Finite Group Databasebeta

← #7211760

Subgroups — #7211760

Order 512.

1158 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#32952C211yesmaximal, characteristic, complemented
2#32950C211yesmaximal, characteristic, complemented
3#32872C211yesmaximal, characteristic, complemented
4#32871C211yesmaximal, characteristic, complemented
5#32699C211yesmaximal, characteristic, complemented
6#32697C211yesmaximal, characteristic, complemented
7#32697C211yesmaximal, characteristic, complemented
8#32696C211yesmaximal, characteristic, complemented
9#31421C211yesmaximal, characteristic, complemented
10#31420C211yesmaximal, characteristic, complemented
11#31419C211yesmaximal, characteristic, complemented
12#31419C211yesmaximal, characteristic, complemented
13#30498C211yesmaximal, characteristic
14#30497C211yesmaximal, characteristic, complemented
15#30443C211yesmaximal, characteristic, complemented
16#30442C211yesmaximal, characteristic, complemented
17#28499C211yesmaximal, characteristic, complemented
18#28184C211yesmaximal, characteristic, complemented
19#28182C211yesmaximal, characteristic, complemented
20#27834C211yesmaximal, characteristic, complemented
21#27834C211yesmaximal, characteristic, complemented
22#27694C211yesmaximal, characteristic, complemented
23#25438C211yesmaximal, characteristic, complemented
24#25437C211yesmaximal, characteristic, complemented
25#24989C211yesmaximal, characteristic, complemented
26#24987C211yesmaximal, characteristic, complemented
27#24810C211yesmaximal, characteristic, complemented
28#24808C211yesmaximal, characteristic, complemented
29#23362C211yesmaximal, characteristic, complemented
30#23360C211yesmaximal, characteristic, complemented
31#21478C211yesmaximal, characteristic, complemented
32#3573C2211yescharacteristic
33#3153C2211yescharacteristic
34#3152C2211yescharacteristic
35C2×#497C2211yescharacteristic, complemented
36#3069C2211yescharacteristic
37#3069C2211yescharacteristic
38#3069C2211yescharacteristic
39#3068C2211yescharacteristic
40C2×#473C2211yescharacteristic
41C2×#473C2211yescharacteristic
42C2×#473C2211yescharacteristic, complemented
43C2×#471C2211yescharacteristic
44C2×#471C2211yescharacteristic
45C2×#471C2211yescharacteristic, complemented
46#3059C2211yescharacteristic
47#3057C2211yescharacteristic
48#3044C2211yescharacteristic
49#3044C2211yescharacteristic
50#3043C2211yescharacteristic
51#3042C2211yescharacteristic
52#3022C2211yescharacteristic
53#3022C2211yescharacteristic
54#3022C2211yescharacteristic
55#3021C2211yescharacteristic
56#3018C2211yescharacteristic
57#2955C2211yescharacteristic
58#2955C2211yescharacteristic
59#2950C2211yescharacteristic, complemented
60#2949C2211yescharacteristic, complemented
61#2932C2211yescharacteristic
62#2916C2211yescharacteristic, complemented
63#2103C2211yescharacteristic, complemented
64#2103C2211yescharacteristic, complemented
65#2103C2211yescharacteristic, complemented
66#2103C2211yescharacteristic, complemented
67#2102C2211yescharacteristic, complemented
68#2102C2211yescharacteristic, complemented
69#2098C2211yescharacteristic
70#2098C2211yescharacteristic
71#2082C2211yescharacteristic, complemented
72#2082C2211yescharacteristic, complemented
73#2082C2211yescharacteristic, complemented
74#2082C2211yescharacteristic, complemented
75#2082C2211yescharacteristic, complemented
76#2082C2211yescharacteristic, complemented
77#2081C2211yescharacteristic, complemented
78#2081C2211yescharacteristic, complemented
79#2080C2211yescharacteristic
80#2080C2211yescharacteristic
81#2080C2211yescharacteristic
82#2080C2211yescharacteristic
83#2070C2211yescharacteristic, complemented
84#2070C2211yescharacteristic, complemented
85#2070C2211yescharacteristic, complemented
86#2069C2211yescharacteristic, complemented
87#2049C2211yescharacteristic
88#2049C2211yescharacteristic
89#2049C2211yescharacteristic
90#2049C2211yescharacteristic
91#2049C2211yescharacteristic
92#2049C2211yescharacteristic
93#2048C2211yescharacteristic
94#2048C2211yescharacteristic
95#2047C2211yescharacteristic, complemented
96#2047C2211yescharacteristic, complemented
97#2046C2211yescharacteristic, complemented
98#2046C2211yescharacteristic, complemented
99#2020C2211yescharacteristic
100#2020C2211yescharacteristic, complemented
101#2019C2211yescharacteristic
102#2019C2211yescharacteristic, complemented
103#2009C2211yescharacteristic
104#2009C2211yescharacteristic
105#2009C2211yescharacteristic
106#2008C2211yescharacteristic
107#2005C2211yescharacteristic
108#2005C2211yescharacteristic
109#2004C2211yescharacteristic
110#2003C2211yescharacteristic
111#1979C2211yescharacteristic, complemented
112#1977C2211yescharacteristic, complemented
113#1967C2211yescharacteristic, complemented
114#1966C2211yescharacteristic, complemented
115#1953C2211yescharacteristic, complemented
116#1953C2211yescharacteristic, complemented
117#1946C2211yescharacteristic, complemented
118#1946C2211yescharacteristic, complemented
119#1932C2211yescharacteristic
120#1932C2211yescharacteristic
121#1932C2211yescharacteristic
122#1932C2211yescharacteristic
123#1915C2211yescharacteristic
124#1915C2211yescharacteristic
125#1915C2211yescharacteristic
126#1914C2211yescharacteristic
127#1912C2211yescharacteristic
128#1912C2211yescharacteristic
129#1912C2211yescharacteristic
130#1911C2211yescharacteristic
131#1905C2211yescharacteristic
132#1905C2211yescharacteristic
133#1905C2211yescharacteristic
134#1905C2211yescharacteristic, complemented
135#1905C2211yescharacteristic, complemented
136#1905C2211yescharacteristic, complemented
137#1904C2211yescharacteristic
138#1904C2211yescharacteristic, complemented
139#1903C2211yescharacteristic
140#1903C2211yescharacteristic
141#1903C2211yescharacteristic, complemented
142#1902C2211yescharacteristic
143#1902C2211yescharacteristic
144#1902C2211yescharacteristic
145#1902C2211yescharacteristic
146#1902C2211yescharacteristic
147#1902C2211yescharacteristic
148#1902C2211yescharacteristic, complemented
149#1902C2211yescharacteristic, complemented
150#1902C2211yescharacteristic, complemented
151#1888C2211yescharacteristic, complemented
152#1886C2211yescharacteristic, complemented
153#1886C2211yescharacteristic, complemented
154#1885C2211yescharacteristic, complemented
155#1884C2211yescharacteristic
156#1884C2211yescharacteristic
157#1884C2211yescharacteristic
158#1881C2211yescharacteristic
159#1881C2211yescharacteristic
160#1868C2211yescharacteristic, complemented
161#1868C2211yescharacteristic, complemented
162#1861C2211yescharacteristic
163#1861C2211yescharacteristic
164#1858C2211yescharacteristic
165#1841C2211yescharacteristic, complemented
166#1841C2211yescharacteristic, complemented
167#1841C2211yescharacteristic, complemented
168#1841C2211yescharacteristic, complemented
169#1833C2211yescharacteristic, complemented
170#1833C2211yescharacteristic, complemented
171#1830C2211yescharacteristic, complemented
172#1830C2211yescharacteristic, complemented
173#1830C2211yescharacteristic, complemented
174#1829C2211yescharacteristic, complemented
175#1814C2211yescharacteristic
176#1814C2211yescharacteristic
177#1814C2211yescharacteristic
178#1814C2211yescharacteristic
179#1813C2211yescharacteristic
180#1813C2211yescharacteristic
181#1812C2211yescharacteristic, complemented
182#1794C2211yescharacteristic
183#1778C2211yescharacteristic, complemented
184#1765C2211yescharacteristic
185#1765C2211yescharacteristic
186#1757C2211yescharacteristic
187#585C2311yescharacteristic
188#575C2311yescharacteristic
189#575C2311yescharacteristic
190C2×#137C2311yescharacteristic
191C2×#137C2311yescharacteristic
192C2×#137C2311yescharacteristic
193C2×#137C2311yescharacteristic
194C2×#137C2311yescharacteristic
195C2×#137C2311yescharacteristic
196C2×#137C2311yescharacteristic
197C2×#137C2311yescharacteristic
198C2×#137C2311yescharacteristic
199C2×AGL(1,ℤ/8)C2311yescharacteristic
200C2×AGL(1,ℤ/8)C2311yescharacteristic
201C2×AGL(1,ℤ/8)C2311yescharacteristic
202C22×Q16C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206#568—41no—
207#568—41no—
208#568—41no—
209#568C2311yescharacteristic
210#568C2311yescharacteristic
211#568C2311yescharacteristic
212#568C2311yescharacteristic
213#568C2311yescharacteristic
214C2×#131—41no—
215C2×#131—41no—
216C2×#131—41no—
217C2×#131C2311yescharacteristic
218C2×#131C2311yescharacteristic
219C2×#131C2311yescharacteristic
220C2×#131C2311yescharacteristic
221#536C2311yescharacteristic
222#536C2311yescharacteristic
223#536C2311yescharacteristic
224#535C2311yescharacteristic
225#532C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#124C2311yescharacteristic
228#519C2311yescharacteristic
229#519C2311yescharacteristic
230#519C2311yescharacteristic
231#518C2311yescharacteristic
232#497—21no—
233#497—21no—
234#497—21no—
235#497—41no—
236#497—41no—
237#496—21no—
238#495—21no—
239#495—21no—
240#494—21no—
241#492—21no—
242#473—41no—
243#473—41no—
244#473—41no—
245#473—41no—
246#473—41no—
247#473—41no—
248#473—41no—
249#473—41no—
250#473—41no—
251#472—41no—
252#471—41no—
253#471—41no—
254#471—41no—
255#471—41no—
256#471—41no—
257#471—41no—
258#471—41no—
259#471—41no—
260#471—41no—
261#471—41no—
262#470—41no—
263#468—41no—
264#467—41no—
265#465—41no—
266#464—41no—
267#464—41no—
268#464—41no—
269#463—41no—
270#462—41no—
271#462—41no—
272#461—41no—
273#460—41no—
274#456—21no—
275#456—41no—
276#456—41no—
277#456—41no—
278#455—21no—
279#455—41no—
280#455—41no—
281#455—41no—
282#454—21no—
283#454—41no—
284#453—21no—
285#453—41no—
286#444—41no—
287#444—41no—
288#443—41no—
289#443—41no—
290#441—41no—
291#440—41no—
292C4×Q16—41no—
293C4×SD16—41no—
294#435—41no—
295#435—41no—
296#430—41no—
297#430C2311yescharacteristic
298#430C2311yescharacteristic
299#430C2311yescharacteristic
300#430C2311yescharacteristic
301#430C2311yescharacteristic
302#430C2311yescharacteristic
303#430C2311yescharacteristic
304#430C2311yescharacteristic
305C2×#108—41no—
306C2×#108C2311yescharacteristic
307C2×#108C2311yescharacteristic
308C2×#108C2311yescharacteristic
309C2×#108C2311yescharacteristic
310#427C2311yescharacteristic
311#427C2311yescharacteristic
312#424C2311yescharacteristic
313#424C2311yescharacteristic
314#424C2311yescharacteristic
315#424C2311yescharacteristic
316#423C2311yescharacteristic
317#421C2311yescharacteristic
318#421C2311yescharacteristic
319#421C2311yescharacteristic
320#421C2311yescharacteristic
321#421C2311yescharacteristic
322#421C2311yescharacteristic
323#421C2311yescharacteristic
324#421C2311yescharacteristic
325#421C2311yescharacteristic
326#421C2311yescharacteristic
327#421C2311yescharacteristic
328#421C2311yescharacteristic
329C2×#104C2311yescharacteristic
330C2×#104C2311yescharacteristic
331#419C2311yescharacteristic
332#419C2311yescharacteristic
333#419C2311yescharacteristic
334#419C2311yescharacteristic
335#419C2311yescharacteristic
336#419C2311yescharacteristic
337#419C2311yescharacteristic
338#419C2311yescharacteristic
339#419C2311yescharacteristic
340#418C2311yescharacteristic
341#418C2311yescharacteristic
342#418C2311yescharacteristic
343#416C2311yescharacteristic
344#416C2311yescharacteristic
345#413C2311yescharacteristic
346#413C2311yescharacteristic
347#413C2311yescharacteristic
348#413C2311yescharacteristic
349#413C2311yescharacteristic
350C2×#101C2311yescharacteristic
351C2×#101C2311yescharacteristic
352C2×#101C2311yescharacteristic
353C2×#101C2311yescharacteristic
354C2×#101C2311yescharacteristic
355C2×#101C2311yescharacteristic
356C2×#101C2311yescharacteristic
357C2×#101C2311yescharacteristic
358C2×#101C2311yescharacteristic
359C2×#101C2311yescharacteristic
360C2×#101C2311yescharacteristic
361C2×#101C2311yescharacteristic
362C2×#100C2311yescharacteristic
363C2×#100C2311yescharacteristic
364C2×#100C2311yescharacteristic
365C2×#100C2311yescharacteristic
366#410C2311yescharacteristic
367#410C2311yescharacteristic
368#410C2311yescharacteristic
369#408C2311yescharacteristic
370#408C2311yescharacteristic
371#405C2311yescharacteristic
372#405C2311yescharacteristic
373C4×M16C2311yescharacteristic
374C4×M16C2311yescharacteristic
375C2×#97C2311yescharacteristic
376#344C2311yescharacteristic
377#344C2311yescharacteristic
378#344C2311yescharacteristic
379#344C2311yescharacteristic
380#344C2311yescharacteristic
381#344C2311yescharacteristic
382#344C2311yescharacteristic
383#344C2311yescharacteristic
384#344C2311yescharacteristic
385#344C2311yescharacteristic
386#344C2311yescharacteristic
387#344C2311yescharacteristic
388#344C2311yescharacteristic
389#344C2311yescharacteristic
390#344C2311yescharacteristic
391#344C2311yescharacteristic
392#344C2311yescharacteristic
393#344C2311yescharacteristic
394#341C2311yescharacteristic
395#341C2311yescharacteristic
396#341C2311yescharacteristic
397#341C2311yescharacteristic
398#339C2311yescharacteristic
399#339C2311yescharacteristic
400#339C2311yescharacteristic
401#339C2311yescharacteristic
402#339C2311yescharacteristic
403#339C2311yescharacteristic
404#338C2311yescharacteristic
405#338C2311yescharacteristic
406#338C2311yescharacteristic
407#338C2311yescharacteristic
408H(3,ℤ/4)C2311yescharacteristic
409H(3,ℤ/4)C2311yescharacteristic
410H(3,ℤ/4)C2311yescharacteristic
411H(3,ℤ/4)C2311yescharacteristic
412H(3,ℤ/4)C2311yescharacteristic
413H(3,ℤ/4)C2311yescharacteristic
4142−1+4—21no—
4152−1+4—21no—
4162−1+4—21no—
417H(5,𝔽2)—21no—
418H(5,𝔽2)—21no—
419H(5,𝔽2)—21no—
420H(5,𝔽2)—41no—
421C2×#41—41no—
422C2×#41—41no—
423C2×#41—41no—
424C2×#41C2411yescharacteristic
425C2×#41C2411yescharacteristic
426C2×#41C2411yescharacteristic
427C2×#41C2411yescharacteristic
428C22×Q8C2411yescharacteristic
429C22×Q8C2411yescharacteristic
430C22×Q8C2411yescharacteristic
431C22×D4C2411yescharacteristic
432#137—21no—
433#137—21no—
434#137—21no—
435#137—21no—
436#137—41no—
437#137—41no—
438#137—41no—
439#137—41no—
440#137—41no—
441#137—41no—
442#137—41no—
443#137—41no—
444#137—41no—
445#137—41no—
446#137—41no—
447#137—41no—
448#137—41no—
449#137—41no—
450#137—41no—
451#137—41no—
452#137—41no—
453#137—41no—
454AGL(1,ℤ/8)—21no—
455AGL(1,ℤ/8)—21no—
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—21no—
458AGL(1,ℤ/8)—41no—
459AGL(1,ℤ/8)—41no—
460AGL(1,ℤ/8)—41no—
461AGL(1,ℤ/8)—41no—
462AGL(1,ℤ/8)—41no—
463AGL(1,ℤ/8)—41no—
464#135—41no—
465#135—41no—
466C2×Q16—21no—
467C2×Q16—21no—
468C2×Q16—21no—
469C2×Q16—21no—
470C2×Q16—21no—
471C2×Q16—21no—
472C2×Q16—21no—
473C2×Q16—21no—
474C2×Q16—21no—
475C2×Q16—21no—
476C2×Q16—21no—
477C2×Q16—21no—
478C2×Q16—21no—
479C2×Q16—21no—
480C2×Q16—21no—
481C2×Q16—41no—
482C2×Q16—41no—
483C2×Q16—41no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—21no—
497C2×SD16—21no—
498C2×SD16—21no—
499C2×SD16—21no—
500C2×SD16—21no—
501C2×SD16—21no—
502C2×SD16—41no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—21no—
508#131—21no—
509#131—21no—
510#131—21no—
511#131—21no—
512#131—21no—
513#131—21no—
514#131—21no—
515#131—21no—
516#131—21no—
517#131—21no—
518#131—21no—
519#131—21no—
520#131—21no—
521#131—21no—
522#131—21no—
523#131—21no—
524#131—41no—
525#131—41no—
526#131—41no—
527#131—41no—
528#131—41no—
529#131—41no—
530#131—41no—
531#131—41no—
532#131—41no—
533#131—41no—
534#131—42no—
535#131—42no—
536#131—42no—
537#131—42no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—21no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—42no—
546C2×M16—42no—
547C2×M16—42no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16C2411yescharacteristic
551C2×M16C2411yescharacteristic
552C2×M16C2411yescharacteristic
553C2×M16C2411yescharacteristic
554C2×M16C2411yescharacteristic
555C2×M16C2411yescharacteristic
556C2×M16C2411yescharacteristic
557C2×M16C2411yescharacteristic
558C2×M16C2411yescharacteristic
559C2×M16C2411yescharacteristic
560C2×M16C2411yescharacteristic
561C2×M16C2411yescharacteristic
562C2×M16C2411yescharacteristic
563C2×M16C2411yescharacteristic
564C22×C8—21no—
565C22×C8—21no—
566C22×C8—21no—
567C22×C8—21no—
568C22×C8—42no—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—21no—
572C4⋊Q8—21no—
573C4⋊Q8—21no—
574C4⋊Q8—21no—
575C4⋊Q8—21no—
576C4⋊Q8—41no—
577C4⋊Q8#4111yescharacteristic
578#127—21no—
579#127#4111yescharacteristic
580#124—21no—
581#124—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#124—21no—
586#124—41no—
587#124#4111yescharacteristic
588#124#4111yescharacteristic
589#123—41no—
590#123—41no—
591#123—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595#121—41no—
596#121—41no—
597#120—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610#117C2411yescharacteristic
611#117C2411yescharacteristic
612#117C2411yescharacteristic
613#117C2411yescharacteristic
614#117C2411yescharacteristic
615#117C2411yescharacteristic
616C2×C4⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C42C2411yescharacteristic
620#108—21no—
621#108—21no—
622#108—21no—
623#108—21no—
624#108—21no—
625#108—21no—
626#108—21no—
627#108—21no—
628#108—41no—
629#108—41no—
630#108—41no—
631#108—41no—
632#108—41no—
633#108—41no—
634#108—41no—
635#108—41no—
636#107—21no—
637#107—21no—
638#106—21no—
639#106—21no—
640C4⋊C8—41no—
641C4⋊C8—41no—
642C4⋊C8—41no—
643C4⋊C8—41no—
644C4⋊C8—41no—
645#104—21no—
646#104—21no—
647#104—21no—
648#104—21no—
649#104—41no—
650#104—41no—
651#104—41no—
652#104—41no—
653#104—41no—
654#104—41no—
655#104—41no—
656#104—41no—
657#104—41no—
658#104—41no—
659#104—41no—
660#104—41no—
661#103—21no—
662#103—21no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#102—21no—
673#102—21no—
674#102—41no—
675#102—41no—
676#102—41no—
677#101—21no—
678#101—21no—
679#101—21no—
680#101—21no—
681#101—21no—
682#101—41no—
683#101—41no—
684#101—41no—
685#101—41no—
686#101—41no—
687#101—41no—
688#101—41no—
689#101—41no—
690#101—41no—
691#101—41no—
692#101—41no—
693#101—41no—
694#100—21no—
695#100—21no—
696#100—21no—
697#100—21no—
698#100—21no—
699#100—41no—
700#100—41no—
701#100—41no—
702#100—41no—
703#99—41no—
704#99—41no—
705#99—41no—
706C22⋊C8—41no—
707C22⋊C8—41no—
708#97—21no—
709#97—21no—
710#97—21no—
711#97—21no—
712#97—21no—
713#97—21no—
714C4×C8—21no—
715C4×C8—21no—
716C4×C8—21no—
717C4×C8—21no—
718C24—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—21no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—42no—
736#41—42no—
737#41—42no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—42no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—41no—
765C2×Q8—41no—
766C2×Q8C2×#4111yescharacteristic
767C2×Q8C2×#4111yescharacteristic
768C2×Q8H(5,𝔽2)11yescharacteristic
769C2×Q8H(5,𝔽2)11yescharacteristic
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—41no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—41no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4C2×#4111yescharacteristic
789C2×D4C2×#4111yescharacteristic
790C2×D4H(5,𝔽2)11yescharacteristic
791C2×D4H(5,𝔽2)11yescharacteristic
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—42no—
801C22×C4—81no—
802C22×C4C2511yescharacteristic
803Q16—41no—
804Q16—41no—
805Q16—41no—
806Q16—41no—
807Q16—41no—
808Q16—41no—
809Q16—81no—
810Q16—81no—
811Q16—81no—
812Q16—81no—
813Q16—81no—
814Q16—81no—
815Q16—81no—
816Q16—81no—
817Q16—81no—
818Q16—82no—
819SD16—41no—
820SD16—41no—
821SD16—41no—
822SD16—41no—
823SD16—41no—
824SD16—41no—
825SD16—41no—
826SD16—41no—
827SD16—81no—
828SD16—81no—
829SD16—81no—
830SD16—81no—
831SD16—81no—
832SD16—81no—
833SD16—81no—
834SD16—81no—
835SD16—81no—
836SD16—81no—
837SD16—81no—
838SD16—81no—
839SD16—82no—
840D8—41no—
841D8—41no—
842D8—81no—
843D8—81no—
844D8—81no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—21no—
858M16—21no—
859M16—21no—
860M16—21no—
861M16—21no—
862M16—21no—
863M16—21no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—21no—
872M16—21no—
873M16—42no—
874M16—42no—
875M16—42no—
876M16—41no—
877M16—41no—
878M16—41no—
879M16—41no—
880M16—41no—
881M16—41no—
882M16—41no—
883M16—41no—
884M16—81no—
885M16—81no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—42no—
904C2×C8—42no—
905C2×C8—42no—
906C2×C8—41no—
907C2×C8—41no—
908C2×C8—41no—
909C2×C8—41no—
910C2×C8—41no—
911C2×C8—41no—
912C2×C8—41no—
913C2×C8—41no—
914C2×C8—81no—
915C2×C8—81no—
916C2×C8H(5,𝔽2)11yescharacteristic
917C2×C8H(5,𝔽2)11yescharacteristic
918C2×C8H(5,𝔽2)11yescharacteristic
919C2×C8H(5,𝔽2)11yescharacteristic
920C2×C8H(5,𝔽2)11yescharacteristic
921C2×C8H(5,𝔽2)11yescharacteristic
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—41no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C22⋊C4—21no—
938C22⋊C4—21no—
939C22⋊C4—21no—
940C22⋊C4—21no—
941C22⋊C4—21no—
942C22⋊C4—21no—
943C22⋊C4—41no—
944C22⋊C4—41no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42C2×#4111yescharacteristic
963C42C2×#4111yescharacteristic
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—42no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—161no—
973C23#58511yescharacteristic
974Q8—21no—
975Q8—21no—
976Q8—21no—
977Q8—21no—
978Q8—21no—
979Q8—21no—
980Q8—21no—
981Q8—21no—
982Q8—42no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—41no—
992Q8—41no—
993Q8—41no—
994Q8—41no—
995D4—21no—
996D4—21no—
997D4—21no—
998D4—21no—
999D4—21no—
1000D4—21no—
1001D4—21no—
1002D4—21no—
1003D4—42no—
1004D4—42no—
1005D4—42no—
1006D4—41no—
1007D4—41no—
1008D4—41no—
1009D4—41no—
1010D4—41no—
1011D4—41no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015D4—41no—
1016D4—41no—
1017D4—41no—
1018D4—161no—
1019D4—321no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—81no—
1053C2×C4—321no—
1054C2×C4C22×#4111yescharacteristic
1055C2×C4C2×H(5,𝔽2)11yescharacteristic
1056C2×C4C2×H(5,𝔽2)11yescharacteristic
1057C2×C4C2×H(5,𝔽2)11yescharacteristic
1058C2×C4C2×H(5,𝔽2)11yescharacteristic
1059C2×C4C2×H(5,𝔽2)11yescharacteristic
1060C8—41no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C8—41no—
1069C8—41no—
1070C8—41no—
1071C8—41no—
1072C8—41no—
1073C8—41no—
1074C8—41no—
1075C8#56011yescharacteristic
1076C8#56011yescharacteristic
1077C8#56011yescharacteristic
1078C8#56011yescharacteristic
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—41no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—161no—
1090C22—161no—
1091C22—161no—
1092C22—162no—
1093C22#350511yescharacteristic
1094C22#354211yescharacteristic
1095C22#354211yescharacteristic
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4#351911yescharacteristic
1112C4#351911yescharacteristic
1113C4C2×#56011yescharacteristic
1114C4#353711yescharacteristic
1115C2—21no—
1116C2—21no—
1117C2—21no—
1118C2—81no—
1119C2—81no—
1120C2—81no—
1121C2—81no—
1122C2—161no—
1123C2#4559911yescharacteristic
subgroupG/H
center, socleC2#45599
commutator, Frattini, cosocleC22×C4C25
prime radical#30498C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #32952C2semidirect
2. #32950C2semidirect
3. #32872C2semidirect
4. #32871C2semidirect
5. #32699C2semidirect
6. #32697C2semidirect
7. #32697C2semidirect
8. #32696C2semidirect
9. #31421C2semidirect
10. #31420C2semidirect
11. #31419C2semidirect
12. #31419C2semidirect
14. #30497C2semidirect
15. #30443C2semidirect
16. #30442C2semidirect
17. #28499C2semidirect
18. #28184C2semidirect
19. #28182C2semidirect
20. #27834C2semidirect
21. #27834C2semidirect
22. #27694C2semidirect
23. #25438C2semidirect
24. #25437C2semidirect
25. #24989C2semidirect
26. #24987C2semidirect
27. #24810C2semidirect
28. #24808C2semidirect
29. #23362C2semidirect
30. #23360C2semidirect
31. #21478C2semidirect
35. C2×#497C22semidirect
42. C2×#473C22semidirect
45. C2×#471C22semidirect
59. #2950C22semidirect
60. #2949C22semidirect
62. #2916C22semidirect
63. #2103C22semidirect
64. #2103C22semidirect
65. #2103C22semidirect
66. #2103C22semidirect
67. #2102C22semidirect
68. #2102C22semidirect
71. #2082C22semidirect
72. #2082C22semidirect
73. #2082C22semidirect
74. #2082C22semidirect
75. #2082C22semidirect
76. #2082C22semidirect
77. #2081C22semidirect
78. #2081C22semidirect
83. #2070C22semidirect
84. #2070C22semidirect
85. #2070C22semidirect
86. #2069C22semidirect
95. #2047C22semidirect
96. #2047C22semidirect
97. #2046C22semidirect
98. #2046C22semidirect
100. #2020C22semidirect
102. #2019C22semidirect
111. #1979C22semidirect
112. #1977C22semidirect
113. #1967C22semidirect
114. #1966C22semidirect
115. #1953C22semidirect
116. #1953C22semidirect
117. #1946C22semidirect
118. #1946C22semidirect
134. #1905C22semidirect
135. #1905C22semidirect
136. #1905C22semidirect
138. #1904C22semidirect
141. #1903C22semidirect
148. #1902C22semidirect
149. #1902C22semidirect
150. #1902C22semidirect
151. #1888C22semidirect
152. #1886C22semidirect
153. #1886C22semidirect
154. #1885C22semidirect
160. #1868C22semidirect
161. #1868C22semidirect
165. #1841C22semidirect
166. #1841C22semidirect
167. #1841C22semidirect
168. #1841C22semidirect
169. #1833C22semidirect
170. #1833C22semidirect
171. #1830C22semidirect
172. #1830C22semidirect
173. #1830C22semidirect
174. #1829C22semidirect
181. #1812C22semidirect
183. #1778C22semidirect

Maximal subgroups

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

subgroupindex
#329522
#329502
#328722
#328712
#326992
#326972
#326962
#314212
#314202
#314192
#304982
#304972
#304432
#304422
#284992
#281842
#281822
#278342
#276942
#254382
#254372
#249892
#249872
#248102
#248082
#233622
#233602
#214782