Finite Group Databasebeta

← #1259348

Subgroups — #1259348

Order 512.

2426 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2581C211yesmaximal, characteristic
2C2×#2584C211yesmaximal, characteristic
3C2×#2462C211yesmaximal, characteristic
4C2×#2351C211yesmaximal, characteristic
5#16964C211yesmaximal, characteristic
6#16705C211yesmaximal, characteristic
7#16634C211yesmaximal, characteristic
8#16517C211yesmaximal, characteristic
9#15969C212yesmaximal
10#15968C212yesmaximal
11#15360C212yesmaximal
12#15347C212yesmaximal
13#15158C211yesmaximal, characteristic
14#14880C211yesmaximal, characteristic
15#14879C211yesmaximal, characteristic
16#14876C211yesmaximal, characteristic
17#14869C211yesmaximal, characteristic
18#14818C212yesmaximal
19#14816C212yesmaximal
20#14404C212yesmaximal
21#14385C212yesmaximal
22#14302C211yesmaximal, characteristic
23#13889C211yesmaximal, characteristic
24C22×#125C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29#2584—28no—
30#2581—28no—
31#2462—28no—
32C2×#400C2211yescharacteristic
33C2×#400C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#398C2211yescharacteristic
36C2×#398C2211yescharacteristic
37C2×#398C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#398C2211yescharacteristic
40C2×#398C2212yes—
41C2×#395C2211yescharacteristic
42C2×#395C2211yescharacteristic
43C2×#395C2211yescharacteristic
44C2×#395C2211yescharacteristic
45C2×#395C2212yes—
46C2×#395C2211yescharacteristic
47#2351—28no—
48C2×#391C2212yes—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2212yes—
54C2×#389C2211yescharacteristic
55C2×#389C2212yes—
56C2×#389C2211yescharacteristic
57C2×#389C2212yes—
58C2×#389C2212yes—
59C2×#389C2212yes—
60C2×#389C2212yes—
61C2×#387C2211yescharacteristic
62C2×#387C2211yescharacteristic
63C2×#387C2211yescharacteristic
64C2×#387C2212yes—
65C2×#387C2211yescharacteristic
66C2×#387C2212yes—
67C2×#387C2212yes—
68C2×#387C2211yescharacteristic
69C2×#387C2211yescharacteristic
70C2×#387C2212yes—
71C2×#382C2212yes—
72C2×#382C2211yescharacteristic
73C2×#382C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2212yes—
76C2×C4×C4⋊C4C2211yescharacteristic
77#1446C2211yescharacteristic
78#1445C2212yes—
79#1445C2211yescharacteristic
80#1445C2211yescharacteristic
81#1445C2212yes—
82#1445C2212yes—
83#1444C2212yes—
84#1444C2212yes—
85#1444C2212yes—
86#1443C2212yes—
87#1443C2212yes—
88#1442C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1442C2211yescharacteristic
92#1442C2212yes—
93#1442C2212yes—
94#1442C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2211yescharacteristic
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1441C2211yescharacteristic
103#1441C2212yes—
104#1441C2212yes—
105#1441C2212yes—
106#1441C2211yescharacteristic
107#1441C2212yes—
108#1441C2212yes—
109#1441C2212yes—
110#1441C2212yes—
111#1441C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117#1436C2212yes—
118#1436C2212yes—
119#1436C2212yes—
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2212yes—
122#1434C2212yes—
123#1434C2211yescharacteristic
124#1434C2211yescharacteristic
125#1434C2212yes—
126#1434C2211yescharacteristic
127C23×Q8C2311yescharacteristic
128C23×Q8C2311yescharacteristic
129C2×#125—24no—
130C2×#125—24no—
131C2×#125—42no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—28no—
140C2×C4×Q8—42no—
141C2×C4×Q8—42no—
142C2×C4×Q8—42no—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C42C2312yes—
176C22×C42C2312yes—
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2312yes—
183C22×C42C2312yes—
184#400—24no—
185#400—24no—
186#400—42no—
187#398—24no—
188#398—24no—
189#398—24no—
190#398—24no—
191#398—42no—
192#398—44no—
193#395—24no—
194#395—24no—
195#395—24no—
196#395—24no—
197#395—44no—
198#395D418yes—
199#391—28no—
200#389—28no—
201#389—28no—
202#389—28no—
203#389—28no—
204#389—28no—
205#389—24no—
206#389—24no—
207#389—24no—
208#389—28no—
209#389—28no—
210#389—28no—
211#389—24no—
212#387—28no—
213#387—24no—
214#387—24no—
215#387—24no—
216#387—24no—
217#387—24no—
218#387—28no—
219#387—28no—
220#387—24no—
221#387—44no—
222#382—24no—
223#382—24no—
224#382—28no—
225C4×C4⋊C4—24no—
226C4×C4⋊C4—28no—
227C4×C4⋊C4D418yes—
228C2×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2311yescharacteristic
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2311yescharacteristic
236C2×#95C2311yescharacteristic
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2311yescharacteristic
240C2×#95C2311yescharacteristic
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2311yescharacteristic
266C2×#95C2312yes—
267C2×#95C2311yescharacteristic
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—24no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—24no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—41no—
294C22×Q8—41no—
295C22×Q8C2×D414yes—
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319#125—416no—
320C4×Q8—232no—
321C4×Q8—416no—
322C4×Q8—416no—
323C4×Q8—416no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
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—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4C2×D414yes—
413C2×C4⋊C4C2×D414yes—
414C2×C4⋊C4C2×D414yes—
415C2×C4⋊C4C2×D418yes—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—41no—
435C2×C42—41no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42C2×D414yes—
439C2×C42C2×D414yes—
440C2×C42C2×D414yes—
441C2×C42#4118yes—
442#95—24no—
443#95—22no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—22no—
466#95—24no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—22no—
477#95—24no—
478#95—24no—
479#95—24no—
480#95—24no—
481#95—24no—
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#95C2×D414yes—
495#95C2×D414yes—
496#95C2×D414yes—
497#95C2×D418yes—
498C24C2511yescharacteristic
499C2×Q8—28no—
500C2×Q8—28no—
501C2×Q8—216no—
502C2×Q8—28no—
503C2×Q8—28no—
504C2×Q8—216no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
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—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4C22×D412yes—
631C22×C4C22×D414yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C22×D414yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4114yes—
645C22×C4H(5,𝔽2)12yes—
646C22×C4H(5,𝔽2)12yes—
647C22×C42−1+414yes—
648C22×C42−1+412yes—
649C22×C42−1+414yes—
650C22×C42−1+412yes—
651C22×C42−1+414yes—
652C4⋊C4—216no—
653C4⋊C4—28no—
654C4⋊C4—216no—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—28no—
658C4⋊C4—216no—
659C4⋊C4—48no—
660C4⋊C4—44no—
661C4⋊C4—48no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—48no—
680C4⋊C4—48no—
681C4⋊C4—84no—
682C4⋊C4—84no—
683C4⋊C4—84no—
684C42—28no—
685C42—216no—
686C42—28no—
687C42—28no—
688C42—48no—
689C42—48no—
690C42—44no—
691C42—44no—
692C42—84no—
693C23C23×D411yescharacteristic
694C23C23×D411yescharacteristic
695C23C22×#4112yes—
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×H(5,𝔽2)11yescharacteristic
698C23C2×2−1+412yes—
699C23C2×2−1+411yescharacteristic
700C23C2×2−1+412yes—
701C23C2×2−1+411yescharacteristic
702C23C2×2−1+412yes—
703C23#58511yescharacteristic
704Q8—232no—
705Q8—416no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4#52514yes—
843C2×C4#53614yes—
844C2×C4#53714yes—
845C2×C4D4214yes—
846C2×C4#54718yes—
847C22C2×#52511yescharacteristic
848C22C2×#53611yescharacteristic
849C22C2×#53711yescharacteristic
850C22C2×D4211yescharacteristic
851C22C2×#54712yes—
852C22#348611yescharacteristic
853C22#348611yescharacteristic
854C22#348612yes—
855C22#348811yescharacteristic
856C22#348911yescharacteristic
857C22#349212yes—
858C22#349512yes—
859C22#349911yescharacteristic
860C22#350912yes—
861C22#350912yes—
862C22#351112yes—
863C22#353611yescharacteristic
864C22#354111yescharacteristic
865C22#355212yes—
866C22#355212yes—
867C22#355512yes—
868C22#355612yes—
869C22#355612yes—
870C4—24no—
871C4—28no—
872C4—24no—
873C4—24no—
874C4—24no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4—44no—
881C4—42no—
882C4—42no—
883C4—44no—
884C4—81no—
885C4—81no—
886C4—82no—
887C4—81no—
888C4—82no—
889C4—81no—
890C4—82no—
891C4—82no—
892C4—81no—
893C2#3529711yescharacteristic
894C2#3608611yescharacteristic
895C2#3610311yescharacteristic
896C2#3764911yescharacteristic
897C2#3767511yescharacteristic
898C2#4279111yescharacteristic
899C2#4281111yescharacteristic
900C2#4533312yes—
901C2#4533412yes—
902C2#5073212yes—
903C2#5135112yes—
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25812
C2×#25842
C2×#24622
C2×#23512
#169642
#167052
#166342
#165172
#159692
#159682
#153602
#153472
#151582
#148802
#148792
#148762
#148692
#148182
#148162
#144042
#143852
#143022
#138892