Finite Group Databasebeta

← #7254802

Subgroups — #7254802

Order 512.

1893 conjugacy classes of subgroups.

The subgroup lattice has 1439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39340C211yesmaximal, characteristic, complemented
2#38950C211yesmaximal, characteristic, complemented
3#32772C211yesmaximal, characteristic, complemented
4#31538C211yesmaximal, characteristic, complemented
5#31520C211yesmaximal, characteristic, complemented
6#31204C211yesmaximal, characteristic, complemented
7#31189C211yesmaximal, characteristic, complemented
8#31145C211yesmaximal, characteristic, complemented
9#31140C211yesmaximal, characteristic, complemented
10#30657C211yesmaximal, characteristic, complemented
11#30655C211yesmaximal, characteristic, complemented
12#30575C211yesmaximal, characteristic, complemented
13#30573C211yesmaximal, characteristic, complemented
14#30566C211yesmaximal, characteristic, complemented
15#30559C211yesmaximal, characteristic, complemented
16#29301C211yesmaximal, characteristic, complemented
17#28782C211yesmaximal, characteristic, complemented
18#28776C211yesmaximal, characteristic, complemented
19#26384C211yesmaximal, characteristic, complemented
20#26382C211yesmaximal, characteristic, complemented
21#25602C211yesmaximal, characteristic, complemented
22#25560C211yesmaximal, characteristic, complemented
23#25549C211yesmaximal, characteristic, complemented
24#25533C211yesmaximal, characteristic, complemented
25#25531C211yesmaximal, characteristic, complemented
26#25422C211yesmaximal, characteristic, complemented
27#25419C211yesmaximal, characteristic, complemented
28#24137C211yesmaximal, characteristic, complemented
29#24116C211yesmaximal, characteristic, complemented
30#24061C211yesmaximal, characteristic, complemented
31#22335C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#537—21no—
36C2×#532C2211yescharacteristic
37C2×#496C2211yescharacteristic
38C2×#489C2211yescharacteristic
39C2×#481C2211yescharacteristic
40C2×#481C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#483C2211yescharacteristic
44C2×#480C2211yescharacteristic
45C2×#478C2211yescharacteristic
46C2×#474C2211yescharacteristic
47C2×#469C2211yescharacteristic
48C2×#468C2211yescharacteristic
49C2×#466C2211yescharacteristic
50C2×#465C2211yescharacteristic
51C2×#440C2211yescharacteristic
52C2×C4×D8C2211yescharacteristic
53#2857C2211yescharacteristic
54#2850C2211yescharacteristic
55#2707—21no—
56#2705—21no—
57#2704—21no—
58#2702—21no—
59#2672—21no—
60#2672—21no—
61#2671—21no—
62#2671—21no—
63#2618—21no—
64#2616—21no—
65#2542C2211yescharacteristic
66#2537C2211yescharacteristic
67#2537C2211yescharacteristic
68#2537C2211yescharacteristic
69#2498—21no—
70#2454C2211yescharacteristic
71#2451C2211yescharacteristic
72#2442C2211yescharacteristic
73#2440C2211yescharacteristic
74#2440C2211yescharacteristic
75#2439C2211yescharacteristic
76#2430—21no—
77#2428C2211yescharacteristic
78#2428C2211yescharacteristic
79#2427C2211yescharacteristic
80#2426C2211yescharacteristic
81#2417—21no—
82#2417C2211yescharacteristic
83#2417C2211yescharacteristic
84#2416C2211yescharacteristic
85#2416C2211yescharacteristic
86#2416C2211yescharacteristic
87#2414C2211yescharacteristic
88#2407—21no—
89D4×C4⋊C4C2211yescharacteristic
90#2311—21no—
91C4×#121C2211yescharacteristic
92C2×#389C2211yescharacteristic
93#2096C2211yescharacteristic
94#2095C2211yescharacteristic
95#2094C2211yescharacteristic
96#2094C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2066C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2058C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2025C2211yescharacteristic
130#2024C2211yescharacteristic
131#2023C2211yescharacteristic
132#2023C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic
139#1999C2211yescharacteristic
140#1999C2211yescharacteristic
141#1993C2211yescharacteristic
142#1992C2211yescharacteristic
143#1990C2211yescharacteristic
144#1972C2211yescharacteristic
145#1968C2211yescharacteristic
146#1961C2211yescharacteristic
147#1955C2211yescharacteristic
148#1954C2211yescharacteristic
149#1944C2211yescharacteristic
150#1943C2211yescharacteristic
151#1943C2211yescharacteristic
152#1943C2211yescharacteristic
153#1943C2211yescharacteristic
154#1941C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1917C2211yescharacteristic
158#1916C2211yescharacteristic
159#1880C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1872C2211yescharacteristic
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic
189#1853C2211yescharacteristic
190#1852C2211yescharacteristic
191#1852C2211yescharacteristic
192#1852C2211yescharacteristic
193#1817C2211yescharacteristic
194#1809C2211yescharacteristic
195#1807C2211yescharacteristic
196#1803C2211yescharacteristic
197#1802C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1749C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41—21no—
204C22×#41—21no—
205C22×#41—21no—
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#552—42no—
213#552—42no—
214#547—42no—
215#547—42no—
216#547—42no—
217#547—42no—
218#537—48no—
219#532—42no—
220#532—42no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#126—21no—
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×#121—21no—
246C2×#121—21no—
247C2×#121—21no—
248C2×#121—21no—
249C2×#121—21no—
250C2×#121—21no—
251C2×#121—21no—
252C2×#121—21no—
253C2×#121—21no—
254C2×#121D411yescharacteristic
255C2×#121C2311yescharacteristic
256C2×#121C2311yescharacteristic
257C2×#121C2311yescharacteristic
258C2×#121C2311yescharacteristic
259C2×#121C2311yescharacteristic
260C2×#121C2311yescharacteristic
261C2×#121C2311yescharacteristic
262C2×#121C2311yescharacteristic
263C2×#121C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×D4—21no—
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×#117—21no—
275C2×#117C2311yescharacteristic
276C22×C4⋊C4—21no—
277C22×C4⋊C4—21no—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C42C2311yescharacteristic
284#496—42no—
285#489—42no—
286#483—42no—
287#482—42no—
288#481—42no—
289#481—42no—
290#481—42no—
291#480—42no—
292#478—42no—
293#474—42no—
294#469—42no—
295#468—42no—
296#466—42no—
297#465—42no—
298#440—42no—
299C4×D8—42no—
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356#400—21no—
357#399—21no—
358#399—21no—
359#399—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#397—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#394—21no—
391#394—21no—
392#393—21no—
393#392—21no—
394#392—21no—
395#392—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#390—21no—
402#390—21no—
403#390D411yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#389—21no—
409#389—21no—
410#389—21no—
411#389D411yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388D411yescharacteristic
427#388D411yescharacteristic
428#387—21no—
429#387—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386D411yescharacteristic
441#386D411yescharacteristic
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#382C2311yescharacteristic
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380D411yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C2×#95—21no—
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503C2×#41—44no—
504C2×#41—44no—
505C2×#41—44no—
506C2×#41—44no—
507C2×#41—44no—
508C2×#41—44no—
509C2×#41—82no—
510C2×#41—82no—
511C2×#41—82no—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8—21no—
515C22×Q8C2411yescharacteristic
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2×D411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×M16—22no—
561C2×M16—41no—
562C2×M16—41no—
563C22×C8—22no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580#127—22no—
581#127—41no—
582#126—44no—
583#125—22no—
584#125—41no—
585#125—44no—
586#124—41no—
587#124—41no—
588#124—44no—
589#123—44no—
590#123—44no—
591#123—44no—
592#123—44no—
593#123—44no—
594C22⋊Q8—22no—
595C22⋊Q8—44no—
596C22⋊Q8—44no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—82no—
607#121—24no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—22no—
613#121—44no—
614#121—44no—
615#121—44no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—44no—
624#121—44no—
625#121—44no—
626#121—44no—
627#121—44no—
628#121—41no—
629#121—41no—
630#121—41no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—82no—
635C4×Q8—22no—
636C4×Q8—41no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—22no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—44no—
654#117—22no—
655#117—41no—
656#117—44no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
697C2×C4⋊C4—44no—
698C2×C4⋊C4—82no—
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—41no—
763C2×C42—41no—
764C2×C42C2×D411yescharacteristic
765C2×C42C2×D411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770#107—22no—
771#107—22no—
772#107—22no—
773#107—22no—
774#107—41no—
775#107—41no—
776#106—22no—
777#106—22no—
778#106—41no—
779#106—41no—
780#106—41no—
781#106—41no—
782#106—41no—
783#106—41no—
784#106—41no—
785#106—41no—
786C4⋊C8—41no—
787C4⋊C8—41no—
788#103—22no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—41no—
802#102—41no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102—41no—
811#102—41no—
812C22⋊C8—22no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815C22⋊C8—22no—
816C22⋊C8—41no—
817C22⋊C8—41no—
818C22⋊C8—41no—
819C22⋊C8—41no—
820C22⋊C8—41no—
821C22⋊C8—41no—
822#97—41no—
823#97—41no—
824#97—41no—
825C4×C8—41no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854C24—21no—
855C24—21no—
856C24—21no—
857C24C22×D411yescharacteristic
858C24C22×D411yescharacteristic
859C24C22×D411yescharacteristic
860#41—816no—
861#41—816no—
862#41—816no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4AGL(1,ℤ/8)14yes—
937C2×D4H(5,𝔽2)12yes—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—22no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—22no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—41no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4—81no—
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C2511yescharacteristic
1017SD16—44no—
1018SD16—82no—
1019D8—44no—
1020D8—82no—
1021M16—82no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—82no—
1045C2×C82−1+412yes—
1046C2×C82−1+412yes—
1047C4⋊C4—24no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4—81no—
1095C4⋊C4—81no—
1096C4⋊C4—81no—
1097C4⋊C4—81no—
1098C4⋊C4—81no—
1099C4⋊C4—81no—
1100C4⋊C4—81no—
1101C4⋊C4—81no—
1102C4⋊C4—81no—
1103C4⋊C4H(5,𝔽2)12yes—
1104C4⋊C4H(5,𝔽2)12yes—
1105C4⋊C4H(5,𝔽2)12yes—
1106C22⋊C4—24no—
1107C22⋊C4—22no—
1108C22⋊C4—22no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—41no—
1159C42—41no—
1160C42—42no—
1161C42—42no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—22no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23C2×AGL(1,ℤ/8)12yes—
1203C23C2×AGL(1,ℤ/8)12yes—
1204C23C23×D411yescharacteristic
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—84no—
1210Q8—84no—
1211Q8—84no—
1212D4—22no—
1213D4—22no—
1214D4—44no—
1215D4—44no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—82no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230D4—84no—
1231D4—84no—
1232D4—84no—
1233D4—84no—
1234D4—84no—
1235D4—162no—
1236D4—162no—
1237D4—162no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—44no—
1273C2×C4—48no—
1274C2×C4—48no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—84no—
1324C2×C4—84no—
1325C2×C4—82no—
1326C2×C4—84no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4—162no—
1330C2×C4—162no—
1331C2×C4—162no—
1332C2×C4C2×AGL(1,ℤ/8)12yes—
1333C2×C4#57712yes—
1334C2×C4C2×H(5,𝔽2)11yescharacteristic
1335C2×C4C2×H(5,𝔽2)11yescharacteristic
1336C2×C4C2×H(5,𝔽2)11yescharacteristic
1337C2×C4C2×H(5,𝔽2)11yescharacteristic
1338C2×C4C2×2−1+411yescharacteristic
1339C2×C4C2×2−1+411yescharacteristic
1340C8—22no—
1341C8—22no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C8—41no—
1346C8—41no—
1347C8—41no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—42no—
1366C22—41no—
1367C22—42no—
1368C22—41no—
1369C22—42no—
1370C22—41no—
1371C22—41no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22#348411yescharacteristic
1391C22#348411yescharacteristic
1392C22#349911yescharacteristic
1393C22C22×AGL(1,ℤ/8)11yescharacteristic
1394C22C2×#57711yescharacteristic
1395C22#358511yescharacteristic
1396C22#358611yescharacteristic
1397C4—22no—
1398C4—22no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—42no—
1404C4—42no—
1405C4—41no—
1406C4—42no—
1407C4—41no—
1408C4—41no—
1409C4—41no—
1410C4—41no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4—81no—
1421C4#353611yescharacteristic
1422C4#353611yescharacteristic
1423C4#354811yescharacteristic
1424C4#354811yescharacteristic
1425C2—42no—
1426C2—42no—
1427C2—81no—
1428C2—82no—
1429C2—161no—
1430C2—161no—
1431C2#4642311yescharacteristic
1432C2#6156911yescharacteristic
1433C2#6160011yescharacteristic
1434C2#6165611yescharacteristic
1435C2#6168611yescharacteristic
1436C2#6250311yescharacteristic
1437C2#6252111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39340C2semidirect
2. #38950C2semidirect
3. #32772C2semidirect
4. #31538C2semidirect
5. #31520C2semidirect
6. #31204C2semidirect
7. #31189C2semidirect
8. #31145C2semidirect
9. #31140C2semidirect
10. #30657C2semidirect
11. #30655C2semidirect
12. #30575C2semidirect
13. #30573C2semidirect
14. #30566C2semidirect
15. #30559C2semidirect
16. #29301C2semidirect
17. #28782C2semidirect
18. #28776C2semidirect
19. #26384C2semidirect
20. #26382C2semidirect
21. #25602C2semidirect
22. #25560C2semidirect
23. #25549C2semidirect
24. #25533C2semidirect
25. #25531C2semidirect
26. #25422C2semidirect
27. #25419C2semidirect
28. #24137C2semidirect
29. #24116C2semidirect
30. #24061C2semidirect
31. #22335C2semidirect

Maximal subgroups

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

subgroupindex
#393402
#389502
#327722
#315382
#315202
#312042
#311892
#311452
#311402
#306572
#306552
#305752
#305732
#305662
#305592
#293012
#287822
#287762
#263842
#263822
#256022
#255602
#255492
#255332
#255312
#254222
#254192
#241372
#241162
#240612
#223352