Finite Group Databasebeta

← #72316524

Subgroups — #72316524

Order 1024.

109761 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3585C212yesmaximal, complemented
2#10586020C211yesmaximal, characteristic, complemented
3C2×#62652C211yesmaximal, characteristic, complemented
4#10574960C2132yesmaximal, complemented
5#10574959C2132yesmaximal, complemented
6#10574957C2132yesmaximal, complemented
7#10574956C2112yesmaximal, complemented
8C2×#60423C2112yesmaximal, complemented
9#10574107C211yesmaximal, characteristic, complemented
10#10574061C212yesmaximal, complemented
11C22×#585C2212yes—
12C23×H(5,𝔽2)C2211yescharacteristic
13C2×#3585—264no—
14C2×#3585C22132yescomplemented
15C2×#3585C22132yescomplemented
16C22×#577C22116yescomplemented
17C22×#576C22116yescomplemented
18C22×#575C22112yescomplemented
19C23×AGL(1,ℤ/8)C22112yescomplemented
20C22×#568C2212yes—
21#62859C22116yescomplemented
22#62853—28no—
23#62852C22116yescomplemented
24#62848—22no—
25#62842—26no—
26#62812C22116yescomplemented
27#62811—216no—
28C2×#3449C22112yescomplemented
29#62652—216no—
30#62652C22132yescomplemented
31C2×C4×H(5,𝔽2)—28no—
32C2×C4×H(5,𝔽2)C22116yescomplemented
33C2×#3428—22no—
34C2×#3428C2211yescharacteristic
35C2×#3428C2211yescharacteristic
36C2×#3428C2216yescomplemented
37C22×#518—26no—
38C22×#518C2216yescomplemented
39#60430C221512yescomplemented
40#60429C221256yescomplemented
41#60428C221256yescomplemented
42#60427C22196yescomplemented
43#60426C22196yescomplemented
44#60425C22196yescomplemented
45#60424C22116yescomplemented
46#60423C22148yescomplemented
47#60423C221192yescomplemented
48#60423C22196yescomplemented
49#60422C221192yescomplemented
50C2×#3042C22196yescomplemented
51C2×#3041C22196yescomplemented
52#60415C22196yescomplemented
53C2×#3036C22196yescomplemented
54#60100C22132yescomplemented
55#60099C22116yescomplemented
56C2×#2905C22112yescomplemented
57#60089C22132yescomplemented
58#60088C22116yescomplemented
59#60087C22116yescomplemented
60#60086C22132yescomplemented
61C2×#2896C22124yescomplemented
62C2×#585—28no—
63C2×#585—28no—
64C2×#585—232no—
65C2×#585—232no—
66C2×#585C23116yes—
67C2×#585C23116yes—
68C22×2−1+4—22no—
69C22×2−1+4C2318yes—
70C22×H(5,𝔽2)—24no—
71C22×H(5,𝔽2)—28no—
72C22×H(5,𝔽2)—216no—
73C22×H(5,𝔽2)—26no—
74C22×H(5,𝔽2)D4132yescomplemented
75C22×H(5,𝔽2)C2318yes—
76C22×H(5,𝔽2)C23116yes—
77C22×H(5,𝔽2)C2318yes—
78C23×#41—28no—
79C23×#41—21no—
80C23×#41C23112yes—
81C23×#41C2313yes—
82C23×#41C2311yescharacteristic
83C24×D4—23no—
84C24×D4C2313yes—
85#3585—2512no—
86#3585—2512no—
87C2×#577—2256no—
88C2×#577C231256yescomplemented
89C2×#576—2256no—
90C2×#576C231256yescomplemented
91C2×#575—2192no—
92C2×#575C23196yes—
93C2×#575C23196yescomplemented
94C22×#137C2318yes—
95C22×#137C23124yescomplemented
96C22×AGL(1,ℤ/8)—2192no—
97C22×AGL(1,ℤ/8)C23196yes—
98C22×AGL(1,ℤ/8)C23124yes—
99C22×AGL(1,ℤ/8)C23148yescomplemented
100C22×AGL(1,ℤ/8)C23196yescomplemented
101C22×AGL(1,ℤ/8)C23124yescomplemented
102C22×#135C23148yescomplemented
103C23×SD16C23124yescomplemented
104C23×D8C23124yescomplemented
105C2×#568—232no—
106C2×#568C23116yes—
107C2×#568C23116yes—
108C22×#131C23116yes—
109C23×M16C23112yes—
110#3500C231128yescomplemented
111#3499C23164yescomplemented
112#3498C23164yescomplemented
113#3497—232no—
114#3496—296no—
115#3489—2128no—
116#3488—2128no—
117#3487—232no—
118#3486—232no—
119#3485—296no—
120#3484—296no—
121D4×#41—2128no—
122#3449—248no—
123#3449—224no—
124#3449—224no—
125#3449C23116yes—
126#3449C23148yescomplemented
127#3449C23196yescomplemented
128C2×#537—224no—
129C2×#536C23148yescomplemented
130C2×#535C23148yescomplemented
131C2×#534—224no—
132C2×#532C23148yescomplemented
133C2×#525—248no—
134C4×H(5,𝔽2)—2256no—
135C4×H(5,𝔽2)—2128no—
136C4×H(5,𝔽2)C231256yescomplemented
137#3428—28no—
138#3428—264no—
139#3428—248no—
140#3428D4116yes—
141#3428C23116yes—
142#3428C23116yes—
143#3428C23196yescomplemented
144C2×#520—216no—
145C2×#520—212no—
146C2×#520D418yes—
147C2×#520C2318yes—
148C2×#520C23124yescomplemented
149C2×#519—21no—
150C2×#519D412yes—
151C2×#519C2314yes—
152C2×#518—23no—
153C2×#518—2192no—
154C2×#518—248no—
155C2×#518—212no—
156C2×#518—212no—
157C2×#518—248no—
158C2×#518—212no—
159C2×#518D416yes—
160C2×#518C23112yes—
161C2×#518C23196yescomplemented
162C2×#518C23124yescomplemented
163C2×C4×#41—24no—
164C2×C4×#41—216no—
165C2×C4×#41—212no—
166C2×C4×#41C2318yes—
167C2×C4×#41C23124yescomplemented
168C22×C4×D4—248no—
169C22×C4×D4—212no—
170C22×C4×D4C23124yescomplemented
171C22×#117—212no—
172C22×#117C2316yes—
173C22×#117C2316yes—
174C23×C22⋊C4—212no—
175#3046C231768yescomplemented
176#3045C231768yescomplemented
177#3044C231128yescomplemented
178#3043C231128yescomplemented
179#3042C231384yescomplemented
180#3042C231768yescomplemented
181#3041C231384yescomplemented
182#3041C231768yescomplemented
183#3040C231384yescomplemented
184#3039C231192yescomplemented
185#3038C231192yescomplemented
186#3037C231128yescomplemented
187#3036C231384yescomplemented
188#3036C231768yescomplemented
189#3035C231768yescomplemented
190C2×#463C231384yescomplemented
191C2×#461C231192yescomplemented
192C2×#459C231192yescomplemented
193#2906C231256yescomplemented
194#2905C23116yes—
195#2905C23148yescomplemented
196#2905C23196yescomplemented
197C2×#424C23196yescomplemented
198C2×#423C23148yescomplemented
199#2898C231256yescomplemented
200#2897C231256yescomplemented
201#2896C23132yes—
202#2896C23196yescomplemented
203#2896C23196yescomplemented
204#2896C23196yescomplemented
205C2×#417C23196yescomplemented
206C2×#419C23148yescomplemented
207C2×#418C23148yescomplemented
208C2×#416C23196yescomplemented
209C26—23no—
210#585—2128no—
211#585—2128no—
212#585—2128no—
213#585—2128no—
214#585—4128no—
215#585—4128no—
216C2×2−1+4—232no—
217C2×2−1+4—216no—
218C2×2−1+4—216no—
219C2×2−1+4—264no—
220C2×2−1+4—264no—
221C2×2−1+4—432no—
222C2×2−1+4C24164yes—
223C2×H(5,𝔽2)—2256no—
224C2×H(5,𝔽2)—2128no—
225C2×H(5,𝔽2)—264no—
226C2×H(5,𝔽2)—232no—
227C2×H(5,𝔽2)—232no—
228C2×H(5,𝔽2)—2128no—
229C2×H(5,𝔽2)—264no—
230C2×H(5,𝔽2)—248no—
231C2×H(5,𝔽2)—248no—
232C2×H(5,𝔽2)—264no—
233C2×H(5,𝔽2)—264no—
234C2×H(5,𝔽2)—496no—
235C2×H(5,𝔽2)C2×D41128yescomplemented
236C2×H(5,𝔽2)C2×D41256yescomplemented
237C2×H(5,𝔽2)C24164yes—
238C2×H(5,𝔽2)C24164yes—
239C22×#41—264no—
240C22×#41—264no—
241C22×#41—232no—
242C22×#41—28no—
243C22×#41—216no—
244C22×#41—28no—
245C22×#41—224no—
246C22×#41—26no—
247C22×#41—212no—
248C22×#41—212no—
249C22×#41—212no—
250C22×#41—224no—
251C22×#41—224no—
252C22×#41—224no—
253C22×#41—296no—
254C22×#41—296no—
255C22×#41—4128no—
256C22×#41C2×D4116yes—
257C22×#41C2×D418yes—
258C22×#41C2×D414yes—
259C22×#41C2×D4148yescomplemented
260C22×#41#41116yes—
261C22×#41C2418yes—
262C22×#41C24124yes—
263C22×#41C24148yes—
264C22×#41C24148yes—
265C22×#41C24112yes—
266C22×#41C24124yes—
267C22×#41C2418yes—
268C22×#41C2414yes—
269C23×Q8—28no—
270C23×Q8C2×D411yescharacteristic
271C23×Q8C24112yes—
272C23×Q8C2411yescharacteristic
273C23×D4—23no—
274C23×D4—296no—
275C23×D4—224no—
276C23×D4—248no—
277C23×D4—212no—
278C23×D4—224no—
279C23×D4—23no—
280C23×D4—26no—
281C23×D4—212no—
282C23×D4—224no—
283C23×D4C2×D413yes—
284C23×D4C2×D4148yescomplemented
285C23×D4C24112yes—
286C23×D4C2413yes—
287C23×D4C24112yes—
288C23×D4C24124yes—
289C24×C4—23no—
290C24×C4—212no—
291C24×C4—224no—
292C24×C4C2413yes—
293#577—22048no—
294#576—22048no—
295#575—2768no—
296#575—2768no—
297C2×#137—2192no—
298C2×#137—264no—
299C2×#137C24132yes—
300C2×#137C241192yes—
301C2×#137C24132yes—
302C2×AGL(1,ℤ/8)—2192no—
303C2×AGL(1,ℤ/8)—2768no—
304C2×AGL(1,ℤ/8)—2768no—
305C2×AGL(1,ℤ/8)—2192no—
306C2×AGL(1,ℤ/8)—2384no—
307C2×AGL(1,ℤ/8)C24196yes—
308C2×AGL(1,ℤ/8)C241384yes—
309C2×AGL(1,ℤ/8)C241192yes—
310C2×AGL(1,ℤ/8)C24196yes—
311C2×#135—2384no—
312C2×#135C241384yes—
313C22×Q16C24116yes—
314C22×SD16—2192no—
315C22×SD16C241192yes—
316C22×SD16C24148yes—
317C22×SD16C24116yes—
318C22×D8—2192no—
319C22×D8C241192yes—
320C22×D8C24148yes—
321#568—2128no—
322#568—2128no—
323C2×#131—2128no—
324C2×#131C241128yes—
325C22×M16—296no—
326C22×M16C24148yes—
327C22×M16C24148yes—
328C22×M16C2418yes—
329C22×M16C24124yes—
330C23×C8C24124yes—
331#550—2128no—
332D4×Q8—2128no—
333#548—2256no—
334#547—2384no—
335#546—2768no—
336D42—2384no—
337#537—232no—
338#537—2192no—
339#537—296no—
340#536—296no—
341#536—296no—
342#536C24164yes—
343#536C241192yescomplemented
344#535—296no—
345#535—296no—
346#535C24164yes—
347#535C241192yescomplemented
348#534—232no—
349#534—2192no—
350#534—296no—
351#532—296no—
352#532—296no—
353#532C24164yes—
354#532C241192yescomplemented
355C2×C4⋊Q8C24148yescomplemented
356C2×#127C24148yescomplemented
357C2×#124C24196yescomplemented
358#525—264no—
359#525—2192no—
360#525—2192no—
361#525—2192no—
362C2×#123—296no—
363C2×C22⋊Q8—296no—
364C2×#121—296no—
365C2×#121—296no—
366C2×#120—296no—
367#520—232no—
368#520—2256no—
369#520—296no—
370#520—2192no—
371#520C2×D41128yes—
372#520C241192yes—
373#520C24164yes—
374#519—216no—
375#519—216no—
376#519C2×D4132yes—
377#519C24132yes—
378#518—248no—
379#518—2768no—
380#518—248no—
381#518—2192no—
382#518—2192no—
383#518—296no—
384#518—2192no—
385#518C2×D4196yes—
386#518C24196yes—
387#518C241192yes—
388C4×#41—264no—
389C4×#41—2256no—
390C4×#41—2192no—
391C4×#41—296no—
392C4×#41C2×D4164yes—
393C4×#41C241192yes—
394C4×#41C24164yes—
395C2×C4×Q8—28no—
396C2×C4×Q8—28no—
397C2×C4×Q8C2×D4116yes—
398C2×C4×Q8C24116yes—
399C2×C4×D4—224no—
400C2×C4×D4—248no—
401C2×C4×D4—2768no—
402C2×C4×D4—224no—
403C2×C4×D4—248no—
404C2×C4×D4—2192no—
405C2×C4×D4—248no—
406C2×C4×D4—248no—
407C2×C4×D4—296no—
408C2×C4×D4—296no—
409C2×C4×D4C2×D4148yes—
410C2×C4×D4C24148yes—
411C2×C4×D4C241192yes—
412C2×#117—26no—
413C2×#117—26no—
414C2×#117—224no—
415C2×#117—2192no—
416C2×#117—224no—
417C2×#117—28no—
418C2×#117—224no—
419C2×#117C2×D4112yes—
420C2×#117C2×D4112yes—
421C2×#117C2×D4148yes—
422C2×#117C24148yes—
423C2×#117C2414yes—
424C2×#117C24112yes—
425C2×#117C24148yes—
426C2×#117C2414yes—
427C2×#117C24112yes—
428C22×C4⋊C4—224no—
429C22×C4⋊C4C2×D4112yes—
430C22×C4⋊C4C24112yes—
431C22×C22⋊C4—26no—
432C22×C22⋊C4—224no—
433C22×C22⋊C4—224no—
434C22×C22⋊C4—248no—
435C22×C22⋊C4—2192no—
436C22×C22⋊C4C2×D4112yes—
437C22×C42—26no—
438C22×C42—224no—
439C22×C42C24112yes—
440#464C241512yescomplemented
441#463C2411536yescomplemented
442#462C241256yescomplemented
443#461C241768yescomplemented
444#460C241256yescomplemented
445#459C241768yescomplemented
446#424C241128yes—
447#424C241384yescomplemented
448#423C24164yes—
449#423C241192yescomplemented
450C2×C4⋊C8C241192yescomplemented
451#419C24164yes—
452#419C241192yescomplemented
453#418C24164yes—
454#418C241192yescomplemented
455#417C241128yes—
456#417C241384yescomplemented
457#416C241128yes—
458#416C241384yescomplemented
459C2×#103C241192yescomplemented
460C2×#102C241192yescomplemented
461C25—23no—
462C25—212no—
463C25—248no—
464C25—224no—
465C25—212no—
466C25—1612no—
467C25C22×D413yes—
4682−1+4—2256no—
4692−1+4—2256no—
4702−1+4—4256no—
4712−1+4—4128no—
4722−1+4—4128no—
473H(5,𝔽2)—2512no—
474H(5,𝔽2)—21024no—
475H(5,𝔽2)—2256no—
476H(5,𝔽2)—2256no—
477H(5,𝔽2)—2256no—
478H(5,𝔽2)—4256no—
479H(5,𝔽2)—4384no—
480H(5,𝔽2)—4384no—
481H(5,𝔽2)C22×D41512yes—
482C2×#41—2256no—
483C2×#41—2128no—
484C2×#41—264no—
485C2×#41—264no—
486C2×#41—2192no—
487C2×#41—2192no—
488C2×#41—296no—
489C2×#41—248no—
490C2×#41—224no—
491C2×#41—28no—
492C2×#41—248no—
493C2×#41—248no—
494C2×#41—248no—
495C2×#41—248no—
496C2×#41—248no—
497C2×#41—28no—
498C2×#41—296no—
499C2×#41—248no—
500C2×#41—296no—
501C2×#41—232no—
502C2×#41—2192no—
503C2×#41—2192no—
504C2×#41—232no—
505C2×#41—296no—
506C2×#41—2192no—
507C2×#41—2192no—
508C2×#41—4512no—
509C2×#41—4512no—
510C2×#41—464no—
511C2×#41—4192no—
512C2×#41—496no—
513C2×#41—496no—
514C2×#41—4192no—
515C2×#41—4192no—
516C2×#41#1211128yes—
517C2×#41#121164yes—
518C2×#41C22×D41192yes—
519C2×#41C22×D4196yes—
520C2×#41C22×D4164yes—
521C2×#41C22×D4132yes—
522C2×#41C22×D4132yes—
523C2×#41C22×D4116yes—
524C2×#41C2×#41164yes—
525C2×#41C2×#41132yes—
526C2×#41C25116yes—
527C2×#41C25196yes—
528C2×#41C25116yes—
529C2×#41C25148yes—
530C2×#41C25116yes—
531C22×Q8—264no—
532C22×Q8—21no—
533C22×Q8—22no—
534C22×Q8—224no—
535C22×Q8—212no—
536C22×Q8—24no—
537C22×Q8—248no—
538C22×Q8—248no—
539C22×Q8—464no—
540C22×Q8#121116yes—
541C22×Q8C22×D418yes—
542C22×Q8C22×D414yes—
543C22×Q8C22×D418yes—
544C22×Q8C25148yes—
545C22×Q8C2518yes—
546C22×Q8C2512yes—
547C22×Q8C2514yes—
548C22×D4—248no—
549C22×D4—212no—
550C22×D4—224no—
551C22×D4—2768no—
552C22×D4—2384no—
553C22×D4—2192no—
554C22×D4—248no—
555C22×D4—248no—
556C22×D4—28no—
557C22×D4—224no—
558C22×D4—2192no—
559C22×D4—248no—
560C22×D4—2192no—
561C22×D4—296no—
562C22×D4—23no—
563C22×D4—212no—
564C22×D4—248no—
565C22×D4—224no—
566C22×D4—26no—
567C22×D4—224no—
568C22×D4—248no—
569C22×D4—224no—
570C22×D4—212no—
571C22×D4—296no—
572C22×D4—212no—
573C22×D4—296no—
574C22×D4—248no—
575C22×D4—248no—
576C22×D4—496no—
577C22×D4—4192no—
578C22×D4#121148yes—
579C22×D4C22×D41192yes—
580C22×D4C22×D4124yes—
581C22×D4C22×D4196yes—
582C22×D4C22×D4112yes—
583C22×D4C22×D4124yes—
584C22×D4C25148yes—
585C22×D4C2518yes—
586C22×D4C2516yes—
587C22×D4C25148yes—
588C22×D4C25112yes—
589C23×C4—21no—
590C23×C4—248no—
591C23×C4—212no—
592C23×C4—224no—
593C23×C4—212no—
594C23×C4—212no—
595C23×C4—248no—
596C23×C4—248no—
597C23×C4—28no—
598C23×C4—224no—
599C23×C4—248no—
600C23×C4—2192no—
601C23×C4—496no—
602C23×C4—1648no—
603C23×C4C22×D4124yes—
604C23×C4C22×D416yes—
605C23×C4C22×D413yes—
606C23×C4C22×D4112yes—
607C23×C4C22×D4124yes—
608C23×C4C2×#41124yes—
609C23×C4C2516yes—
610C23×C4C25112yes—
611C23×C4C2511yescharacteristic
612#137—2768no—
613#137—2128no—
614#137—2128no—
615AGL(1,ℤ/8)—2768no—
616AGL(1,ℤ/8)—2384no—
617AGL(1,ℤ/8)—2384no—
618AGL(1,ℤ/8)—21536no—
619#135—21536no—
620C2×Q16—264no—
621C2×Q16C25164yes—
622C2×SD16—264no—
623C2×SD16—2192no—
624C2×SD16—2768no—
625C2×SD16C251192yes—
626C2×SD16C25164yes—
627C2×D8—2192no—
628C2×D8—2768no—
629C2×D8C251192yes—
630#131—2512no—
631C2×M16—232no—
632C2×M16—296no—
633C2×M16—2192no—
634C2×M16—2192no—
635C2×M16C25116yes—
636C2×M16C25116yes—
637C2×M16C25196yes—
638C22×C8—296no—
639C22×C8C25116yes—
640C22×C8C25196yes—
641C4⋊Q8—296no—
642C4⋊Q8C25164yes—
643#127—296no—
644#127C25164yes—
645#124—2192no—
646#124C251128yes—
647#123—2128no—
648#123—2384no—
649C22⋊Q8—2128no—
650C22⋊Q8—2384no—
651#121—2128no—
652#121—2384no—
653#121—2128no—
654#121—2384no—
655#120—2128no—
656#120—2384no—
657C4×Q8—264no—
658C4×Q8—264no—
659C4×Q8—232no—
660C4×Q8C22×D41128yes—
661C4×Q8C25164yes—
662C4×D4—2192no—
663C4×D4—2384no—
664C4×D4—2384no—
665C4×D4—2192no—
666C4×D4—2384no—
667C4×D4—2384no—
668C4×D4—296no—
669C4×D4—2128no—
670C4×D4—2384no—
671C4×D4C22×D41384yes—
672C4×D4C251192yes—
673#117—28no—
674#117—248no—
675#117—248no—
676#117—224no—
677#117—2192no—
678#117—264no—
679#117—2192no—
680#117C22×D4196yes—
681#117C22×D4116yes—
682#117C22×D4196yes—
683#117C22×D4148yes—
684#117C25116yes—
685#117C25148yes—
686#117C25116yes—
687#117C25148yes—
688C2×C4⋊C4—216no—
689C2×C4⋊C4—212no—
690C2×C4⋊C4—224no—
691C2×C4⋊C4—296no—
692C2×C4⋊C4—2192no—
693C2×C4⋊C4C22×D4124yes—
694C2×C4⋊C4C22×D418yes—
695C2×C4⋊C4C22×D4196yes—
696C2×C4⋊C4C2518yes—
697C2×C4⋊C4C25148yes—
698C2×C22⋊C4—24no—
699C2×C22⋊C4—212no—
700C2×C22⋊C4—248no—
701C2×C22⋊C4—248no—
702C2×C22⋊C4—2192no—
703C2×C22⋊C4—2192no—
704C2×C22⋊C4—2192no—
705C2×C22⋊C4—2384no—
706C2×C22⋊C4C22×D418yes—
707C2×C22⋊C4C22×D4124yes—
708C2×C22⋊C4C22×D4196yes—
709C2×C42—216no—
710C2×C42—24no—
711C2×C42—212no—
712C2×C42—248no—
713C2×C42—2192no—
714C2×C42C22×D4124yes—
715C2×C42C22×D4148yes—
716C2×C42C2518yes—
717C2×C42C25148yes—
718C4⋊C8C251256yes—
719#103C251256yes—
720#102C251256yes—
721C24—26no—
722C24—212no—
723C24—248no—
724C24—224no—
725C24—296no—
726C24—2192no—
727C24—248no—
728C24—28no—
729C24—448no—
730C24—86no—
731C24—848no—
732C24—812no—
733C24—1624no—
734C24—1648no—
735C24—1696no—
736C24C2×#121124yes—
737C24C23×D411yescharacteristic
738C24C23×D4112yes—
739C24C23×D416yes—
740#41—2512no—
741#41—296no—
742#41—2192no—
743#41—2384no—
744#41—2192no—
745#41—232no—
746#41—232no—
747#41—232no—
748#41—232no—
749#41—2192no—
750#41—4256no—
751#41—4768no—
752#41—432no—
753#41—4192no—
754#41—4192no—
755#41—432no—
756#41—4192no—
757#41—4192no—
758#41—4192no—
759#41C2×#1211128yes—
760#41C2×#1211256yes—
761#41C23×D41192yes—
762#41C23×D4164yes—
763#41C22×#41164yes—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—28no—
767C2×Q8—248no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—216no—
771C2×Q8—28no—
772C2×Q8—216no—
773C2×Q8—296no—
774C2×Q8—216no—
775C2×Q8—296no—
776C2×Q8—4256no—
777C2×Q8—448no—
778C2×Q8—496no—
779C2×Q8C2×#121164yes—
780C2×Q8C2×#121132yes—
781C2×Q8C23×D4116yes—
782C2×Q8C23×D418yes—
783C2×Q8C23×D4116yes—
784C2×Q8C26116yes—
785C2×Q8C2614yes—
786C2×D4—248no—
787C2×D4—296no—
788C2×D4—2192no—
789C2×D4—21536no—
790C2×D4—216no—
791C2×D4—296no—
792C2×D4—216no—
793C2×D4—212no—
794C2×D4—248no—
795C2×D4—26no—
796C2×D4—216no—
797C2×D4—296no—
798C2×D4—28no—
799C2×D4—248no—
800C2×D4—2128no—
801C2×D4—224no—
802C2×D4—212no—
803C2×D4—296no—
804C2×D4—216no—
805C2×D4—296no—
806C2×D4—2192no—
807C2×D4—296no—
808C2×D4—248no—
809C2×D4—224no—
810C2×D4—2192no—
811C2×D4—2384no—
812C2×D4—432no—
813C2×D4—496no—
814C2×D4—4192no—
815C2×D4—4192no—
816C2×D4—4768no—
817C2×D4—448no—
818C2×D4—496no—
819C2×D4—1696no—
820C2×D4C2×#1211192yes—
821C2×D4C2×#121196yes—
822C2×D4C23×D4148yes—
823C2×D4C23×D41192yes—
824C2×D4C23×D4124yes—
825C2×D4C23×D4148yes—
826C2×D4C26116yes—
827C2×D4C26112yes—
828C22×C4—22no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—248no—
832C22×C4—2192no—
833C22×C4—296no—
834C22×C4—28no—
835C22×C4—248no—
836C22×C4—28no—
837C22×C4—248no—
838C22×C4—216no—
839C22×C4—296no—
840C22×C4—216no—
841C22×C4—2192no—
842C22×C4—448no—
843C22×C4—432no—
844C22×C4—496no—
845C22×C4—4192no—
846C22×C4—4192no—
847C22×C4—824no—
848C22×C4—896no—
849C22×C4—824no—
850C22×C4—16192no—
851C22×C4C2×#121124yes—
852C22×C4C2×#121196yes—
853C22×C4C2×#121148yes—
854C22×C4C23×D4116yes—
855C22×C4C23×D4196yes—
856C22×C4C23×D4148yes—
857C22×C4C23×D414yes—
858C22×C4C23×D4124yes—
859C22×C4C23×D411yescharacteristic
860C22×C4C23×D416yes—
861C22×C4C23×D4124yes—
862C22×C4C23×D4112yes—
863C22×C4C23×D412yes—
864C22×C4C23×D4112yes—
865C22×C4C22×#4114yes—
866C22×C4C22×#41148yes—
867C22×C4C22×#41124yes—
868C22×C4C2611yescharacteristic
869C22×C4C26112yes—
870C22×C4C2612yes—
871Q16—2128no—
872SD16—2128no—
873SD16—2384no—
874D8—2384no—
875M16—232no—
876M16—232no—
877M16—2192no—
878C2×C8—232no—
879C2×C8—2192no—
880C2×C8C26132yes—
881C4⋊C4—264no—
882C4⋊C4—248no—
883C4⋊C4—28no—
884C4⋊C4—2128no—
885C4⋊C4C23×D4196yes—
886C4⋊C4C23×D4132yes—
887C4⋊C4C26116yes—
888C22⋊C4—216no—
889C22⋊C4—248no—
890C22⋊C4—2192no—
891C22⋊C4—2256no—
892C22⋊C4C23×D4132yes—
893C22⋊C4C23×D4196yes—
894C42—264no—
895C42—216no—
896C42—248no—
897C42C23×D4196yes—
898C42C23×D4116yes—
899C42C26116yes—
900C23—212no—
901C23—224no—
902C23—248no—
903C23—2192no—
904C23—216no—
905C23—412no—
906C23—42no—
907C23—424no—
908C23—424no—
909C23—416no—
910C23—496no—
911C23—896no—
912C23—824no—
913C23—816no—
914C23—896no—
915C23—824no—
916C23—8192no—
917C23—848no—
918C23—16192no—
919C23—1696no—
920C23C22×#12114yes—
921C23C22×#121148yes—
922C23C22×#121124yes—
923C23C24×D412yes—
924C23C24×D4112yes—
925C23C24×D411yescharacteristic
926Q8—24no—
927Q8—28no—
928Q8—216no—
929Q8—216no—
930Q8—216no—
931Q8—496no—
932Q8—416no—
933Q8C22×#121164yes—
934Q8C24×D418yes—
935D4—2192no—
936D4—216no—
937D4—212no—
938D4—216no—
939D4—2192no—
940D4—224no—
941D4—248no—
942D4—432no—
943D4—432no—
944D4—4192no—
945D4—496no—
946D4—416no—
947D4—8128no—
948D4C22×#1211192yes—
949D4C24×D4124yes—
950C2×C4—24no—
951C2×C4—216no—
952C2×C4—28no—
953C2×C4—2192no—
954C2×C4—216no—
955C2×C4—216no—
956C2×C4—416no—
957C2×C4—496no—
958C2×C4—416no—
959C2×C4—416no—
960C2×C4—496no—
961C2×C4—432no—
962C2×C4—432no—
963C2×C4—4192no—
964C2×C4—8192no—
965C2×C4—848no—
966C2×C4C22×#121148yes—
967C2×C4C22×#121124yes—
968C2×C4C22×#12118yes—
969C2×C4C22×#121148yes—
970C2×C4C22×#121196yes—
971C2×C4C22×#12114yes—
972C2×C4C24×D4132yes—
973C2×C4C24×D414yes—
974C2×C4C24×D4124yes—
975C2×C4C24×D412yes—
976C2×C4C24×D412yes—
977C2×C4C24×D4112yes—
978C2×C4C24×D411yescharacteristic
979C2×C4C23×#4114yes—
980C2×C4C23×#4112yes—
981C2×C4C23×#41124yes—
982C2×C4C2711yescharacteristic
983C8—232no—
984C22—22no—
985C22—224no—
986C22—24no—
987C22—224no—
988C22—44no—
989C22—424no—
990C22—448no—
991C22—448no—
992C22—424no—
993C22—416no—
994C22—432no—
995C22—8192no—
996C22—848no—
997C22—832no—
998C22—1696no—
999C22C23×#12114yes—
1000C22C23×#12112yes—
1001C22C23×#121124yes—
1002C22C25×D411yescharacteristic
1003C4—28no—
1004C4—232no—
1005C4—416no—
1006C4—416no—
1007C4C23×#121124yes—
1008C4C23×#12112yes—
1009C4C23×#12114yes—
1010C4C25×D411yescharacteristic
1011C4C24×#4111yescharacteristic
1012C2—22no—
1013C2—24no—
1014C2—224no—
1015C2—424no—
1016C2—816no—
1017C2C24×#12111yescharacteristic
1018C2#1058699912yes—
subgroupG/H
center, socleC22C25×D4
commutator, Frattini, cosocleC2×C4C27
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#3428 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#3585C2semidirect
2. #10586020C2semidirect
3. C2×#62652C2semidirect
4. #10574960C2semidirect
5. #10574959C2semidirect
6. #10574957C2semidirect
7. #10574956C2semidirect
8. C2×#60423C2semidirect
9. #10574107C2semidirect
10. #10574061C2semidirect
14. C2×#3585C22semidirect
15. C2×#3585C22semidirect
16. C22×#577C22semidirect
17. C22×#576C22semidirect
18. C22×#575C22semidirect
19. C23×AGL(1,ℤ/8)C22semidirect
21. #62859C22semidirect
23. #62852C22semidirect
26. #62812C22semidirect
28. C2×#3449C22semidirect
30. #62652C22semidirect
32. C2×C4×H(5,𝔽2)C22semidirect
36. C2×#3428C22semidirect
38. C22×#518C22semidirect
39. #60430C22semidirect
40. #60429C22semidirect
41. #60428C22semidirect
42. #60427C22semidirect
43. #60426C22semidirect
44. #60425C22semidirect
45. #60424C22semidirect
46. #60423C22semidirect
47. #60423C22semidirect
48. #60423C22semidirect
49. #60422C22semidirect
50. C2×#3042C22semidirect
51. C2×#3041C22semidirect
52. #60415C22semidirect
53. C2×#3036C22semidirect
54. #60100C22semidirect
55. #60099C22semidirect
56. C2×#2905C22semidirect
57. #60089C22semidirect
58. #60088C22semidirect
59. #60087C22semidirect
60. #60086C22semidirect
61. C2×#2896C22semidirect
74. C22×H(5,𝔽2)D4semidirect
88. C2×#577C23semidirect
90. C2×#576C23semidirect
93. C2×#575C23semidirect
95. C22×#137C23semidirect
99. C22×AGL(1,ℤ/8)C23semidirect
100. C22×AGL(1,ℤ/8)C23semidirect
101. C22×AGL(1,ℤ/8)C23semidirect
102. C22×#135C23semidirect
103. C23×SD16C23semidirect
104. C23×D8C23semidirect
110. #3500C23semidirect
111. #3499C23semidirect
112. #3498C23semidirect
126. #3449C23semidirect
127. #3449C23semidirect
129. C2×#536C23semidirect
130. C2×#535C23semidirect
132. C2×#532C23semidirect
136. C4×H(5,𝔽2)C23semidirect
143. #3428C23semidirect
148. C2×#520C23semidirect
161. C2×#518C23semidirect
162. C2×#518C23semidirect
167. C2×C4×#41C23semidirect
170. C22×C4×D4C23semidirect
175. #3046C23semidirect
176. #3045C23semidirect
177. #3044C23semidirect
178. #3043C23semidirect
179. #3042C23semidirect
180. #3042C23semidirect
181. #3041C23semidirect
182. #3041C23semidirect
183. #3040C23semidirect
184. #3039C23semidirect
185. #3038C23semidirect
186. #3037C23semidirect
187. #3036C23semidirect
188. #3036C23semidirect
189. #3035C23semidirect
190. C2×#463C23semidirect
191. C2×#461C23semidirect
192. C2×#459C23semidirect
193. #2906C23semidirect
195. #2905C23semidirect
196. #2905C23semidirect
197. C2×#424C23semidirect
198. C2×#423C23semidirect
199. #2898C23semidirect
200. #2897C23semidirect
202. #2896C23semidirect
203. #2896C23semidirect
204. #2896C23semidirect
205. C2×#417C23semidirect
206. C2×#419C23semidirect
207. C2×#418C23semidirect
208. C2×#416C23semidirect
235. C2×H(5,𝔽2)C2×D4semidirect
236. C2×H(5,𝔽2)C2×D4semidirect
259. C22×#41C2×D4semidirect
284. C23×D4C2×D4semidirect
343. #536C24semidirect
347. #535C24semidirect
354. #532C24semidirect
355. C2×C4⋊Q8C24semidirect
356. C2×#127C24semidirect
357. C2×#124C24semidirect
440. #464C24semidirect
441. #463C24semidirect
442. #462C24semidirect
443. #461C24semidirect
444. #460C24semidirect
445. #459C24semidirect
447. #424C24semidirect
449. #423C24semidirect
450. C2×C4⋊C8C24semidirect
452. #419C24semidirect
454. #418C24semidirect
456. #417C24semidirect
458. #416C24semidirect
459. C2×#103C24semidirect
460. C2×#102C24semidirect

Maximal subgroups

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

subgroupindex
C22×#35852
#105860202
C2×#626522
#105749602
#105749592
#105749572
#105749562
C2×#604232
#105741072
#105740612