no—
276Q8×C83—22no—
277Q8×C83—42no—
278Q8×C83C2×#4114yes—
279C2×C4×C83—24no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—42no—
287C2×C4×C83—42no—
288C2×C4×C83—42no—
289C2×C4×C83C22×D412yes—
290C2×C4×C83C22×D412yes—
291C2×C4×C83C22×D411yescharacteristic
292C2×C4×C83C2×#4112yes—
293C2×C4×C832−1+412yes—
294C2×C4×C83C2511yescharacteristic
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—42no—
302C2×Dic83—42no—
303C2×Dic83—42no—
304C2×Dic83#13714yes—
305C2×Dic83C22×D412yes—
306C2×Dic83C22×D412yes—
307C2×Dic83C22×D412yes—
308C2×Dic83C22×D412yes—
309D332—22no—
310D332—22no—
311D332—42no—
312C4×D83—48no—
313Dic166—28no—
314Dic166—22no—
315Dic166—22no—
316Dic166—42no—
317Dic166—84no—
318Dic166—84no—
319Dic166—84no—
320C8×C83—22no—
321C8×C83—22no—
322C83⋊C8—22no—
323C83⋊C8—22no—
324C22×C83#54812yes—
325C22×C83C2×#13712yes—
326C22×C83#57712yes—
327C22×C83C23×D411yescharacteristic
328C2×D83—42no—
329C2×D83—42no—
330C2×D83—42no—
331C2×D83—84no—
332C4×C83—24no—
333C4×C83—22no—
334C4×C83—22no—
335C4×C83—42no—
336C4×C83—42no—
337C4×C83—42no—
338C4×C83#54812yes—
339C4×C83C22×#4111yescharacteristic
340C4×C83C2×2−1+411yescharacteristic
341Dic83—22no—
342Dic83—22no—
343Dic83—22no—
344Dic83—42no—
345Dic83—42no—
346Dic83—42no—
347Dic83C2×#13714yes—
348C2×#3369—831nomaximal, Sylow
349C2×C83#336914yescomplemented
350C2×C83C2×#54811yescharacteristic
351C2×C83C22×#13711yescharacteristic
352C2×C83C2×#57711yescharacteristic
353D83—82no—
354C2×Q82—831no—
355C2×#556—831no—
356#3369—8316no—
357C2×#489—831no—
358C2×#489—831no—
359C2×#487—831no—
360C2×#475—831no—
361C2×#475—831no—
362C2×#476—831no—
363C2×#464—831no—
364C2×#464—831no—
365C2×#462—831no—
366C2×#446—831no—
367C2×#441—831no—
368C2×#441D8311yescharacteristic, complemented
369C2×C4×SD16—831no—
370C83C2×#336911yescharacteristic, complemented, Sylow
371C22×Q16—831no—
372C22×Q16C2×D8311yescharacteristic
373C22×SD16—831no—
374Q82—838no—
375Q82—1664no—
376#556—838no—
377#556—1664no—
378C2×C4⋊Q8—831no—
379C2×C4⋊Q8—831no—
380C2×C4⋊Q8—831no—
381C2×C4⋊Q8—831no—
382C2×C4⋊Q8—1661no—
383C2×C4⋊Q8—1661no—
384C2×C4⋊Q8—1661no—
385C2×#126—1661no—
386C2×#126—1661no—
387C2×#124—831no—
388C2×#124—831no—
389C2×C22⋊Q8—1661no—
390C2×C4×Q8—831no—
391C2×C4×Q8—831no—
392C2×C4×Q8—831no—
393C2×C4×Q8—831no—
394C2×C4×Q8—1661no—
395C2×C4×Q8C2×D8311yescharacteristic
396C2×C4×Q8C2×D8311yescharacteristic
397C2×C4×D4—831no—
398C2×#117—1661no—
399#489—838no—
400#489—838no—
401#487—838no—
402#476—838no—
403#475—838no—
404#475—838no—
405#464—838no—
406#464—838no—
407#462—838no—
408#446—838no—
409#441—838no—
410#441C2×D8318yescomplemented
411C4×SD16—838no—
412C2×#106—831no—
413C2×#106—831no—
414C2×#106C2×D8311yescharacteristic
415C2×C4⋊C8—831no—
416C2×C4⋊C8—831no—
417C2×C4⋊C8—831no—
418C2×#103—831no—
419C2×#103—831no—
420C2×#103—831no—
421C2×#103—831no—
422C2×#103—831no—
423C2×#103C2×D8311yescharacteristic
424C2×#103C2×D8311yescharacteristic
425C2×#102—831no—
426C2×#102—831no—
427C2×#102—831no—
428C2×#97—831no—
429C2×#97C2×D8311yescharacteristic
430C2×C4×C8—831no—
431C22×Q8—831no—
432C22×Q8—831no—
433C22×Q8—1661no—
434C22×Q8—1661no—
435C22×Q8—1661no—
436C22×Q8C22×D8311yescharacteristic
437C22×Q8C22×D8311yescharacteristic
438C22×D4—831no—
439C23×C4—1661no—
440C2×Q16—24no—
441C2×Q16—834no—
442C2×Q16—1664no—
443C2×Q16C22×D8314yes—
444C2×SD16—834no—
445C2×SD16—1664no—
446C22×C8—831no—
447C22×C8—831no—
448C22×C8C22×D8311yescharacteristic
449C22×C8C22×D8311yescharacteristic
450C4⋊Q8—834no—
451C4⋊Q8—834no—
452C4⋊Q8—834no—
453C4⋊Q8—834no—
454C4⋊Q8—1668no—
455C4⋊Q8—1662no—
456C4⋊Q8—1662no—
457C4⋊Q8—1662no—
458C4⋊Q8—1668no—
459C4⋊Q8—1668no—
460C4⋊Q8—1662no—
461#126—1668no—
462#126—1668no—
463#124—834no—
464#124—834no—
465#124—1662no—
466#124—1662no—
467C22⋊Q8—1668no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—834no—
471C4×Q8—834no—
472C4×Q8—834no—
473C4×Q8—834no—
474C4×Q8—834no—
475C4×Q8—1668no—
476C4×Q8—1662no—
477C4×Q8—1662no—
478C4×Q8—1662no—
479C4×Q8C22×D8314yes—
480C4×Q8C22×D8314yes—
481C4×D4—834no—
482C4×D4—1662no—
483#117—1668no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4—1661no—
492C2×C4⋊C4—1661no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1661no—
497C2×C4⋊C4—1661no—
498C2×C4⋊C4—1661no—
499C2×C4⋊C4C22×D8311yescharacteristic
500C2×C4⋊C4C22×D8311yescharacteristic
501C2×C22⋊C4—1661no—
502C2×C22⋊C4—1661no—
503C2×C22⋊C4—1661no—
504C2×C22⋊C4—1661no—
505C2×C22⋊C4—1661no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—831no—
509C2×C42—831no—
510C2×C42—1661no—
511C2×C42—1661no—
512C2×C42—1661no—
513C2×C42C22×D8311yescharacteristic
514#106—834no—
515#106—834no—
516#106C22×D8314yes—
517C4⋊C8—834no—
518C4⋊C8—834no—
519C4⋊C8—834no—
520#103—834no—
521#103—834no—
522#103—834no—
523#103—834no—
524#103—834no—
525#103C22×D8314yes—
526#103C22×D8314yes—
527#102—834no—
528#102—834no—
529#102—834no—
530#97—834no—
531#97C22×D8314yes—
532C4×C8—834no—
533C24—1661no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—834no—
540C2×Q8—832no—
541C2×Q8—6642no—
542C2×Q8—6642no—
543C2×Q8—6642no—
544C2×Q8—1664no—
545C2×Q8—1664no—
546C2×Q8—1664no—
547C2×Q8—1662no—
548C2×Q8—1662no—
549C2×Q8—1661no—
550C2×Q8—1664no—
551C2×Q8#1305059014yes—
552C2×Q8C23×D8312yes—
553C2×Q8C23×D8312yes—
554C2×D4—832no—
555C2×D4—1661no—
556C2×D4—1662no—
557C2×D4—1662no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—3324no—
563C22×C4—831no—
564C22×C4—831no—
565C22×C4—831no—
566C22×C4—831no—
567C22×C4—1664no—
568C22×C4—1661no—
569C22×C4—1661no—
570C22×C4—1661no—
571C22×C4D4×D8311yescharacteristic
572C22×C4D4×D8311yescharacteristic
573C22×C4C23×D8311yescharacteristic
574Q16—28no—
575Q16—1668no—
576SD16—1668no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—832no—
580C2×C8—832no—
581C2×C8—1662no—
582C2×C8—1662no—
583C2×C8C23×D8312yes—
584C2×C8C23×D8312yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—834no—
590C4⋊C4—834no—
591C4⋊C4—834no—
592C4⋊C4—832no—
593C4⋊C4—832no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4—1664no—
599C4⋊C4—1664no—
600C4⋊C4—1664no—
601C4⋊C4—1661no—
602C4⋊C4—1661no—
603C4⋊C4—1664no—
604C4⋊C4C23×D8312yes—
605C4⋊C4C23×D8312yes—
606C22⋊C4—1664no—
607C22⋊C4—1664no—
608C22⋊C4—1664no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C42—24no—
612C42—24no—
613C42—832no—
614C42—832no—
615C42—832no—
616C42—832no—
617C42—1664no—
618C42—1664no—
619C42—1664no—
620C42D4×D8312yes—
621C42C23×D8312yes—
622C23—3322no—
623C23—3322no—
624C23—3322no—
625C23—1662no—
626C23C2×D4×D8311yescharacteristic
627Q8—24no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—3322no—
633Q8—6644no—
634Q8—6644no—
635Q8—6644no—
636Q8—1668no—
637Q8—1662no—
638Q8—1662no—
639Q8C2×#1305059014yes—
640D4—3322no—
641D4—1662no—
642D4—1662no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—3328no—
654C2×C4—3322no—
655C2×C4—3322no—
656C2×C4—3322no—
657C2×C4—834no—
658C2×C4—832no—
659C2×C4—832no—
660C2×C4—832no—
661C2×C4—832no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4C2×D4×D8312yes—
669C2×C4C2×D4×D8312yes—
670C2×C4C2×D4×D8311yescharacteristic
671C2×C4C2×#1305059012yes—
672C2×C4#1458183912yes—
673C2×C4C24×D8311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1662no—
677C8—1662no—
678C22—3322no—
679C22—3322no—
680C22—3322no—
681C22—6644no—
682C22#1912836012yes—
683C22#137×D8312yes—
684C22#1912851012yes—
685C22C22×D4×D8311yescharacteristic
686C4—22no—
687C4—24no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—3322no—
693C4—3322no—
694C4—3322no—
695C4—834no—
696C4—1662no—
697C4—1662no—
698C4—1662no—
699C4#1912836012yes—
700C4C22×#1305059011yescharacteristic
701C4C2×#1458183911yescharacteristic
702C2—6642no—
703C2#2492020414yesdirect product factor
704C2C2×#1912836011yescharacteristic
705C2C2×#137×D8311yescharacteristic
706C2C2×#1912851011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#441×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenterC2×#441D83
hypocenterC83C2×#3369
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic166C2semidirect
3. #24920204C2direct (N × H)
6. C2×#19128050C2semidirect
7. C2×#19127986C2semidirect
8. C2×#19127985C2semidirect
12. C2×#19127909C2semidirect
13. C2×#19127829C2semidirect
14. C2×#19127805C2semidirect
16. C2×#441×C83C2semidirect
20. Q8×Dic166C22semidirect
44. #19128050C22semidirect
46. #19127986C22semidirect
47. #19127985C22semidirect
50. #19127909C22semidirect
51. #19127829C22semidirect
52. #19127805C22semidirect
72. #441×C83C22semidirect
349. C2×C83#3369semidirect
368. C2×#441D83semidirect
370. C83C2×#3369semidirect
410. #441C2×D83semidirect
703. C2#24920204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1662
C2×#191284232
#249202042
C2×#191280622
C2×#191280612
C2×#191280502
C2×#191279862
C2×#191279852
C2×#191279902
C2×#191279252
C2×#191279232
C2×#191279092
C2×#191278292
C2×#191278052
C2×#191277862
C2×#441×C832
C2×#336983