Finite Group Databasebeta

← C2×#18008 #6344909

Subgroups — C2×#18008 #6344909

Order 512.

1944 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3105C211yesmaximal, characteristic
2C2×#2969C211yesmaximal, characteristic, complemented
3C2×D4×M16C211yesmaximal, characteristic, complemented
4#18008C2116yesmaximal, direct product factor
5C2×#1592C211yesmaximal, characteristic, complemented
6C2×#1589C211yesmaximal, characteristic, complemented
7C2×#1586C211yesmaximal, characteristic, complemented
8C2×#1585C211yesmaximal, characteristic, complemented
9C2×#1583C211yesmaximal, characteristic, complemented
10C2×#1581C211yesmaximal, characteristic, complemented
11C2×#1580C211yesmaximal, characteristic, complemented
12C2×C8×SD16C211yesmaximal, characteristic, complemented
13C2×#1574C211yesmaximal, characteristic, complemented
14C2×#1495C211yesmaximal, characteristic, complemented
15C2×#1478C211yesmaximal, characteristic, complemented
16C2×#1453C211yesmaximal, characteristic, complemented
17C23×M16—21no—
18C2×#529C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20#3105C418yes—
21#3105C2218yes—
22C2×#484C411yescharacteristic
23C2×#481C411yescharacteristic
24C2×#478C411yescharacteristic
25C2×#478C411yescharacteristic
26C2×#463C411yescharacteristic
27C2×#463C411yescharacteristic
28C2×#450C411yescharacteristic
29C2×#447C411yescharacteristic
30#2969—24no—
31#2969C2218yescomplemented
32C2×#446C2211yescharacteristic, complemented
33C2×C8×Q8C2211yescharacteristic, complemented
34C2×C4×SD16C2211yescharacteristic
35C2×C4×SD16C2211yescharacteristic
36C2×C4×D8C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38D4×M16—24no—
39D4×M16C2218yescomplemented
40C2×#436—21no—
41C2×#436C2211yescharacteristic
42C2×#436C2211yescharacteristic
43C2×#436C2211yescharacteristic, complemented
44C2×#435—21no—
45C2×#435—21no—
46C2×#435—21no—
47C2×C8×D4C2211yescharacteristic
48C2×C8×D4C2211yescharacteristic
49C2×C8×D4C2211yescharacteristic, complemented
50C2×#433—21no—
51C2×#431C2211yescharacteristic
52C2×#431C2211yescharacteristic
53C2×#431C2211yescharacteristic
54C2×#423C2211yescharacteristic
55C2×#407—21no—
56C2×#405—21no—
57C2×C4×M16C2211yescharacteristic
58#1592C2218yescomplemented
59#1589C2218yescomplemented
60#1586C2218yescomplemented
61#1585C2218yescomplemented
62#1583C2218yescomplemented
63#1581C2218yescomplemented
64#1580C2218yescomplemented
65C8×SD16C2218yescomplemented
66#1574C2218yescomplemented
67C2×#335C2211yescharacteristic, complemented
68C2×#335C2211yescharacteristic, complemented
69C2×#334C2211yescharacteristic, complemented
70C2×#334C2211yescharacteristic, complemented
71#1495C2218yescomplemented
72#1478C2218yescomplemented
73C2×Q8⋊C8C2211yescharacteristic, complemented
74C2×Q8⋊C8C2211yescharacteristic, complemented
75C2×D4⋊C8C2211yescharacteristic
76C2×D4⋊C8C2211yescharacteristic
77C2×D4⋊C8C2211yescharacteristic
78C2×D4⋊C8C2211yescharacteristic
79C2×D4⋊C8C2211yescharacteristic, complemented
80C2×D4⋊C8C2211yescharacteristic, complemented
81#1453C2218yescomplemented
82C2×#322C2211yescharacteristic, complemented
83C2×#322C2211yescharacteristic, complemented
84C2×#322C2211yescharacteristic, complemented
85C2×C82C2211yescharacteristic, complemented
86C23×D4C2×C411yescharacteristic
87C24×C4—21no—
88C22×SD16C2×C411yescharacteristic
89C22×SD16C2×C411yescharacteristic
90C22×D8C2×C411yescharacteristic
91C22×D8C2×C411yescharacteristic
92C22×M16—21no—
93C22×M16—28no—
94C22×M16—21no—
95C22×M16—21no—
96C22×M16—21no—
97C22×M16—48no—
98C22×M16D411yescharacteristic
99C22×M16D411yescharacteristic
100C23×C8—21no—
101C23×C8—21no—
102C23×C8—21no—
103#529—22no—
104#529—22no—
105#529C2×C414yes—
106#529C2314yes—
107C2×#126—21no—
108C2×#125C2×C411yescharacteristic
109C2×#124C2×C411yescharacteristic
110C2×#123—21no—
111C2×C22⋊Q8C2×C411yescharacteristic
112C2×#121C2×C411yescharacteristic
113C2×C4×Q8C2311yescharacteristic
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—22no—
117C2×C4×D4—21no—
118C2×C4×D4—22no—
119C2×C4×D4C2×C411yescharacteristic
120C2×C4×D4C2×C411yescharacteristic
121C2×C4×D4C2×C414yes—
122C2×C4×D4C2314yes—
123C2×C4×D4C2311yescharacteristic
124C2×C4×D4C2311yescharacteristic
125C2×C4×D4C2311yescharacteristic
126C2×#117—21no—
127C22×C4⋊C4C2×C411yescharacteristic
128C22×C22⋊C4—21no—
129C22×C42C2311yescharacteristic
130#484C2×C418yes—
131#481C2×C418yes—
132#478C2×C418yes—
133#478C2×C418yes—
134#463C2×C418yes—
135#463C2×C418yes—
136#450C2×C418yes—
137#447C2×C418yes—
138#446—22no—
139#446C2314yescomplemented
140C8×Q8—22no—
141C8×Q8C2314yescomplemented
142C4×SD16C2×C414yes—
143C4×SD16C2×C414yes—
144C4×SD16C2314yes—
145C4×SD16C2314yes—
146C4×D8C2×C414yes—
147C4×D8C2×C414yes—
148C4×D8C2314yes—
149C4×D8C2314yes—
150#436—28no—
151#436—22no—
152#436—22no—
153#436—22no—
154#436C2314yes—
155#436C2314yes—
156#436C2314yescomplemented
157#435—28no—
158#435—28no—
159#435—28no—
160C8×D4—22no—
161C8×D4—22no—
162C8×D4—22no—
163C8×D4C2314yes—
164C8×D4C2314yes—
165C8×D4C2314yescomplemented
166#433—28no—
167#431—22no—
168#431—22no—
169#431C2×C414yes—
170#431C2314yes—
171#431C2314yes—
172#431C2314yes—
173C2×#107C2×C411yescharacteristic
174C2×#107C2×C411yescharacteristic
175C2×#106C2×C411yescharacteristic
176C2×#106C2×C411yescharacteristic
177#423—22no—
178#423C2314yes—
179C2×C4⋊C8—21no—
180C2×C4⋊C8—21no—
181C2×C4⋊C8—21no—
182C2×C4⋊C8—21no—
183C2×C4⋊C8C2×C411yescharacteristic
184C2×C4⋊C8C2×C411yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189C2×#103C2×C411yescharacteristic
190C2×#103C2×C411yescharacteristic
191C2×#102C2×C411yescharacteristic
192C2×#102C2×C411yescharacteristic
193C2×#102C2×C411yescharacteristic
194C2×#102C2×C411yescharacteristic
195C2×#102C2×C411yescharacteristic
196C2×#102C2×C411yescharacteristic
197#407—28no—
198C2×C22⋊C8—21no—
199C2×C22⋊C8—21no—
200C2×C22⋊C8—21no—
201C2×C22⋊C8—21no—
202C2×C22⋊C8—21no—
203C2×C22⋊C8—21no—
204C2×C22⋊C8—21no—
205C2×C22⋊C8—21no—
206C2×C22⋊C8C2×C411yescharacteristic
207C2×C22⋊C8C2×C411yescharacteristic
208#405—28no—
209C4×M16D414yes—
210C4×M16C2314yes—
211C2×#97—21no—
212C2×#97D411yescharacteristic
213C2×#97D411yescharacteristic
214C2×C4×C8—21no—
215C2×C4×C8—21no—
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2311yescharacteristic
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2311yescharacteristic
222#335C2314yescomplemented
223#335C2314yescomplemented
224#334C2314yescomplemented
225#334C2314yescomplemented
226Q8⋊C8C2314yescomplemented
227Q8⋊C8C2314yescomplemented
228D4⋊C8C2314yes—
229D4⋊C8C2314yes—
230D4⋊C8C2314yes—
231D4⋊C8C2314yes—
232D4⋊C8C2314yescomplemented
233D4⋊C8C2314yescomplemented
234#322C2314yescomplemented
235#322C2314yescomplemented
236#322C2314yescomplemented
237C82C2314yescomplemented
238C25—21no—
239C22×Q8C22×C411yescharacteristic
240C22×D4—24no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—22no—
244C22×D4—42no—
245C22×D4C22×C411yescharacteristic
246C22×D4C22×C411yescharacteristic
247C22×D4C22×C414yes—
248C22×D4C22×C411yescharacteristic
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4C22×C411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4#4111yescharacteristic
262C2×SD16—24no—
263C2×SD16—42no—
264C2×SD16C22×C414yes—
265C2×SD16C22×C414yes—
266C2×D8—24no—
267C2×D8—42no—
268C2×D8C22×C414yes—
269C2×D8C22×C414yes—
270C2×M16—24no—
271C2×M16—24no—
272C2×M16—24no—
273C2×M16—24no—
274C2×M16—24no—
275C2×M16—42no—
276C2×M16—44no—
277C2×M16—432no—
278C2×M16—44no—
279C2×M16—44no—
280C2×M16—44no—
281C2×M16C2×D414yes—
282C2×M16C2×D414yes—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—24no—
290C22×C8—24no—
291C22×C8—24no—
292C22×C8—44no—
293C22×C8—44no—
294C22×C8—44no—
295C22×C8C22×C411yescharacteristic
296C22×C8C22×C411yescharacteristic
297C22×C8C22×C411yescharacteristic
298C22×C8C22×C411yescharacteristic
299C22×C8C2×D411yescharacteristic
300C22×C8C2×D411yescharacteristic
301C22×C8C2×D411yescharacteristic
302C22×C8C2×D411yescharacteristic
303#126—24no—
304#126—24no—
305#125—22no—
306#125C22×C414yes—
307#124—22no—
308#124C22×C414yes—
309#123—24no—
310#123—24no—
311C22⋊Q8—22no—
312C22⋊Q8C22×C414yes—
313#121—22no—
314#121C22×C414yes—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8C22×C412yes—
318C4×Q8C2412yes—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—24no—
325C4×D4—21no—
326C4×D4—24no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—24no—
332C4×D4—21no—
333C4×D4C22×C412yes—
334C4×D4C22×C412yes—
335C4×D4C22×C414yes—
336C4×D4C22×C414yes—
337C4×D4C22×C412yes—
338C4×D4C2412yes—
339C4×D4C2412yes—
340C4×D4C2412yes—
341#117—24no—
342#117—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C22×C411yescharacteristic
350C2×C4⋊C4C22×C411yescharacteristic
351C2×C4⋊C4C22×C414yes—
352C2×C4⋊C4C22×C411yescharacteristic
353C2×C4⋊C4C22×C411yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—21no—
365C2×C42—21no—
366C2×C42C22×C411yescharacteristic
367C2×C42C22×C412yes—
368C2×C42C2×D412yes—
369C2×C42C2×D411yescharacteristic
370C2×C42#4111yescharacteristic
371C2×C42#4112yes—
372C2×C42C2412yes—
373C2×C42C2411yescharacteristic
374#107C22×C414yes—
375#107C22×C414yes—
376#106C22×C414yes—
377#106C22×C414yes—
378C4⋊C8—24no—
379C4⋊C8—24no—
380C4⋊C8—24no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—24no—
386C4⋊C8C22×C414yes—
387C4⋊C8C22×C414yes—
388C4⋊C8C2412yes—
389C4⋊C8C2412yes—
390C4⋊C8C2412yes—
391C4⋊C8C2412yes—
392#103C22×C414yes—
393#103C22×C414yes—
394#102C22×C414yes—
395#102C22×C414yes—
396#102C22×C414yes—
397#102C22×C414yes—
398#102C22×C414yes—
399#102C22×C414yes—
400C22⋊C8—24no—
401C22⋊C8—24no—
402C22⋊C8—24no—
403C22⋊C8—24no—
404C22⋊C8—24no—
405C22⋊C8—24no—
406C22⋊C8—24no—
407C22⋊C8—24no—
408C22⋊C8C22×C414yes—
409C22⋊C8C22×C414yes—
410#97—24no—
411#97C2×D414yes—
412#97C2×D414yes—
413C4×C8—24no—
414C4×C8—24no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8C22×C412yes—
418C4×C8C22×C412yes—
419C4×C8C2×D412yes—
420C4×C8C2×D412yes—
421C4×C8C2412yes—
422C4×C8C2412yes—
423C4×C8C2412yes—
424C4×C8C2412yes—
425C4×C8C2412yes—
426C4×C8C2412yes—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—24no—
431C24—44no—
432C24—44no—
433C24—82no—
434C24C4×D411yescharacteristic
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8C23×C412yes—
439C2×D4—28no—
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—44no—
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—82no—
454C2×D4#13114yes—
455C2×D4C23×C412yes—
456C2×D4C23×C412yes—
457C2×D4C23×C412yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—42no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—416no—
481C22×C4—48no—
482C22×C4—44no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4C4×D411yescharacteristic
490C22×C4C4×D411yescharacteristic
491C22×C4C4×D412yes—
492C22×C4C4×D411yescharacteristic
493C22×C4C4×D412yes—
494C22×C4C4×D412yes—
495C22×C4C23×C412yes—
496C22×C4C23×C411yescharacteristic
497C22×C4C22×D412yes—
498C22×C4C22×D411yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4C2×#4112yes—
501SD16—28no—
502SD16—44no—
503D8—28no—
504D8—44no—
505M16—28no—
506M16—44no—
507M16—48no—
508M16—48no—
509M16—48no—
510M16—48no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—48no—
525C2×C8—48no—
526C2×C8—42no—
527C2×C8—42no—
528C2×C8—42no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8—48no—
533C2×C8AGL(1,ℤ/8)14yes—
534C2×C8C23×C412yes—
535C2×C8C23×C412yes—
536C2×C8C23×C412yes—
537C2×C8C23×C412yes—
538C2×C8C22×D412yes—
539C2×C8C22×D412yes—
540C2×C8C22×D412yes—
541C2×C8C22×D412yes—
542C4⋊C4—24no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—22no—
552C4⋊C4C23×C412yes—
553C4⋊C4C23×C412yes—
554C4⋊C4C23×C412yes—
555C4⋊C4C23×C412yes—
556C22⋊C4—24no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—22no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C42—22no—
569C42—22no—
570C42C4×D412yes—
571C42C4×D412yes—
572C42C4×D412yes—
573C42C23×C411yescharacteristic
574C42C23×C412yes—
575C42C22×D412yes—
576C42C22×D411yescharacteristic
577C42C2×#4111yescharacteristic
578C42C2×#4112yes—
579C42C2511yescharacteristic
580C23—22no—
581C23—22no—
582C23—24no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—48no—
588C23—48no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—84no—
598C23—816no—
599C23C2×C4×D412yes—
600C23C2×C4×D411yescharacteristic
601Q8—22no—
602Q8—22no—
603Q8—42no—
604D4—24no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—48no—
611D4—42no—
612D4—42no—
613D4—84no—
614D4C2×#13114yes—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—48no—
633C2×C4—48no—
634C2×C4—48no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4C2×C4×D412yes—
650C2×C4C2×C4×D411yescharacteristic
651C2×C4C2×C4×D412yes—
652C2×C4C2×C4×D412yes—
653C2×C4C2×C4×D411yescharacteristic
654C2×C4C2×C4×D411yescharacteristic
655C2×C4C2×#13112yes—
656C2×C4#56812yes—
657C2×C4C2×AGL(1,ℤ/8)12yes—
658C2×C4#57512yes—
659C2×C4C24×C411yescharacteristic
660C2×C4C23×D411yescharacteristic
661C2×C4C22×#4111yescharacteristic
662C8—22no—
663C8—22no—
664C8—22no—
665C8—22no—
666C8—22no—
667C8—22no—
668C8—22no—
669C8—42no—
670C8—42no—
671C8—42no—
672C8—42no—
673C8—42no—
674C8—42no—
675C8C2×AGL(1,ℤ/8)14yes—
676C22—22no—
677C22—22no—
678C22—24no—
679C22—22no—
680C22—42no—
681C22—44no—
682C22—48no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—816no—
691C22—84no—
692C22—84no—
693C22#293312yes—
694C22C4×AGL(1,ℤ/8)12yes—
695C22#295712yes—
696C22C22×C4×D411yescharacteristic
697C4—21no—
698C4—21no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4#293312yes—
708C4C4×AGL(1,ℤ/8)12yes—
709C4C22×#13111yescharacteristic
710C4C2×#56811yescharacteristic
711C4C22×AGL(1,ℤ/8)11yescharacteristic
712C4C2×#57511yescharacteristic
713C2—42no—
714C2—44no—
715C2—82no—
716C2—82no—
717C2#1800814yesdirect product factor
718C2C2×#293311yescharacteristic
719C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
720C2C2×#295711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC23C2×C4×D4
prime radicalC2×#447C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×M16 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2969C2semidirect
3. C2×D4×M16C2semidirect
4. #18008C2direct (N × H)
5. C2×#1592C2semidirect
6. C2×#1589C2semidirect
7. C2×#1586C2semidirect
8. C2×#1585C2semidirect
9. C2×#1583C2semidirect
10. C2×#1581C2semidirect
11. C2×#1580C2semidirect
12. C2×C8×SD16C2semidirect
13. C2×#1574C2semidirect
14. C2×#1495C2semidirect
15. C2×#1478C2semidirect
16. C2×#1453C2semidirect
31. #2969C22semidirect
32. C2×#446C22semidirect
33. C2×C8×Q8C22semidirect
39. D4×M16C22semidirect
43. C2×#436C22semidirect
49. C2×C8×D4C22semidirect
58. #1592C22semidirect
59. #1589C22semidirect
60. #1586C22semidirect
61. #1585C22semidirect
62. #1583C22semidirect
63. #1581C22semidirect
64. #1580C22semidirect
65. C8×SD16C22semidirect
66. #1574C22semidirect
67. C2×#335C22semidirect
68. C2×#335C22semidirect
69. C2×#334C22semidirect
70. C2×#334C22semidirect
71. #1495C22semidirect
72. #1478C22semidirect
73. C2×Q8⋊C8C22semidirect
74. C2×Q8⋊C8C22semidirect
79. C2×D4⋊C8C22semidirect
80. C2×D4⋊C8C22semidirect
81. #1453C22semidirect
82. C2×#322C22semidirect
83. C2×#322C22semidirect
84. C2×#322C22semidirect
85. C2×C82C22semidirect
139. #446C23semidirect
141. C8×Q8C23semidirect
156. #436C23semidirect
165. C8×D4C23semidirect
222. #335C23semidirect
223. #335C23semidirect
224. #334C23semidirect
225. #334C23semidirect
226. Q8⋊C8C23semidirect
227. Q8⋊C8C23semidirect
232. D4⋊C8C23semidirect
233. D4⋊C8C23semidirect
234. #322C23semidirect
235. #322C23semidirect
236. #322C23semidirect
237. C82C23semidirect
717. C2#18008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31052
C2×#29692
C2×D4×M162
#180082
C2×#15922
C2×#15892
C2×#15862
C2×#15852
C2×#15832
C2×#15812
C2×#15802
C2×C8×SD162
C2×#15742
C2×#14952
C2×#14782
C2×#14532