Finite Group Databasebeta

← C2×#24920241 #36284064

Subgroups — C2×#24920241 #36284064

Order 21248.

1854 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×#19128426C211yesmaximal, characteristic, complemented
2C2×#19128407C211yesmaximal, characteristic
3#24920241C2116yesmaximal, direct product factor
4C2×#19128068C211yesmaximal, characteristic, complemented
5C2×#19128050C211yesmaximal, characteristic, complemented
6C2×#19128010C211yesmaximal, characteristic, complemented
7C2×#19128005C211yesmaximal, characteristic, complemented
8C2×#19127994C211yesmaximal, characteristic, complemented
9C2×#19127905C211yesmaximal, characteristic
10C2×#19127905C211yesmaximal, characteristic
11C2×#19127903C211yesmaximal, characteristic
12C2×#19127829C211yesmaximal, characteristic, complemented
13C2×#19127804C211yesmaximal, characteristic
14C2×#19127803C211yesmaximal, characteristic
15C2×#19127786C211yesmaximal, characteristic
16C2×#491×C83C211yesmaximal, characteristic, complemented
17C22×#13050579C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20#19128426—24no—
21#19128426C2218yescomplemented
22#19128407—24no—
23#19128407C2218yes—
24C2×#14581791C2211yescharacteristic
25C2×#14581790C2211yescharacteristic
26C2×#14581790C2211yescharacteristic
27C2×#14581783—21no—
28C2×#14581783C2211yescharacteristic
29C2×#14581782—21no—
30C2×#14581782—21no—
31C2×#14581772—21no—
32C2×#14581770—21no—
33C2×#14581770—21no—
34C2×Q8×Dic83C2211yescharacteristic
35C2×Q8×Dic83C2211yescharacteristic
36C2×C4×Dic166C2211yescharacteristic
37C2×C4×Dic166C2211yescharacteristic
38C2×#14581757—21no—
39C2×C4×D332C2211yescharacteristic
40C2×#14581754C2211yescharacteristic
41C2×#14581754C2211yescharacteristic
42C2×C4⋊C4×D83—21no—
43#19128068C2218yescomplemented
44#19128050C2218yescomplemented
45#19128010C2218yescomplemented
46#19128005C2218yescomplemented
47#19127994C2218yescomplemented
48#19127905C2218yes—
49#19127905C2218yes—
50#19127903C2218yes—
51#19127829C2218yescomplemented
52#19127804C2218yes—
53#19127803C2218yes—
54#19127786C2218yes—
55C2×#14581726C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×C4⋊(C83⋊C8)C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×Dic83⋊C8C2211yescharacteristic
61C2×#14581717C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581715C2211yescharacteristic
65C2×#14581715C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581702C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×C4⋊Q8×C83C2211yescharacteristic
70C2×#125×C83C2211yescharacteristic
71#491×C83C2218yescomplemented
72C2×#103×C83C2211yescharacteristic
73C2×#103×C83C2211yescharacteristic
74C2×#103×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166D411yescharacteristic
79C22×Dic166C2311yescharacteristic
80C22×D332C2311yescharacteristic
81C22×C4×D83—21no—
82C22×C4×D83—21no—
83C22×C4×D83—21no—
84C2×#13050579—24no—
85C2×#13050579C2314yes—
86C2×#13050577—24no—
87C2×#13050577—24no—
88C2×#13050577C2314yes—
89C2×#13050577C2314yes—
90C22×C83⋊C8C2311yescharacteristic
91C22×C83⋊C8C2311yescharacteristic
92#14581791—22no—
93#14581791C2314yes—
94#14581790—22no—
95#14581790—22no—
96#14581790C2314yes—
97#14581790C2314yes—
98#14581783—28no—
99#14581783—22no—
100#14581783C2314yes—
101#14581782—28no—
102#14581782—28no—
103#14581772—28no—
104#14581770—28no—
105#14581770—28no—
106Q8×Dic83—22no—
107Q8×Dic83—22no—
108Q8×Dic83C2314yes—
109Q8×Dic83C2314yes—
110C4×Dic166—22no—
111C4×Dic166D414yes—
112C4×Dic166C2314yes—
113C4×Dic166C2314yes—
114#14581757—28no—
115C4×D332—22no—
116C4×D332C2314yes—
117#14581754—22no—
118#14581754—22no—
119#14581754C2314yes—
120#14581754C2314yes—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83—21no—
124C2×C4⋊Dic83D411yescharacteristic
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⋊C4—21no—
134C2×Dic83⋊C4D411yescharacteristic
135C2×Dic83⋊C4D411yescharacteristic
136C4⋊C4×D83—28no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83—21no—
143C2×C4×Dic83C2311yescharacteristic
144C2×C4×Dic83C2311yescharacteristic
145#14581726C2314yes—
146#14581725C2314yes—
147#14581723C2314yes—
148C4⋊(C83⋊C8)C2314yes—
149Dic83⋊C8C2314yes—
150Dic83⋊C8C2314yes—
151#14581717C2314yes—
152#14581716C2314yes—
153#14581716C2314yes—
154#14581715C2314yes—
155#14581715C2314yes—
156#14581714C2314yes—
157#14581702C2314yes—
158C8×Dic83C2314yes—
159C22×Q8×C83C2311yescharacteristic
160C22×Q8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C4⋊Q8×C83—22no—
164C4⋊Q8×C83C2314yes—
165#125×C83—22no—
166#125×C83C2314yes—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83—21no—
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C42×C83C2311yescharacteristic
174#103×C83C2314yes—
175#103×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—82no—
186C2×Dic166C2×D414yes—
187C2×Dic166C2412yes—
188C2×D332—21no—
189C2×D332—22no—
190C2×D332#4114yes—
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—82no—
204C2×C4×D83—82no—
205#13050579—28no—
206#13050577—28no—
207#13050577—28no—
208C2×C83⋊C8—22no—
209C2×C83⋊C8—22no—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83—24no—
215C4⋊Dic83—24no—
216C4⋊Dic83—24no—
217C4⋊Dic83C2×D414yes—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4C2×D414yes—
228Dic83⋊C4C2×D414yes—
229(C2×D83)⋊C4—24no—
230(C2×D83)⋊C4—24no—
231(C2×D83)⋊C4—24no—
232C4×Dic83—24no—
233C4×Dic83—24no—
234C4×Dic83—24no—
235C4×Dic83C2×D412yes—
236C4×Dic83C2×D412yes—
237C4×Dic83C2412yes—
238C4×Dic83C2412yes—
239C2×Q8×C83—21no—
240C2×Q8×C83—21no—
241C2×Q8×C83—22no—
242C2×Q8×C83—22no—
243C2×Q8×C83—22no—
244C2×Q8×C83—22no—
245C2×Q8×C83C2412yes—
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—24no—
260C4⋊C4×C83—24no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—21no—
264C4⋊C4×C83C2412yes—
265C4⋊C4×C83C2412yes—
266C42×C83C2×D412yes—
267C42×C83C2412yes—
268C23×C83C22×D411yescharacteristic
269C22×D83—24no—
270C22×D83—22no—
271C22×D83—42no—
272C22×D83—42no—
273Q8×C83—22no—
274Q8×C83—22no—
275Q8×C83—22no—
276Q8×C83—22no—
277Q8×C83—42no—
278Q8×C83—42no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—42no—
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—24no—
310D332—22no—
311D332C2×#4114yes—
312C4×D83—48no—
313C4×D83—84no—
314C4×D83—84no—
315Dic166—28no—
316Dic166—22no—
317Dic166—22no—
318Dic166—42no—
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—24no—
329C2×D83—48no—
330C2×D83—42no—
331C2×D83—42no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—42no—
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×#3372—831nomaximal, Sylow
349C2×C83#337214yescomplemented
350C2×C83C2×#54811yescharacteristic
351C2×C83C22×#13711yescharacteristic
352C2×C83C2×#57711yescharacteristic
353D83—44no—
354C2×#557—831no—
355C2×#554—831no—
356#3372—8316no—
357C2×#491—831no—
358C2×#491D8311yescharacteristic, complemented
359C2×#487—831no—
360C2×#479—831no—
361C2×#479—831no—
362C2×#477—831no—
363C2×#461—831no—
364C2×#461—831no—
365C2×#461—831no—
366C2×#446—831no—
367C2×#440—831no—
368C2×#440—831no—
369C2×C4×SD16—831no—
370C83C2×#337211yescharacteristic, complemented, Sylow
371C22×SD16—831no—
372C22×SD16—831no—
373C22×SD16—831no—
374#557—838no—
375#557—1664no—
376#554—838no—
377#554—1664no—
378C2×C4⋊Q8—831no—
379C2×C4⋊Q8—831no—
380C2×C4⋊Q8—831no—
381C2×C4⋊Q8C2×D8311yescharacteristic
382C2×#125—831no—
383C2×#125—1661no—
384C2×#125—1661no—
385C2×#125—1661no—
386C2×#125C2×D8311yescharacteristic
387C2×C22⋊Q8—1661no—
388C2×C22⋊Q8—1661no—
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×D4—831no—
396C2×C4×D4—831no—
397C2×C4×D4—831no—
398C22×C4⋊C4—1661no—
399#491—838no—
400#491C2×D8318yescomplemented
401#487—838no—
402#479—838no—
403#479—838no—
404#477—838no—
405#461—838no—
406#461—838no—
407#461—838no—
408#446—838no—
409#440—838no—
410#440—838no—
411C4×SD16—838no—
412C2×#107—831no—
413C2×#107—831no—
414C2×#106—831no—
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×#103C2×D8311yescharacteristic
426C2×#103C2×D8311yescharacteristic
427C2×#102—831no—
428C2×#97—831no—
429C2×#97C2×D8311yescharacteristic
430C2×C4×C8—831no—
431C22×Q8—831no—
432C22×Q8—831no—
433C22×Q8—1661no—
434C22×Q8C22×D8311yescharacteristic
435C22×Q8C22×D8311yescharacteristic
436C22×D4—831no—
437C23×C4—1661no—
438C23×C4—1661no—
439C23×C4—1661no—
440C2×SD16—834no—
441C2×SD16—834no—
442C2×SD16—834no—
443C2×SD16—1664no—
444C2×SD16—1664no—
445C2×SD16—1664no—
446C22×C8—831no—
447C22×C8—831no—
448C22×C8C22×D8311yescharacteristic
449C22×C8C22×D8311yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8—834no—
452C4⋊Q8—834no—
453C4⋊Q8—834no—
454C4⋊Q8—1662no—
455C4⋊Q8—1662no—
456C4⋊Q8—1662no—
457C4⋊Q8C22×D8314yes—
458#125—22no—
459#125—834no—
460#125—1662no—
461#125—1668no—
462#125—1668no—
463#125—1668no—
464#125C22×D8314yes—
465C22⋊Q8—1668no—
466C22⋊Q8—1668no—
467C22⋊Q8—1668no—
468C4×Q8—834no—
469C4×Q8—834no—
470C4×Q8—834no—
471C4×Q8—834no—
472C4×Q8—834no—
473C4×Q8—1662no—
474C4×Q8—1662no—
475C4×Q8—1668no—
476C4×Q8—1662no—
477C4×D4—834no—
478C4×D4—834no—
479C4×D4—834no—
480C4×D4—1662no—
481C4×D4—1662no—
482C4×D4—1662no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4—831no—
492C2×C4⋊C4—1668no—
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⋊C4—1661no—
500C2×C4⋊C4—1661no—
501C2×C4⋊C4—1661no—
502C2×C4⋊C4—1661no—
503C2×C4⋊C4C22×D8311yescharacteristic
504C2×C4⋊C4C22×D8311yescharacteristic
505C2×C22⋊C4—1661no—
506C2×C22⋊C4—1661no—
507C2×C22⋊C4—1661no—
508C2×C42—831no—
509C2×C42—831no—
510C2×C42—1661no—
511C2×C42—1661no—
512C2×C42—1661no—
513C2×C42C22×D8311yescharacteristic
514#107—834no—
515#107—834no—
516#106—834no—
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#103C22×D8314yes—
528#103C22×D8314yes—
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—22no—
540C2×Q8—834no—
541C2×Q8—832no—
542C2×Q8—6642no—
543C2×Q8—1664no—
544C2×Q8—1664no—
545C2×Q8—1662no—
546C2×Q8—1662no—
547C2×Q8—1661no—
548C2×Q8C23×D8312yes—
549C2×Q8C23×D8312yes—
550C2×D4—834no—
551C2×D4—832no—
552C2×D4—1661no—
553C2×D4—1662no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—3324no—
559C22×C4—831no—
560C22×C4—831no—
561C22×C4—831no—
562C22×C4—831no—
563C22×C4—6642no—
564C22×C4—6642no—
565C22×C4—1664no—
566C22×C4—1664no—
567C22×C4—1661no—
568C22×C4—1661no—
569C22×C4—1661no—
570C22×C4—1664no—
571C22×C4D4×D8311yescharacteristic
572C22×C4D4×D8311yescharacteristic
573C22×C4C23×D8311yescharacteristic
574SD16—1668no—
575SD16—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—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—834no—
592C4⋊C4—834no—
593C4⋊C4—834no—
594C4⋊C4—832no—
595C4⋊C4—832no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4—1664no—
599C4⋊C4—1664no—
600C4⋊C4—1664no—
601C4⋊C4—1664no—
602C4⋊C4—1664no—
603C4⋊C4—1664no—
604C4⋊C4—1664no—
605C4⋊C4—1661no—
606C4⋊C4—1661no—
607C4⋊C4—1664no—
608C4⋊C4C23×D8312yes—
609C4⋊C4C23×D8312yes—
610C22⋊C4—1664no—
611C22⋊C4—1664no—
612C22⋊C4—1664no—
613C42—832no—
614C42—832no—
615C42—832no—
616C42—832no—
617C42—1664no—
618C42—1664no—
619C42—1664no—
620C42D4×D8312yes—
621C42C23×D8312yes—
622C23—3322no—
623C23—3322no—
624C23—1664no—
625C23—1662no—
626C23C2×D4×D8311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—42no—
633Q8—3322no—
634Q8—6644no—
635Q8—1668no—
636Q8—1662no—
637Q8—1662no—
638D4—834no—
639D4—1664no—
640D4—1662no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—3328no—
652C2×C4—3322no—
653C2×C4—3322no—
654C2×C4—3322no—
655C2×C4—834no—
656C2×C4—832no—
657C2×C4—832no—
658C2×C4—832no—
659C2×C4—832no—
660C2×C4—6644no—
661C2×C4—6644no—
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×C4#41×D8312yes—
672C2×C4#1458183912yes—
673C2×C4C24×D8311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1662no—
677C8—1662no—
678C22—3322no—
679C22—3322no—
680C22—3328no—
681C22—1664no—
682C22#1912835912yes—
683C22#137×D8312yes—
684C22#1912851012yes—
685C22C22×D4×D8311yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—3322no—
693C4—3322no—
694C4—3322no—
695C4—834no—
696C4—1662no—
697C4—1662no—
698C4—1662no—
699C4#1912835912yes—
700C4C2×#41×D8311yescharacteristic
701C4C2×#1458183911yescharacteristic
702C2—3324no—
703C2#2492024114yesdirect product factor
704C2C2×#1912835911yescharacteristic
705C2C2×#137×D8311yescharacteristic
706C2C2×#1912851011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#491×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenterC2×#491D83
hypocenterC83C2×#3372
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#19128426C2semidirect
3. #24920241C2direct (N × H)
4. C2×#19128068C2semidirect
5. C2×#19128050C2semidirect
6. C2×#19128010C2semidirect
7. C2×#19128005C2semidirect
8. C2×#19127994C2semidirect
12. C2×#19127829C2semidirect
16. C2×#491×C83C2semidirect
21. #19128426C22semidirect
43. #19128068C22semidirect
44. #19128050C22semidirect
45. #19128010C22semidirect
46. #19128005C22semidirect
47. #19127994C22semidirect
51. #19127829C22semidirect
71. #491×C83C22semidirect
349. C2×C83#3372semidirect
358. C2×#491D83semidirect
370. C83C2×#3372semidirect
400. #491C2×D83semidirect
703. C2#24920241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284262
C2×#191284072
#249202412
C2×#191280682
C2×#191280502
C2×#191280102
C2×#191280052
C2×#191279942
C2×#191279052
C2×#191279032
C2×#191278292
C2×#191278042
C2×#191278032
C2×#191277862
C2×#491×C832
C2×#337283