Finite Group Databasebeta

← C22×#62812 #72279343

Subgroups — C22×#62812 #72279343

Order 1024.

827517 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#585C212yesmaximal, complemented
2C2×#62812C21192yesmaximal, direct product factor
3C22×#3500C218yesmaximal, complemented
4C22×#3499C214yesmaximal, complemented
5C22×#3498C214yesmaximal, complemented
6C22×#3497C214yesmaximal, complemented
7C22×#3496C2112yesmaximal, complemented
8C22×D4×#41C2116yesmaximal, complemented
9C22×#3449C216yesmaximal, complemented
10C23×#532C216yesmaximal, complemented
11C23×C4×#41C211yesmaximal, characteristic, complemented
12C22×#585—2128no—
13C22×#585C221192yescomplemented
14C23×2−1+4C2214yescomplemented
15C23×2−1+4C2218yescomplemented
16C23×H(5,𝔽2)C22112yescomplemented
17C23×H(5,𝔽2)C2218yescomplemented
18C24×#41C2211yescharacteristic
19C24×#41C22112yescomplemented
20C24×#41C22116yescomplemented
21#62812C2214096yesdirect product factor
22C2×#3500C221768yescomplemented
23C2×#3499C221384yescomplemented
24C2×#3498C221384yescomplemented
25C2×#3497C221384yescomplemented
26C2×#3496C2211152yescomplemented
27C2×D4×#41C2211536yescomplemented
28C22×#550C22116yescomplemented
29C22×#547C22148yescomplemented
30C22×#548C22132yescomplemented
31C22×#546C22196yescomplemented
32C22×D4×Q8C22116yescomplemented
33C22×D42C22148yescomplemented
34C2×#3449C221576yescomplemented
35C22×#536C22124yescomplemented
36C22×#537C22124yescomplemented
37C22×#535C22124yescomplemented
38C22×#534C22124yescomplemented
39C22×#532C2214yescomplemented
40C22×#532C22112yescomplemented
41C22×#532C22124yescomplemented
42C22×#532C22124yescomplemented
43C22×#532C22112yescomplemented
44C22×#532C22112yescomplemented
45C22×#532C221576yescomplemented
46C23×C4⋊Q8C2216yescomplemented
47C23×#127C2216yescomplemented
48C23×#124C22112yescomplemented
49C22×#525C22148yescomplemented
50C23×#121C22124yescomplemented
51C22×C4×#41C2218yescomplemented
52C22×C4×#41C2214yescomplemented
53C22×C4×#41C2214yescomplemented
54C22×C4×#41C22196yescomplemented
55C23×C4×Q8C2212yescomplemented
56C23×C4×D4C2216yescomplemented
57C23×C4×D4C22124yescomplemented
58C23×#117C2213yescomplemented
59C24×C42C2213yescomplemented
60C2×#585—26144no—
61C2×#585C2312048yescomplemented
62C22×2−1+4—2256no—
63C22×2−1+4—2128no—
64C22×2−1+4C231192yescomplemented
65C22×2−1+4C231384yescomplemented
66C22×H(5,𝔽2)—2256no—
67C22×H(5,𝔽2)—2384no—
68C22×H(5,𝔽2)C231576yescomplemented
69C22×H(5,𝔽2)C231384yescomplemented
70C23×#41—2512no—
71C23×#41—2384no—
72C23×#41D4164yescomplemented
73C23×#41C23124yes—
74C23×#41C2318yes—
75C23×#41C23124yes—
76C23×#41C23124yes—
77C23×#41C23148yes—
78C23×#41C23116yes—
79C23×#41C2314yes—
80C23×#41C2314yes—
81C23×#41C23148yes—
82C23×#41C231576yescomplemented
83C23×#41C231768yescomplemented
84C24×Q8C23112yes—
85C24×Q8C23116yes—
86C24×Q8C2311yescharacteristic
87C24×D4C23124yes—
88C24×D4C23112yes—
89C24×D4C23148yes—
90C24×D4C23124yes—
91C24×D4C2313yes—
92C25×C4C23124yes—
93C25×C4C2316yes—
94C25×C4C2313yes—
95#3500C2318192yescomplemented
96#3499C2314096yescomplemented
97#3498C2314096yescomplemented
98#3497C2314096yescomplemented
99#3496C23112288yescomplemented
100D4×#41C23116384yescomplemented
101C2×#550C231768yescomplemented
102C2×D4×Q8C231768yescomplemented
103C2×#548C2311536yescomplemented
104C2×#547C2312304yescomplemented
105C2×#546C2314608yescomplemented
106C2×D42C2312304yescomplemented
107#3449C2316144yescomplemented
108C2×#537C2311152yescomplemented
109C2×#536C2311152yescomplemented
110C2×#535C2311152yescomplemented
111C2×#534C2311152yescomplemented
112C2×#532C2311152yescomplemented
113C2×#532C231576yescomplemented
114C2×#532C231576yescomplemented
115C2×#532C231192yescomplemented
116C2×#532C231576yescomplemented
117C2×#532C2311152yescomplemented
118C2×#532C2316144yescomplemented
119C22×C4⋊Q8C2314yes—
120C22×C4⋊Q8C23112yes—
121C22×C4⋊Q8C23124yes—
122C22×C4⋊Q8C231288yescomplemented
123C22×#127C2314yes—
124C22×#127C23112yes—
125C22×#127C23124yes—
126C22×#127C231288yescomplemented
127C22×#124C2318yes—
128C22×#124C23124yes—
129C22×#124C23148yes—
130C22×#124C231576yescomplemented
131C2×#525C2312304yescomplemented
132C22×#123C23196yes—
133C22×C22⋊Q8C23196yes—
134C22×#121C23116yes—
135C22×#121C23148yes—
136C22×#121C23148yes—
137C22×#121C23148yes—
138C22×#121C23196yes—
139C22×#121C2311152yescomplemented
140C22×#120C23196yes—
141C2×C4×#41C231192yescomplemented
142C2×C4×#41C231192yescomplemented
143C2×C4×#41C231384yescomplemented
144C2×C4×#41C2311024yescomplemented
145C22×C4×Q8C2318yes—
146C22×C4×Q8C2318yes—
147C22×C4×Q8C23196yescomplemented
148C22×C4×D4C23116yes—
149C22×C4×D4C23124yes—
150C22×C4×D4C23124yes—
151C22×C4×D4C23148yes—
152C22×C4×D4C23148yes—
153C22×C4×D4C23148yes—
154C22×C4×D4C231288yescomplemented
155C22×C4×D4C2311152yescomplemented
156C22×#117C23112yes—
157C22×#117C23112yes—
158C22×#117C231144yescomplemented
159C23×C4⋊C4C2316yes—
160C23×C4⋊C4C23124yes—
161C23×C22⋊C4C2316yes—
162C23×C22⋊C4C23148yes—
163C23×C42C2311yescharacteristic
164C23×C42C2313yes—
165C23×C42C23112yes—
166C23×C42C2316yes—
167C23×C42C2316yes—
168C23×C42C2316yes—
169C23×C42C231144yescomplemented
170C26C24124yes—
171C26C2413yes—
172#585—232768no—
173C2×2−1+4—26144no—
174C2×2−1+4—23072no—
175C2×2−1+4C2411024yescomplemented
176C2×2−1+4C2412048yescomplemented
177C2×H(5,𝔽2)—26144no—
178C2×H(5,𝔽2)—29216no—
179C2×H(5,𝔽2)C2413072yescomplemented
180C2×H(5,𝔽2)C2412048yescomplemented
181C22×#41—212288no—
182C22×#41—2256no—
183C22×#41—2768no—
184C22×#41—2384no—
185C22×#41—2128no—
186C22×#41—2384no—
187C22×#41—2384no—
188C22×#41—29216no—
189C22×#41C2×D41128yescomplemented
190C22×#41C2×D41128yescomplemented
191C22×#41C2×D411536yescomplemented
192C22×#41C241576yes—
193C22×#41C241192yes—
194C22×#41C241576yes—
195C22×#41C241576yes—
196C22×#41C2411152yes—
197C22×#41C241384yes—
198C22×#41C24196yes—
199C22×#41C24196yes—
200C22×#41C241256yes—
201C22×#41C2413072yescomplemented
202C22×#41C2414096yescomplemented
203C23×Q8—2256no—
204C23×Q8—2192no—
205C23×Q8C2×D4132yescomplemented
206C23×Q8C24124yes—
207C23×Q8C2418yes—
208C23×Q8C241288yes—
209C23×Q8C241384yes—
210C23×Q8C2414yes—
211C23×Q8C24124yes—
212C23×D4—2384no—
213C23×D4—2768no—
214C23×D4—2192no—
215C23×D4—4192no—
216C23×D4C2×D4196yescomplemented
217C23×D4C24148yes—
218C23×D4C24116yes—
219C23×D4C24124yes—
220C23×D4C2418yes—
221C23×D4C24116yes—
222C23×D4C241576yes—
223C23×D4C241288yes—
224C23×D4C2411152yes—
225C23×D4C24148yes—
226C23×D4C241576yes—
227C23×D4C24112yes—
228C23×D4C24172yes—
229C24×C4—2384no—
230C24×C4—448no—
231C24×C4C2×D4196yescomplemented
232C24×C4C2412yes—
233C24×C4C24112yes—
234C24×C4C24124yes—
235C24×C4C24148yes—
236C24×C4C241576yes—
237C24×C4C24116yes—
238C24×C4C24112yes—
239C24×C4C2416yes—
240C24×C4C241144yes—
241C24×C4C2416yes—
242C24×C4C2413yes—
243C24×C4C2416yes—
244C24×C4C2411yescharacteristic
245C24×C4C24172yes—
246#550C2414096yescomplemented
247D4×Q8C2414096yescomplemented
248#548C2418192yescomplemented
249#547C24112288yescomplemented
250#546C24124576yescomplemented
251D42C24112288yescomplemented
252#537C2416144yescomplemented
253#536C2416144yescomplemented
254#535C2416144yescomplemented
255#534C2416144yescomplemented
256#532C2411024yescomplemented
257#532C2413072yescomplemented
258#532C2416144yescomplemented
259#532C2416144yescomplemented
260#532C2413072yescomplemented
261#532C2413072yescomplemented
262C2×C4⋊Q8C24196yes—
263C2×C4⋊Q8C241288yes—
264C2×C4⋊Q8C241576yes—
265C2×C4⋊Q8C2411536yescomplemented
266C2×#127C24196yes—
267C2×#127C241288yes—
268C2×#127C241576yes—
269C2×#127C2411536yescomplemented
270C2×#124C241192yes—
271C2×#124C241576yes—
272C2×#124C2411152yes—
273C2×#124C2413072yescomplemented
274#525C24112288yescomplemented
275C2×#123C2412304yes—
276C2×C22⋊Q8C2412304yes—
277C2×#121C241384yes—
278C2×#121C2411152yes—
279C2×#121C2411152yes—
280C2×#121C2411152yes—
281C2×#121C2412304yes—
282C2×#121C2416144yescomplemented
283C2×#120C2412304yes—
284C4×#41C2412048yescomplemented
285C4×#41C2411024yescomplemented
286C4×#41C2411024yescomplemented
287C2×C4×Q8C241192yes—
288C2×C4×Q8C241192yes—
289C2×C4×Q8C241512yescomplemented
290C2×C4×D4C241384yes—
291C2×C4×D4C241576yes—
292C2×C4×D4C241576yes—
293C2×C4×D4C2411152yes—
294C2×C4×D4C2411152yes—
295C2×C4×D4C2411152yes—
296C2×C4×D4C2411536yescomplemented
297C2×C4×D4C2416144yescomplemented
298C2×#117C241288yes—
299C2×#117C241288yes—
300C2×#117C241768yescomplemented
301C22×C4⋊C4C24116yes—
302C22×C4⋊C4C24124yes—
303C22×C4⋊C4C241144yes—
304C22×C4⋊C4C24148yes—
305C22×C4⋊C4C241576yes—
306C22×C22⋊C4C24132yes—
307C22×C22⋊C4C24124yes—
308C22×C22⋊C4C241144yes—
309C22×C22⋊C4C24196yes—
310C22×C22⋊C4C2411152yes—
311C22×C42C2411yescharacteristic
312C22×C42C2411yescharacteristic
313C22×C42C2416yes—
314C22×C42C24112yes—
315C22×C42C24112yes—
316C22×C42C24124yes—
317C22×C42C24172yes—
318C22×C42C241288yes—
319C22×C42C241144yes—
320C22×C42C241144yes—
321C22×C42C241144yes—
322C22×C42C2412yes—
323C22×C42C2416yes—
324C22×C42C241768yescomplemented
325C25—2192no—
326C25—424no—
327C25—4192no—
328C25C22×D4148yes—
329C25C25116yes—
330C25C2516yes—
331C25C2511yescharacteristic
332C25C251288yes—
333C25C25136yes—
3342−1+4—216384no—
3352−1+4—28192no—
336H(5,𝔽2)—216384no—
337H(5,𝔽2)—224576no—
338C2×#41—232768no—
339C2×#41—23072no—
340C2×#41—29216no—
341C2×#41—24608no—
342C2×#41—21536no—
343C2×#41—24608no—
344C2×#41—24608no—
345C2×#41—224576no—
346C2×#41C22×D411536yescomplemented
347C2×#41C22×D411536yescomplemented
348C2×#41C22×D414096yescomplemented
349C2×#41C2511536yes—
350C2×#41C251512yes—
351C2×#41C2511536yes—
352C2×#41C2511536yes—
353C2×#41C2513072yes—
354C2×#41C2511024yes—
355C2×#41C251256yes—
356C2×#41C251256yes—
357C22×Q8—23072no—
358C22×Q8—2192no—
359C22×Q8—264no—
360C22×Q8—22304no—
361C22×Q8C22×D4164yes—
362C22×Q8C22×D41384yescomplemented
363C22×Q8C251288yes—
364C22×Q8C25196yes—
365C22×Q8C251768yes—
366C22×Q8C2511024yes—
367C22×Q8C25148yes—
368C22×Q8C25164yes—
369C22×D4—2384no—
370C22×D4—2128no—
371C22×D4—24608no—
372C22×D4—29216no—
373C22×D4—2192no—
374C22×D4—264no—
375C22×D4—22304no—
376C22×D4—2128no—
377C22×D4—42304no—
378C22×D4—4192no—
379C22×D4C22×D41192yes—
380C22×D4C22×D411152yescomplemented
381C22×D4C251192yes—
382C22×D4C251576yes—
383C22×D4C251192yes—
384C22×D4C251288yes—
385C22×D4C2511536yes—
386C22×D4C25196yes—
387C22×D4C251768yes—
388C22×D4C2513072yes—
389C22×D4C251576yes—
390C22×D4C2511536yes—
391C22×D4C251144yes—
392C22×D4C251192yes—
393C23×C4—2192no—
394C23×C4—2128no—
395C23×C4—2384no—
396C23×C4—24608no—
397C23×C4—216no—
398C23×C4—296no—
399C23×C4—4576no—
400C23×C4—448no—
401C23×C4—424no—
402C23×C4C22×D4196yes—
403C23×C4C22×D4116yes—
404C23×C4C22×D4196yes—
405C23×C4C22×D4148yes—
406C23×C4C22×D411152yescomplemented
407C23×C4C2512yes—
408C23×C4C25112yes—
409C23×C4C25116yes—
410C23×C4C251288yes—
411C23×C4C251144yes—
412C23×C4C251192yes—
413C23×C4C251576yes—
414C23×C4C2511536yes—
415C23×C4C25124yes—
416C23×C4C251144yes—
417C23×C4C25172yes—
418C23×C4C251384yes—
419C23×C4C2516yes—
420C23×C4C25136yes—
421C23×C4C25172yes—
422C23×C4C25172yes—
423C23×C4C2511yescharacteristic
424C23×C4C25112yes—
425C23×C4C251192yes—
426C23×C4C2512yes—
427C23×C4C2511yescharacteristic
428C4⋊Q8C251256yes—
429C4⋊Q8C251768yes—
430C4⋊Q8C2511536yes—
431#127C251256yes—
432#127C251768yes—
433#127C2511536yes—
434#124C251512yes—
435#124C2511536yes—
436#124C2513072yes—
437#123C2516144yes—
438C22⋊Q8C2516144yes—
439#121C2511024yes—
440#121C2513072yes—
441#121C2513072yes—
442#121C2513072yes—
443#121C2516144yes—
444#120C2516144yes—
445C4×Q8C251512yes—
446C4×Q8C251512yes—
447C4×D4C2511024yes—
448C4×D4C2511536yes—
449C4×D4C2511536yes—
450C4×D4C2513072yes—
451C4×D4C2513072yes—
452C4×D4C2513072yes—
453#117C251768yes—
454#117C251768yes—
455C2×C4⋊C4C251192yes—
456C2×C4⋊C4C251288yes—
457C2×C4⋊C4C251384yes—
458C2×C4⋊C4C251576yes—
459C2×C4⋊C4C2511536yes—
460C2×C22⋊C4C251384yes—
461C2×C22⋊C4C251288yes—
462C2×C22⋊C4C251384yes—
463C2×C22⋊C4C2511152yes—
464C2×C22⋊C4C2513072yes—
465C2×C42C25172yes—
466C2×C42C25172yes—
467C2×C42C251192yes—
468C2×C42C25124yes—
469C2×C42C251144yes—
470C2×C42C251144yes—
471C2×C42C251768yes—
472C2×C42C251384yes—
473C2×C42C251384yes—
474C2×C42C251384yes—
475C2×C42C25112yes—
476C2×C42C25112yes—
477C2×C42C25164yes—
478C24—28no—
479C24—248no—
480C24—264no—
481C24—2128no—
482C24—21152no—
483C24—4144no—
484C24—4192no—
485C24—41152no—
486C24—8768no—
487C24C23×D4148yes—
488C24C23×D418yes—
489C24C23×D41288yes—
490C24C26196yes—
491C24C26136yes—
492C24C2616yes—
493C24C261384yes—
494C24C26148yes—
495C24C2611yescharacteristic
496#41—24096no—
497#41—212288no—
498#41—26144no—
499#41—22048no—
500#41—26144no—
501#41—26144no—
502#41C23×D412048yescomplemented
503#41C23×D412048yescomplemented
504C2×Q8—24096no—
505C2×Q8—21152no—
506C2×Q8—2384no—
507C2×Q8—23072no—
508C2×Q8C23×D41384yes—
509C2×Q8C23×D41512yescomplemented
510C2×Q8C261384yes—
511C2×Q8C261128yes—
512C2×Q8C26164yes—
513C2×D4—22304no—
514C2×D4—2768no—
515C2×D4—26144no—
516C2×D4—212288no—
517C2×D4—21152no—
518C2×D4—2384no—
519C2×D4—23072no—
520C2×D4—2768no—
521C2×D4—43072no—
522C2×D4—41152no—
523C2×D4C23×D411152yes—
524C2×D4C23×D411536yescomplemented
525C2×D4C261256yes—
526C2×D4C261768yes—
527C2×D4C261256yes—
528C2×D4C261384yes—
529C2×D4C261128yes—
530C2×D4C261768yes—
531C2×D4C261192yes—
532C22×C4—264no—
533C22×C4—21152no—
534C22×C4—28no—
535C22×C4—248no—
536C22×C4—2768no—
537C22×C4—22304no—
538C22×C4—26144no—
539C22×C4—296no—
540C22×C4—2576no—
541C22×C4—4768no—
542C22×C4—4288no—
543C22×C4—4144no—
544C22×C4C23×D418yes—
545C22×C4C23×D4148yes—
546C22×C4C23×D41576yes—
547C22×C4C23×D418yes—
548C22×C4C23×D4196yes—
549C22×C4C23×D41576yes—
550C22×C4C23×D41288yes—
551C22×C4C23×D411536yescomplemented
552C22×C4#585116yescomplemented
553C22×C4C26112yes—
554C22×C4C26132yes—
555C22×C4C26172yes—
556C22×C4C261192yes—
557C22×C4C26196yes—
558C22×C4C261384yes—
559C22×C4C261256yes—
560C22×C4C261768yes—
561C22×C4C261192yes—
562C22×C4C26196yes—
563C22×C4C2616yes—
564C22×C4C2616yes—
565C22×C4C26116yes—
566C22×C4C26136yes—
567C22×C4C26148yes—
568C22×C4C26196yes—
569C22×C4C26196yes—
570C22×C4C26112yes—
571C4⋊C4C261256yes—
572C4⋊C4C261384yes—
573C4⋊C4C261768yes—
574C22⋊C4C261512yes—
575C22⋊C4C261384yes—
576C22⋊C4C2611536yes—
577C42C26132yes—
578C42C26116yes—
579C42C26116yes—
580C42C26196yes—
581C42C26196yes—
582C42C261192yes—
583C42C261192yes—
584C23—232no—
585C23—2192no—
586C23—224no—
587C23—2144no—
588C23—2192no—
589C23—2384no—
590C23—2768no—
591C23—496no—
592C23—4576no—
593C23—4768no—
594C23—4256no—
595C23—82304no—
596C23C24×D41144yes—
597C23C24×D4124yes—
598C23C24×D41192yes—
599C23C24×D414yes—
600C23C2×#58518yes—
601C23C27164yes—
602C23C27124yes—
603C23C2714yes—
604C23C2713yes—
605Q8—2768no—
606Q8—2256no—
607Q8C24×D41256yes—
608D4—21536no—
609D4—2512no—
610D4—2768no—
611D4—2256no—
612D4—2512no—
613D4—4768no—
614D4C24×D41768yes—
615C2×C4—2192no—
616C2×C4—2768no—
617C2×C4—224no—
618C2×C4—2144no—
619C2×C4—2512no—
620C2×C4—21536no—
621C2×C4—264no—
622C2×C4—2384no—
623C2×C4—4192no—
624C2×C4—496no—
625C2×C4C24×D4124yes—
626C2×C4C24×D41144yes—
627C2×C4C24×D41384yes—
628C2×C4C24×D4124yes—
629C2×C4C24×D4164yes—
630C2×C4C24×D41384yes—
631C2×C4C24×D41192yes—
632C2×C4C2×#585148yescomplemented
633C2×C4C2718yes—
634C2×C4C27148yes—
635C2×C4C27164yes—
636C2×C4C2714yes—
637C2×C4C2714yes—
638C2×C4C27124yes—
639C2×C4C2718yes—
640C22—28no—
641C22—248no—
642C22—248no—
643C22—2288no—
644C22—264no—
645C22—2128no—
646C22—4192no—
647C22—4384no—
648C22—8768no—
649C22#62812116yesdirect product factor
650C22C25×D4148yes—
651C22C25×D418yes—
652C22C25×D416yes—
653C22C22×#585112yes—
654C22C2811yescharacteristic
655C4—264no—
656C4—28no—
657C4—248no—
658C4C25×D418yes—
659C4C25×D4148yes—
660C4C25×D418yes—
661C4C22×#585116yescomplemented
662C2—28no—
663C2—248no—
664C2—464no—
665C2C2×#62812112yesdirect product factor
666C2C26×D411yescharacteristic
667C2C23×#58512yes—
subgroupG/H
center, socleC23×C4C25
commutator, Frattini, cosocleC22C28
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#585C2semidirect
2. C2×#62812C2direct (N × H)
3. C22×#3500C2semidirect
4. C22×#3499C2semidirect
5. C22×#3498C2semidirect
6. C22×#3497C2semidirect
7. C22×#3496C2semidirect
8. C22×D4×#41C2semidirect
9. C22×#3449C2semidirect
10. C23×#532C2semidirect
11. C23×C4×#41C2semidirect
13. C22×#585C22semidirect
14. C23×2−1+4C22semidirect
15. C23×2−1+4C22semidirect
16. C23×H(5,𝔽2)C22semidirect
17. C23×H(5,𝔽2)C22semidirect
19. C24×#41C22semidirect
20. C24×#41C22semidirect
21. #62812C22direct (N × H)
22. C2×#3500C22semidirect
23. C2×#3499C22semidirect
24. C2×#3498C22semidirect
25. C2×#3497C22semidirect
26. C2×#3496C22semidirect
27. C2×D4×#41C22semidirect
28. C22×#550C22semidirect
29. C22×#547C22semidirect
30. C22×#548C22semidirect
31. C22×#546C22semidirect
32. C22×D4×Q8C22semidirect
33. C22×D42C22semidirect
34. C2×#3449C22semidirect
35. C22×#536C22semidirect
36. C22×#537C22semidirect
37. C22×#535C22semidirect
38. C22×#534C22semidirect
39. C22×#532C22semidirect
40. C22×#532C22semidirect
41. C22×#532C22semidirect
42. C22×#532C22semidirect
43. C22×#532C22semidirect
44. C22×#532C22semidirect
45. C22×#532C22semidirect
46. C23×C4⋊Q8C22semidirect
47. C23×#127C22semidirect
48. C23×#124C22semidirect
49. C22×#525C22semidirect
50. C23×#121C22semidirect
51. C22×C4×#41C22semidirect
52. C22×C4×#41C22semidirect
53. C22×C4×#41C22semidirect
54. C22×C4×#41C22semidirect
55. C23×C4×Q8C22semidirect
56. C23×C4×D4C22semidirect
57. C23×C4×D4C22semidirect
58. C23×#117C22semidirect
59. C24×C42C22semidirect
61. C2×#585C23semidirect
64. C22×2−1+4C23semidirect
65. C22×2−1+4C23semidirect
68. C22×H(5,𝔽2)C23semidirect
69. C22×H(5,𝔽2)C23semidirect
72. C23×#41D4semidirect
82. C23×#41C23semidirect
83. C23×#41C23semidirect
95. #3500C23semidirect
96. #3499C23semidirect
97. #3498C23semidirect
98. #3497C23semidirect
99. #3496C23semidirect
100. D4×#41C23semidirect
101. C2×#550C23semidirect
102. C2×D4×Q8C23semidirect
103. C2×#548C23semidirect
104. C2×#547C23semidirect
105. C2×#546C23semidirect
106. C2×D42C23semidirect
107. #3449C23semidirect
108. C2×#537C23semidirect
109. C2×#536C23semidirect
110. C2×#535C23semidirect
111. C2×#534C23semidirect
112. C2×#532C23semidirect
113. C2×#532C23semidirect
114. C2×#532C23semidirect
115. C2×#532C23semidirect
116. C2×#532C23semidirect
117. C2×#532C23semidirect
118. C2×#532C23semidirect
122. C22×C4⋊Q8C23semidirect
126. C22×#127C23semidirect
130. C22×#124C23semidirect
131. C2×#525C23semidirect
139. C22×#121C23semidirect
141. C2×C4×#41C23semidirect
142. C2×C4×#41C23semidirect
143. C2×C4×#41C23semidirect
144. C2×C4×#41C23semidirect
147. C22×C4×Q8C23semidirect
154. C22×C4×D4C23semidirect
155. C22×C4×D4C23semidirect
158. C22×#117C23semidirect
169. C23×C42C23semidirect
175. C2×2−1+4C24semidirect
176. C2×2−1+4C24semidirect
179. C2×H(5,𝔽2)C24semidirect
180. C2×H(5,𝔽2)C24semidirect
189. C22×#41C2×D4semidirect
190. C22×#41C2×D4semidirect
191. C22×#41C2×D4semidirect
201. C22×#41C24semidirect
202. C22×#41C24semidirect
205. C23×Q8C2×D4semidirect
216. C23×D4C2×D4semidirect
231. C24×C4C2×D4semidirect
246. #550C24semidirect
247. D4×Q8C24semidirect
248. #548C24semidirect
249. #547C24semidirect
250. #546C24semidirect
251. D42C24semidirect
252. #537C24semidirect
253. #536C24semidirect
254. #535C24semidirect
255. #534C24semidirect
256. #532C24semidirect
257. #532C24semidirect
258. #532C24semidirect
259. #532C24semidirect
260. #532C24semidirect
261. #532C24semidirect
265. C2×C4⋊Q8C24semidirect
269. C2×#127C24semidirect
273. C2×#124C24semidirect
274. #525C24semidirect
282. C2×#121C24semidirect
284. C4×#41C24semidirect
285. C4×#41C24semidirect
286. C4×#41C24semidirect
289. C2×C4×Q8C24semidirect
296. C2×C4×D4C24semidirect
297. C2×C4×D4C24semidirect
300. C2×#117C24semidirect
324. C22×C42C24semidirect
346. C2×#41C22×D4semidirect
347. C2×#41C22×D4semidirect
348. C2×#41C22×D4semidirect
362. C22×Q8C22×D4semidirect
380. C22×D4C22×D4semidirect
406. C23×C4C22×D4semidirect
502. #41C23×D4semidirect
503. #41C23×D4semidirect
509. C2×Q8C23×D4semidirect
524. C2×D4C23×D4semidirect
551. C22×C4C23×D4semidirect
552. C22×C4#585semidirect
632. C2×C4C2×#585semidirect
649. C22#62812direct (N × H)
661. C4C22×#585semidirect
665. C2C2×#62812direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5852
C2×#628122
C22×#35002
C22×#34992
C22×#34982
C22×#34972
C22×#34962
C22×D4×#412
C22×#34492
C23×#5322
C23×C4×#412