Finite Group Databasebeta

← #641357

Subgroups — #641357

Order 512.

2770 conjugacy classes of subgroups.

The subgroup lattice has 775 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2442C211yesmaximal, characteristic
2C2×#2440C211yesmaximal, characteristic
3#16828C214yesmaximal, complemented
4#16827C214yesmaximal, complemented
5#15231C211yesmaximal, characteristic, complemented
6#15228C211yesmaximal, characteristic, complemented
7#15145C211yesmaximal, characteristic, complemented
8#15143C211yesmaximal, characteristic, complemented
9#14758C214yesmaximal
10#14736C214yesmaximal
11#14686C211yesmaximal, characteristic
12#14283C211yesmaximal, characteristic, complemented
13#14282C211yesmaximal, characteristic, complemented
14#14277C211yesmaximal, characteristic, complemented
15#14276C211yesmaximal, characteristic, complemented
16#13881C211yesmaximal, characteristic
17#13880C211yesmaximal, characteristic
18C2×C4⋊#95C211yesmaximal, characteristic
19#13753C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2442—28no—
27#2440—28no—
28C2×#400C2212yes—
29C2×#398C2212yes—
30C2×#398C2212yes—
31C2×#398C2214yes—
32C2×#395C2212yes—
33C2×#395C2214yes—
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2214yes—
41C2×#384C2211yescharacteristic
42C2×#384C2211yescharacteristic
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#382C2211yescharacteristic
47C2×#382C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2214yes—
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×#376C2211yescharacteristic
56C2×#376C2211yescharacteristic
57C22×#95C2214yes—
58#1446C2214yes—
59#1445C2214yes—
60#1444C2214yes—
61#1444C2214yes—
62#1444C2214yes—
63#1444C2214yes—
64#1444C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74C4⋊#95C2211yescharacteristic
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2214yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86#1434C2212yes—
87#1434C2212yes—
88C22⋊#95C2214yes—
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2312yes—
94C24×C4C2312yes—
95C24×C4C2312yes—
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—42no—
101C2×#125—24no—
102C2×#125—24no—
103C2×#125—42no—
104C2×C22⋊Q8—28no—
105C2×C22⋊Q8—48no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C42—42no—
141C22×C42—42no—
142C22×C42Q818yescomplemented
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150#400—28no—
151#398—28no—
152#398—28no—
153#398—48no—
154#395—28no—
155#395—48no—
156#389—24no—
157#389—24no—
158#389—24no—
159#389—24no—
160#385—28no—
161#385—28no—
162#385—48no—
163#384—24no—
164#384—24no—
165#384—42no—
166#384—42no—
167#384—42no—
168#382—24no—
169#382—24no—
170#382—42no—
171#380—24no—
172#380—24no—
173#380—28no—
174#380—48no—
175C4×C22⋊C4D418yes—
176C4×C22⋊C4Q818yescomplemented
177#376—42no—
178#376—42no—
179C2×#95—48no—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C25C2411yescharacteristic
212C22×Q8—24no—
213C22×Q8—24no—
214C22×Q8—44no—
215C22×Q8—42no—
216C22×Q8—44no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—28no—
228C23×C4—28no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—44no—
236C23×C4—44no—
237C23×C4C2×D414yes—
238C23×C4C2×Q818yes—
239C23×C4C2×Q814yes—
240C23×C4C2×Q814yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C4⋊Q8—416no—
260#125—416no—
261C22⋊Q8—432no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—416no—
304C2×C4⋊C4—416no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4#4114yes—
326C2×C4⋊C4#4114yes—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4C2×D414yes—
336C2×C22⋊C4C2×D414yes—
337C2×C22⋊C4C2×Q818yes—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—416no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42C2×D414yes—
354C2×C42C2×D414yes—
355C2×C42C2×Q814yes—
356C2×C42C2×Q814yes—
357C2×C42C2×Q814yes—
358C2×C42C2×Q814yes—
359C2×C42C2×Q818yes—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—44no—
376#95—44no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95C2×D414yes—
389#95C2×D414yes—
390#95C2×Q818yes—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—22no—
397C24C22×D412yes—
398C24C22×Q812yes—
399C24C22×Q812yes—
400C24H(5,𝔽2)14yes—
401C242−1+414yes—
402C24C2511yescharacteristic
403C2×Q8—48no—
404C2×Q8—48no—
405C2×Q8—84no—
406C2×Q8—88no—
407C2×Q8—88no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—216no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—216no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—416no—
504C22×C4—416no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—84no—
508C22×C4—84no—
509C22×C4—88no—
510C22×C4—88no—
511C22×C4C4⋊Q8116yes—
512C22×C4C22×D412yes—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×Q814yes—
519C22×C4C22×Q814yes—
520C22×C4C22×Q814yes—
521C22×C4C22×Q812yes—
522C22×C4C22×Q812yes—
523C22×C4C22×Q814yes—
524C22×C4C22×Q812yes—
525C22×C4C22×Q812yes—
526C22×C4C2×#4114yes—
527C22×C4C2×#4114yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4H(5,𝔽2)14yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C42−1+414yes—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—48no—
537C4⋊C4—48no—
538C4⋊C4—48no—
539C4⋊C4—48no—
540C4⋊C4—48no—
541C4⋊C4—48no—
542C4⋊C4—48no—
543C4⋊C4—48no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C4⋊C4—44no—
550C4⋊C4—88no—
551C4⋊C4—88no—
552C4⋊C4—84no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C4⋊C4—88no—
556C4⋊C4—88no—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4—216no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C42—28no—
563C42—28no—
564C42—28no—
565C42—28no—
566C42—28no—
567C42—28no—
568C42—48no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23C2×C4⋊Q814yes—
588C23#53514yes—
589C23#53614yes—
590C23#54418yes—
591C23#54418yes—
592C23C23×D411yescharacteristic
593C23C23×Q811yescharacteristic
594C23C23×Q811yescharacteristic
595C23C22×#4111yescharacteristic
596C23C22×#4111yescharacteristic
597C23C2×H(5,𝔽2)12yes—
598C23C2×H(5,𝔽2)11yescharacteristic
599C23C2×H(5,𝔽2)11yescharacteristic
600C23C2×H(5,𝔽2)12yes—
601C23C2×2−1+412yes—
602C23C2×2−1+412yes—
603Q8—816no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—232no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—432no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—816no—
700C2×C4—816no—
701C2×C4C2×C4⋊Q814yes—
702C2×C4C2×C4⋊Q814yes—
703C2×C4#53314yes—
704C2×C4#54314yes—
705C2×C4#54418yes—
706C2×C4#54614yes—
707C2×C4#54614yes—
708C2×C4#55414yes—
709C2×C4#55414yes—
710C22—24no—
711C22—28no—
712C22—28no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—24no—
718C22—28no—
719C22—28no—
720C22#266018yes—
721C22C22×C4⋊Q811yescharacteristic
722C22C2×#53311yescharacteristic
723C22C2×#53511yescharacteristic
724C22C2×#53611yescharacteristic
725C22C2×#54311yescharacteristic
726C22C2×#54412yes—
727C22C2×#54412yes—
728C22C2×#54412yes—
729C22C2×#54611yescharacteristic
730C22C2×#54611yescharacteristic
731C22C2×#55411yescharacteristic
732C22C2×#55411yescharacteristic
733C22#349811yescharacteristic
734C22#349911yescharacteristic
735C22#350312yes—
736C22#351912yes—
737C22#352012yes—
738C22#352212yes—
739C22#352312yes—
740C22#353612yes—
741C22#353612yes—
742C22#353712yes—
743C22#353812yes—
744C4—24no—
745C4—28no—
746C4—44no—
747C4—42no—
748C4—44no—
749C4—42no—
750C4—44no—
751C4—42no—
752C4—42no—
753C4—44no—
754C4—44no—
755C4—82no—
756C4—82no—
757C4—82no—
758C4—82no—
759C4—82no—
760C4—82no—
761C4#254918yes—
762C2—28no—
763C2C2×#266011yescharacteristic
764C2C2×#254911yescharacteristic
765C2#3523912yes—
766C2#3527511yescharacteristic
767C2#3747712yes—
768C2#3807811yescharacteristic
769C2#3807911yescharacteristic
770C2#3808011yescharacteristic
771C2#3808111yescharacteristic
772C2#3809812yes—
773C2#3809912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #16828C2semidirect
4. #16827C2semidirect
5. #15231C2semidirect
6. #15228C2semidirect
7. #15145C2semidirect
8. #15143C2semidirect
12. #14283C2semidirect
13. #14282C2semidirect
14. #14277C2semidirect
15. #14276C2semidirect
142. C22×C42Q8semidirect
176. C4×C22⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24422
C2×#24402
#168282
#168272
#152312
#152282
#151452
#151432
#147582
#147362
#146862
#142832
#142822
#142772
#142762
#138812
#138802
C2×C4⋊#952
#137532