Finite Group Databasebeta

← #62318

Subgroups — #62318

Order 256.

931 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic, complemented
2#3540C211yesmaximal, characteristic, complemented
3#3354C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3347C211yesmaximal, characteristic, complemented
6#3340C211yesmaximal, characteristic, complemented
7#3324C211yesmaximal, characteristic, complemented
8#3323C211yesmaximal, characteristic, complemented
9#3319C211yesmaximal, characteristic, complemented
10#3319C211yesmaximal, characteristic, complemented
11#3311C211yesmaximal, characteristic, complemented
12#3308C211yesmaximal, characteristic, complemented
13#3305C211yesmaximal, characteristic, complemented
14#3301C211yesmaximal, characteristic, complemented
15#3280C211yesmaximal, characteristic, complemented
16#3275C211yesmaximal, characteristic, complemented
17#3271C211yesmaximal, characteristic, complemented
18#3264C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3200C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3191C211yesmaximal, characteristic, complemented
24#3188C211yesmaximal, characteristic, complemented
25#3179C211yesmaximal, characteristic, complemented
26#3173C211yesmaximal, characteristic, complemented
27#3063C211yesmaximal, characteristic, complemented
28#3058C211yesmaximal, characteristic, complemented
29#3055C211yesmaximal, characteristic, complemented
30#3054C211yesmaximal, characteristic, complemented
31#2933C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic, complemented
35C22×D8C2211yescharacteristic, complemented
36C2×#131C2211yescharacteristic, complemented
37C22×M16C2211yescharacteristic, complemented
38#562—21no—
39H(3,𝔽4)—21no—
40#560—21no—
41#560—21no—
42#559—21no—
43#556C2211yescharacteristic
44#556C2211yescharacteristic, complemented
45#555C2211yescharacteristic
46#555C2211yescharacteristic, complemented
47#555C2211yescharacteristic, complemented
48#553C2211yescharacteristic, complemented
49#552C2211yescharacteristic
50#551—21no—
51#551—21no—
52#550C2211yescharacteristic, complemented
53#548C2211yescharacteristic, complemented
54#548C2211yescharacteristic, complemented
55#547C2211yescharacteristic, complemented
56#546—21no—
57#546C2211yescharacteristic
58#546C2211yescharacteristic
59#546C2211yescharacteristic, complemented
60#546C2211yescharacteristic, complemented
61D42C2211yescharacteristic
62#542—21no—
63#542—21no—
64#542C2211yescharacteristic, complemented
65#542C2211yescharacteristic, complemented
66#542C2211yescharacteristic, complemented
67#540—21no—
68#540C2211yescharacteristic, complemented
69#538—21no—
70#538—21no—
71#538—21no—
72#537C2211yescharacteristic
73#536C2211yescharacteristic, complemented
74#535—21no—
75#535C2211yescharacteristic
76#535C2211yescharacteristic, complemented
77#534—21no—
78#525C2211yescharacteristic
79#525C2211yescharacteristic, complemented
80#525C2211yescharacteristic, complemented
81#525C2211yescharacteristic, complemented
82C2×#121C2211yescharacteristic, complemented
83#501C2211yescharacteristic, complemented
84#498C2211yescharacteristic, complemented
85#496C2211yescharacteristic, complemented
86#495C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#486C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#482C2211yescharacteristic, complemented
98#482C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#481C2211yescharacteristic, complemented
105#481C2211yescharacteristic, complemented
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#477C2211yescharacteristic, complemented
111#476C2211yescharacteristic, complemented
112#474C2211yescharacteristic, complemented
113#474C2211yescharacteristic, complemented
114#474C2211yescharacteristic, complemented
115#470C2211yescharacteristic, complemented
116#470C2211yescharacteristic, complemented
117#470C2211yescharacteristic, complemented
118#469C2211yescharacteristic
119#469C2211yescharacteristic
120#469C2211yescharacteristic, complemented
121#469C2211yescharacteristic, complemented
122#469C2211yescharacteristic, complemented
123#469C2211yescharacteristic, 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, complemented
136#466C2211yescharacteristic, complemented
137#466C2211yescharacteristic, complemented
138#466C2211yescharacteristic, complemented
139#466C2211yescharacteristic, complemented
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, complemented
150#463C2211yescharacteristic, complemented
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#459C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#450C2211yescharacteristic, complemented
158#450C2211yescharacteristic, complemented
159#450C2211yescharacteristic, complemented
160#450C2211yescharacteristic, complemented
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#449C2211yescharacteristic, complemented
166#449C2211yescharacteristic, complemented
167#448C2211yescharacteristic, complemented
168#448C2211yescharacteristic, complemented
169#447C2211yescharacteristic
170#447C2211yescharacteristic, complemented
171#442C2211yescharacteristic, complemented
172#442C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic
182#435C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185C8×D4C2211yescharacteristic, complemented
186C8×D4C2211yescharacteristic, complemented
187#428C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190#427C2211yescharacteristic, complemented
191#424C2211yescharacteristic, complemented
192#418C2211yescharacteristic, complemented
193#418C2211yescharacteristic, complemented
194#418C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198#416C2211yescharacteristic, complemented
199C2×#103C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201C2×C22⋊C8C2211yescharacteristic, complemented
202#405C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C22×D4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216#137—42no—
217AGL(1,ℤ/8)—42no—
218#135—42no—
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×D8—42no—
230C2×D8C2311yescharacteristic
231C2×D8C2311yescharacteristic
232C2×D8C2311yescharacteristic
233C2×D8C2311yescharacteristic
234C2×D8C2311yescharacteristic
235C2×D8C2311yescharacteristic
236#131—42no—
237C2×M16—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⋊Q8C2311yescharacteristic
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254#127—21no—
255#127—21no—
256#127—21no—
257#127C2311yescharacteristic
258#126—21no—
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#125—21no—
268#125C2311yescharacteristic
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
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#124—21no—
284#124—21no—
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—
305#123—21no—
306#123D411yescharacteristic
307#123D411yescharacteristic
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8D411yescharacteristic
316C22⋊Q8D411yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
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#121D411yescharacteristic
347#121D411yescharacteristic
348#121C2311yescharacteristic
349#121C2311yescharacteristic
350#121C2311yescharacteristic
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#120—21no—
364#120—21no—
365#120—21no—
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#120D411yescharacteristic
377#120D411yescharacteristic
378C4×Q8—21no—
379C4×Q8—21no—
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×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#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409#117C2311yescharacteristic
410#117C2311yescharacteristic
411#117C2311yescharacteristic
412#117C2311yescharacteristic
413C2×C4⋊C4C2311yescharacteristic
414C2×C4⋊C4C2311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
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—
487C24C2×D411yescharacteristic
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—82no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8C2×D411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×D4—21no—
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—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—82no—
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×D4C2411yescharacteristic
549C2×D4C2411yescharacteristic
550C2×D4C2411yescharacteristic
551C2×D4C2411yescharacteristic
552C2×D4C2411yescharacteristic
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—41no—
566C22×C4—41no—
567C22×C4C2×D411yescharacteristic
568C22×C4C2×D411yescharacteristic
569C22×C4C2×D411yescharacteristic
570C22×C4C2411yescharacteristic
571C22×C4C2411yescharacteristic
572C22×C4C2411yescharacteristic
573C22×C4C2411yescharacteristic
574C22×C4C2411yescharacteristic
575Q16—22no—
576Q16—41no—
577SD16—22no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582SD16—41no—
583SD16—41no—
584SD16—41no—
585D8—22no—
586D8—22no—
587D8—41no—
588D8—41no—
589D8—41no—
590D8—41no—
591M16—22no—
592M16—22no—
593M16—22no—
594M16—41no—
595M16—41no—
596M16—41no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8C2411yescharacteristic
604C2×C8C2411yescharacteristic
605C2×C8C2411yescharacteristic
606C2×C8C2411yescharacteristic
607C2×C8C2411yescharacteristic
608C2×C8C2411yescharacteristic
609C2×C8C2411yescharacteristic
610C2×C8C2411yescharacteristic
611C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
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—
702C42—21no—
703C42—21no—
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23C22×D411yescharacteristic
724C23C22×D411yescharacteristic
725C23C22×D411yescharacteristic
726C23C22×D411yescharacteristic
727C23C22×D411yescharacteristic
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—21no—
734Q8—41no—
735Q8—81no—
736Q8—81no—
737Q8—81no—
738Q8—81no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—42no—
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—
779D4—81no—
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—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
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—82no—
865C22—162no—
866C22—162no—
867C22—162no—
868C22C23×D411yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4C2×H(5,𝔽2)11yescharacteristic
890C4#58511yescharacteristic
891C2—41no—
892C2—41no—
893C2—41no—
894C2—41no—
895C2—41no—
896C2—81no—
897C2—81no—
898C2—81no—
899C2—81no—
900C2—81no—
901C2#349611yescharacteristic
902C2#358411yescharacteristic
903C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3542C2semidirect
2. #3540C2semidirect
3. #3354C2semidirect
4. #3349C2semidirect
5. #3347C2semidirect
6. #3340C2semidirect
7. #3324C2semidirect
8. #3323C2semidirect
9. #3319C2semidirect
10. #3319C2semidirect
11. #3311C2semidirect
12. #3308C2semidirect
13. #3305C2semidirect
14. #3301C2semidirect
15. #3280C2semidirect
16. #3275C2semidirect
17. #3271C2semidirect
18. #3264C2semidirect
19. #3262C2semidirect
20. #3257C2semidirect
21. #3200C2semidirect
22. #3198C2semidirect
23. #3191C2semidirect
24. #3188C2semidirect
25. #3179C2semidirect
26. #3173C2semidirect
27. #3063C2semidirect
28. #3058C2semidirect
29. #3055C2semidirect
30. #3054C2semidirect
31. #2933C2semidirect
32. C2×#137C22semidirect
34. C2×#135C22semidirect
35. C22×D8C22semidirect
36. C2×#131C22semidirect
37. C22×M16C22semidirect
44. #556C22semidirect
46. #555C22semidirect
47. #555C22semidirect
48. #553C22semidirect
52. #550C22semidirect
53. #548C22semidirect
54. #548C22semidirect
55. #547C22semidirect
59. #546C22semidirect
60. #546C22semidirect
64. #542C22semidirect
65. #542C22semidirect
66. #542C22semidirect
68. #540C22semidirect
73. #536C22semidirect
76. #535C22semidirect
79. #525C22semidirect
80. #525C22semidirect
81. #525C22semidirect
82. C2×#121C22semidirect
83. #501C22semidirect
84. #498C22semidirect
85. #496C22semidirect
86. #495C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #486C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #484C22semidirect
97. #482C22semidirect
98. #482C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #481C22semidirect
105. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #477C22semidirect
111. #476C22semidirect
112. #474C22semidirect
113. #474C22semidirect
114. #474C22semidirect
115. #470C22semidirect
116. #470C22semidirect
117. #470C22semidirect
120. #469C22semidirect
121. #469C22semidirect
122. #469C22semidirect
123. #469C22semidirect
124. #468C22semidirect
125. #468C22semidirect
126. #468C22semidirect
127. #468C22semidirect
128. #468C22semidirect
129. #468C22semidirect
130. #468C22semidirect
131. #467C22semidirect
132. #467C22semidirect
135. #466C22semidirect
136. #466C22semidirect
137. #466C22semidirect
138. #466C22semidirect
139. #466C22semidirect
140. #465C22semidirect
141. #465C22semidirect
142. #465C22semidirect
143. #465C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #463C22semidirect
150. #463C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #460C22semidirect
154. #459C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #450C22semidirect
158. #450C22semidirect
159. #450C22semidirect
160. #450C22semidirect
163. #449C22semidirect
164. #449C22semidirect
165. #449C22semidirect
166. #449C22semidirect
167. #448C22semidirect
168. #448C22semidirect
170. #447C22semidirect
171. #442C22semidirect
172. #442C22semidirect
173. #441C22semidirect
174. #440C22semidirect
175. C4×SD16C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
178. C4×D8C22semidirect
180. #436C22semidirect
182. #435C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. C8×D4C22semidirect
186. C8×D4C22semidirect
187. #428C22semidirect
188. #428C22semidirect
189. #427C22semidirect
190. #427C22semidirect
191. #424C22semidirect
192. #418C22semidirect
193. #418C22semidirect
194. #418C22semidirect
195. #417C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. #416C22semidirect
199. C2×#103C22semidirect
200. #408C22semidirect
201. C2×C22⋊C8C22semidirect
202. #405C22semidirect

Maximal subgroups

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

subgroupindex
#35422
#35402
#33542
#33492
#33472
#33402
#33242
#33232
#33192
#33112
#33082
#33052
#33012
#32802
#32752
#32712
#32642
#32622
#32572
#32002
#31982
#31912
#31882
#31792
#31732
#30632
#30582
#30552
#30542
#29332