Finite Group Databasebeta

← #62347

Subgroups — #62347

Order 256.

929 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3551C211yesmaximal, characteristic, complemented
2#3546C211yesmaximal, characteristic, complemented
3#3351C211yesmaximal, characteristic, complemented
4#3350C211yesmaximal, characteristic, complemented
5#3343C211yesmaximal, characteristic, complemented
6#3339C211yesmaximal, characteristic, complemented
7#3326C211yesmaximal, characteristic, complemented
8#3322C211yesmaximal, characteristic, complemented
9#3318C211yesmaximal, characteristic, complemented
10#3317C211yesmaximal, characteristic, complemented
11#3313C211yesmaximal, characteristic, complemented
12#3306C211yesmaximal, characteristic, complemented
13#3297C211yesmaximal, characteristic, complemented
14#3296C211yesmaximal, characteristic, complemented
15#3282C211yesmaximal, characteristic, complemented
16#3273C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3250C211yesmaximal, characteristic, complemented
20#3247C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3199C211yesmaximal, characteristic, complemented
24#3198C211yesmaximal, characteristic, complemented
25#3183C211yesmaximal, characteristic, complemented
26#3171C211yesmaximal, characteristic, complemented
27#3062C211yesmaximal, characteristic, complemented
28#3062C211yesmaximal, characteristic, complemented
29#3061C211yesmaximal, characteristic, complemented
30#3057C211yesmaximal, characteristic, complemented
31#2935C211yesmaximal, characteristic, complemented
32C2×AGL(1,ℤ/8)C2211yescharacteristic
33C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
34C2×#135C2211yescharacteristic, complemented
35C22×SD16C2211yescharacteristic, complemented
36C2×#131C2211yescharacteristic, complemented
37C2×#131C2211yescharacteristic, complemented
38#563—21no—
39#560—21no—
40#560—21no—
41#560—21no—
42#556C2211yescharacteristic, complemented
43#555—21no—
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#553C2211yescharacteristic, complemented
47#553C2211yescharacteristic, complemented
48#552C2211yescharacteristic, complemented
49#552C2211yescharacteristic, complemented
50#551—21no—
51#550—21no—
52#550C2211yescharacteristic
53#548C2211yescharacteristic
54#548C2211yescharacteristic, complemented
55#547C2211yescharacteristic
56#546—21no—
57#546C2211yescharacteristic
58#546C2211yescharacteristic, complemented
59#546C2211yescharacteristic, complemented
60#546C2211yescharacteristic, complemented
61D42C2211yescharacteristic, complemented
62#542—21no—
63#540—21no—
64#540—21no—
65#538—21no—
66#538—21no—
67#538—21no—
68#538—21no—
69#537C2211yescharacteristic
70#537C2211yescharacteristic, complemented
71#537C2211yescharacteristic, complemented
72#537C2211yescharacteristic, complemented
73#536C2211yescharacteristic, complemented
74#535—21no—
75#535C2211yescharacteristic
76#535C2211yescharacteristic, complemented
77#535C2211yescharacteristic, complemented
78#532C2211yescharacteristic
79#532C2211yescharacteristic, complemented
80#529C2211yescharacteristic, complemented
81#529C2211yescharacteristic, complemented
82#529C2211yescharacteristic, complemented
83#501C2211yescharacteristic, complemented
84#499C2211yescharacteristic, complemented
85#496C2211yescharacteristic
86#495C2211yescharacteristic
87#490C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic, complemented
94#483C2211yescharacteristic, complemented
95#483C2211yescharacteristic, complemented
96#483C2211yescharacteristic, complemented
97#482C2211yescharacteristic
98#482C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#481C2211yescharacteristic, complemented
104#481C2211yescharacteristic, complemented
105#481C2211yescharacteristic, complemented
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#478C2211yescharacteristic, complemented
110#478C2211yescharacteristic, complemented
111#478C2211yescharacteristic, complemented
112#478C2211yescharacteristic, complemented
113#477C2211yescharacteristic, complemented
114#476C2211yescharacteristic, complemented
115#470C2211yescharacteristic, complemented
116#469C2211yescharacteristic
117#469C2211yescharacteristic
118#469C2211yescharacteristic
119#469C2211yescharacteristic, complemented
120#469C2211yescharacteristic, complemented
121#468C2211yescharacteristic
122#468C2211yescharacteristic, complemented
123#468C2211yescharacteristic, complemented
124#468C2211yescharacteristic, complemented
125#468C2211yescharacteristic, complemented
126#468C2211yescharacteristic, complemented
127#468C2211yescharacteristic, complemented
128#468C2211yescharacteristic, complemented
129#468C2211yescharacteristic, complemented
130#468C2211yescharacteristic, complemented
131#467C2211yescharacteristic, complemented
132#467C2211yescharacteristic, complemented
133#466C2211yescharacteristic
134#466C2211yescharacteristic
135#466C2211yescharacteristic
136#466C2211yescharacteristic, complemented
137#466C2211yescharacteristic, complemented
138#466C2211yescharacteristic, complemented
139#465C2211yescharacteristic
140#465C2211yescharacteristic, complemented
141#465C2211yescharacteristic, complemented
142#465C2211yescharacteristic, complemented
143#465C2211yescharacteristic, complemented
144#465C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#464C2211yescharacteristic, complemented
148#464C2211yescharacteristic, complemented
149#463C2211yescharacteristic
150#463C2211yescharacteristic
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#459C2211yescharacteristic
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#451C2211yescharacteristic, complemented
160#450C2211yescharacteristic, complemented
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#448C2211yescharacteristic, complemented
166#447C2211yescharacteristic
167#447C2211yescharacteristic
168#447C2211yescharacteristic
169#447C2211yescharacteristic
170#447C2211yescharacteristic, complemented
171#442C2211yescharacteristic
172#441C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×D8C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic, complemented
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185C8×D4C2211yescharacteristic, complemented
186C8×D4C2211yescharacteristic, complemented
187#428C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190C2×#107C2211yescharacteristic, complemented
191C2×C4⋊C8C2211yescharacteristic, complemented
192#419C2211yescharacteristic, complemented
193#418C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201#408C2211yescharacteristic, complemented
202C4×M16C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C2×#41C2311yescharacteristic
211C22×Q8C2311yescharacteristic
212C22×D4—21no—
213C22×D4C2311yescharacteristic
214C22×D4C2311yescharacteristic
215C22×D4C2311yescharacteristic
216AGL(1,ℤ/8)—42no—
217AGL(1,ℤ/8)—42no—
218#135—42no—
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×SD16—42no—
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×D8C2311yescharacteristic
231C2×D8C2311yescharacteristic
232C2×D8C2311yescharacteristic
233C2×D8C2311yescharacteristic
234C2×D8C2311yescharacteristic
235C2×D8C2311yescharacteristic
236#131—42no—
237#131—42no—
238C2×M16C2311yescharacteristic
239C2×M16C2311yescharacteristic
240C2×M16C2311yescharacteristic
241C2×M16C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C22×C8C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C4⋊Q8—21no—
251C4⋊Q8D411yescharacteristic
252C4⋊Q8C2311yescharacteristic
253#127—21no—
254#127—21no—
255#127—21no—
256#127—21no—
257#127D411yescharacteristic
258#127C2311yescharacteristic
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#126—21no—
269#126—21no—
270#125—21no—
271#125—21no—
272#125C2311yescharacteristic
273#125C2311yescharacteristic
274#125C2311yescharacteristic
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124—21no—
281#124—21no—
282#124—21no—
283#124D411yescharacteristic
284#124D411yescharacteristic
285#124C2311yescharacteristic
286#124C2311yescharacteristic
287#124C2311yescharacteristic
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121D411yescharacteristic
348#121D411yescharacteristic
349#121D411yescharacteristic
350#121D411yescharacteristic
351#121C2311yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354#121C2311yescharacteristic
355#121C2311yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#121C2311yescharacteristic
360#121C2311yescharacteristic
361#121C2311yescharacteristic
362#121C2311yescharacteristic
363#121C2311yescharacteristic
364#121C2311yescharacteristic
365#121C2311yescharacteristic
366#120—21no—
367#120—21no—
368#120—21no—
369#120—21no—
370#120—21no—
371#120—21no—
372#120—21no—
373#120—21no—
374#120—21no—
375#120—21no—
376#120—21no—
377#120—21no—
378C4×Q8—21no—
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401C4×D4C2311yescharacteristic
402#117—21no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409#117C2311yescharacteristic
410#117C2311yescharacteristic
411C2×C4⋊C4C2311yescharacteristic
412C2×C4⋊C4C2311yescharacteristic
413C2×C4⋊C4C2311yescharacteristic
414C2×C4⋊C4C2311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42C2311yescharacteristic
420#107C2311yescharacteristic
421#107C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#107C2311yescharacteristic
427#107C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430#106C2311yescharacteristic
431#106C2311yescharacteristic
432#106C2311yescharacteristic
433#106C2311yescharacteristic
434#106C2311yescharacteristic
435#106C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478C22⋊C8C2311yescharacteristic
479C22⋊C8C2311yescharacteristic
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24—21no—
486C24—21no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—82no—
500#41—82no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8C2×D411yescharacteristic
506C2×Q8C2×D411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—82no—
541C2×D4C2×D411yescharacteristic
542C2×D4C2×D411yescharacteristic
543C2×D4C2×D411yescharacteristic
544C2×D4C2×D411yescharacteristic
545C2×D4C2×D411yescharacteristic
546C2×D4C2×D411yescharacteristic
547C2×D4C2×D411yescharacteristic
548C2×D4C2×D411yescharacteristic
549C2×D4C2×D411yescharacteristic
550C2×D4C2×D411yescharacteristic
551C2×D4C2411yescharacteristic
552C2×D4C2411yescharacteristic
553C2×D4C2411yescharacteristic
554C2×D4C2411yescharacteristic
555C2×D4C2411yescharacteristic
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4C2×D411yescharacteristic
571C22×C4C2×D411yescharacteristic
572C22×C4C2411yescharacteristic
573C22×C4C2411yescharacteristic
574C22×C4C2411yescharacteristic
575C22×C4C2411yescharacteristic
576C22×C4C2411yescharacteristic
577Q16—41no—
578Q16—41no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582SD16—41no—
583SD16—41no—
584SD16—41no—
585SD16—41no—
586SD16—41no—
587D8—22no—
588D8—41no—
589D8—41no—
590D8—41no—
591D8—41no—
592D8—41no—
593M16—22no—
594M16—22no—
595M16—22no—
596M16—41no—
597M16—41no—
598M16—41no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8C2411yescharacteristic
606C2×C8C2411yescharacteristic
607C2×C8C2411yescharacteristic
608C2×C8C2411yescharacteristic
609C2×C8C2411yescharacteristic
610C2×C8C2411yescharacteristic
611C2×C8C2411yescharacteristic
612C2×C8C2411yescharacteristic
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C22⋊C4C2×D411yescharacteristic
691C22⋊C4C2×D411yescharacteristic
692C22⋊C4C2×D411yescharacteristic
693C22⋊C4C2×D411yescharacteristic
694C22⋊C4C2×D411yescharacteristic
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42C2×D411yescharacteristic
703C42C2×D411yescharacteristic
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23C22×D411yescharacteristic
721C23C22×D411yescharacteristic
722C23C22×D411yescharacteristic
723C23C22×D411yescharacteristic
724C23C22×D411yescharacteristic
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—41no—
732Q8—41no—
733Q8—42no—
734Q8—81no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—42no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4—81no—
760D4—81no—
761D4—81no—
762D4—81no—
763D4—81no—
764D4—81no—
765D4—81no—
766D4—81no—
767D4—81no—
768D4—81no—
769D4—81no—
770D4—81no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4C22×D411yescharacteristic
817C2×C4C22×D411yescharacteristic
818C2×C4C22×D411yescharacteristic
819C2×C4C22×D411yescharacteristic
820C2×C4C22×D411yescharacteristic
821C2×C4C22×D411yescharacteristic
822C2×C4C22×D411yescharacteristic
823C2×C4C22×D411yescharacteristic
824C2×C4C22×D411yescharacteristic
825C2×C4C2511yescharacteristic
826C8—21no—
827C8—21no—
828C8—21no—
829C8—21no—
830C8—21no—
831C8—21no—
832C8—21no—
833C8H(5,𝔽2)12yes—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—162no—
865C22—162no—
866C22—162no—
867C22C23×D411yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4C2×H(5,𝔽2)11yescharacteristic
889C4#58511yescharacteristic
890C2—41no—
891C2—41no—
892C2—41no—
893C2—41no—
894C2—41no—
895C2—81no—
896C2—81no—
897C2—81no—
898C2—81no—
899C2—81no—
900C2#349611yescharacteristic
901C2#358411yescharacteristic
902C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3551C2semidirect
2. #3546C2semidirect
3. #3351C2semidirect
4. #3350C2semidirect
5. #3343C2semidirect
6. #3339C2semidirect
7. #3326C2semidirect
8. #3322C2semidirect
9. #3318C2semidirect
10. #3317C2semidirect
11. #3313C2semidirect
12. #3306C2semidirect
13. #3297C2semidirect
14. #3296C2semidirect
15. #3282C2semidirect
16. #3273C2semidirect
17. #3268C2semidirect
18. #3265C2semidirect
19. #3250C2semidirect
20. #3247C2semidirect
21. #3204C2semidirect
22. #3201C2semidirect
23. #3199C2semidirect
24. #3198C2semidirect
25. #3183C2semidirect
26. #3171C2semidirect
27. #3062C2semidirect
28. #3062C2semidirect
29. #3061C2semidirect
30. #3057C2semidirect
31. #2935C2semidirect
33. C2×AGL(1,ℤ/8)C22semidirect
34. C2×#135C22semidirect
35. C22×SD16C22semidirect
36. C2×#131C22semidirect
37. C2×#131C22semidirect
42. #556C22semidirect
46. #553C22semidirect
47. #553C22semidirect
48. #552C22semidirect
49. #552C22semidirect
54. #548C22semidirect
58. #546C22semidirect
59. #546C22semidirect
60. #546C22semidirect
61. D42C22semidirect
70. #537C22semidirect
71. #537C22semidirect
72. #537C22semidirect
73. #536C22semidirect
76. #535C22semidirect
77. #535C22semidirect
79. #532C22semidirect
80. #529C22semidirect
81. #529C22semidirect
82. #529C22semidirect
83. #501C22semidirect
84. #499C22semidirect
87. #490C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #488C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #484C22semidirect
94. #483C22semidirect
95. #483C22semidirect
96. #483C22semidirect
98. #482C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #481C22semidirect
104. #481C22semidirect
105. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #478C22semidirect
110. #478C22semidirect
111. #478C22semidirect
112. #478C22semidirect
113. #477C22semidirect
114. #476C22semidirect
115. #470C22semidirect
119. #469C22semidirect
120. #469C22semidirect
122. #468C22semidirect
123. #468C22semidirect
124. #468C22semidirect
125. #468C22semidirect
126. #468C22semidirect
127. #468C22semidirect
128. #468C22semidirect
129. #468C22semidirect
130. #468C22semidirect
131. #467C22semidirect
132. #467C22semidirect
136. #466C22semidirect
137. #466C22semidirect
138. #466C22semidirect
140. #465C22semidirect
141. #465C22semidirect
142. #465C22semidirect
143. #465C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #460C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #451C22semidirect
160. #450C22semidirect
163. #449C22semidirect
164. #449C22semidirect
165. #448C22semidirect
170. #447C22semidirect
172. #441C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×SD16C22semidirect
176. C4×SD16C22semidirect
177. C4×D8C22semidirect
178. C4×D8C22semidirect
179. #436C22semidirect
180. #436C22semidirect
181. #435C22semidirect
182. #435C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. C8×D4C22semidirect
186. C8×D4C22semidirect
187. #428C22semidirect
188. #428C22semidirect
189. #427C22semidirect
190. C2×#107C22semidirect
191. C2×C4⋊C8C22semidirect
192. #419C22semidirect
193. #418C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. C2×#102C22semidirect
199. C2×#102C22semidirect
200. #408C22semidirect
201. #408C22semidirect
202. C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#35512
#35462
#33512
#33502
#33432
#33392
#33262
#33222
#33182
#33172
#33132
#33062
#32972
#32962
#32822
#32732
#32682
#32652
#32502
#32472
#32042
#32012
#31992
#31982
#31832
#31712
#30622
#30612
#30572
#29352