Finite Group Databasebeta

← C2×#82751 #10963128

Subgroups — C2×#82751 #10963128

Order 768.

5566 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
1C23×D3×Q8C211yesmaximal, characteristic, complemented
2C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×#924C211yesmaximal, characteristic, complemented
4C22×C4×#67C211yesmaximal, characteristic
5C2×#5229C211yesmaximal, characteristic, complemented
6#82751C2116yesmaximal, direct product factor
7C2×#4989C212yesmaximal, complemented
8C2×#4987C211yesmaximal, characteristic, complemented
9C2×#4979C212yesmaximal, complemented
10C2×#4973C211yesmaximal, characteristic, complemented
11C2×#4956C212yesmaximal
12C2×#4947C212yesmaximal, complemented
13C2×#2409—31nomaximal, Sylow
14C23×C3×Q8C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C22×D3×Q8—28no—
18C22×D3×Q8—28no—
19C22×D3×Q8—28no—
20C22×D3×Q8C2218yescomplemented
21C23×C4×D3C2212yes—
22C23×C4×D3C2211yescharacteristic
23C23×Dic6C2212yes—
24C23×Dic6C2211yescharacteristic
25C2×C3×C22⋊Q8—28no—
26C2×C3×C22⋊Q8C2218yescomplemented
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2212yes—
29C22×C3×C22⋊C4C2212yes—
30C22×#217C2211yescharacteristic
31C22×#217C2212yes—
32C2×C4×#67—28no—
33C2×C4×#67C2218yes—
34C22×(C2×D3)⋊C4C2212yes—
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C2×#924—28no—
38C2×#924C2218yescomplemented
39C22×Dic3⋊C4C2212yes—
40C22×Dic3⋊C4C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42#5229C2218yescomplemented
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2212yes—
45C2×C3⋊#95C2212yes—
46C2×C3⋊#95C2212yes—
47C2×C3⋊#95C2212yes—
48#4989C22116yescomplemented
49#4987C2218yescomplemented
50#4979C22116yescomplemented
51#4973C2218yescomplemented
52#4956C22116yes—
53#4947C22116yescomplemented
54C24×Q8—31no—
55C22×C22⋊Q8—31no—
56C22×C22⋊Q8D311yescharacteristic, complemented
57C22×C4×D4—31no—
58#2409—316no—
59C2×#395—32no—
60C2×#393—32no—
61C2×#391—31no—
62C2×#391—31no—
63C2×#386—32no—
64C2×#385—32no—
65C2×#380—31no—
66C25×C3C2311yescharacteristic
67C24×D3C2311yescharacteristic
68C22×C3×Q8—24no—
69C22×C3×Q8—24no—
70C22×C3×Q8D418yescomplemented
71C22×C3×Q8C2314yes—
72C23×C3×C4—24no—
73C23×C3×C4—24no—
74C23×C3×C4—24no—
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2314yes—
77C23×C3×C4C2312yes—
78C23×C3×C4C2312yes—
79C23×C3×C4C2311yescharacteristic
80C22×#67—24no—
81C22×#67—24no—
82C22×#67Q818yescomplemented
83C22×#67C2314yes—
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2312yes—
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2312yes—
88C23×Dic3C2311yescharacteristic
89C2×D3×Q8—2128no—
90C2×D3×Q8—232no—
91C2×D3×Q8—232no—
92C2×D3×Q8—232no—
93C22×C4×D3—28no—
94C22×C4×D3—24no—
95C22×C4×D3—28no—
96C22×C4×D3—24no—
97C22×C4×D3—28no—
98C22×C4×D3D418yes—
99C22×C4×D3C2318yes—
100C22×C4×D3C2314yes—
101C22×Dic6—24no—
102C22×Dic6—28no—
103C22×Dic6—24no—
104C22×Dic6—28no—
105C22×Dic6—28no—
106C22×Dic6D418yescomplemented
107C22×Dic6C2318yes—
108C22×Dic6C2314yes—
109C3×C22⋊Q8—232no—
110C2×C3×C4⋊C4—24no—
111C2×C3×C4⋊C4—28no—
112C2×C3×C4⋊C4C2314yes—
113C2×C3×C4⋊C4C2318yes—
114C2×C3×C22⋊C4—28no—
115C2×C3×C22⋊C4C2318yes—
116C2×#217—28no—
117C2×#217—24no—
118C2×#217C2314yes—
119C2×#217C2318yes—
120C4×#67—232no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—28no—
123C2×(C2×D3)⋊C4C2318yes—
124C2×(C2×D3)⋊C4C2314yes—
125C2×C4⋊Dic3—24no—
126C2×C4⋊Dic3C2314yes—
127#924—232no—
128C2×Dic3⋊C4—28no—
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4C2314yes—
131C2×Dic3⋊C4C2318yes—
132C2×C4×Dic3—24no—
133C2×C4×Dic3C2314yes—
134C3⋊#95C2318yes—
135C3⋊#95C2318yes—
136C3⋊#95C2318yes—
137C3⋊#95C2318yes—
138C3⋊#95C2318yes—
139C23×Q8—38no—
140C23×Q8—31no—
141C23×Q8—32no—
142C23×Q8—68no—
143C23×Q8—68no—
144C23×Q8—68no—
145C23×Q8C2×D311yescharacteristic
146C23×D4—31no—
147C24×C4—31no—
148C24×C4—32no—
149C24×C4C2×D311yescharacteristic
150C2×C22⋊Q8—28no—
151C2×C22⋊Q8—38no—
152C2×C22⋊Q8—68no—
153C2×C22⋊Q8C2×D318yescomplemented
154C2×C4×D4—38no—
155C2×C4×D4—68no—
156C22×C4⋊C4—31no—
157C22×C4⋊C4—32no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4C2×D312yes—
160C22×C4⋊C4C2×D311yescharacteristic
161C22×C22⋊C4—31no—
162C22×C22⋊C4—32no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—32no—
165C22×C22⋊C4C2×D312yes—
166C22×C42—31no—
167#395—316no—
168#393—316no—
169#391—38no—
170#391—38no—
171#386—316no—
172#385—316no—
173#380—38no—
174C2×#95—32no—
175C2×#95—32no—
176C2×#95—32no—
177C2×#95—32no—
178C2×#95—32no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3C2×Q814yescomplemented
186C24×C3C2412yes—
187C24×C3C2411yescharacteristic
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3C2×D414yes—
193C23×D3C2×Q814yes—
194C23×D3#4114yes—
195C23×D3C2412yes—
196C2×C3×Q8—232no—
197C2×C3×Q8—28no—
198C2×C3×Q8—28no—
199C2×C3×Q8C2×D4116yescomplemented
200C22×C3×C4—24no—
201C22×C3×C4—24no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—24no—
205C22×C3×C4—22no—
206C22×C3×C4—24no—
207C22×C3×C4—24no—
208C22×C3×C4—28no—
209C22×C3×C4—28no—
210C22×C3×C4—28no—
211C22×C3×C4—416no—
212C22×C3×C4C2×D414yes—
213C22×C3×C4C2×D414yes—
214C22×C3×C4C2×D418yes—
215C22×C3×C4C2×D414yes—
216C22×C3×C4C2414yes—
217C22×C3×C4C2412yes—
218C22×C3×C4C2414yes—
219C22×C3×C4C2412yes—
220C2×#67—232no—
221C2×#67—28no—
222C2×#67—28no—
223C2×#67C2×Q8116yescomplemented
224C22×Dic3—22no—
225C22×Dic3—24no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—24no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—24no—
232C22×Dic3—24no—
233C22×Dic3—22no—
234C22×Dic3—24no—
235C22×Dic3—22no—
236C22×Dic3C2×D414yes—
237C22×Dic3C2×D418yes—
238C22×Dic3C2×Q814yescomplemented
239C22×Dic3C2412yes—
240C22×Dic3C2414yes—
241C22×Dic3C2412yes—
242C22×Dic3C2414yes—
243C22×Dic3C2412yes—
244D3×Q8—2256no—
245C2×C4×D3—264no—
246C2×C4×D3—216no—
247C2×C4×D3—232no—
248C2×C4×D3—28no—
249C2×C4×D3—216no—
250C2×C4×D3—28no—
251C2×C4×D3—216no—
252C2×C4×D3C2×D4116yes—
253C2×Dic6—264no—
254C2×Dic6—232no—
255C2×Dic6—28no—
256C2×Dic6—216no—
257C2×Dic6—28no—
258C2×Dic6—216no—
259C2×Dic6—216no—
260C2×Dic6C2×D4116yescomplemented
261C3×C4⋊C4—28no—
262C3×C4⋊C4—216no—
263C3×C22⋊C4—216no—
264#217—216no—
265#217—28no—
266(C2×D3)⋊C4—28no—
267(C2×D3)⋊C4—216no—
268C4⋊Dic3—28no—
269Dic3⋊C4—216no—
270Dic3⋊C4—28no—
271C4×Dic3—28no—
272C25—31no—
273C25C22×D311yescharacteristic
274C22×Q8—24no—
275C22×Q8—24no—
276C22×Q8—38no—
277C22×Q8—34no—
278C22×Q8—38no—
279C22×Q8—68no—
280C22×Q8—68no—
281C22×Q8—632no—
282C22×Q8—632no—
283C22×Q8—6128no—
284C22×Q8—632no—
285C22×Q8—64no—
286C22×Q8—68no—
287C22×Q8—64no—
288C22×Q8#6718yescomplemented
289C22×Q8C22×D314yes—
290C22×D4—38no—
291C22×D4—34no—
292C22×D4—64no—
293C22×D4—64no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—31no—
298C23×C4—32no—
299C23×C4—31no—
300C23×C4—38no—
301C23×C4—34no—
302C23×C4—32no—
303C23×C4—31no—
304C23×C4—38no—
305C23×C4—68no—
306C23×C4—68no—
307C23×C4—64no—
308C23×C4—68no—
309C23×C4—64no—
310C23×C4C22×D314yes—
311C23×C4C22×D312yes—
312C23×C4C22×D311yescharacteristic
313C23×C4C22×D312yes—
314C23×C4C22×D311yescharacteristic
315C22⋊Q8—232no—
316C22⋊Q8—632no—
317C4×D4—632no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—34no—
321C2×C4⋊C4—34no—
322C2×C4⋊C4—38no—
323C2×C4⋊C4—64no—
324C2×C4⋊C4—68no—
325C2×C4⋊C4—64no—
326C2×C4⋊C4C22×D314yes—
327C2×C4⋊C4C22×D318yes—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—34no—
330C2×C22⋊C4—38no—
331C2×C22⋊C4—34no—
332C2×C22⋊C4—38no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—68no—
335C2×C22⋊C4—64no—
336C2×C22⋊C4—68no—
337C2×C22⋊C4C22×D318yes—
338C2×C42—34no—
339C2×C42—64no—
340#95—38no—
341#95—38no—
342#95—38no—
343#95—38no—
344#95—38no—
345C23×C3—28no—
346C23×C3—28no—
347C23×C3—28no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—44no—
355C23×C3—44no—
356C23×C3—44no—
357C23×C3—44no—
358C23×C3C22×D412yes—
359C23×C3C22×D412yes—
360C23×C3C22×D412yes—
361C23×C3C22×Q812yes—
362C23×C3C22×Q814yescomplemented
363C23×C3C2×#4112yes—
364C23×C32−1+412yes—
365C23×C32−1+412yes—
366C23×C3C2511yescharacteristic
367C22×D3—28no—
368C22×D3—28no—
369C22×D3—28no—
370C22×D3—28no—
371C22×D3—28no—
372C22×D3—28no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3C22⋊Q8116yescomplemented
378C22×D3C22×D414yes—
379C22×D3C22×Q814yes—
380C22×D3C2×#4114yes—
381C3×Q8—232no—
382C2×C3×C4—216no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—22no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—44no—
392C2×C3×C4—48no—
393C2×C3×C4—416no—
394C2×C3×C4#120116yes—
395C2×C3×C4C22×D414yes—
396C2×C3×C4C22×D414yes—
397C2×C3×C4C22×D418yes—
398C2×C3×C4C22×D414yes—
399#67—232no—
400C2×Dic3—28no—
401C2×Dic3—216no—
402C2×Dic3—28no—
403C2×Dic3—22no—
404C2×Dic3—24no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—24no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—24no—
414C2×Dic3—22no—
415C2×Dic3—44no—
416C2×Dic3—48no—
417C2×Dic3C22×D414yes—
418C2×Dic3C22×D418yes—
419C2×Dic3C22×Q814yescomplemented
420C4×D3—264no—
421C4×D3—232no—
422Dic6—264no—
423Dic6—232no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—34no—
431C24—34no—
432C24—34no—
433C24—32no—
434C24—62no—
435C24—62no—
436C24—62no—
437C24—62no—
438C24D3×Q814yescomplemented
439C24C23×D312yes—
440C24C23×D311yescharacteristic
441C2×Q8—232no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—316no—
445C2×Q8—616no—
446C2×Q8—616no—
447C2×Q8—664no—
448C2×Q8—6256no—
449C2×Q8—632no—
450C2×Q8—68no—
451C2×Q8—616no—
452C2×Q8—68no—
453C2×Q8C2×#67116yescomplemented
454C2×D4—316no—
455C2×D4—68no—
456C2×D4—68no—
457C2×D4—632no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—34no—
470C22×C4—38no—
471C22×C4—34no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—34no—
475C22×C4—316no—
476C22×C4—32no—
477C22×C4—34no—
478C22×C4—416no—
479C22×C4—616no—
480C22×C4—616no—
481C22×C4—664no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—64no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—64no—
488C22×C4—632no—
489C22×C4—68no—
490C22×C4—616no—
491C22×C4—68no—
492C22×C4—62no—
493C22×C4—64no—
494C22×C4—64no—
495C22×C4—62no—
496C22×C4—64no—
497C22×C4—62no—
498C22×C4D3×D414yes—
499C22×C4D3×D414yes—
500C22×C4C2×#6718yes—
501C22×C4C2×#6714yes—
502C22×C4C23×D314yes—
503C22×C4C23×D312yes—
504C22×C4C23×D314yes—
505C22×C4C23×D312yes—
506C4⋊C4—28no—
507C4⋊C4—216no—
508C4⋊C4—68no—
509C4⋊C4—616no—
510C4⋊C4—68no—
511C22⋊C4—216no—
512C22⋊C4—68no—
513C22⋊C4—616no—
514C22⋊C4—68no—
515C22⋊C4—616no—
516C42—68no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—42no—
521C22×C3—416no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3C2×#12014yes—
526C22×C3C2×C22⋊Q814yes—
527C22×C3#53614yes—
528C22×C3#54814yes—
529C22×C3#54814yes—
530C22×C3D4×Q814yes—
531C22×C3D4×Q814yes—
532C22×C3C23×D411yescharacteristic
533C22×C3C23×D411yescharacteristic
534C22×C3C23×D411yescharacteristic
535C22×C3C23×Q811yescharacteristic
536C22×C3C22×#4111yescharacteristic
537C22×C3C2×2−1+411yescharacteristic
538C22×C3C2×2−1+411yescharacteristic
539C2×D3—24no—
540C2×D3—232no—
541C2×D3—24no—
542C2×D3—24no—
543C2×D3—24no—
544C2×D3—24no—
545C2×D3—24no—
546C2×D3C2×C22⋊Q818yescomplemented
547C3×C4—28no—
548C3×C4—42no—
549C3×C4—44no—
550C3×C4C2×#12018yes—
551Dic3—24no—
552Dic3—28no—
553Dic3—24no—
554Dic3—42no—
555Dic3—44no—
556C23—28no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—28no—
564C23—28no—
565C23—34no—
566C23—34no—
567C23—34no—
568C23—316no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—44no—
573C23—68no—
574C23—68no—
575C23—62no—
576C23—62no—
577C23—62no—
578C23—62no—
579C23—68no—
580C23—68no—
581C23—68no—
582C23—68no—
583C23C2×D3×D412yes—
584C23C2×D3×D412yes—
585C23C2×D3×Q812yes—
586C23C2×D3×Q814yescomplemented
587C23#100712yes—
588C23D3×#4112yes—
589C23#101012yes—
590C23C22×#6712yes—
591C23C24×D311yescharacteristic
592Q8—232no—
593Q8—664no—
594Q8—632no—
595D4—632no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—216no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—34no—
606C2×C4—38no—
607C2×C4—34no—
608C2×C4—44no—
609C2×C4—48no—
610C2×C4—416no—
611C2×C4—664no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—64no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—64no—
618C2×C4—68no—
619C2×C4—616no—
620C2×C4—68no—
621C2×C4—632no—
622C2×C4—62no—
623C2×C4—64no—
624C2×C4—62no—
625C2×C4—64no—
626C2×C4—64no—
627C2×C4—62no—
628C2×C4—128no—
629C2×C4—124no—
630C2×C4#937116yes—
631C2×C4C2×D3×D414yes—
632C2×C4C2×D3×D414yes—
633C2×C4C22×#6718yes—
634C2×C4C22×#6714yes—
635C2×C3—44no—
636C2×C3#240918yescomplemented
637C2×C3C22×#12011yescharacteristic
638C2×C3C22×C22⋊Q811yescharacteristic
639C2×C3C2×#53611yescharacteristic
640C2×C3C2×#54811yescharacteristic
641C2×C3C2×#54811yescharacteristic
642C2×C3C2×D4×Q811yescharacteristic
643C2×C3C2×D4×Q811yescharacteristic
644D3—28no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—38no—
649C22—416no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—632no—
655C22—64no—
656C22—64no—
657C22—64no—
658C22—64no—
659C22—64no—
660C22—64no—
661C22D3×C22⋊Q814yes—
662C22#562814yes—
663C22#563214yes—
664C22#563314yes—
665C22C2×#93714yes—
666C22Q8×#6714yes—
667C22#583114yes—
668C22C22×D3×D411yescharacteristic
669C22C22×D3×D411yescharacteristic
670C22C22×D3×Q811yescharacteristic
671C22C2×#100711yescharacteristic
672C22C2×D3×#4111yescharacteristic
673C22C2×#101011yescharacteristic
674C22C23×#6711yescharacteristic
675C4—28no—
676C4—42no—
677C4—44no—
678C4—64no—
679C4—68no—
680C4—64no—
681C4—122no—
682C4—124no—
683C4C2×#93718yes—
684C3C2×#240911yescharacteristic, complemented, Sylow
685C2—44no—
686C2—68no—
687C2#8275118yesdirect product factor
688C2C2×#563211yescharacteristic
689C2C2×D3×C22⋊Q811yescharacteristic
690C2C2×#562811yescharacteristic
691C2C2×#563311yescharacteristic
692C2C22×#93711yescharacteristic
693C2C2×Q8×#6711yescharacteristic
694C2C2×#583111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×C22⋊Q8C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3C2×#2409
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×D3×Q8C2semidirect
2. C22×C3×C22⋊Q8C2semidirect
3. C22×#924C2semidirect
5. C2×#5229C2semidirect
6. #82751C2direct (N × H)
7. C2×#4989C2semidirect
8. C2×#4987C2semidirect
9. C2×#4979C2semidirect
10. C2×#4973C2semidirect
12. C2×#4947C2semidirect
20. C22×D3×Q8C22semidirect
26. C2×C3×C22⋊Q8C22semidirect
38. C2×#924C22semidirect
42. #5229C22semidirect
48. #4989C22semidirect
49. #4987C22semidirect
50. #4979C22semidirect
51. #4973C22semidirect
53. #4947C22semidirect
56. C22×C22⋊Q8D3semidirect
70. C22×C3×Q8D4semidirect
82. C22×#67Q8semidirect
106. C22×Dic6D4semidirect
153. C2×C22⋊Q8C2×D3semidirect
185. C24×C3C2×Q8semidirect
199. C2×C3×Q8C2×D4semidirect
223. C2×#67C2×Q8semidirect
238. C22×Dic3C2×Q8semidirect
260. C2×Dic6C2×D4semidirect
288. C22×Q8#67semidirect
362. C23×C3C22×Q8semidirect
377. C22×D3C22⋊Q8semidirect
419. C2×Dic3C22×Q8semidirect
438. C24D3×Q8semidirect
453. C2×Q8C2×#67semidirect
546. C2×D3C2×C22⋊Q8semidirect
586. C23C2×D3×Q8semidirect
636. C2×C3#2409semidirect
684. C3C2×#2409semidirect
687. C2#82751direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×Q82
C22×C3×C22⋊Q82
C22×#9242
C22×C4×#672
C2×#52292
#827512
C2×#49892
C2×#49872
C2×#49792
C2×#49732
C2×#49562
C2×#49472
C2×#24093