Finite Group Databasebeta

← C2×#24917998 #36274033

Subgroups — C2×#24917998 #36274033

Order 21248.

1854 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128331C211yesmaximal, characteristic
2C2×#19128328C211yesmaximal, characteristic
3#24917998C2116yesmaximal, direct product factor
4C2×#19128110C211yesmaximal, characteristic, complemented
5C2×#19128109C211yesmaximal, characteristic, complemented
6C2×#19128108C211yesmaximal, characteristic, complemented
7C2×#19128105C211yesmaximal, characteristic, complemented
8C2×#19128104C211yesmaximal, characteristic, complemented
9C2×#19128101C211yesmaximal, characteristic, complemented
10C2×#19128100C211yesmaximal, characteristic, complemented
11C2×#19127742C211yesmaximal, characteristic
12C2×#19127740C211yesmaximal, characteristic
13C2×#19127736C211yesmaximal, characteristic
14C2×#107×D83C211yesmaximal, characteristic
15C2×#19127658C211yesmaximal, characteristic
16C2×#501×C83C211yesmaximal, characteristic, complemented
17C22×#13050573C2211yescharacteristic
18C22×C8×D83C2211yescharacteristic
19#19128331—24no—
20#19128331C2218yes—
21#19128328—24no—
22#19128328C2218yes—
23C2×#14581792C2211yescharacteristic
24C2×#14581791—21no—
25C2×#14581791C2211yescharacteristic
26C2×#14581791C2211yescharacteristic
27C2×#14581790—21no—
28C2×#14581784C2211yescharacteristic
29C2×#14581783C2211yescharacteristic
30C2×#14581783C2211yescharacteristic
31C2×#14581782—21no—
32C2×#14581782—21no—
33C2×#14581772—21no—
34C2×#14581770—21no—
35C2×#14581770—21no—
36C2×#14581768—21no—
37C2×#14581750C2211yescharacteristic
38C2×#14581750C2211yescharacteristic
39C2×#14581749C2211yescharacteristic
40C2×C4⋊C4×D83C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128110C2218yescomplemented
43#19128109C2218yescomplemented
44#19128108C2218yescomplemented
45#19128105C2218yescomplemented
46#19128104C2218yescomplemented
47#19128101C2218yescomplemented
48#19128100C2218yescomplemented
49#19127742C2218yes—
50#19127740C2218yes—
51#19127736C2218yes—
52C2×#14581726C2211yescharacteristic
53C2×#14581726C2211yescharacteristic
54C2×#14581725C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58C2×#14581725C2211yescharacteristic
59C2×#14581725C2211yescharacteristic
60#107×D83C2218yes—
61C2×#14581724C2211yescharacteristic
62C2×#14581724C2211yescharacteristic
63C2×#14581723C2211yescharacteristic
64C2×#14581723C2211yescharacteristic
65#19127658C2218yes—
66C2×#14581702C2211yescharacteristic
67C2×C4×C83⋊C8C2211yescharacteristic
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×C4×D83—21no—
81C22×C4×D83—21no—
82C22×C4×D83C2311yescharacteristic
83C2×#13050573Q818yescomplemented
84C2×#13050573C2314yes—
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2311yescharacteristic
87C2×C8×D83Q818yescomplemented
88C2×C8×D83C2314yes—
89#14581792—22no—
90#14581792C2314yes—
91#14581791—28no—
92#14581791—22no—
93#14581791—22no—
94#14581791C2314yes—
95#14581791C2314yes—
96#14581790—28no—
97#14581784—22no—
98#14581784C2314yes—
99#14581783—22no—
100#14581783—22no—
101#14581783C2314yes—
102#14581783C2314yes—
103#14581782—28no—
104#14581782—28no—
105#14581772—28no—
106#14581770—28no—
107#14581770—28no—
108#14581768—28no—
109#14581750—22no—
110#14581750—22no—
111#14581750C2314yes—
112#14581750C2314yes—
113#14581749D414yes—
114#14581749C2314yes—
115C2×C4⋊Dic83—21no—
116C2×C4⋊Dic83—21no—
117C2×C4⋊Dic83—21no—
118C2×C4⋊Dic83C2311yescharacteristic
119C2×C4⋊Dic83C2311yescharacteristic
120C2×C4⋊Dic83C2311yescharacteristic
121C2×C4⋊Dic83C2311yescharacteristic
122C2×Dic83⋊C4—21no—
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—22no—
133C4⋊C4×D83—22no—
134C4⋊C4×D83C2314yes—
135C4⋊C4×D83C2314yes—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4D411yescharacteristic
139C2×(C2×D83)⋊C4D411yescharacteristic
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83C2311yescharacteristic
143#14581726C2314yes—
144#14581726C2314yes—
145#14581725C2314yes—
146#14581725C2314yes—
147#14581725C2314yes—
148#14581725C2314yes—
149#14581725C2314yes—
150#14581725C2314yes—
151#14581724C2314yes—
152#14581724C2314yes—
153#14581723C2314yes—
154#14581723C2314yes—
155#14581702C2314yes—
156C4×C83⋊C8C2314yes—
157C8×Dic83C2314yes—
158C22×Q8×C83—21no—
159C22×C8×C83C2311yescharacteristic
160C22×C8×C83C2311yescharacteristic
161C4⋊Q8×C83—22no—
162C4⋊Q8×C83C2314yes—
163#125×C83—22no—
164#125×C83C2314yes—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C42×C83C2311yescharacteristic
173#107×C83C2314yes—
174#107×C83C2314yes—
175#106×C83C2314yes—
176#106×C83C2314yes—
177#97×C83C2314yes—
178C23×D83C2×D411yescharacteristic
179C2×Dic166—24no—
180C2×Dic166—24no—
181C2×Dic166—24no—
182C2×Dic166—82no—
183C2×Dic166—82no—
184C2×Dic166—82no—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C22×Dic83C2×D411yescharacteristic
190C22×Dic83C2×D411yescharacteristic
191C22×Dic83C2×D411yescharacteristic
192C2×C4×D83—24no—
193C2×C4×D83—24no—
194C2×C4×D83—82no—
195C2×C4×D83—82no—
196C2×C4×D83C2×D412yes—
197C2×C4×D83C2×Q814yes—
198C2×C4×D83C2×Q814yes—
199C2×C4×D83C2412yes—
200#13050573C2×Q8116yescomplemented
201C2×C83⋊C8C2×Q814yes—
202C2×C83⋊C8C2×Q814yes—
203C2×C83⋊C8C2412yes—
204C2×C83⋊C8C2412yes—
205C8×D83C2×Q8116yescomplemented
206C4⋊Dic83—24no—
207C4⋊Dic83—21no—
208C4⋊Dic83—21no—
209C4⋊Dic83—21no—
210C4⋊Dic83—21no—
211C4⋊Dic83—24no—
212C4⋊Dic83—24no—
213C4⋊Dic83C2412yes—
214C4⋊Dic83C2412yes—
215C4⋊Dic83C2412yes—
216C4⋊Dic83C2412yes—
217Dic83⋊C4—24no—
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)⋊C4C2×D414yes—
230(C2×D83)⋊C4C2×D414yes—
231C4×Dic83—24no—
232C4×Dic83—24no—
233C4×Dic83C2×D412yes—
234C4×Dic83C2412yes—
235C2×Q8×C83—24no—
236C2×Q8×C83—82no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83C2×D411yescharacteristic
242C22×C4×C83C2×D411yescharacteristic
243C22×C4×C83C2411yescharacteristic
244C2×C8×C83C2×Q814yes—
245C2×C8×C83C2×Q814yes—
246C2×C8×C83C2412yes—
247C2×C8×C83C2412yes—
248C4⋊C4×C83—24no—
249C4⋊C4×C83—24no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—21no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83C2412yes—
256C4⋊C4×C83C2412yes—
257C4⋊C4×C83C2412yes—
258C4⋊C4×C83C2412yes—
259C42×C83C2×D412yes—
260C42×C83C2412yes—
261C23×C83C22×D411yescharacteristic
262C22×D83—22no—
263C22×D83—22no—
264C22×D83C4⋊Q814yes—
265C22×D83C22×D412yes—
266Q8×C83—84no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—42no—
274C2×C4×C83—42no—
275C2×C4×C83—42no—
276C2×C4×C83—42no—
277C2×C4×C83C22×D412yes—
278C2×C4×C83C22×D412yes—
279C2×C4×C83C22×D411yescharacteristic
280C2×C4×C83C22×Q812yes—
281C2×C4×C83C22×Q812yes—
282C2×C4×C83C2511yescharacteristic
283C2×Dic83—22no—
284C2×Dic83—22no—
285C2×Dic83—22no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—42no—
290C2×Dic83—42no—
291C2×Dic83—42no—
292C2×Dic83—42no—
293C2×Dic83C4⋊Q814yes—
294C2×Dic83C22×D412yes—
295C2×Dic83C22×D412yes—
296C2×Dic83C22×D412yes—
297C4×D83—84no—
298C4×D83—84no—
299C4×D83C4⋊Q818yes—
300C4×D83C22×Q814yes—
301C4×D83C22×Q814yes—
302Dic166—84no—
303Dic166—84no—
304Dic166—84no—
305C8×C83C22×Q814yes—
306C8×C83C22×Q814yes—
307C83⋊C8C22×Q814yes—
308C83⋊C8C22×Q814yes—
309C22×C83C2×C4⋊Q812yes—
310C22×C83#57612yes—
311C22×C83#57812yes—
312C22×C83C23×D411yescharacteristic
313C2×D83—28no—
314C2×D83—22no—
315C2×D83—22no—
316C2×D83C2×C4⋊Q814yes—
317C4×C83—22no—
318C4×C83—22no—
319C4×C83—42no—
320C4×C83—42no—
321C4×C83—42no—
322C4×C83—42no—
323C4×C83C2×C4⋊Q812yes—
324C4×C83C23×Q811yescharacteristic
325C4×C83C23×Q811yescharacteristic
326Dic83—22no—
327Dic83—22no—
328Dic83—42no—
329Dic83—42no—
330Dic83—42no—
331Dic83—42no—
332Dic83C2×C4⋊Q814yes—
333C2×#3164—831nomaximal, Sylow
334C2×C83#316414yescomplemented
335C2×C83C22×C4⋊Q811yescharacteristic
336C2×C83C2×#57611yescharacteristic
337C2×C83C2×#57811yescharacteristic
338D83—24no—
339C2×#544—831no—
340C2×#544—831no—
341#3164—8316no—
342C2×#501—831no—
343C2×#501—831no—
344C2×#501—831no—
345C2×#501D8311yescharacteristic, complemented
346C2×#500—831no—
347C2×#500—831no—
348C2×#499—831no—
349C2×#499—831no—
350C2×#428—831no—
351C2×#428—831no—
352C2×#427—831no—
353C22×#107—831no—
354C2×#405—831no—
355C83C2×#316411yescharacteristic, complemented, Sylow
356C22×M16—831no—
357C23×C8—831no—
358#544—838no—
359#544—838no—
360#544—1664no—
361#544—1664no—
362C2×C4⋊Q8—831no—
363C2×C4⋊Q8—831no—
364C2×C4⋊Q8—831no—
365C2×C4⋊Q8—1661no—
366C2×C4⋊Q8—1661no—
367C2×C4⋊Q8C2×D8311yescharacteristic
368C2×#125—831no—
369C2×#125—831no—
370C2×#125—831no—
371C2×#125—1661no—
372C2×#125—1661no—
373C2×#125C2×D8311yescharacteristic
374C2×C22⋊Q8—1661no—
375C2×C22⋊Q8—1661no—
376C2×C22⋊Q8—1661no—
377C2×C22⋊Q8—1661no—
378C2×#117—831no—
379C2×#117—831no—
380C2×#117—831no—
381C22×C4⋊C4—831no—
382C22×C4⋊C4—831no—
383#501—838no—
384#501—838no—
385#501—838no—
386#501C2×D8318yescomplemented
387#500—838no—
388#500—838no—
389#499—838no—
390#499—838no—
391#428—838no—
392#428—838no—
393#427—838no—
394C2×#107—831no—
395C2×#107—831no—
396C2×#107—831no—
397C2×#107—831no—
398C2×#107—831no—
399C2×#107—831no—
400C2×#107—831no—
401C2×#107—831no—
402C2×#107—838no—
403C2×#107C2×D8311yescharacteristic
404C2×#107C2×D8311yescharacteristic
405C2×#106—831no—
406C2×#106—831no—
407C2×#106—831no—
408C2×#106—831no—
409C2×#106C2×D8311yescharacteristic
410C2×#106C2×D8311yescharacteristic
411#405—838no—
412C2×#97—831no—
413C2×#97C2×D8311yescharacteristic
414C2×C4×C8—831no—
415C2×C4×C8—831no—
416C22×Q8—21no—
417C22×Q8—1661no—
418C22×Q8—1661no—
419C22×Q8—1661no—
420C23×C4—831no—
421C23×C4—1661no—
422C23×C4—1661no—
423C2×M16—838no—
424C2×M16—834no—
425C22×C8—831no—
426C22×C8—831no—
427C22×C8—838no—
428C22×C8—834no—
429C22×C8C22×D8311yescharacteristic
430C22×C8C22×D8311yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—834no—
433C4⋊Q8—834no—
434C4⋊Q8—834no—
435C4⋊Q8—1662no—
436C4⋊Q8—1662no—
437C4⋊Q8—1668no—
438C4⋊Q8—1668no—
439C4⋊Q8—1662no—
440C4⋊Q8C22×D8314yes—
441#125—22no—
442#125—834no—
443#125—834no—
444#125—834no—
445#125—1662no—
446#125—1662no—
447#125—1668no—
448#125—1668no—
449#125—1662no—
450#125C22×D8314yes—
451C22⋊Q8—1668no—
452C22⋊Q8—1668no—
453C22⋊Q8—1668no—
454C22⋊Q8—1668no—
455#117—834no—
456#117—834no—
457#117—834no—
458#117—834no—
459#117—1662no—
460#117—1662no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—831no—
465C2×C4⋊C4—831no—
466C2×C4⋊C4—831no—
467C2×C4⋊C4—831no—
468C2×C4⋊C4—831no—
469C2×C4⋊C4—831no—
470C2×C4⋊C4—834no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—1662no—
473C2×C4⋊C4—1662no—
474C2×C4⋊C4—1661no—
475C2×C4⋊C4—1661no—
476C2×C4⋊C4—1661no—
477C2×C4⋊C4—1661no—
478C2×C4⋊C4—1661no—
479C2×C4⋊C4—1661no—
480C2×C4⋊C4—1661no—
481C2×C4⋊C4—1661no—
482C2×C4⋊C4—1661no—
483C2×C4⋊C4—1661no—
484C2×C4⋊C4—1661no—
485C2×C4⋊C4C22×D8311yescharacteristic
486C2×C4⋊C4C22×D8311yescharacteristic
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C22⋊C4—831no—
490C2×C22⋊C4—831no—
491C2×C22⋊C4—1661no—
492C2×C22⋊C4—1661no—
493C2×C42—831no—
494C2×C42—1661no—
495C2×C42—1661no—
496C2×C42C22×D8311yescharacteristic
497#107—834no—
498#107—834no—
499#107—834no—
500#107—834no—
501#107—834no—
502#107—834no—
503#107—834no—
504#107—834no—
505#107C22×D8314yes—
506#107C22×D8314yes—
507#106—834no—
508#106—834no—
509#106—834no—
510#106—834no—
511#106C22×D8314yes—
512#106C22×D8314yes—
513#97—834no—
514#97C22×D8314yes—
515C4×C8—834no—
516C4×C8—834no—
517C24—831no—
518C2×Q8—24no—
519C2×Q8—82no—
520C2×Q8—6642no—
521C2×Q8—6642no—
522C2×Q8—6642no—
523C2×Q8—1664no—
524C2×Q8—1664no—
525C2×Q8—1664no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—831no—
531C22×C4—832no—
532C22×C4—834no—
533C22×C4—834no—
534C22×C4—832no—
535C22×C4—831no—
536C22×C4—831no—
537C22×C4—6642no—
538C22×C4—6642no—
539C22×C4—1664no—
540C22×C4—1664no—
541C22×C4—1661no—
542C22×C4—1661no—
543C22×C4—1661no—
544C22×C4—1661no—
545C22×C4D4×D8311yescharacteristic
546C22×C4D4×D8311yescharacteristic
547C22×C4C23×D8311yescharacteristic
548M16—8316no—
549C2×C8—834no—
550C2×C8—834no—
551C2×C8—832no—
552C2×C8—832no—
553C2×C8—8316no—
554C2×C8Q8×D8314yes—
555C2×C8Q8×D8314yes—
556C2×C8C23×D8312yes—
557C2×C8C23×D8312yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—834no—
566C4⋊C4—834no—
567C4⋊C4—832no—
568C4⋊C4—832no—
569C4⋊C4—832no—
570C4⋊C4—832no—
571C4⋊C4—1664no—
572C4⋊C4—1664no—
573C4⋊C4—1664no—
574C4⋊C4—1664no—
575C4⋊C4—1664no—
576C4⋊C4—1664no—
577C4⋊C4—1664no—
578C4⋊C4—1664no—
579C4⋊C4—1661no—
580C4⋊C4—1661no—
581C4⋊C4—1661no—
582C4⋊C4—1661no—
583C4⋊C4—1664no—
584C4⋊C4—1664no—
585C4⋊C4—1664no—
586C4⋊C4C23×D8312yes—
587C4⋊C4C23×D8312yes—
588C4⋊C4C23×D8312yes—
589C4⋊C4C23×D8312yes—
590C22⋊C4—834no—
591C22⋊C4—834no—
592C22⋊C4—1664no—
593C22⋊C4—1664no—
594C42—832no—
595C42—832no—
596C42—1664no—
597C42—1664no—
598C42D4×D8312yes—
599C42C23×D8312yes—
600C23—834no—
601C23—832no—
602C23—1662no—
603C23—1662no—
604C23C2×D4×D8311yescharacteristic
605Q8—84no—
606Q8—6644no—
607Q8—6644no—
608Q8—6644no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—3322no—
620C2×C4—3322no—
621C2×C4—3322no—
622C2×C4—3322no—
623C2×C4—834no—
624C2×C4—832no—
625C2×C4—838no—
626C2×C4—834no—
627C2×C4—834no—
628C2×C4—832no—
629C2×C4—832no—
630C2×C4—6644no—
631C2×C4—6644no—
632C2×C4—1662no—
633C2×C4—1662no—
634C2×C4—1662no—
635C2×C4—1662no—
636C2×C4—1662no—
637C2×C4—1662no—
638C2×C4C2×D4×D8312yes—
639C2×C4C2×D4×D8312yes—
640C2×C4C2×D4×D8311yescharacteristic
641C2×C4C2×Q8×D8312yes—
642C2×C4C2×Q8×D8312yes—
643C2×C4C24×D8311yescharacteristic
644C8—834no—
645C8—834no—
646C8C2×Q8×D8314yes—
647C8C2×Q8×D8314yes—
648C22—834no—
649C22—1662no—
650C22—1662no—
651C22—1668no—
652C22C4⋊Q8×D8312yes—
653C22#1912850512yes—
654C22#1912851712yes—
655C22C22×D4×D8311yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—3322no—
663C4—3322no—
664C4—3322no—
665C4—3322no—
666C4—834no—
667C4—1662no—
668C4—1662no—
669C4C4⋊Q8×D8312yes—
670C4C22×Q8×D8311yescharacteristic
671C4C22×Q8×D8311yescharacteristic
672C2—1664no—
673C2#2491799814yesdirect product factor
674C2C2×C4⋊Q8×D8311yescharacteristic
675C2C2×#1912850511yescharacteristic
676C2C2×#1912851711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#501×C83C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
hypercenterC2×#501D83
hypocenterC83C2×#3164
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
3. #24917998C2direct (N × H)
4. C2×#19128110C2semidirect
5. C2×#19128109C2semidirect
6. C2×#19128108C2semidirect
7. C2×#19128105C2semidirect
8. C2×#19128104C2semidirect
9. C2×#19128101C2semidirect
10. C2×#19128100C2semidirect
16. C2×#501×C83C2semidirect
42. #19128110C22semidirect
43. #19128109C22semidirect
44. #19128108C22semidirect
45. #19128105C22semidirect
46. #19128104C22semidirect
47. #19128101C22semidirect
48. #19128100C22semidirect
71. #501×C83C22semidirect
83. C2×#13050573Q8semidirect
87. C2×C8×D83Q8semidirect
200. #13050573C2×Q8semidirect
205. C8×D83C2×Q8semidirect
334. C2×C83#3164semidirect
345. C2×#501D83semidirect
355. C83C2×#3164semidirect
386. #501C2×D83semidirect
673. C2#24917998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283312
C2×#191283282
#249179982
C2×#191281102
C2×#191281092
C2×#191281082
C2×#191281052
C2×#191281042
C2×#191281012
C2×#191281002
C2×#191277422
C2×#191277402
C2×#191277362
C2×#107×D832
C2×#191276582
C2×#501×C832
C2×#316483