Finite Group Databasebeta

← #1393416

Subgroups — #1393416

Order 512.

2366 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2453C211yesmaximal, characteristic
2C2×#2634C211yesmaximal, characteristic
3C2×#2399C211yesmaximal, characteristic
4C2×#2365C211yesmaximal, characteristic
5#17070C211yesmaximal, characteristic
6#16813C211yesmaximal, characteristic
7#16683C211yesmaximal, characteristic
8#16663C211yesmaximal, characteristic
9#16529C212yesmaximal
10#16507C212yesmaximal
11#16337C212yesmaximal
12#16281C212yesmaximal
13#15164C211yesmaximal, characteristic
14#14908C211yesmaximal, characteristic
15#14884C211yesmaximal, characteristic
16#14881C211yesmaximal, characteristic
17#14879C211yesmaximal, characteristic
18#14791C212yesmaximal
19#14787C212yesmaximal
20#14314C211yesmaximal, characteristic
21#14191C212yesmaximal
22#14117C212yesmaximal
23#13900C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29#2634—28no—
30#2453—28no—
31#2399—28no—
32C2×#400C2211yescharacteristic
33C2×#400C2211yescharacteristic
34C2×#400C2212yes—
35C2×#400C2212yes—
36C2×#400C2211yescharacteristic
37C2×#398C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#398C2212yes—
40C2×#398C2212yes—
41C2×#398C2212yes—
42C2×#398C2211yescharacteristic
43C2×#395C2211yescharacteristic
44C2×#395C2211yescharacteristic
45C2×#395C2212yes—
46C2×#395C2212yes—
47C2×#395C2211yescharacteristic
48#2365—28no—
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2212yes—
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#387C2211yescharacteristic
59C2×#387C2211yescharacteristic
60C2×#387C2212yes—
61C2×#387C2212yes—
62C2×#387C2212yes—
63C2×#387C2211yescharacteristic
64C2×#387C2211yescharacteristic
65C2×#387C2212yes—
66C2×#383C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2212yes—
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C4⋊C4C2212yes—
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×#376C2211yescharacteristic
74#1446C2211yescharacteristic
75#1446C2212yes—
76#1446C2212yes—
77#1445C2212yes—
78#1445C2211yescharacteristic
79#1445C2211yescharacteristic
80#1445C2212yes—
81#1445C2212yes—
82#1445C2212yes—
83#1445C2212yes—
84#1444C2212yes—
85#1444C2212yes—
86#1444C2212yes—
87#1444C2212yes—
88#1443C2212yes—
89#1443C2212yes—
90#1443C2212yes—
91#1442C2212yes—
92#1442C2211yescharacteristic
93#1442C2212yes—
94#1442C2212yes—
95#1442C2212yes—
96#1442C2212yes—
97#1442C2212yes—
98#1442C2212yes—
99#1441C2211yescharacteristic
100#1441C2212yes—
101#1441C2211yescharacteristic
102#1441C2211yescharacteristic
103#1441C2212yes—
104#1441C2212yes—
105#1441C2212yes—
106#1441C2212yes—
107#1441C2212yes—
108#1441C2212yes—
109#1441C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117#1436C2212yes—
118#1436C2212yes—
119#1436C2212yes—
120#1436C2212yes—
121#1436C2212yes—
122C4⋊#95C2211yescharacteristic
123#1434C2211yescharacteristic
124#1434C2211yescharacteristic
125#1434C2212yes—
126#1434C2211yescharacteristic
127C23×Q8C2311yescharacteristic
128C23×Q8C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C2×C4⋊Q8—24no—
131C2×C4⋊Q8—24no—
132C2×C4⋊Q8—24no—
133C2×#125—24no—
134C2×#125—24no—
135C2×#125—42no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—24no—
140C2×C4×Q8—24no—
141C2×C4×Q8—24no—
142C2×C4×Q8—42no—
143C2×C4×Q8—42no—
144C2×C4×Q8—42no—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183#400—24no—
184#400—28no—
185#400—24no—
186#400—28no—
187#400—42no—
188#398—24no—
189#398—24no—
190#398—28no—
191#398—28no—
192#398—28no—
193#398D418yes—
194#395—28no—
195#395—28no—
196#395—24no—
197#395—24no—
198#395—42no—
199#391—24no—
200#391—24no—
201#391—24no—
202#391—24no—
203#389—24no—
204#389—28no—
205#389—24no—
206#389—24no—
207#389—24no—
208#387—28no—
209#387—24no—
210#387—24no—
211#387—28no—
212#387—24no—
213#387—24no—
214#387—28no—
215#387—28no—
216#383—24no—
217C4×C4⋊C4—24no—
218C4×C4⋊C4—24no—
219C4×C4⋊C4—28no—
220C4×C4⋊C4—24no—
221C4×C4⋊C4—28no—
222C4×C4⋊C4D418yes—
223#376—24no—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2311yescharacteristic
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—24no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—41no—
297C22×Q8—41no—
298C22×Q8—42no—
299C22×Q8—41no—
300C22×Q8—41no—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C4⋊Q8—232no—
325#125—416no—
326C4×Q8—416no—
327C4×Q8—416no—
328C4×Q8—416no—
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—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
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—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4C2×D414yes—
402C2×C4⋊C4C2×D414yes—
403C2×C4⋊C4C2×D414yes—
404C2×C4⋊C4C2×D414yes—
405C2×C4⋊C4C2×D418yes—
406C2×C4⋊C4#4114yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—41no—
428C2×C42—41no—
429C2×C42—42no—
430C2×C42—41no—
431C2×C42—41no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436C2×C42C2×D414yes—
437C2×C42#4114yes—
438#95—22no—
439#95—24no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
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—22no—
475#95—24no—
476#95—24no—
477#95—24no—
478#95—24no—
479#95—24no—
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#95C2×D414yes—
493#95C2×D418yes—
494#95C2×D414yes—
495#95C2×D414yes—
496C24C2511yescharacteristic
497C2×Q8—28no—
498C2×Q8—28no—
499C2×Q8—28no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—48no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—48no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
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—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4C22×D412yes—
635C22×C4C22×D414yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D414yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C22×D412yes—
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4C2×#4112yes—
649C22×C4C2×#4112yes—
650C22×C4C2×#4112yes—
651C22×C4C2×#4112yes—
652C22×C4H(5,𝔽2)12yes—
653C22×C42−1+414yes—
654C22×C42−1+414yes—
655C22×C42−1+414yes—
656C22×C42−1+412yes—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—216no—
665C4⋊C4—44no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—84no—
683C4⋊C4—84no—
684C42—216no—
685C42—28no—
686C42—28no—
687C42—28no—
688C42—44no—
689C42—44no—
690C42—44no—
691C42—48no—
692C42—44no—
693C42—44no—
694C42—44no—
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×2−1+412yes—
701C23C2×2−1+411yescharacteristic
702C23C2×2−1+412yes—
703C23C2×2−1+412yes—
704C23#58512yes—
705C23#58511yescharacteristic
706Q8—416no—
707Q8—416no—
708Q8—416no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
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—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4#52514yes—
847C2×C4#53614yes—
848C2×C4D4214yes—
849C2×C4#54714yes—
850C22C2×#52511yescharacteristic
851C22C2×#53611yescharacteristic
852C22#344911yescharacteristic
853C22#346112yes—
854C22#346112yes—
855C22C2×D4211yescharacteristic
856C22C2×#54711yescharacteristic
857C22D4×#4111yescharacteristic
858C22#348611yescharacteristic
859C22#348612yes—
860C22#348911yescharacteristic
861C22#348912yes—
862C22#349911yescharacteristic
863C22#350611yescharacteristic
864C22#350912yes—
865C22#352011yescharacteristic
866C22#352312yes—
867C22#353512yes—
868C22#355212yes—
869C22#355512yes—
870C22#355512yes—
871C22#355612yes—
872C22#356412yes—
873C4—24no—
874C4—24no—
875C4—24no—
876C4—24no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—44no—
884C4—42no—
885C4—42no—
886C4—44no—
887C4—42no—
888C4—44no—
889C4—81no—
890C4—81no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—82no—
896C2#3460211yescharacteristic
897C2#3574911yescharacteristic
898C2#3610011yescharacteristic
899C2#3765311yescharacteristic
900C2#3767511yescharacteristic
901C2#3779312yes—
902C2#3781112yes—
903C2#4102412yes—
904C2#4119412yes—
905C2#4231511yescharacteristic
906C2#4281111yescharacteristic
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×#24532
C2×#26342
C2×#23992
C2×#23652
#170702
#168132
#166832
#166632
#165292
#165072
#163372
#162812
#151642
#149082
#148842
#148812
#148792
#147912
#147872
#143142
#141912
#141172
#139002