Finite Group Databasebeta

← #62338

Subgroups — #62338

Order 256.

918 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3551C211yesmaximal, characteristic, complemented
2#3548C211yesmaximal, characteristic, complemented
3#3346C211yesmaximal, characteristic, complemented
4#3345C211yesmaximal, characteristic, complemented
5#3344C211yesmaximal, characteristic, complemented
6#3343C211yesmaximal, characteristic, complemented
7#3317C211yesmaximal, characteristic, complemented
8#3316C211yesmaximal, characteristic, complemented
9#3315C211yesmaximal, characteristic, complemented
10#3314C211yesmaximal, characteristic, complemented
11#3309C211yesmaximal, characteristic, complemented
12#3308C211yesmaximal, characteristic, complemented
13#3307C211yesmaximal, characteristic, complemented
14#3306C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3269C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3267C211yesmaximal, characteristic, complemented
19#3252C211yesmaximal, characteristic, complemented
20#3251C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3203C211yesmaximal, characteristic, complemented
23#3201C211yesmaximal, characteristic, complemented
24#3198C211yesmaximal, characteristic, complemented
25#3181C211yesmaximal, characteristic, complemented
26#3180C211yesmaximal, characteristic, complemented
27#3063C211yesmaximal, characteristic, complemented
28#3062C211yesmaximal, characteristic, complemented
29#3061C211yesmaximal, characteristic, complemented
30#3060C211yesmaximal, characteristic, complemented
31#2932C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C2×#135C2211yescharacteristic
36C2×#131C2211yescharacteristic
37C2×#131C2211yescharacteristic, complemented
38#563—21no—
39#562—21no—
40#562—21no—
41#560—21no—
42#555—21no—
43#554—21no—
44#554C2211yescharacteristic
45#554C2211yescharacteristic, complemented
46#553C2211yescharacteristic
47#553C2211yescharacteristic
48#552C2211yescharacteristic
49#552C2211yescharacteristic
50#551—21no—
51#550—21no—
52#550C2211yescharacteristic
53#550C2211yescharacteristic, complemented
54#548C2211yescharacteristic
55#548C2211yescharacteristic
56#547C2211yescharacteristic
57#547C2211yescharacteristic
58#547C2211yescharacteristic, complemented
59#547C2211yescharacteristic, complemented
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#540—21no—
63#540—21no—
64#540—21no—
65#540—21no—
66#538—21no—
67#538—21no—
68#537—21no—
69#537—21no—
70#537C2211yescharacteristic
71#537C2211yescharacteristic
72#537C2211yescharacteristic
73#537C2211yescharacteristic
74#537C2211yescharacteristic, complemented
75#537C2211yescharacteristic, complemented
76#536C2211yescharacteristic
77#535C2211yescharacteristic
78#533C2211yescharacteristic, complemented
79#532C2211yescharacteristic
80#532C2211yescharacteristic, complemented
81#529C2211yescharacteristic
82#529C2211yescharacteristic
83#501C2211yescharacteristic, complemented
84#501C2211yescharacteristic, complemented
85#497C2211yescharacteristic
86#496C2211yescharacteristic
87#491C2211yescharacteristic, complemented
88#490C2211yescharacteristic, complemented
89#489C2211yescharacteristic
90#489C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#482C2211yescharacteristic, complemented
101#481C2211yescharacteristic
102#481C2211yescharacteristic
103#481C2211yescharacteristic, complemented
104#480C2211yescharacteristic
105#480C2211yescharacteristic
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#478C2211yescharacteristic, complemented
110#478C2211yescharacteristic, complemented
111#477C2211yescharacteristic, complemented
112#476C2211yescharacteristic
113#475C2211yescharacteristic, complemented
114#474C2211yescharacteristic
115#470C2211yescharacteristic
116#470C2211yescharacteristic, complemented
117#470C2211yescharacteristic, complemented
118#470C2211yescharacteristic, complemented
119#469C2211yescharacteristic
120#469C2211yescharacteristic
121#469C2211yescharacteristic
122#469C2211yescharacteristic
123#468C2211yescharacteristic
124#468C2211yescharacteristic
125#468C2211yescharacteristic
126#468C2211yescharacteristic
127#468C2211yescharacteristic
128#468C2211yescharacteristic, complemented
129#468C2211yescharacteristic, complemented
130#468C2211yescharacteristic, complemented
131#467C2211yescharacteristic
132#467C2211yescharacteristic, complemented
133#467C2211yescharacteristic, complemented
134#467C2211yescharacteristic, complemented
135#466C2211yescharacteristic
136#466C2211yescharacteristic
137#466C2211yescharacteristic
138#466C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#465C2211yescharacteristic
142#465C2211yescharacteristic
143#465C2211yescharacteristic
144#465C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#464C2211yescharacteristic
148#464C2211yescharacteristic
149#463C2211yescharacteristic
150#463C2211yescharacteristic
151#462C2211yescharacteristic, complemented
152#461C2211yescharacteristic
153#460C2211yescharacteristic, complemented
154#459C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#450C2211yescharacteristic
163#449C2211yescharacteristic
164#449C2211yescharacteristic
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic
168#449C2211yescharacteristic
169#448C2211yescharacteristic, complemented
170#447C2211yescharacteristic
171#442C2211yescharacteristic
172#442C2211yescharacteristic
173#441C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#440C2211yescharacteristic
176#440C2211yescharacteristic
177#440C2211yescharacteristic, complemented
178#440C2211yescharacteristic, complemented
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186#435C2211yescharacteristic, complemented
187#428C2211yescharacteristic
188#428C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#423C2211yescharacteristic, complemented
192#417C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic
197#416C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic
200#408C2211yescharacteristic
201#408C2211yescharacteristic, complemented
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C2×#41C2311yescharacteristic
211C2×#41C2311yescharacteristic
212C2×#41C2311yescharacteristic
213C2×#41C2311yescharacteristic
214C22×Q8C2311yescharacteristic
215C22×D4C2311yescharacteristic
216#137—42no—
217AGL(1,ℤ/8)—42no—
218#135—42no—
219#135—42no—
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
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
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255#127—21no—
256#127—21no—
257#127—21no—
258#127D411yescharacteristic
259#127C2311yescharacteristic
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124D411yescharacteristic
279#124D411yescharacteristic
280#124C2311yescharacteristic
281#124C2311yescharacteristic
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
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—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
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#121—21no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121D411yescharacteristic
359#121D411yescharacteristic
360#121D411yescharacteristic
361#121D411yescharacteristic
362#121C2311yescharacteristic
363#121C2311yescharacteristic
364#121C2311yescharacteristic
365#121C2311yescharacteristic
366#121C2311yescharacteristic
367#121C2311yescharacteristic
368#121C2311yescharacteristic
369#121C2311yescharacteristic
370#121C2311yescharacteristic
371#121C2311yescharacteristic
372#121C2311yescharacteristic
373#121C2311yescharacteristic
374#120—21no—
375#120—21no—
376#120—21no—
377#120—21no—
378C4×Q8—21no—
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×Q8C2311yescharacteristic
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×D4—21no—
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
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4C2311yescharacteristic
412C2×C4⋊C4C2311yescharacteristic
413C2×C4⋊C4C2311yescharacteristic
414C2×C4⋊C4C2311yescharacteristic
415C2×C4⋊C4C2311yescharacteristic
416C2×C4⋊C4C2311yescharacteristic
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#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
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
482#97C2311yescharacteristic
483#97C2311yescharacteristic
484C24—21no—
485#41—41no—
486#41—41no—
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—41no—
500#41—41no—
501#41—82no—
502#41—82no—
503#41—82no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8C2×D411yescharacteristic
510C2×Q8C2×D411yescharacteristic
511C2×Q8C2411yescharacteristic
512C2×Q8C2411yescharacteristic
513C2×Q8C2411yescharacteristic
514C2×Q8C2411yescharacteristic
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—21no—
535C2×D4—21no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4C2×D411yescharacteristic
539C2×D4C2×D411yescharacteristic
540C2×D4C2×D411yescharacteristic
541C2×D4C2×D411yescharacteristic
542C2×D4C2×D411yescharacteristic
543C2×D4C2×D411yescharacteristic
544C2×D4C2×D411yescharacteristic
545C2×D4C2×D411yescharacteristic
546C2×D4C2×D411yescharacteristic
547C2×D4C2×D411yescharacteristic
548C2×D4C2411yescharacteristic
549C2×D4C2411yescharacteristic
550C2×D4C2411yescharacteristic
551C2×D4C2411yescharacteristic
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
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×C4C2×D411yescharacteristic
570C22×C4C2×D411yescharacteristic
571C22×C4C2411yescharacteristic
572C22×C4C2411yescharacteristic
573C22×C4C2411yescharacteristic
574C22×C4C2411yescharacteristic
575C22×C4C2411yescharacteristic
576Q16—22no—
577Q16—41no—
578Q16—41no—
579Q16—41no—
580SD16—22no—
581SD16—22no—
582SD16—41no—
583SD16—41no—
584SD16—41no—
585SD16—41no—
586SD16—41no—
587SD16—41no—
588D8—22no—
589D8—41no—
590D8—41no—
591D8—41no—
592M16—22no—
593M16—22no—
594M16—41no—
595M16—41no—
596M16—41no—
597M16—41no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8C2411yescharacteristic
605C2×C8C2411yescharacteristic
606C2×C8C2411yescharacteristic
607C2×C8C2411yescharacteristic
608C2×C8C2411yescharacteristic
609C2×C8C2411yescharacteristic
610C2×C8C2411yescharacteristic
611C2×C8C2411yescharacteristic
612C4⋊C4—21no—
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⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4C2×D411yescharacteristic
643C4⋊C4C2×D411yescharacteristic
644C4⋊C4C2×D411yescharacteristic
645C4⋊C4C2×D411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
649C4⋊C4C2411yescharacteristic
650C4⋊C4C2411yescharacteristic
651C4⋊C4C2411yescharacteristic
652C4⋊C4C2411yescharacteristic
653C4⋊C4C2411yescharacteristic
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⋊C4—21no—
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C22⋊C4C2×D411yescharacteristic
691C22⋊C4C2×D411yescharacteristic
692C22⋊C4C2×D411yescharacteristic
693C22⋊C4C2×D411yescharacteristic
694C22⋊C4C2×D411yescharacteristic
695C22⋊C4C2×D411yescharacteristic
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—81no—
711C23—81no—
712C23—81no—
713C23C22×D411yescharacteristic
714C23C22×D411yescharacteristic
715C23C22×D411yescharacteristic
716C23C22×D411yescharacteristic
717C23C22×D411yescharacteristic
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—41no—
727Q8—41no—
728Q8—42no—
729Q8—81no—
730Q8—81no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—42no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754D4—81no—
755D4—81no—
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—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
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—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
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×C4C22×D411yescharacteristic
812C2×C4C22×D411yescharacteristic
813C2×C4C22×D411yescharacteristic
814C2×C4C22×D411yescharacteristic
815C2×C4C22×D411yescharacteristic
816C2×C4C22×D411yescharacteristic
817C2×C4C22×D411yescharacteristic
818C2×C4C22×D411yescharacteristic
819C2×C4C22×D411yescharacteristic
820C2×C4C2511yescharacteristic
821C8—21no—
822C8—21no—
823C8—21no—
824C8—21no—
825C8—21no—
826C8—21no—
827C8—21no—
828C8H(5,𝔽2)12yes—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—162no—
857C22C23×D411yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4C2×H(5,𝔽2)11yescharacteristic
880C4#58511yescharacteristic
881C2—41no—
882C2—41no—
883C2—41no—
884C2—41no—
885C2—41no—
886C2—81no—
887C2—81no—
888C2—81no—
889C2—81no—
890C2#349611yescharacteristic
891C2#358511yescharacteristic
892C2#358611yescharacteristic
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. #3548C2semidirect
3. #3346C2semidirect
4. #3345C2semidirect
5. #3344C2semidirect
6. #3343C2semidirect
7. #3317C2semidirect
8. #3316C2semidirect
9. #3315C2semidirect
10. #3314C2semidirect
11. #3309C2semidirect
12. #3308C2semidirect
13. #3307C2semidirect
14. #3306C2semidirect
15. #3271C2semidirect
16. #3269C2semidirect
17. #3268C2semidirect
18. #3267C2semidirect
19. #3252C2semidirect
20. #3251C2semidirect
21. #3204C2semidirect
22. #3203C2semidirect
23. #3201C2semidirect
24. #3198C2semidirect
25. #3181C2semidirect
26. #3180C2semidirect
27. #3063C2semidirect
28. #3062C2semidirect
29. #3061C2semidirect
30. #3060C2semidirect
31. #2932C2semidirect
32. C2×#137C22semidirect
37. C2×#131C22semidirect
45. #554C22semidirect
53. #550C22semidirect
58. #547C22semidirect
59. #547C22semidirect
74. #537C22semidirect
75. #537C22semidirect
78. #533C22semidirect
80. #532C22semidirect
83. #501C22semidirect
84. #501C22semidirect
87. #491C22semidirect
88. #490C22semidirect
92. #485C22semidirect
94. #484C22semidirect
95. #484C22semidirect
97. #483C22semidirect
98. #483C22semidirect
100. #482C22semidirect
103. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #478C22semidirect
110. #478C22semidirect
111. #477C22semidirect
113. #475C22semidirect
116. #470C22semidirect
117. #470C22semidirect
118. #470C22semidirect
128. #468C22semidirect
129. #468C22semidirect
130. #468C22semidirect
132. #467C22semidirect
133. #467C22semidirect
134. #467C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
151. #462C22semidirect
153. #460C22semidirect
159. #452C22semidirect
160. #452C22semidirect
161. #451C22semidirect
169. #448C22semidirect
173. #441C22semidirect
174. #441C22semidirect
177. #440C22semidirect
178. #440C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. #435C22semidirect
188. #428C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #423C22semidirect
194. #417C22semidirect
195. #417C22semidirect
197. #416C22semidirect
198. C2×#103C22semidirect
201. #408C22semidirect
202. C2×#97C22semidirect

Maximal subgroups

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

subgroupindex
#35512
#35482
#33462
#33452
#33442
#33432
#33172
#33162
#33152
#33142
#33092
#33082
#33072
#33062
#32712
#32692
#32682
#32672
#32522
#32512
#32042
#32032
#32012
#31982
#31812
#31802
#30632
#30622
#30612
#30602
#29322