Finite Group Databasebeta

← C2×#24920370 #36284890

Subgroups — C2×#24920370 #36284890

Order 21248.

1854 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128431C211yesmaximal, characteristic, complemented
2C2×#19128407C211yesmaximal, characteristic
3#24920370C2116yesmaximal, direct product factor
4C2×#19128108C211yesmaximal, characteristic, complemented
5C2×#19128105C211yesmaximal, characteristic, complemented
6C2×#19128011C211yesmaximal, characteristic, complemented
7C2×#19128005C211yesmaximal, characteristic, complemented
8C2×#19127995C211yesmaximal, characteristic, complemented
9C2×#19127990C211yesmaximal, characteristic
10C2×#19127980C211yesmaximal, characteristic
11C2×#19127978C211yesmaximal, characteristic
12C2×#19127829C211yesmaximal, characteristic, complemented
13C2×#19127803C211yesmaximal, characteristic
14C2×#19127800C211yesmaximal, characteristic
15C2×#19127788C211yesmaximal, characteristic
16C2×#501×C83C211yesmaximal, characteristic, complemented
17C22×#13050579C2211yescharacteristic
18#19128431—24no—
19#19128431C2218yescomplemented
20#19128407—24no—
21#19128407C2218yes—
22C2×#14581791—21no—
23C2×#14581791C2211yescharacteristic
24C2×#14581791C2211yescharacteristic
25C2×#14581791C2211yescharacteristic
26C2×#14581790—21no—
27C2×#14581790—21no—
28C2×#14581783C2211yescharacteristic
29C2×#14581772—21no—
30C2×#14581770—21no—
31C2×#14581770—21no—
32C2×C4×Dic166C2211yescharacteristic
33C2×C4×Dic166C2211yescharacteristic
34C2×#14581757—21no—
35C2×#14581757C2211yescharacteristic
36C2×#14581757C2211yescharacteristic
37C2×C4×D332C2211yescharacteristic
38C2×#14581754C2211yescharacteristic
39C2×#14581754C2211yescharacteristic
40C2×C4⋊C4×D83—21no—
41#19128108C2218yescomplemented
42#19128105C2218yescomplemented
43#19128011C2218yescomplemented
44#19128005C2218yescomplemented
45#19127995C2218yescomplemented
46#19127990C2218yes—
47#19127980C2218yes—
48#19127978C2218yes—
49#19127829C2218yescomplemented
50#19127803C2218yes—
51#19127800C2218yes—
52#19127788C2218yes—
53C2×#14581726C2211yescharacteristic
54C2×#14581725C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×C4⋊(C83⋊C8)C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×Dic83⋊C8C2211yescharacteristic
61C2×#14581717C2211yescharacteristic
62C2×#14581715C2211yescharacteristic
63C2×#14581715C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×#14581712C2211yescharacteristic
67C2×#14581702C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×C4⋊Q8×C83C2211yescharacteristic
70C2×#125×C83C2211yescharacteristic
71#501×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#107×C83C2211yescharacteristic
74C2×#106×C83C2211yescharacteristic
75C2×#106×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166—21no—
80C22×Dic166D411yescharacteristic
81C22×Dic166C2311yescharacteristic
82C22×D332C2311yescharacteristic
83C22×C4×D83—21no—
84C22×C4×D83—21no—
85C22×C4×D83—21no—
86C2×#13050579Q818yescomplemented
87C2×#13050579C2314yes—
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90#14581791—28no—
91#14581791—22no—
92#14581791—22no—
93#14581791—22no—
94#14581791C2314yes—
95#14581791C2314yes—
96#14581791C2314yes—
97#14581790—28no—
98#14581790—28no—
99#14581783—22no—
100#14581783C2314yes—
101#14581772—28no—
102#14581770—28no—
103#14581770—28no—
104C4×Dic166—22no—
105C4×Dic166D414yes—
106C4×Dic166C2314yes—
107C4×Dic166C2314yes—
108#14581757—28no—
109#14581757—22no—
110#14581757—22no—
111#14581757C2314yes—
112#14581757C2314yes—
113C4×D332—22no—
114C4×D332C2314yes—
115#14581754—22no—
116#14581754—22no—
117#14581754C2314yes—
118#14581754C2314yes—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83D411yescharacteristic
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×Dic83⋊C4—21no—
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4D411yescharacteristic
131C2×Dic83⋊C4D411yescharacteristic
132C4⋊C4×D83—28no—
133C2×(C2×D83)⋊C4—21no—
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4—21no—
136C2×C4×Dic83—21no—
137C2×C4×Dic83—21no—
138C2×C4×Dic83—21no—
139C2×C4×Dic83C2311yescharacteristic
140C2×C4×Dic83C2311yescharacteristic
141#14581726C2314yes—
142#14581725C2314yes—
143#14581725C2314yes—
144#14581725C2314yes—
145#14581723C2314yes—
146C4⋊(C83⋊C8)C2314yes—
147Dic83⋊C8C2314yes—
148Dic83⋊C8C2314yes—
149#14581717C2314yes—
150#14581715C2314yes—
151#14581715C2314yes—
152#14581714C2314yes—
153#14581712C2314yes—
154#14581712C2314yes—
155#14581702C2314yes—
156C8×Dic83C2314yes—
157C22×Q8×C83—21no—
158C22×C8×C83C2311yescharacteristic
159C22×C8×C83C2311yescharacteristic
160C4⋊Q8×C83—22no—
161C4⋊Q8×C83C2314yes—
162#125×C83—22no—
163#125×C83C2314yes—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83C2311yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C42×C83C2311yescharacteristic
172#107×C83C2314yes—
173#107×C83C2314yes—
174#106×C83C2314yes—
175#106×C83C2314yes—
176#97×C83C2314yes—
177C23×D83—21no—
178C2×Dic166—21no—
179C2×Dic166—22no—
180C2×Dic166—24no—
181C2×Dic166—24no—
182C2×Dic166—24no—
183C2×Dic166—24no—
184C2×Dic166—82no—
185C2×Dic166—82no—
186C2×Dic166—82no—
187C2×Dic166C2×D414yes—
188C2×Dic166C2×Q814yes—
189C2×Dic166C2412yes—
190C2×D332—21no—
191C2×D332—22no—
192C2×D332C2×Q814yes—
193C2×D332C2412yes—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83C2×D411yescharacteristic
198C22×Dic83C2×D411yescharacteristic
199C22×Dic83C2×D411yescharacteristic
200C22×Dic83C2×D411yescharacteristic
201C2×C4×D83—24no—
202C2×C4×D83—24no—
203C2×C4×D83—24no—
204C2×C4×D83—44no—
205C2×C4×D83—82no—
206C2×C4×D83—82no—
207#13050579C2×Q8116yescomplemented
208C2×C83⋊C8—22no—
209C2×C83⋊C8—22no—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83—24no—
215C4⋊Dic83C2×D414yes—
216C4⋊Dic83C2412yes—
217C4⋊Dic83C2412yes—
218Dic83⋊C4—24no—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4C2×D414yes—
226Dic83⋊C4C2×D414yes—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—24no—
229(C2×D83)⋊C4—24no—
230C4×Dic83—24no—
231C4×Dic83—24no—
232C4×Dic83—24no—
233C4×Dic83C2×D412yes—
234C4×Dic83C2×D412yes—
235C4×Dic83C2412yes—
236C4×Dic83C2412yes—
237C2×Q8×C83—24no—
238C2×Q8×C83—82no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83C2×D411yescharacteristic
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2411yescharacteristic
246C2×C8×C83—22no—
247C2×C8×C83C2×Q814yes—
248C2×C8×C83C2412yes—
249C2×C8×C83C2412yes—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—24no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—24no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83—21no—
256C4⋊C4×C83—21no—
257C4⋊C4×C83C2412yes—
258C4⋊C4×C83C2412yes—
259C4⋊C4×C83C2412yes—
260C4⋊C4×C83C2412yes—
261C42×C83C2×D412yes—
262C42×C83C2412yes—
263C23×C83C22×D411yescharacteristic
264C22×D83—24no—
265C22×D83—22no—
266C22×D83—42no—
267C22×D83—42no—
268Q8×C83—84no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—42no—
276C2×C4×C83—42no—
277C2×C4×C83—42no—
278C2×C4×C83—42no—
279C2×C4×C83C22×D412yes—
280C2×C4×C83C22×D412yes—
281C2×C4×C83C22×D411yescharacteristic
282C2×C4×C83C22×Q812yes—
283C2×C4×C832−1+412yes—
284C2×C4×C83C2511yescharacteristic
285C2×Dic83—24no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—42no—
293C2×Dic83—42no—
294C2×Dic83#13714yes—
295C2×Dic83C22×D412yes—
296C2×Dic83C22×D412yes—
297C2×Dic83C22×D412yes—
298C2×Dic83C22×D412yes—
299D332—24no—
300D332—22no—
301D332C22×Q814yes—
302C4×D83—48no—
303C4×D83—84no—
304C4×D83—84no—
305Dic166—24no—
306Dic166—22no—
307Dic166—28no—
308Dic166—84no—
309Dic166—84no—
310Dic166—84no—
311Dic166C22×Q814yes—
312C8×C83—22no—
313C8×C83C22×Q814yes—
314C83⋊C8—22no—
315C83⋊C8—22no—
316C22×C83D4×Q812yes—
317C22×C83C2×#13712yes—
318C22×C83#57612yes—
319C22×C83C23×D411yescharacteristic
320C2×D83—24no—
321C2×D83—48no—
322C2×D83—42no—
323C2×D83—42no—
324C4×C83—22no—
325C4×C83—22no—
326C4×C83—42no—
327C4×C83—42no—
328C4×C83—42no—
329C4×C83—42no—
330C4×C83D4×Q812yes—
331C4×C83C23×Q811yescharacteristic
332C4×C83C2×2−1+411yescharacteristic
333Dic83—24no—
334Dic83—22no—
335Dic83—22no—
336Dic83—22no—
337Dic83—42no—
338Dic83—42no—
339Dic83C2×#13714yes—
340C2×#3385—831nomaximal, Sylow
341C2×C83#338514yescomplemented
342C2×C83C2×D4×Q811yescharacteristic
343C2×C83C22×#13711yescharacteristic
344C2×C83C2×#57611yescharacteristic
345D83—44no—
346C2×Q82—831no—
347C2×#554—831no—
348#3385—8316no—
349C2×#501—831no—
350C2×#501D8311yescharacteristic, complemented
351C2×#500—831no—
352C2×#479—831no—
353C2×#479—831no—
354C2×#477—831no—
355C2×#476—831no—
356C2×#474—831no—
357C2×#474—831no—
358C2×#446—831no—
359C2×#440—831no—
360C2×#440—831no—
361C2×C4×SD16—831no—
362C83C2×#338511yescharacteristic, complemented, Sylow
363C22×SD16—831no—
364Q82—838no—
365Q82—1664no—
366#554—838no—
367#554—1664no—
368C2×C4⋊Q8—831no—
369C2×C4⋊Q8—831no—
370C2×C4⋊Q8—831no—
371C2×C4⋊Q8—1661no—
372C2×C4⋊Q8—1661no—
373C2×C4⋊Q8—1661no—
374C2×C4⋊Q8C2×D8311yescharacteristic
375C2×#125—831no—
376C2×#125C2×D8311yescharacteristic
377C2×C22⋊Q8—1661no—
378C2×C22⋊Q8—1661no—
379C2×C22⋊Q8—1661no—
380C2×C4×Q8—831no—
381C2×C4×Q8—831no—
382C2×C4×Q8—831no—
383C2×C4×Q8—831no—
384C2×C4×Q8—1661no—
385C2×C4×D4—831no—
386C2×C4×D4—831no—
387C2×C4×D4—831no—
388C22×C4⋊C4—1661no—
389#501—838no—
390#501C2×D8318yescomplemented
391#500—838no—
392#479—838no—
393#479—838no—
394#477—838no—
395#476—838no—
396#474—838no—
397#474—838no—
398#446—838no—
399#440—838no—
400#440—838no—
401C4×SD16—838no—
402C2×#107—831no—
403C2×#107—831no—
404C2×#107—831no—
405C2×#107—831no—
406C2×#107C2×D8311yescharacteristic
407C2×#107C2×D8311yescharacteristic
408C2×#106—831no—
409C2×#106C2×D8311yescharacteristic
410C2×#106C2×D8311yescharacteristic
411C2×C4⋊C8—831no—
412C2×C4⋊C8—831no—
413C2×C4⋊C8—831no—
414C2×#103—831no—
415C2×#103—831no—
416C2×#103—831no—
417C2×#102—831no—
418C2×#102—831no—
419C2×#102—831no—
420C2×#97—831no—
421C2×#97C2×D8311yescharacteristic
422C2×C4×C8—831no—
423C22×Q8—21no—
424C22×Q8—831no—
425C22×Q8—831no—
426C22×Q8—1661no—
427C22×Q8—1661no—
428C22×Q8—1661no—
429C22×D4—831no—
430C23×C4—1661no—
431C23×C4—1661no—
432C23×C4—1661no—
433C2×SD16—838no—
434C2×SD16—834no—
435C22×C8—831no—
436C22×C8—831no—
437C22×C8C22×D8311yescharacteristic
438C22×C8C22×D8311yescharacteristic
439C4⋊Q8—22no—
440C4⋊Q8—834no—
441C4⋊Q8—834no—
442C4⋊Q8—834no—
443C4⋊Q8—1662no—
444C4⋊Q8—1662no—
445C4⋊Q8—1662no—
446C4⋊Q8—1668no—
447C4⋊Q8—1668no—
448C4⋊Q8—1668no—
449C4⋊Q8C22×D8314yes—
450#125—22no—
451#125—834no—
452#125—1662no—
453#125C22×D8314yes—
454C22⋊Q8—1668no—
455C22⋊Q8—1668no—
456C22⋊Q8—1668no—
457C4×Q8—834no—
458C4×Q8—834no—
459C4×Q8—834no—
460C4×Q8—834no—
461C4×Q8—834no—
462C4×Q8—1662no—
463C4×Q8—1662no—
464C4×Q8—1668no—
465C4×Q8—1662no—
466C4×D4—834no—
467C4×D4—834no—
468C4×D4—834no—
469C4×D4—1662no—
470C4×D4—1662no—
471C4×D4—1662no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—831no—
476C2×C4⋊C4—831no—
477C2×C4⋊C4—831no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—1668no—
481C2×C4⋊C4—1661no—
482C2×C4⋊C4—1661no—
483C2×C4⋊C4—1661no—
484C2×C4⋊C4—1661no—
485C2×C4⋊C4—1661no—
486C2×C4⋊C4—1661no—
487C2×C4⋊C4—1661no—
488C2×C4⋊C4—1661no—
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C4⋊C4C22×D8311yescharacteristic
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8311yescharacteristic
493C2×C22⋊C4—1661no—
494C2×C22⋊C4—1661no—
495C2×C22⋊C4—1661no—
496C2×C42—831no—
497C2×C42—831no—
498C2×C42—1661no—
499C2×C42—1661no—
500C2×C42—1661no—
501C2×C42C22×D8311yescharacteristic
502#107—834no—
503#107—834no—
504#107—834no—
505#107—834no—
506#107C22×D8314yes—
507#107C22×D8314yes—
508#106—834no—
509#106C22×D8314yes—
510#106C22×D8314yes—
511C4⋊C8—834no—
512C4⋊C8—834no—
513C4⋊C8—834no—
514#103—834no—
515#103—834no—
516#103—834no—
517#102—834no—
518#102—834no—
519#102—834no—
520#97—834no—
521#97C22×D8314yes—
522C4×C8—834no—
523C24—1661no—
524C2×Q8—24no—
525C2×Q8—82no—
526C2×Q8—834no—
527C2×Q8—834no—
528C2×Q8—832no—
529C2×Q8—6642no—
530C2×Q8—6642no—
531C2×Q8—6642no—
532C2×Q8—1664no—
533C2×Q8—1664no—
534C2×Q8—1664no—
535C2×Q8—1664no—
536C2×Q8—1661no—
537C2×Q8—1662no—
538C2×D4—834no—
539C2×D4—832no—
540C2×D4—1661no—
541C2×D4—1662no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—3324no—
547C22×C4—831no—
548C22×C4—831no—
549C22×C4—831no—
550C22×C4—831no—
551C22×C4—6642no—
552C22×C4—6642no—
553C22×C4—1664no—
554C22×C4—1664no—
555C22×C4—1661no—
556C22×C4—1661no—
557C22×C4—1664no—
558C22×C4—1661no—
559C22×C4D4×D8311yescharacteristic
560C22×C4D4×D8311yescharacteristic
561C22×C4C23×D8311yescharacteristic
562SD16—8316no—
563C2×C8—22no—
564C2×C8—832no—
565C2×C8—832no—
566C2×C8—1662no—
567C2×C8—1662no—
568C2×C8Q8×D8314yes—
569C2×C8C23×D8312yes—
570C2×C8C23×D8312yes—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—834no—
579C4⋊C4—834no—
580C4⋊C4—834no—
581C4⋊C4—832no—
582C4⋊C4—832no—
583C4⋊C4—1664no—
584C4⋊C4—1664no—
585C4⋊C4—1664no—
586C4⋊C4—1664no—
587C4⋊C4—1664no—
588C4⋊C4—1664no—
589C4⋊C4—1664no—
590C4⋊C4—1661no—
591C4⋊C4—1661no—
592C4⋊C4—1664no—
593C4⋊C4C23×D8312yes—
594C4⋊C4C23×D8312yes—
595C4⋊C4C23×D8312yes—
596C4⋊C4C23×D8312yes—
597C22⋊C4—1664no—
598C22⋊C4—1664no—
599C22⋊C4—1664no—
600C42—832no—
601C42—832no—
602C42—832no—
603C42—832no—
604C42—1664no—
605C42—1664no—
606C42—1664no—
607C42D4×D8312yes—
608C42C23×D8312yes—
609C23—3322no—
610C23—3322no—
611C23—1664no—
612C23—1662no—
613C23C2×D4×D8311yescharacteristic
614Q8—84no—
615Q8—834no—
616Q8—6644no—
617Q8—6644no—
618Q8—6644no—
619Q8—1668no—
620Q8—1664no—
621Q8—1662no—
622D4—834no—
623D4—1664no—
624D4—1662no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—3328no—
636C2×C4—3322no—
637C2×C4—3322no—
638C2×C4—834no—
639C2×C4—832no—
640C2×C4—832no—
641C2×C4—832no—
642C2×C4—832no—
643C2×C4—6644no—
644C2×C4—6644no—
645C2×C4—1662no—
646C2×C4—1662no—
647C2×C4—1664no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4C2×D4×D8312yes—
653C2×C4C2×D4×D8312yes—
654C2×C4C2×D4×D8311yescharacteristic
655C2×C4C2×Q8×D8312yes—
656C2×C4#1458184012yes—
657C2×C4C24×D8311yescharacteristic
658C8—22no—
659C8—1662no—
660C8—1662no—
661C8C2×Q8×D8314yes—
662C22—3328no—
663C22—3322no—
664C22—3322no—
665C22—1664no—
666C22#1912836612yes—
667C22#137×D8312yes—
668C22#1912850512yes—
669C22C22×D4×D8311yescharacteristic
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—3322no—
677C4—3322no—
678C4—834no—
679C4—1662no—
680C4—1662no—
681C4—1662no—
682C4—1664no—
683C4#1912836612yes—
684C4C22×Q8×D8311yescharacteristic
685C4C2×#1458184011yescharacteristic
686C2—3324no—
687C2#2492037014yesdirect product factor
688C2C2×#1912836611yescharacteristic
689C2C2×#137×D8311yescharacteristic
690C2C2×#1912850511yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#501×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenterC2×#501D83
hypocenterC83C2×#3385
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#19128431C2semidirect
3. #24920370C2direct (N × H)
4. C2×#19128108C2semidirect
5. C2×#19128105C2semidirect
6. C2×#19128011C2semidirect
7. C2×#19128005C2semidirect
8. C2×#19127995C2semidirect
12. C2×#19127829C2semidirect
16. C2×#501×C83C2semidirect
19. #19128431C22semidirect
41. #19128108C22semidirect
42. #19128105C22semidirect
43. #19128011C22semidirect
44. #19128005C22semidirect
45. #19127995C22semidirect
49. #19127829C22semidirect
71. #501×C83C22semidirect
86. C2×#13050579Q8semidirect
207. #13050579C2×Q8semidirect
341. C2×C83#3385semidirect
350. C2×#501D83semidirect
362. C83C2×#3385semidirect
390. #501C2×D83semidirect
687. C2#24920370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284312
C2×#191284072
#249203702
C2×#191281082
C2×#191281052
C2×#191280112
C2×#191280052
C2×#191279952
C2×#191279902
C2×#191279802
C2×#191279782
C2×#191278292
C2×#191278032
C2×#191278002
C2×#191277882
C2×#501×C832
C2×#338583