Finite Group Databasebeta

← #61550

Subgroups — #61550

Order 256.

890 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3521C211yesmaximal, characteristic, complemented
2#3516C211yesmaximal, characteristic, complemented
3#3393C211yesmaximal, characteristic, complemented
4#3381C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3376C211yesmaximal, characteristic, complemented
7#3356C211yesmaximal, characteristic, complemented
8#3355C211yesmaximal, characteristic, complemented
9#3352C211yesmaximal, characteristic, complemented
10#3320C211yesmaximal, characteristic, complemented
11#3314C211yesmaximal, characteristic, complemented
12#3313C211yesmaximal, characteristic, complemented
13#3307C211yesmaximal, characteristic, complemented
14#3300C211yesmaximal, characteristic, complemented
15#3296C211yesmaximal, characteristic, complemented
16#3276C211yesmaximal, characteristic, complemented
17#3275C211yesmaximal, characteristic, complemented
18#3275C211yesmaximal, characteristic, complemented
19#3183C211yesmaximal, characteristic, complemented
20#3177C211yesmaximal, characteristic, complemented
21#3173C211yesmaximal, characteristic, complemented
22#3124C211yesmaximal, characteristic, complemented
23#3123C211yesmaximal, characteristic, complemented
24#3121C211yesmaximal, characteristic, complemented
25#3120C211yesmaximal, characteristic, complemented
26#3108C211yesmaximal, characteristic, complemented
27#3102C211yesmaximal, characteristic, complemented
28#2969C211yesmaximal, characteristic, complemented
29#2947C211yesmaximal, characteristic, complemented
30#2946C211yesmaximal, characteristic, complemented
31C4×#137C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic
34C2×AGL(1,ℤ/8)C2211yescharacteristic
35#557C2211yescharacteristic, complemented
36#556—21no—
37#556C2211yescharacteristic
38#556C2211yescharacteristic
39#556C2211yescharacteristic, complemented
40#554—21no—
41#554C2211yescharacteristic
42#554C2211yescharacteristic
43#553—21no—
44#553—21no—
45#553C2211yescharacteristic
46#553C2211yescharacteristic, complemented
47#552—21no—
48#552—21no—
49#552C2211yescharacteristic
50#552C2211yescharacteristic
51#551—21no—
52#551—21no—
53D4×Q8C2211yescharacteristic, complemented
54#548C2211yescharacteristic
55#548C2211yescharacteristic
56#547C2211yescharacteristic
57#546C2211yescharacteristic
58#546C2211yescharacteristic
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic, complemented
62#541—21no—
63#541C2211yescharacteristic
64#541C2211yescharacteristic
65#539—21no—
66#538—21no—
67#529—21no—
68#529—21no—
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#529C2211yescharacteristic, complemented
73C2×#126—21no—
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76#519C2211yescharacteristic, complemented
77#518C2211yescharacteristic
78C4×#41C2211yescharacteristic
79C2×C4×Q8C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#499C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#495C2211yescharacteristic
84#495C2211yescharacteristic
85#494C2211yescharacteristic, complemented
86#491C2211yescharacteristic, complemented
87#491C2211yescharacteristic, complemented
88#489C2211yescharacteristic
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic
91#488C2211yescharacteristic, complemented
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic
101#482C2211yescharacteristic, complemented
102#480C2211yescharacteristic
103#480C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic
111#478C2211yescharacteristic, complemented
112#477C2211yescharacteristic, complemented
113#477C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#474C2211yescharacteristic
116#470C2211yescharacteristic
117#470C2211yescharacteristic
118#470C2211yescharacteristic, complemented
119#470C2211yescharacteristic, complemented
120#469C2211yescharacteristic
121#469C2211yescharacteristic
122#468C2211yescharacteristic
123#468C2211yescharacteristic, complemented
124#467C2211yescharacteristic
125#467C2211yescharacteristic
126#465C2211yescharacteristic
127#465C2211yescharacteristic, complemented
128#464C2211yescharacteristic
129#464C2211yescharacteristic
130#464C2211yescharacteristic
131#464C2211yescharacteristic
132#464C2211yescharacteristic, complemented
133#464C2211yescharacteristic, complemented
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#462C2211yescharacteristic, complemented
137#461C2211yescharacteristic
138#461C2211yescharacteristic
139#461C2211yescharacteristic, complemented
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#452C2211yescharacteristic
143#452C2211yescharacteristic
144#451C2211yescharacteristic, complemented
145#451C2211yescharacteristic, complemented
146#450C2211yescharacteristic
147#450C2211yescharacteristic
148#449C2211yescharacteristic
149#449C2211yescharacteristic
150#448C2211yescharacteristic
151#448C2211yescharacteristic
152#446C2211yescharacteristic, complemented
153C8×Q8C2211yescharacteristic, complemented
154#442C2211yescharacteristic
155#442C2211yescharacteristic
156#441C2211yescharacteristic, complemented
157#441C2211yescharacteristic, complemented
158#441C2211yescharacteristic, complemented
159#441C2211yescharacteristic, complemented
160#440C2211yescharacteristic
161#440C2211yescharacteristic
162#440C2211yescharacteristic
163#440C2211yescharacteristic
164#440C2211yescharacteristic
165#440C2211yescharacteristic, complemented
166C4×Q16C2211yescharacteristic, complemented
167C4×Q16C2211yescharacteristic, complemented
168C4×Q16C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×Q16C2211yescharacteristic, complemented
171C4×Q16C2211yescharacteristic, complemented
172C4×SD16C2211yescharacteristic
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic
175C4×SD16C2211yescharacteristic
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic
178C4×SD16C2211yescharacteristic
179C4×SD16C2211yescharacteristic, complemented
180C4×D8C2211yescharacteristic
181C4×D8C2211yescharacteristic
182#436C2211yescharacteristic
183#436C2211yescharacteristic
184#436C2211yescharacteristic, complemented
185#435C2211yescharacteristic
186#435C2211yescharacteristic, complemented
187C8×D4C2211yescharacteristic
188#433C2211yescharacteristic
189#433C2211yescharacteristic, complemented
190#431C2211yescharacteristic, complemented
191#428C2211yescharacteristic
192#428C2211yescharacteristic, complemented
193#428C2211yescharacteristic, complemented
194#419C2211yescharacteristic, complemented
195#417C2211yescharacteristic
196#416C2211yescharacteristic
197#416C2211yescharacteristic
198C2×#103C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic, complemented
202C4×M16C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4C2311yescharacteristic
209#137—24no—
210#137—24no—
211AGL(1,ℤ/8)—24no—
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×Q16C2311yescharacteristic
217C2×Q16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C2×D8C2311yescharacteristic
228C2×M16C2311yescharacteristic
229C2×M16C2311yescharacteristic
230C2×M16C2311yescharacteristic
231C2×M16C2311yescharacteristic
232C22×C8C2311yescharacteristic
233C22×C8C2311yescharacteristic
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126D411yescharacteristic
259#126D411yescharacteristic
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125D411yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#125C2311yescharacteristic
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124D411yescharacteristic
280#124C2311yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
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#123D411yescharacteristic
297#123D411yescharacteristic
298C22⋊Q8—21no—
299C22⋊Q8—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⋊Q8D411yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121D411yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#120—21no—
333#120—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C2311yescharacteristic
402C2×C4⋊C4C2311yescharacteristic
403C2×C4⋊C4C2311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#107C2311yescharacteristic
417#107C2311yescharacteristic
418#107C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
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#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C4×C8C2311yescharacteristic
479C4×C8C2311yescharacteristic
480C4×C8C2311yescharacteristic
481C24—21no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—41no—
486#41—41no—
487#41—41no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8C2×D411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—41no—
512C2×D4C2×D411yescharacteristic
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4C2×D411yescharacteristic
535C22×C4C2×D411yescharacteristic
536C22×C4C2411yescharacteristic
537C22×C4C2411yescharacteristic
538C22×C4C2411yescharacteristic
539Q16—22no—
540Q16—22no—
541Q16—22no—
542Q16—22no—
543Q16—41no—
544Q16—41no—
545SD16—22no—
546SD16—22no—
547SD16—22no—
548SD16—41no—
549SD16—41no—
550SD16—41no—
551SD16—41no—
552SD16#4114yes—
553D8—22no—
554D8—22no—
555M16—22no—
556M16—22no—
557M16—22no—
558M16—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8C2411yescharacteristic
562C2×C8C2411yescharacteristic
563C2×C8C2411yescharacteristic
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42C2×D411yescharacteristic
681C42C2×D411yescharacteristic
682C42C2411yescharacteristic
683C42C2411yescharacteristic
684C42C2411yescharacteristic
685C42C2411yescharacteristic
686C23—21no—
687C23—21no—
688C23—21no—
689C23—42no—
690C23—81no—
691C23—81no—
692C23C22×D411yescharacteristic
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—41no—
705Q8—42no—
706Q8—42no—
707Q8—81no—
708Q8—81no—
709Q8C2×#4112yes—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4C2×#4112yes—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4C22×D411yescharacteristic
765C2×C4C22×D411yescharacteristic
766C2×C4C22×D411yescharacteristic
767C2×C4C22×D411yescharacteristic
768C2×C4C22×D411yescharacteristic
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C2511yescharacteristic
776C8—21no—
777C8—21no—
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C8C2×#4112yes—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—162no—
803C22C23×D411yescharacteristic
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4C22×#4111yescharacteristic
829C4#58511yescharacteristic
830C2—41no—
831C2—41no—
832C2—41no—
833C2—42no—
834C2—81no—
835C2—81no—
836C2D4×#4111yescharacteristic
837C2#358411yescharacteristic
838C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3521C2semidirect
2. #3516C2semidirect
3. #3393C2semidirect
4. #3381C2semidirect
5. #3377C2semidirect
6. #3376C2semidirect
7. #3356C2semidirect
8. #3355C2semidirect
9. #3352C2semidirect
10. #3320C2semidirect
11. #3314C2semidirect
12. #3313C2semidirect
13. #3307C2semidirect
14. #3300C2semidirect
15. #3296C2semidirect
16. #3276C2semidirect
17. #3275C2semidirect
18. #3275C2semidirect
19. #3183C2semidirect
20. #3177C2semidirect
21. #3173C2semidirect
22. #3124C2semidirect
23. #3123C2semidirect
24. #3121C2semidirect
25. #3120C2semidirect
26. #3108C2semidirect
27. #3102C2semidirect
28. #2969C2semidirect
29. #2947C2semidirect
30. #2946C2semidirect
31. C4×#137C2semidirect
35. #557C22semidirect
39. #556C22semidirect
46. #553C22semidirect
53. D4×Q8C22semidirect
61. #542C22semidirect
72. #529C22semidirect
76. #519C22semidirect
79. C2×C4×Q8C22semidirect
80. #499C22semidirect
81. #499C22semidirect
82. #498C22semidirect
85. #494C22semidirect
86. #491C22semidirect
87. #491C22semidirect
89. #489C22semidirect
91. #488C22semidirect
94. #485C22semidirect
95. #485C22semidirect
97. #484C22semidirect
99. #483C22semidirect
101. #482C22semidirect
103. #480C22semidirect
104. #479C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #479C22semidirect
111. #478C22semidirect
112. #477C22semidirect
113. #477C22semidirect
114. #475C22semidirect
118. #470C22semidirect
119. #470C22semidirect
123. #468C22semidirect
127. #465C22semidirect
132. #464C22semidirect
133. #464C22semidirect
136. #462C22semidirect
139. #461C22semidirect
144. #451C22semidirect
145. #451C22semidirect
152. #446C22semidirect
153. C8×Q8C22semidirect
156. #441C22semidirect
157. #441C22semidirect
158. #441C22semidirect
159. #441C22semidirect
165. #440C22semidirect
166. C4×Q16C22semidirect
167. C4×Q16C22semidirect
168. C4×Q16C22semidirect
169. C4×Q16C22semidirect
170. C4×Q16C22semidirect
171. C4×Q16C22semidirect
179. C4×SD16C22semidirect
184. #436C22semidirect
186. #435C22semidirect
189. #433C22semidirect
190. #431C22semidirect
192. #428C22semidirect
193. #428C22semidirect
194. #419C22semidirect
198. C2×#103C22semidirect
201. #405C22semidirect
202. C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#35212
#35162
#33932
#33812
#33772
#33762
#33562
#33552
#33522
#33202
#33142
#33132
#33072
#33002
#32962
#32762
#32752
#31832
#31772
#31732
#31242
#31232
#31212
#31202
#31082
#31022
#29692
#29472
#29462
C4×#1372