Finite Group Databasebeta

← #6345197

Subgroups — #6345197

Order 512.

1815 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60949C211yesmaximal, characteristic
2C2×#2966C211yesmaximal, characteristic, complemented
3C2×#2931C211yesmaximal, characteristic, complemented
4#17985C214yesmaximal, complemented
5#17964C214yesmaximal, complemented
6#17938C214yesmaximal, complemented
7#17936C212yesmaximal, complemented
8#17935C212yesmaximal, complemented
9#17910C214yesmaximal, complemented
10#17901C212yesmaximal, complemented
11#17900C212yesmaximal, complemented
12#17822C211yesmaximal, characteristic, complemented
13#17495C211yesmaximal, characteristic, complemented
14#17492C211yesmaximal, characteristic, complemented
15#17323C211yesmaximal, characteristic, complemented
16C22×#131—21no—
17C2×#532C2211yescharacteristic
18C2×#529C2211yescharacteristic
19#3251C414yes—
20#3239C412yes—
21#3234C412yes—
22#3217C412yes—
23#3213C412yes—
24#3193C412yes—
25#3192C412yes—
26#3171C2214yes—
27#3105C2214yes—
28#3103C2212yes—
29#3100C2212yes—
30#2966—21no—
31#2966—21no—
32#2966—21no—
33#2966—21no—
34#2966C2212yes—
35#2966C2212yes—
36#2966C2212yescomplemented
37#2966C2212yescomplemented
38C2×#446C2211yescharacteristic, complemented
39C2×C8×Q8C2211yescharacteristic, complemented
40#2931—21no—
41#2931—21no—
42#2931—21no—
43#2931—21no—
44#2931C2212yes—
45#2931C2212yes—
46#2931C2212yescomplemented
47#2931C2212yescomplemented
48C2×#436—21no—
49C2×#436C2211yescharacteristic, complemented
50C2×#436C2212yescomplemented
51C2×#435—21no—
52C2×C8×D4—21no—
53C2×C8×D4—21no—
54C2×C8×D4C2211yescharacteristic, complemented
55C2×C8×D4C2212yescomplemented
56#2920C2211yescharacteristic
57#2920C2211yescharacteristic
58C2×#433—21no—
59C2×#432C2211yescharacteristic
60C2×#423C2211yescharacteristic
61C2×#408—21no—
62C2×#405—21no—
63C22×C4×C8C2211yescharacteristic
64#1594C2218yescomplemented
65#1592C2218yescomplemented
66#1586C2218yescomplemented
67#1585C2218yescomplemented
68#1583C2218yescomplemented
69#1581C2218yescomplemented
70C8×SD16C2218yescomplemented
71C8×D8C2218yescomplemented
72#1573C2214yescomplemented
73#1571C2212yescomplemented
74#1570C2212yescomplemented
75#1569C2214yescomplemented
76#1496C2214yescomplemented
77#1495C2214yescomplemented
78#1490C2214yescomplemented
79#1487C2212yescomplemented
80#1486C2212yescomplemented
81#1483C2214yes—
82#1480C2212yes—
83#1480C2212yes—
84#1452C2212yescomplemented
85#1451C2212yescomplemented
86#1451C2212yescomplemented
87#1450C2212yescomplemented
88C8×M16C2212yescomplemented
89C8×M16C2212yescomplemented
90C22×#41—21no—
91C2×#131—22no—
92C2×#131—22no—
93C2×#131—22no—
94C2×#131—22no—
95C2×#131—48no—
96C22×M16—21no—
97C22×M16—21no—
98C22×M16—22no—
99C23×C8—21no—
100C23×C8—22no—
101C23×C8D411yescharacteristic
102C23×C8D411yescharacteristic
103#532—21no—
104#532—21no—
105#532—21no—
106#532—21no—
107#532C2×C412yes—
108#532C2×C412yes—
109#532C2312yes—
110#532C2312yes—
111C2×C4⋊Q8C2×C411yescharacteristic
112C2×#127C2×C411yescharacteristic
113#529—21no—
114#529—21no—
115#529—21no—
116#529—21no—
117#529C2×C412yes—
118#529C2×C412yes—
119#529C2312yes—
120#529C2312yes—
121C2×#126—21no—
122C2×#125C2×C411yescharacteristic
123C2×#124—21no—
124C2×#124C2×C411yescharacteristic
125C2×#123—21no—
126C2×C22⋊Q8C2×C411yescharacteristic
127C2×#121—21no—
128C2×#121C2×C411yescharacteristic
129C2×#121C2×C412yes—
130C2×C4×Q8C2311yescharacteristic
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4C2311yescharacteristic
134C2×C4×D4C2312yes—
135C2×#117—21no—
136C22×C42C2311yescharacteristic
137#501C2×C414yes—
138#496C2×C414yes—
139#490C2×C414yes—
140#489C2×C414yes—
141#484C2×C414yes—
142#481C2×C414yes—
143#481C2×C414yes—
144#480C2×C414yes—
145#478C2×C418yes—
146#475C2×C414yes—
147#474C2×C414yes—
148#469C2×C418yes—
149#468C2×C418yes—
150#463C2×C418yes—
151#460C2×C414yes—
152#459C2×C414yes—
153#450C2×C414yes—
154#448C2×C414yes—
155#447C2×C414yes—
156#447C2×C414yes—
157#446—21no—
158#446—21no—
159#446C2312yes—
160#446C2312yes—
161C8×Q8—21no—
162C8×Q8—21no—
163C8×Q8C2312yes—
164C8×Q8C2312yes—
165C4×SD16C2318yes—
166C4×D8C2318yes—
167#436—22no—
168#436—22no—
169#436—22no—
170#436—22no—
171#436—22no—
172#436—22no—
173#436—21no—
174#436—21no—
175#436C2314yes—
176#436C2312yes—
177#436C2314yes—
178#436C2312yes—
179#435—22no—
180#435—22no—
181#435—22no—
182#435—22no—
183C8×D4—22no—
184C8×D4—22no—
185C8×D4—22no—
186C8×D4—22no—
187C8×D4—22no—
188C8×D4—22no—
189C8×D4—22no—
190C8×D4—22no—
191C8×D4—22no—
192C8×D4—22no—
193C8×D4—21no—
194C8×D4—21no—
195C8×D4C2312yes—
196C8×D4C2314yes—
197C8×D4C2312yes—
198C8×D4C2314yes—
199#433—22no—
200#433—22no—
201#433—22no—
202#433—22no—
203#432—21no—
204#432—21no—
205#432—21no—
206#432—21no—
207#432C2×C412yes—
208#432C2×C412yes—
209#432C2312yes—
210#432C2312yes—
211#431C2312yes—
212#431C2312yes—
213#431C2312yes—
214#431C2312yes—
215#423—21no—
216#423—21no—
217#423—21no—
218#423C2×C412yes—
219#423C2312yes—
220#423C2312yes—
221C2×C4⋊C8—21no—
222C2×C4⋊C8—21no—
223C2×C4⋊C8—21no—
224C2×C4⋊C8C2311yescharacteristic
225C2×C4⋊C8C2311yescharacteristic
226C2×C4⋊C8C2312yes—
227#408—22no—
228#408—22no—
229#408—22no—
230#408—22no—
231#407—21no—
232#407C2×C412yes—
233C2×C22⋊C8—21no—
234C2×C22⋊C8—22no—
235C2×C22⋊C8—22no—
236C2×C22⋊C8—21no—
237C2×C22⋊C8—21no—
238#405—22no—
239#405—22no—
240#405—22no—
241#405—22no—
242C4×M16C2312yes—
243C4×M16C2312yes—
244C2×#97—21no—
245C2×#97—21no—
246C2×C4×C8—21no—
247C2×C4×C8D411yescharacteristic
248C2×C4×C8D411yescharacteristic
249C2×C4×C8D411yescharacteristic
250C2×C4×C8D411yescharacteristic
251C2×C4×C8D411yescharacteristic
252C2×C4×C8D411yescharacteristic
253C2×C4×C8C2311yescharacteristic
254C2×C4×C8C2311yescharacteristic
255C2×C4×C8C2311yescharacteristic
256C2×C4×C8C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259#335C2318yes—
260#334C2318yes—
261Q8⋊C8C2318yes—
262D4⋊C8C2318yes—
263D4⋊C8C2318yes—
264D4⋊C8C2318yes—
265#322C2314yes—
266#322C2314yes—
267#322C2314yes—
268C82C2314yes—
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41—22no—
273C2×#41—44no—
274C2×#41—44no—
275C22×Q8—21no—
276C22×Q8C22×C411yescharacteristic
277C22×D4—21no—
278C22×D4—22no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4C22×C411yescharacteristic
282C22×D4C22×C412yes—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4C22×C411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4#4111yescharacteristic
288C2×SD16C22×C418yes—
289C2×D8C22×C418yes—
290#131—48no—
291#131—48no—
292#131—48no—
293#131—48no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—44no—
302C2×M16—48no—
303C2×M16—44no—
304C2×M16C22×C414yes—
305C22×C8—24no—
306C22×C8—22no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—24no—
310C22×C8—22no—
311C22×C8—24no—
312C22×C8—22no—
313C22×C8—42no—
314C22×C8—48no—
315C22×C8—44no—
316C22×C8C2×D411yescharacteristic
317C22×C8C2×D411yescharacteristic
318C22×C8C2×D411yescharacteristic
319C22×C8C2×D411yescharacteristic
320C22×C8C2×D411yescharacteristic
321C22×C8C2×D411yescharacteristic
322C22×C8C2×D411yescharacteristic
323C22×C8C2×D411yescharacteristic
324C22×C8C2×D411yescharacteristic
325C22×C8C2×D411yescharacteristic
326C22×C8C2×D411yescharacteristic
327C22×C8C2×D411yescharacteristic
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8C22×C412yes—
331C4⋊Q8C22×C412yes—
332#127—21no—
333#127—21no—
334#127C22×C412yes—
335#127C22×C412yes—
336#126—22no—
337#126—22no—
338#126—22no—
339#126—22no—
340#125—21no—
341#125—21no—
342#125C22×C412yes—
343#125C22×C412yes—
344#124—22no—
345#124—22no—
346#124—21no—
347#124—21no—
348#124—22no—
349#124—22no—
350#124C22×C412yes—
351#124C22×C412yes—
352#123—22no—
353#123—22no—
354#123—22no—
355#123—22no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8C22×C412yes—
359C22⋊Q8C22×C412yes—
360#121—22no—
361#121—22no—
362#121—21no—
363#121—21no—
364#121—22no—
365#121—22no—
366#121—22no—
367#121—22no—
368#121C22×C412yes—
369#121C22×C412yes—
370#121C22×C414yes—
371#121C22×C414yes—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C22×C412yes—
375C4×Q8C2412yes—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4—21no—
387C4×D4—22no—
388C4×D4C22×C412yes—
389C4×D4C22×C414yes—
390C4×D4C2412yes—
391C4×D4C2414yes—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C22×C412yes—
402C2×C4⋊C4C22×C411yescharacteristic
403C2×C4⋊C4C22×C411yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C42—21no—
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42#4111yescharacteristic
419C2×C42#4111yescharacteristic
420C2×C42#4111yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424#107C22×C418yes—
425#106C22×C418yes—
426C4⋊C8—22no—
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C4⋊C8C22×C414yes—
438C4⋊C8C22×C414yes—
439C4⋊C8C2412yes—
440C4⋊C8C2412yes—
441C4⋊C8C2414yes—
442#103C22×C418yes—
443#102C22×C418yes—
444#102C22×C418yes—
445#102C22×C418yes—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—24no—
451C22⋊C8—24no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—22no—
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—22no—
458C22⋊C8C22×C414yes—
459C22⋊C8C22×C414yes—
460#97—22no—
461#97—22no—
462#97—22no—
463#97—22no—
464#97—22no—
465#97C22×C414yes—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8C2×D411yescharacteristic
469C4×C8C2×D411yescharacteristic
470C4×C8C2×D411yescharacteristic
471C4×C8C2×D411yescharacteristic
472C4×C8C2×D411yescharacteristic
473C4×C8C2×D411yescharacteristic
474C4×C8C2×D411yescharacteristic
475C4×C8C2×D411yescharacteristic
476C4×C8C2×D411yescharacteristic
477C4×C8C2×D411yescharacteristic
478C4×C8C2×D411yescharacteristic
479C4×C8C2×D411yescharacteristic
480C4×C8C2414yes—
481C4×C8C2414yes—
482C4×C8C2411yescharacteristic
483C4×C8C2411yescharacteristic
484C4×C8C2411yescharacteristic
485C4×C8C2411yescharacteristic
486C24—21no—
487C24—22no—
488C24C4×D411yescharacteristic
489#41—44no—
490#41—48no—
491#41—48no—
492#41—44no—
493#41—44no—
494#41—44no—
495C2×Q8—21no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—42no—
499C2×Q8—44no—
500C2×Q8C23×C412yes—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—44no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—48no—
517C2×D4C23×C412yes—
518C2×D4C23×C414yes—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4C4×D411yescharacteristic
536C22×C4C4×D411yescharacteristic
537C22×C4C4×D411yescharacteristic
538C22×C4C4×D411yescharacteristic
539C22×C4C4×D411yescharacteristic
540C22×C4C4×D411yescharacteristic
541C22×C4C4×D411yescharacteristic
542C22×C4C4×D411yescharacteristic
543C22×C4C4×D411yescharacteristic
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553SD16—48no—
554D8—48no—
555M16—44no—
556M16—44no—
557M16—44no—
558M16—48no—
559M16—44no—
560M16—44no—
561M16—44no—
562M16—48no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—48no—
579C2×C8—44no—
580C2×C8—42no—
581C2×C8—42no—
582C2×C8—44no—
583C2×C8—44no—
584C2×C8—48no—
585C2×C8AGL(1,ℤ/8)14yes—
586C2×C8C23×C418yes—
587C2×C8C22×D411yescharacteristic
588C2×C8C22×D411yescharacteristic
589C2×C8C22×D411yescharacteristic
590C2×C8C22×D411yescharacteristic
591C2×C8C22×D411yescharacteristic
592C2×C8C22×D411yescharacteristic
593C2×C8C22×D411yescharacteristic
594C2×C8C22×D411yescharacteristic
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4C23×C412yes—
609C4⋊C4C23×C412yes—
610C4⋊C4C23×C414yes—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C42—22no—
626C42—22no—
627C42C4×D411yescharacteristic
628C42C4×D411yescharacteristic
629C42C4×D411yescharacteristic
630C42C4×D411yescharacteristic
631C42C4×D411yescharacteristic
632C42C4×D411yescharacteristic
633C42C23×C411yescharacteristic
634C42C23×C411yescharacteristic
635C42C23×C411yescharacteristic
636C42C22×D411yescharacteristic
637C42C22×D411yescharacteristic
638C42C22×D411yescharacteristic
639C42C2×#4111yescharacteristic
640C42C2×#4111yescharacteristic
641C42C2×#4111yescharacteristic
642C42C2511yescharacteristic
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—41no—
648C23—44no—
649C23—42no—
650C23—42no—
651C23—44no—
652C23—42no—
653C23—44no—
654C23C2×C4×D411yescharacteristic
655C23C2×C4×D411yescharacteristic
656C23C2×C4×D411yescharacteristic
657Q8—24no—
658Q8—42no—
659Q8—44no—
660Q8—44no—
661D4—24no—
662D4—28no—
663D4—44no—
664D4—44no—
665D4—44no—
666D4—42no—
667D4—44no—
668D4—44no—
669D4—48no—
670D4—48no—
671D4—44no—
672D4—44no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—48no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4C2×C4×D411yescharacteristic
707C2×C4C2×C4×D411yescharacteristic
708C2×C4C2×C4×D411yescharacteristic
709C2×C4C2×C4×D411yescharacteristic
710C2×C4C2×C4×D411yescharacteristic
711C2×C4C2×C4×D411yescharacteristic
712C2×C4C2×C4×D411yescharacteristic
713C2×C4C2×C4×D411yescharacteristic
714C2×C4C2×C4×D411yescharacteristic
715C2×C4C2×AGL(1,ℤ/8)12yes—
716C2×C4#57512yes—
717C2×C4C24×C411yescharacteristic
718C2×C4C23×D411yescharacteristic
719C2×C4C22×#4111yescharacteristic
720C8—28no—
721C8—21no—
722C8—21no—
723C8—21no—
724C8—21no—
725C8—21no—
726C8—21no—
727C8—44no—
728C8—42no—
729C8—44no—
730C8—42no—
731C8C2×AGL(1,ℤ/8)12yes—
732C8C2×AGL(1,ℤ/8)12yes—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—44no—
745C22—44no—
746C22—42no—
747C22—88no—
748C22—84no—
749C22C4×AGL(1,ℤ/8)12yes—
750C22#295512yes—
751C22C22×C4×D411yescharacteristic
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—44no—
765C4C4×AGL(1,ℤ/8)12yes—
766C4#357312yes—
767C4C22×AGL(1,ℤ/8)11yescharacteristic
768C4C2×#57511yescharacteristic
769C2—22no—
770C2—22no—
771C2—41no—
772C2—84no—
773C2—82no—
774C2#6014011yescharacteristic
775C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
776C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C8C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60949C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8 ◁ C22×C4×C8 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2966C2semidirect
3. C2×#2931C2semidirect
4. #17985C2semidirect
5. #17964C2semidirect
6. #17938C2semidirect
7. #17936C2semidirect
8. #17935C2semidirect
9. #17910C2semidirect
10. #17901C2semidirect
11. #17900C2semidirect
12. #17822C2semidirect
13. #17495C2semidirect
14. #17492C2semidirect
15. #17323C2semidirect
36. #2966C22semidirect
37. #2966C22semidirect
38. C2×#446C22semidirect
39. C2×C8×Q8C22semidirect
46. #2931C22semidirect
47. #2931C22semidirect
49. C2×#436C22semidirect
50. C2×#436C22semidirect
54. C2×C8×D4C22semidirect
55. C2×C8×D4C22semidirect
64. #1594C22semidirect
65. #1592C22semidirect
66. #1586C22semidirect
67. #1585C22semidirect
68. #1583C22semidirect
69. #1581C22semidirect
70. C8×SD16C22semidirect
71. C8×D8C22semidirect
72. #1573C22semidirect
73. #1571C22semidirect
74. #1570C22semidirect
75. #1569C22semidirect
76. #1496C22semidirect
77. #1495C22semidirect
78. #1490C22semidirect
79. #1487C22semidirect
80. #1486C22semidirect
84. #1452C22semidirect
85. #1451C22semidirect
86. #1451C22semidirect
87. #1450C22semidirect
88. C8×M16C22semidirect
89. C8×M16C22semidirect

Maximal subgroups

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

subgroupindex
#609492
C2×#29662
C2×#29312
#179852
#179642
#179382
#179362
#179352
#179102
#179012
#179002
#178222
#174952
#174922
#173232