Finite Group Databasebeta

← #1295166

Subgroups — #1295166

Order 512.

2371 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2494C211yesmaximal, characteristic, complemented
2C2×#2476C211yesmaximal, characteristic
3#17029C211yesmaximal, characteristic, complemented
4#16986C211yesmaximal, characteristic, complemented
5#16982C211yesmaximal, characteristic, complemented
6#16363C211yesmaximal, characteristic
7#15748C212yesmaximal, complemented
8#15610C212yesmaximal, complemented
9#15415C212yesmaximal, complemented
10#15401C212yesmaximal, complemented
11#15175C211yesmaximal, characteristic, complemented
12#15047C211yesmaximal, characteristic, complemented
13#14910C211yesmaximal, characteristic, complemented
14#14893C211yesmaximal, characteristic, complemented
15#14826C211yesmaximal, characteristic, complemented
16#14802C212yesmaximal, complemented
17#14741C212yesmaximal, complemented
18#14573C212yesmaximal, complemented
19#14571C212yesmaximal, complemented
20#14271C211yesmaximal, characteristic
21#14231C211yesmaximal, characteristic, complemented
22#13957C211yesmaximal, characteristic, complemented
23#13809C211yesmaximal, characteristic, complemented
24C22×#121C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2494—28no—
27#2476—28no—
28C2×#401C2212yes—
29C2×#400C2211yescharacteristic
30C2×#399C2211yescharacteristic
31C2×#399C2211yescharacteristic
32C2×#398C2211yescharacteristic
33C2×#397C2212yes—
34C2×#394C2211yescharacteristic
35C2×#394C2211yescharacteristic
36C2×#394C2212yes—
37C2×#394C2211yescharacteristic
38C2×#394C2212yes—
39C2×#390C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#388C2211yescharacteristic
44C2×#388C2211yescharacteristic
45C2×#388C2211yescharacteristic
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#387C2211yescharacteristic
51C2×#387C2212yes—
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#385C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×#376C2211yescharacteristic
64C22×#95C2211yescharacteristic
65#1445C2212yes—
66#1445C2212yes—
67#1445C2211yescharacteristic
68#1444C2212yes—
69#1444C2212yes—
70#1444C2212yes—
71#1444C2211yescharacteristic
72#1444C2211yescharacteristic
73#1443C2212yes—
74#1443C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1442C2211yescharacteristic
81#1442C2212yes—
82#1441C2211yescharacteristic
83#1441C2212yes—
84#1441C2211yescharacteristic
85#1441C2211yescharacteristic
86#1440C2212yes—
87#1440C2212yes—
88#1439C2212yes—
89#1439C2211yescharacteristic
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2211yescharacteristic
94#1439C2212yes—
95#1439C2211yescharacteristic
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2211yescharacteristic
101#1439C2211yescharacteristic
102#1438C2212yes—
103#1438C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111C4⋊#95C2212yes—
112#1434C2212yes—
113#1434C2211yescharacteristic
114#1434C2211yescharacteristic
115#1434C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2211yescharacteristic
125C23×D4C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2312yes—
130C24×C4C2311yescharacteristic
131C2×#121—24no—
132C2×#121—24no—
133C2×#121—42no—
134C2×#117—24no—
135C2×#117—24no—
136C2×#117—42no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2312yes—
177C22×C42C2311yescharacteristic
178C22×C42C2312yes—
179C22×C42C2311yescharacteristic
180C22×C42C2312yes—
181C22×C42C2312yes—
182C22×C42C2311yescharacteristic
183#401—28no—
184#400—42no—
185#399—24no—
186#399—42no—
187#398—24no—
188#397—28no—
189#394—24no—
190#394—24no—
191#394—28no—
192#394—28no—
193#394—24no—
194#390—24no—
195#389—24no—
196#389—24no—
197#389—44no—
198#388—28no—
199#388—24no—
200#388—24no—
201#388—24no—
202#388—44no—
203#388—44no—
204#387—24no—
205#387—28no—
206#387—44no—
207#386—24no—
208#386—24no—
209#386—44no—
210#386—44no—
211#385—24no—
212#382—24no—
213#380—24no—
214#380—24no—
215C4×C4⋊C4—24no—
216C4×C22⋊C4—28no—
217C4×C22⋊C4D418yes—
218#376—42no—
219C2×#95—42no—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2311yescharacteristic
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2311yescharacteristic
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C25C2411yescharacteristic
268C25C2411yescharacteristic
269C25C2411yescharacteristic
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—41no—
279C22×D4—41no—
280C22×D4—41no—
281C22×D4—42no—
282C22×D4—42no—
283C22×D4—42no—
284C22×D4—42no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—24no—
292C23×C4—41no—
293C23×C4—41no—
294C23×C4—41no—
295C23×C4—41no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4C2×D414yes—
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2411yescharacteristic
321C23×C4C2412yes—
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324#121—416no—
325#117—416no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
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—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
431C2×C22⋊C4C2×D414yes—
432C2×C22⋊C4#4114yes—
433C2×C22⋊C4#4118yes—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—24no—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—24no—
442C2×C42—41no—
443C2×C42—42no—
444C2×C42—42no—
445C2×C42—42no—
446C2×C42—42no—
447C2×C42—42no—
448C2×C42—42no—
449C2×C42C2×D414yes—
450C2×C42C2×D414yes—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95—24no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—24no—
477#95—24no—
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#95C2×D414yes—
497#95C2×D414yes—
498C24—21no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—22no—
509C24—22no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—22no—
519C24—21no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—22no—
527C24—22no—
528C24C22×D412yes—
529C24C2×#4112yes—
530C24C2×#4114yes—
531C24C2511yescharacteristic
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—48no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—48no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—82no—
541C2×D4—82no—
542C2×D4—84no—
543C2×D4—84no—
544C2×D4—82no—
545C2×D4—84no—
546C2×D4—84no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
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—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—28no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
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—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—48no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—48no—
666C22×C4—84no—
667C22×C4—84no—
668C22×C4—84no—
669C22×C4—84no—
670C22×C4—84no—
671C22×C4—84no—
672C22×C4—84no—
673C22×C4C22×D412yes—
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×#4112yes—
683C22×C4H(5,𝔽2)14yes—
684C22×C4H(5,𝔽2)12yes—
685C22×C42−1+412yes—
686C4⋊C4—48no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—48no—
693C4⋊C4—44no—
694C4⋊C4—48no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—82no—
698C4⋊C4—84no—
699C4⋊C4—82no—
700C4⋊C4—84no—
701C4⋊C4—84no—
702C22⋊C4—28no—
703C22⋊C4—28no—
704C22⋊C4—44no—
705C22⋊C4—48no—
706C22⋊C4—44no—
707C22⋊C4—48no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—82no—
715C22⋊C4—82no—
716C22⋊C4—84no—
717C22⋊C4—84no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C22⋊C4—84no—
721C22⋊C4—84no—
722C22⋊C4—82no—
723C22⋊C4—84no—
724C22⋊C4—84no—
725C22⋊C4—84no—
726C42—28no—
727C42—44no—
728C42—48no—
729C42—44no—
730C42—84no—
731C42—84no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—24no—
736C23—22no—
737C23—22no—
738C23—24no—
739C23—24no—
740C23—22no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—24no—
746C23—22no—
747C23—22no—
748C23—24no—
749C23—41no—
750C23—41no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—41no—
755C23—41no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—41no—
773C23—41no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—42no—
782C23—41no—
783C23—41no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—41no—
788C23—41no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23#53214yes—
801C23C23×D411yescharacteristic
802C23C22×#4112yes—
803C23C22×#4111yescharacteristic
804C23C2×H(5,𝔽2)11yescharacteristic
805C23C2×H(5,𝔽2)12yes—
806C23C2×2−1+411yescharacteristic
807C23#58511yescharacteristic
808C23#58512yes—
809C23#58511yescharacteristic
810C23#58512yes—
811C23#58511yescharacteristic
812D4—88no—
813D4—88no—
814D4—88no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—416no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—42no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—42no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—41no—
909C2×C4—42no—
910C2×C4—41no—
911C2×C4—41no—
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—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—88no—
936C2×C4—816no—
937C2×C4#54614yes—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—44no—
942C22—42no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—44no—
950C22—42no—
951C22—44no—
952C22—42no—
953C22—42no—
954C22—81no—
955C22—81no—
956C22—82no—
957C22—82no—
958C22—81no—
959C22—81no—
960C22—82no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—82no—
965C22—82no—
966C22—82no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#53211yescharacteristic
972C22#344911yescharacteristic
973C22#344911yescharacteristic
974C22C2×#54611yescharacteristic
975C22#348112yes—
976C22#348511yescharacteristic
977C22#348911yescharacteristic
978C22#349112yes—
979C22#349311yescharacteristic
980C22#349312yes—
981C22#349511yescharacteristic
982C22#349811yescharacteristic
983C22#351512yes—
984C22#351912yes—
985C22#352112yes—
986C22#352112yes—
987C22#353312yes—
988C22#353912yes—
989C22#354011yescharacteristic
990C22#354111yescharacteristic
991C22#354512yes—
992C22#354712yes—
993C22#356012yes—
994C4—24no—
995C4—44no—
996C4—42no—
997C4—42no—
998C4—44no—
999C4—44no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—82no—
1006C4—81no—
1007C4—82no—
1008C4—81no—
1009C4—82no—
1010C4—82no—
1011C4—81no—
1012C4—82no—
1013C4—81no—
1014C2—44no—
1015C2—82no—
1016C2—161no—
1017C2#3511911yescharacteristic
1018C2#3604511yescharacteristic
1019C2#3636211yescharacteristic
1020C2#3784411yescharacteristic
1021C2#3890111yescharacteristic
1022C2#4195411yescharacteristic
1023C2#4230311yescharacteristic
1024C2#4377612yes—
1025C2#4468212yes—
1026C2#4846012yes—
1027C2#4847012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2494C2semidirect
3. #17029C2semidirect
4. #16986C2semidirect
5. #16982C2semidirect
7. #15748C2semidirect
8. #15610C2semidirect
9. #15415C2semidirect
10. #15401C2semidirect
11. #15175C2semidirect
12. #15047C2semidirect
13. #14910C2semidirect
14. #14893C2semidirect
15. #14826C2semidirect
16. #14802C2semidirect
17. #14741C2semidirect
18. #14573C2semidirect
19. #14571C2semidirect
21. #14231C2semidirect
22. #13957C2semidirect
23. #13809C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24942
C2×#24762
#170292
#169862
#169822
#163632
#157482
#156102
#154152
#154012
#151752
#150472
#149102
#148932
#148262
#148022
#147412
#145732
#145712
#142712
#142312
#139572
#138092