Finite Group Databasebeta

← #1409587

Subgroups — #1409587

Order 512.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic, complemented
2C2×#2455C211yesmaximal, characteristic
3#17074C211yesmaximal, characteristic, complemented
4#17022C212yesmaximal
5#17011C212yesmaximal, complemented
6#16980C211yesmaximal, characteristic, complemented
7#16892C211yesmaximal, characteristic, complemented
8#16844C212yesmaximal, complemented
9#16781C212yesmaximal, complemented
10#16360C211yesmaximal, characteristic, complemented
11#15256C211yesmaximal, characteristic, complemented
12#15114C211yesmaximal, characteristic, complemented
13#14998C212yesmaximal, complemented
14#14964C212yesmaximal, complemented
15#14841C211yesmaximal, characteristic, complemented
16#14841C211yesmaximal, characteristic, complemented
17#14825C211yesmaximal, characteristic, complemented
18#14322C211yesmaximal, characteristic, complemented
19#14287C211yesmaximal, characteristic, complemented
20#14070C212yesmaximal, complemented
21#14060C212yesmaximal, complemented
22#13839C211yesmaximal, characteristic, complemented
23#13820C211yesmaximal, characteristic, complemented
24C22×#123C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2485—28no—
30#2455—28no—
31C2×#400C2211yescharacteristic
32C2×#400C2211yescharacteristic
33C2×#399C2211yescharacteristic
34C2×#399C2211yescharacteristic
35C2×#397C2212yes—
36C2×#394C2211yescharacteristic
37C2×#394C2211yescharacteristic
38C2×#394C2212yes—
39C2×#392C2211yescharacteristic
40C2×#390C2212yes—
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#389C2211yescharacteristic
46C2×#388C2211yescharacteristic
47C2×#388C2211yescharacteristic
48C2×#388C2212yes—
49C2×#388C2212yes—
50C2×#387C2212yes—
51C2×#387C2212yes—
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#1445C2212yes—
63#1445C2212yes—
64#1445C2212yes—
65#1445C2211yescharacteristic
66#1444C2211yescharacteristic
67#1442C2211yescharacteristic
68#1442C2212yes—
69#1442C2211yescharacteristic
70#1442C2212yes—
71#1442C2212yes—
72#1441C2211yescharacteristic
73#1441C2211yescharacteristic
74#1441C2211yescharacteristic
75#1441C2211yescharacteristic
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1441C2212yes—
80#1441C2212yes—
81#1441C2211yescharacteristic
82#1441C2211yescharacteristic
83#1441C2212yes—
84#1440C2212yes—
85#1440C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1439C2212yes—
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2212yes—
97#1439C2212yes—
98#1439C2211yescharacteristic
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1437C2212yes—
108#1437C2212yes—
109#1437C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114C4⋊#95C2211yescharacteristic
115#1434C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118#1434C2212yes—
119#1434C2212yes—
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yes—
122C22⋊#95C2211yescharacteristic
123C4×#95C2212yes—
124C4×#95C2211yescharacteristic
125C23×D4C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C2×#123—24no—
132C2×#123—24no—
133C2×#123—24no—
134C2×#123—44no—
135C2×#123—42no—
136C2×C4×D4—24no—
137C2×C4×D4—24no—
138C2×C4×D4—44no—
139C2×C4×D4—42no—
140C2×C4×D4D418yes—
141C2×#117—24no—
142C2×#117—44no—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C42C2312yes—
186C22×C42C2311yescharacteristic
187C22×C42C2312yes—
188C22×C42C2312yes—
189C22×C42C2311yescharacteristic
190C22×C42C2312yes—
191#400—42no—
192#400—42no—
193#399—24no—
194#399—24no—
195#397—28no—
196#394—24no—
197#394—28no—
198#394—24no—
199#392—24no—
200#390—28no—
201#389—24no—
202#389—24no—
203#389—24no—
204#389—24no—
205#389—28no—
206#388—24no—
207#388—28no—
208#388—24no—
209#388—28no—
210#387—28no—
211#387—44no—
212#385—24no—
213#385—24no—
214#385—24no—
215#380—24no—
216#380—24no—
217#380—24no—
218C4×C4⋊C4—44no—
219C4×C22⋊C4—42no—
220C4×C22⋊C4—42no—
221C4×C22⋊C4—44no—
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2311yescharacteristic
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C25C2411yescharacteristic
268C25C2411yescharacteristic
269C25C2411yescharacteristic
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—42no—
277C22×D4—41no—
278C22×D4—41no—
279C22×D4—41no—
280C22×D4—41no—
281C22×D4—41no—
282C22×D4—41no—
283C22×D4—41no—
284C22×D4—42no—
285C22×D4—42no—
286C22×D4C2×D414yes—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—24no—
295C23×C4—42no—
296C23×C4—41no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322#123—416no—
323#123—416no—
324C4×D4—416no—
325C4×D4—416no—
326#117—416no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4C2×D414yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4C2×D414yes—
437C2×C22⋊C4C2×D414yes—
438C2×C22⋊C4#4114yes—
439C2×C42—24no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—24no—
443C2×C42—24no—
444C2×C42—24no—
445C2×C42—42no—
446C2×C42—41no—
447C2×C42—42no—
448C2×C42—42no—
449C2×C42—42no—
450C2×C42—42no—
451C2×C42—42no—
452C2×C42—42no—
453C2×C42—42no—
454C2×C42C2×D414yes—
455C2×C42#4118yes—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—24no—
464#95—22no—
465#95—24no—
466#95—22no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—24no—
476#95—24no—
477#95—42no—
478#95—42no—
479#95—42no—
480#95—42no—
481#95—42no—
482#95—42no—
483#95—42no—
484#95—42no—
485#95—42no—
486#95—42no—
487#95—42no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95—42no—
492#95—42no—
493#95—42no—
494#95—42no—
495#95—42no—
496#95—42no—
497#95—42no—
498#95—42no—
499#95—42no—
500#95—42no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—22no—
517C24—21no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24C22×D412yes—
532C24C22×D412yes—
533C24C2×#4112yes—
534C24C2511yescharacteristic
535C2×D4—28no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—82no—
550C2×D4—84no—
551C2×D4—84no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—44no—
663C22×C4—48no—
664C22×C4—48no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—48no—
669C22×C4—44no—
670C22×C4—82no—
671C22×C4—84no—
672C22×C4—84no—
673C22×C4—84no—
674C22×C4C22×D412yes—
675C22×C4C22×D412yes—
676C22×C4C22×D412yes—
677C22×C4C22×D412yes—
678C22×C4C22×D412yes—
679C22×C4C2×#4114yes—
680C22×C4C2×#4114yes—
681C22×C4C2×#4112yes—
682C22×C4C2×#4114yes—
683C22×C4C2×#4112yes—
684C22×C4H(5,𝔽2)14yes—
685C22×C4H(5,𝔽2)12yes—
686C22×C42−1+412yes—
687C4⋊C4—28no—
688C4⋊C4—48no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—48no—
692C4⋊C4—44no—
693C4⋊C4—48no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—48no—
699C4⋊C4—44no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—82no—
704C4⋊C4—84no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—44no—
708C22⋊C4—48no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—44no—
717C22⋊C4—48no—
718C22⋊C4—44no—
719C22⋊C4—48no—
720C22⋊C4—44no—
721C22⋊C4—48no—
722C22⋊C4—44no—
723C22⋊C4—84no—
724C22⋊C4—84no—
725C22⋊C4—82no—
726C22⋊C4—84no—
727C22⋊C4—84no—
728C22⋊C4—84no—
729C42—44no—
730C42—48no—
731C42—44no—
732C42—48no—
733C42—84no—
734C42—84no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—24no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23C23×D411yescharacteristic
805C23C22×#4112yes—
806C23C22×#4111yescharacteristic
807C23C2×H(5,𝔽2)12yes—
808C23C2×H(5,𝔽2)11yescharacteristic
809C23C2×2−1+411yescharacteristic
810C23#58511yescharacteristic
811C23#58511yescharacteristic
812C23#58512yes—
813C23#58512yes—
814C23#58511yescharacteristic
815D4—416no—
816D4—416no—
817D4—88no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—416no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—42no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—41no—
926C2×C4—42no—
927C2×C4—41no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—88no—
937C2×C4—88no—
938C2×C4#53214yes—
939C2×C4#53414yes—
940C2×C4#54614yes—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—44no—
947C22—44no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—81no—
961C22—82no—
962C22—82no—
963C22—82no—
964C22—82no—
965C22—82no—
966C22—82no—
967C22—82no—
968C22—82no—
969C22—82no—
970C22—82no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22C2×#53211yescharacteristic
975C22C2×#53411yescharacteristic
976C22#344911yescharacteristic
977C22#345912yes—
978C22#346012yes—
979C22C2×#54611yescharacteristic
980C22#347512yes—
981C22#348511yescharacteristic
982C22#348911yescharacteristic
983C22#349311yescharacteristic
984C22#349511yescharacteristic
985C22#350011yescharacteristic
986C22#350612yes—
987C22#350712yes—
988C22#351012yes—
989C22#351312yes—
990C22#353412yes—
991C22#353911yescharacteristic
992C22#353912yes—
993C22#354111yescharacteristic
994C22#354712yes—
995C22#356612yes—
996C22#356712yes—
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—44no—
1001C4—42no—
1002C4—44no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—82no—
1007C4—81no—
1008C4—82no—
1009C4—82no—
1010C4—82no—
1011C4—81no—
1012C4—81no—
1013C4—81no—
1014C4—82no—
1015C4—81no—
1016C4—82no—
1017C2—82no—
1018C2—82no—
1019C2—82no—
1020C2#3457511yescharacteristic
1021C2#3595911yescharacteristic
1022C2#3641511yescharacteristic
1023C2#3784711yescharacteristic
1024C2#3802211yescharacteristic
1025C2#3874312yes—
1026C2#3875312yes—
1027C2#4101712yes—
1028C2#4102512yes—
1029C2#4138211yescharacteristic
1030C2#4299211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2485C2semidirect
3. #17074C2semidirect
5. #17011C2semidirect
6. #16980C2semidirect
7. #16892C2semidirect
8. #16844C2semidirect
9. #16781C2semidirect
10. #16360C2semidirect
11. #15256C2semidirect
12. #15114C2semidirect
13. #14998C2semidirect
14. #14964C2semidirect
15. #14841C2semidirect
16. #14841C2semidirect
17. #14825C2semidirect
18. #14322C2semidirect
19. #14287C2semidirect
20. #14070C2semidirect
21. #14060C2semidirect
22. #13839C2semidirect
23. #13820C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24552
#170742
#170222
#170112
#169802
#168922
#168442
#167812
#163602
#152562
#151142
#149982
#149642
#148412
#148252
#143222
#142872
#140702
#140602
#138392
#138202