Finite Group Databasebeta

← #6556557

Subgroups — #6556557

Order 512.

1576 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38112C211yesmaximal, characteristic, complemented
2#37893C211yesmaximal, characteristic, complemented
3#30389C211yesmaximal, characteristic, complemented
4#30329C211yesmaximal, characteristic, complemented
5#30189C211yesmaximal, characteristic, complemented
6#29584C211yesmaximal, characteristic, complemented
7#29505C211yesmaximal, characteristic, complemented
8#29096C211yesmaximal, characteristic, complemented
9#29072C211yesmaximal, characteristic, complemented
10#29000C211yesmaximal, characteristic, complemented
11#28976C211yesmaximal, characteristic, complemented
12#28584C211yesmaximal, characteristic, complemented
13#28301C211yesmaximal, characteristic, complemented
14#28022C211yesmaximal, characteristic, complemented
15#28013C211yesmaximal, characteristic, complemented
16#27952C211yesmaximal, characteristic, complemented
17#27868C211yesmaximal, characteristic, complemented
18#25250C211yesmaximal, characteristic, complemented
19#25232C211yesmaximal, characteristic, complemented
20#25124C211yesmaximal, characteristic, complemented
21#25108C211yesmaximal, characteristic, complemented
22#25048C211yesmaximal, characteristic, complemented
23#25032C211yesmaximal, characteristic, complemented
24#23770C211yesmaximal, characteristic, complemented
25#23688C211yesmaximal, characteristic, complemented
26C2×#2073C211yesmaximal, characteristic, complemented
27#22938C211yesmaximal, characteristic, complemented
28#22916C211yesmaximal, characteristic, complemented
29#22870C211yesmaximal, characteristic, complemented
30#22858C211yesmaximal, characteristic, complemented
31#20557C211yesmaximal, characteristic, complemented
32C2×#480C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#469C2211yescharacteristic
35C2×#466C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#442C2211yescharacteristic
39C2×C4×D8C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×#102C2211yescharacteristic
44#2856C2211yescharacteristic
45#2851C2211yescharacteristic
46#2797—21no—
47#2786—21no—
48#2761—21no—
49#2761—21no—
50#2753—21no—
51#2753—21no—
52#2752—21no—
53#2740—21no—
54#2647C2211yescharacteristic, complemented
55#2644C2211yescharacteristic
56#2624C2211yescharacteristic
57#2619C2211yescharacteristic, complemented
58#2543—21no—
59#2543—21no—
60#2513C2211yescharacteristic
61#2513C2211yescharacteristic, complemented
62#2513C2211yescharacteristic, complemented
63#2490C2211yescharacteristic
64#2486C2211yescharacteristic
65#2483—21no—
66#2482—21no—
67#2454C2211yescharacteristic
68#2444—21no—
69#2444—21no—
70#2420C2211yescharacteristic
71#2420C2211yescharacteristic, complemented
72#2420C2211yescharacteristic, complemented
73#2416C2211yescharacteristic
74#2416C2211yescharacteristic
75#2412—21no—
76#2411—21no—
77#2408C2211yescharacteristic
78#2361C2211yescharacteristic
79#2361C2211yescharacteristic
80#2344C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82#2328C2211yescharacteristic, complemented
83#2324C2211yescharacteristic
84#2319C2211yescharacteristic
85#2314C2211yescharacteristic, complemented
86C2×#390C2211yescharacteristic
87#2290C2211yescharacteristic
88C2×#382C2211yescharacteristic
89#2100C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2075C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic, complemented
110#2073C2211yescharacteristic, complemented
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic, complemented
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic, complemented
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2041C2211yescharacteristic, complemented
118#2041C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic, complemented
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2025C2211yescharacteristic, complemented
124#2025C2211yescharacteristic, complemented
125#2011C2211yescharacteristic
126#2011C2211yescharacteristic
127#1999C2211yescharacteristic
128#1999C2211yescharacteristic
129#1991C2211yescharacteristic, complemented
130#1991C2211yescharacteristic, complemented
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1970C2211yescharacteristic
136#1970C2211yescharacteristic
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1944C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1942C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic, complemented
146#1936C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic, complemented
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic, complemented
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic, complemented
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic, complemented
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1846C2211yescharacteristic, complemented
180#1846C2211yescharacteristic, complemented
181#1809C2211yescharacteristic, complemented
182#1808C2211yescharacteristic, complemented
183#1776C2211yescharacteristic, complemented
184C4×#107C2211yescharacteristic, complemented
185#1771C2211yescharacteristic, complemented
186C8×C4⋊C4C2211yescharacteristic, complemented
187#1768C2211yescharacteristic, complemented
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic, complemented
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic
198#1746C2211yescharacteristic, complemented
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201#1729C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#123—21no—
215C2×#121—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C42C2311yescharacteristic
242#480—24no—
243#480—24no—
244#469—42no—
245#466—42no—
246#447—24no—
247#447—24no—
248#442—42no—
249C4×D8—42no—
250#435—24no—
251C8×D4—24no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#102—42no—
267C2×#102—42no—
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#400—21no—
306#399—21no—
307#399—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#392—21no—
342#392—21no—
343#392—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388D411yescharacteristic
389#388D411yescharacteristic
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387D411yescharacteristic
397#387D411yescharacteristic
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386D411yescharacteristic
413#386D411yescharacteristic
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385D411yescharacteristic
421#385D411yescharacteristic
422#384C2311yescharacteristic
423#382—21no—
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#381—21no—
433#381—21no—
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376C2311yescharacteristic
454C2×#95—21no—
455C2×#95—21no—
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4C2×D411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×D8—22no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—22no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×M16—22no—
535C2×M16—41no—
536C2×M16—41no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554#127—41no—
555#127—41no—
556#125—41no—
557#125—41no—
558#123—82no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—82no—
572#121—82no—
573#121—82no—
574#121—82no—
575#120—82no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—82no—
587C4×D4—82no—
588#117—41no—
589#117—41no—
590#117—82no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—82no—
676C2×C22⋊C4—82no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—41no—
691C2×C42—41no—
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#107—22no—
700#107—22no—
701#107—22no—
702#107—22no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711C4⋊C8—22no—
712C4⋊C8—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8#4114yes—
740C22⋊C8#4114yes—
741#97—22no—
742#97—41no—
743#97—41no—
744C4×C8—22no—
745C4×C8—41no—
746C4×C8—41no—
747C4×C8—41no—
748C4×C8—41no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—42no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—82no—
842C2×D4—82no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4H(5,𝔽2)12yes—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C2×#4112yes—
922C22×C4C2×#4112yes—
923C22×C4C2511yescharacteristic
924D8—44no—
925D8—44no—
926D8—82no—
927D8—82no—
928M16—82no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—82no—
950C2×C8—82no—
951C2×C8—82no—
952C2×C8C2×#4112yes—
953C2×C8C2×#4112yes—
954C2×C8C2×#4112yes—
955C2×C8C2×#4112yes—
956C4⋊C4—22no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—41no—
1065C42—41no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—22no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—84no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23#53212yes—
1117C23#57612yes—
1118C23#57612yes—
1119C23C23×D411yescharacteristic
1120D4—22no—
1121D4—22no—
1122D4—44no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140D4—162no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144D4—162no—
1145D4—162no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—82no—
1226C2×C4—82no—
1227C2×C4—84no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4#53212yes—
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C22×#4111yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4#58511yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C8—22no—
1242C8—22no—
1243C8—22no—
1244C8—22no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—42no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—168no—
1291C22#317614yes—
1292C22C2×#53211yescharacteristic
1293C22#348511yescharacteristic
1294C22#348811yescharacteristic
1295C22C2×#57611yescharacteristic
1296C22C2×#57611yescharacteristic
1297C22#358411yescharacteristic
1298C22#358411yescharacteristic
1299C4—22no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4#351311yescharacteristic
1324C4#351311yescharacteristic
1325C4#352111yescharacteristic
1326C4#352111yescharacteristic
1327C2—24no—
1328C2—81no—
1329C2—82no—
1330C2—161no—
1331C2—161no—
1332C2—161no—
1333C2#3585011yescharacteristic
1334C2C2×#317611yescharacteristic
1335C2#6072411yescharacteristic
1336C2#6177211yescharacteristic
1337C2#6177211yescharacteristic
1338C2#6206411yescharacteristic
1339C2#6206411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38112C2semidirect
2. #37893C2semidirect
3. #30389C2semidirect
4. #30329C2semidirect
5. #30189C2semidirect
6. #29584C2semidirect
7. #29505C2semidirect
8. #29096C2semidirect
9. #29072C2semidirect
10. #29000C2semidirect
11. #28976C2semidirect
12. #28584C2semidirect
13. #28301C2semidirect
14. #28022C2semidirect
15. #28013C2semidirect
16. #27952C2semidirect
17. #27868C2semidirect
18. #25250C2semidirect
19. #25232C2semidirect
20. #25124C2semidirect
21. #25108C2semidirect
22. #25048C2semidirect
23. #25032C2semidirect
24. #23770C2semidirect
25. #23688C2semidirect
26. C2×#2073C2semidirect
27. #22938C2semidirect
28. #22916C2semidirect
29. #22870C2semidirect
30. #22858C2semidirect
31. #20557C2semidirect
54. #2647C22semidirect
57. #2619C22semidirect
61. #2513C22semidirect
62. #2513C22semidirect
71. #2420C22semidirect
72. #2420C22semidirect
82. #2328C22semidirect
85. #2314C22semidirect
89. #2100C22semidirect
90. #2100C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2076C22semidirect
100. #2075C22semidirect
109. #2073C22semidirect
110. #2073C22semidirect
112. #2067C22semidirect
114. #2065C22semidirect
117. #2041C22semidirect
118. #2041C22semidirect
120. #2034C22semidirect
122. #2033C22semidirect
123. #2025C22semidirect
124. #2025C22semidirect
129. #1991C22semidirect
130. #1991C22semidirect
139. #1944C22semidirect
140. #1943C22semidirect
141. #1942C22semidirect
142. #1942C22semidirect
145. #1936C22semidirect
146. #1936C22semidirect
149. #1934C22semidirect
150. #1934C22semidirect
152. #1926C22semidirect
154. #1925C22semidirect
155. #1921C22semidirect
156. #1921C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
160. #1895C22semidirect
166. #1893C22semidirect
172. #1864C22semidirect
174. #1862C22semidirect
179. #1846C22semidirect
180. #1846C22semidirect
181. #1809C22semidirect
182. #1808C22semidirect
183. #1776C22semidirect
184. C4×#107C22semidirect
185. #1771C22semidirect
186. C8×C4⋊C4C22semidirect
187. #1768C22semidirect
189. #1762C22semidirect
191. C4×#102C22semidirect
192. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
196. #1750C22semidirect
198. #1746C22semidirect
201. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#381122
#378932
#303892
#303292
#301892
#295842
#295052
#290962
#290722
#290002
#289762
#285842
#283012
#280222
#280132
#279522
#278682
#252502
#252322
#251242
#251082
#250482
#250322
#237702
#236882
C2×#20732
#229382
#229162
#228702
#228582
#205572