Finite Group Databasebeta

← #522470

Subgroups — #522470

Order 512.

3898 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2362C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic
4#14384C212yesmaximal, complemented
5#14383C212yesmaximal, complemented
6#14366C212yesmaximal
7#14365C212yesmaximal
8#14269C212yesmaximal, complemented
9#14138C211yesmaximal, characteristic, complemented
10#14129C211yesmaximal, characteristic, complemented
11#14075C212yesmaximal, complemented
12#14067C212yesmaximal, complemented
13#13997C211yesmaximal, characteristic, complemented
14#13997C211yesmaximal, characteristic, complemented
15#13994C211yesmaximal, characteristic, complemented
16#13993C211yesmaximal, characteristic, complemented
17#13974C211yesmaximal, characteristic, complemented
18#13973C211yesmaximal, characteristic, complemented
19#13969C211yesmaximal, characteristic, complemented
20#13969C211yesmaximal, characteristic, complemented
21#13801C211yesmaximal, characteristic, complemented
22#13789C212yesmaximal, complemented
23C4×#379C211yesmaximal, characteristic
24C25×C4C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic, complemented
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2848C4116yescomplemented
32#2362—28no—
33C2×#391C2211yescharacteristic, complemented
34C2×#391C2211yescharacteristic, complemented
35C2×#391C2211yescharacteristic, complemented
36C2×#389C2211yescharacteristic, complemented
37C2×#389C2211yescharacteristic, complemented
38C2×#389C2211yescharacteristic, complemented
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#387C2212yescomplemented
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47#2280—28no—
48C2×#381C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#379C2211yescharacteristic
57C2×#379C2212yes—
58C2×#379C2211yescharacteristic
59C2×#379C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic, complemented
61C2×C4×C4⋊C4C2212yescomplemented
62C2×C4×C4⋊C4C2211yescharacteristic, complemented
63C2×C4×C4⋊C4C2211yescharacteristic, complemented
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67C2×C4×C22⋊C4C2212yes—
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72#1445C2212yescomplemented
73#1445C2212yescomplemented
74#1443C2212yescomplemented
75#1443C2212yescomplemented
76#1442C2212yescomplemented
77#1442C2212yescomplemented
78#1441C2212yescomplemented
79#1441C2212yescomplemented
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1440C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1437C2212yes—
93#1437C2212yes—
94#1437C2212yes—
95#1437C2212yes—
96#1437C2212yes—
97#1437C2212yes—
98#1437C2212yes—
99#1437C2212yes—
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107#1436C2212yescomplemented
108C4⋊#95C2212yescomplemented
109C4⋊#95C2212yescomplemented
110C4⋊#95C2211yescharacteristic, complemented
111C4⋊#95C2211yescharacteristic, complemented
112C4⋊#95C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2211yescharacteristic, complemented
116#1434C2212yescomplemented
117#1434C2212yescomplemented
118#1434C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C4×#95C2212yescomplemented
126C26C2311yescharacteristic
127C23×Q8C2311yescharacteristic
128C24×C4—24no—
129C24×C4—24no—
130C24×C4—42no—
131C24×C4—42no—
132C24×C4—42no—
133C24×C4—42no—
134C24×C4C2×C418yes—
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—42no—
144C2×C22⋊Q8—42no—
145C2×C22⋊Q8—42no—
146C2×C22⋊Q8—42no—
147C2×C22⋊Q8C2×C418yes—
148C2×C22⋊Q8C2×C418yes—
149C2×C22⋊Q8C2×C418yes—
150C2×C4×Q8—24no—
151C2×C4×Q8—42no—
152C2×C4×Q8—42no—
153C2×#117—24no—
154C2×#117—42no—
155C2×#117—42no—
156C2×#117—42no—
157C2×#117—42no—
158C2×#117D418yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204C22×C42C2312yes—
205C22×C42C2312yes—
206C22×C42C2312yes—
207#391—24no—
208#391—42no—
209#391—42no—
210#389—24no—
211#389—42no—
212#389—42no—
213#388—28no—
214#388—28no—
215#388—28no—
216#388—28no—
217#387—28no—
218#385C2×C4116yes—
219#385C2×C4116yes—
220#385C2×C4116yes—
221#381—28no—
222#380—24no—
223#380—24no—
224#380—24no—
225#380—24no—
226#380C2×C418yes—
227#380C2×C418yes—
228#380C2×C418yes—
229#379—28no—
230#379—24no—
231#379—24no—
232#379C2×C4116yes—
233C4×C4⋊C4—24no—
234C4×C4⋊C4—28no—
235C4×C4⋊C4—42no—
236C4×C4⋊C4—42no—
237C4×C22⋊C4—24no—
238C4×C22⋊C4—24no—
239C4×C22⋊C4—28no—
240C4×C22⋊C4—28no—
241C4×C22⋊C4—42no—
242C4×C22⋊C4—42no—
243C4×C22⋊C4—42no—
244C4×C22⋊C4—42no—
245C2×#95C2311yescharacteristic
246C2×#95C2312yes—
247C2×#95C2311yescharacteristic
248C2×#95C2311yescharacteristic
249C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C25—22no—
289C25—22no—
290C25—22no—
291C25—22no—
292C25—22no—
293C25—22no—
294C25—41no—
295C25—41no—
296C25—41no—
297C25—41no—
298C25—41no—
299C25—41no—
300C25—41no—
301C25—41no—
302C25C22×C414yes—
303C25C2411yescharacteristic
304C25C2411yescharacteristic
305C25C2411yescharacteristic
306C22×Q8—22no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8C22×C414yes—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—232no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—416no—
337C23×C4—416no—
338C23×C4—41no—
339C23×C4—41no—
340C23×C4—41no—
341C23×C4—41no—
342C23×C4—41no—
343C23×C4—41no—
344C23×C4—41no—
345C23×C4—41no—
346C23×C4—41no—
347C23×C4—41no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—416no—
351C23×C4—416no—
352C23×C4—416no—
353C23×C4—416no—
354C23×C4C22×C414yes—
355C23×C4C22×C414yes—
356C23×C4C22×C414yes—
357C23×C4C22×C414yes—
358C23×C4C22×C414yes—
359C23×C4C22×C414yes—
360C23×C4C2×D414yes—
361C23×C4#4114yes—
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2411yescharacteristic
367C23×C4C2411yescharacteristic
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C22⋊Q8—232no—
383C22⋊Q8—416no—
384C22⋊Q8—416no—
385C4×Q8—416no—
386#117—416no—
387#117—416no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4C22×C414yes—
423C2×C4⋊C4C22×C414yes—
424C2×C4⋊C4C22×C414yes—
425C2×C4⋊C4C22×C418yes—
426C2×C4⋊C4C22×C418yes—
427C2×C4⋊C4C22×C418yes—
428C2×C4⋊C4C2×D414yes—
429C2×C4⋊C4C2×D414yes—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—41no—
466C2×C22⋊C4—41no—
467C2×C22⋊C4—41no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4—41no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—41no—
476C2×C22⋊C4—41no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—41no—
489C2×C22⋊C4—41no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4C22×C418yes—
494C2×C22⋊C4C22×C418yes—
495C2×C22⋊C4C22×C418yes—
496C2×C22⋊C4C22×C418yes—
497C2×C22⋊C4C22×C418yes—
498C2×C22⋊C4C22×C418yes—
499C2×C22⋊C4C2×D418yes—
500C2×C22⋊C4#4114yes—
501C2×C22⋊C4#4114yes—
502C2×C42—24no—
503C2×C42—22no—
504C2×C42—24no—
505C2×C42—22no—
506C2×C42—24no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—24no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—24no—
519C2×C42—42no—
520C2×C42—42no—
521C2×C42—42no—
522C2×C42—42no—
523C2×C42—42no—
524C2×C42—42no—
525C2×C42—42no—
526C2×C42—42no—
527C2×C42—42no—
528C2×C42—42no—
529C2×C42—42no—
530C2×C42—42no—
531C2×C42C2×D418yes—
532#95—22no—
533#95—24no—
534#95—24no—
535#95—24no—
536#95—24no—
537#95—22no—
538#95—24no—
539#95—24no—
540#95—24no—
541#95—24no—
542#95—22no—
543#95—22no—
544#95—24no—
545#95—24no—
546#95—24no—
547#95—24no—
548#95—42no—
549#95—42no—
550#95—42no—
551#95—42no—
552#95—42no—
553#95—42no—
554#95—42no—
555#95—42no—
556#95—41no—
557#95—41no—
558#95—41no—
559#95—41no—
560#95—41no—
561#95—41no—
562#95—41no—
563#95—41no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95—42no—
568#95—42no—
569#95—42no—
570#95—42no—
571#95—42no—
572#95C22×C418yes—
573#95C22×C418yes—
574#95C22×C418yes—
575C24—21no—
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C24—21no—
581C24—21no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—28no—
612C24—28no—
613C24—28no—
614C24—44no—
615C24—44no—
616C24—44no—
617C24—44no—
618C24—44no—
619C24—44no—
620C24—44no—
621C24—44no—
622C24—44no—
623C24—44no—
624C24—44no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24—44no—
634C24—44no—
635C24—44no—
636C24—44no—
637C24—44no—
638C24—44no—
639C24—44no—
640C24—44no—
641C24—44no—
642C24—44no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24C23×C412yes—
647C24C23×C412yes—
648C24C23×C412yes—
649C24C22×D412yes—
650C24C2×#4112yes—
651C24C2×#4112yes—
652C24C2×#4112yes—
653C242−1+412yes—
654C242−1+412yes—
655C24C2511yescharacteristic
656C2×Q8—28no—
657C2×Q8—28no—
658C2×Q8—28no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—44no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—4128no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4C4×D4116yes—
824C22×C4C23×C414yes—
825C22×C4C23×C414yes—
826C22×C4C23×C414yes—
827C22×C4C23×C412yes—
828C22×C4C23×C412yes—
829C22×C4C23×C414yes—
830C22×C4C23×C412yes—
831C22×C4C23×C412yes—
832C22×C4C22×D414yes—
833C22×C4C22×D414yes—
834C22×C4C22×D412yes—
835C22×C4C22×D412yes—
836C22×C4C2×#4112yes—
837C22×C4C2×#4112yes—
838C22×C4C2×#4112yes—
839C22×C4C2×#4112yes—
840C22×C4C2×#4112yes—
841C22×C4C2×#4112yes—
842C22×C4H(5,𝔽2)12yes—
843C22×C4H(5,𝔽2)12yes—
844C22×C4H(5,𝔽2)12yes—
845C22×C4H(5,𝔽2)12yes—
846C4⋊C4—28no—
847C4⋊C4—216no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—84no—
859C4⋊C4—84no—
860C22⋊C4—216no—
861C22⋊C4—216no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C42—48no—
885C42—48no—
886C42—48no—
887C42—48no—
888C42—44no—
889C42—44no—
890C42—44no—
891C42—44no—
892C42—84no—
893C42—84no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—416no—
949C23—416no—
950C23—416no—
951C23—416no—
952C23—416no—
953C23—416no—
954C23—416no—
955C23—416no—
956C23—416no—
957C23—416no—
958C23—416no—
959C23—416no—
960C23—416no—
961C23—416no—
962C23—416no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23C2×C4×D414yes—
1012C23C4×#4114yes—
1013C23#51914yes—
1014C23C24×C411yescharacteristic
1015C23C23×D411yescharacteristic
1016C23C22×#4111yescharacteristic
1017C23C22×#4111yescharacteristic
1018C23C22×#4111yescharacteristic
1019C23C2×H(5,𝔽2)11yescharacteristic
1020C23C2×H(5,𝔽2)11yescharacteristic
1021C23C2×H(5,𝔽2)11yescharacteristic
1022C23C2×H(5,𝔽2)11yescharacteristic
1023C23C2×2−1+411yescharacteristic
1024C23C2×2−1+411yescharacteristic
1025C23#58511yescharacteristic
1026C23#58511yescharacteristic
1027C23#58511yescharacteristic
1028C23#58511yescharacteristic
1029Q8—416no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—232no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—416no—
1074C2×C4—416no—
1075C2×C4—416no—
1076C2×C4—41no—
1077C2×C4—42no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—42no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—416no—
1125C2×C4—416no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4C2×C4×D414yes—
1169C2×C4C2×C4×D414yes—
1170C2×C4#51814yes—
1171C2×C4#51814yes—
1172C2×C4#53414yes—
1173C2×C4#53514yes—
1174C2×C4#53814yes—
1175C2×C4#53814yes—
1176C22—24no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—24no—
1181C22—24no—
1182C22—24no—
1183C22—24no—
1184C22—24no—
1185C22—464no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22C22×C4×D411yescharacteristic
1223C22C2×C4×#4111yescharacteristic
1224C22C2×#51811yescharacteristic
1225C22C2×#51811yescharacteristic
1226C22C2×#51911yescharacteristic
1227C22#342811yescharacteristic
1228C22#342811yescharacteristic
1229C22C2×#53411yescharacteristic
1230C22C2×#53511yescharacteristic
1231C22C2×#53811yescharacteristic
1232C22C2×#53811yescharacteristic
1233C22D4×#4111yescharacteristic
1234C22D4×#4111yescharacteristic
1235C22#347511yescharacteristic
1236C22#347511yescharacteristic
1237C22#348911yescharacteristic
1238C22#348911yescharacteristic
1239C22#349511yescharacteristic
1240C22#349511yescharacteristic
1241C22#350511yescharacteristic
1242C22#350511yescharacteristic
1243C22#350611yescharacteristic
1244C22#350611yescharacteristic
1245C22#352011yescharacteristic
1246C22#352011yescharacteristic
1247C22#352011yescharacteristic
1248C22#352011yescharacteristic
1249C22#353911yescharacteristic
1250C22#353911yescharacteristic
1251C22#354011yescharacteristic
1252C22#354011yescharacteristic
1253C22#354111yescharacteristic
1254C22#354111yescharacteristic
1255C22#354111yescharacteristic
1256C22#354111yescharacteristic
1257C4—24no—
1258C4—42no—
1259C4—42no—
1260C4—44no—
1261C4—44no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C4—42no—
1266C4—44no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—82no—
1271C4—81no—
1272C4—81no—
1273C4—82no—
1274C4—81no—
1275C4—81no—
1276C4#232118yes—
1277C2—44no—
1278C2—44no—
1279C2—44no—
1280C2C2×#232111yescharacteristic
1281C2#3413611yescharacteristic
1282C2#3420311yescharacteristic
1283C2#3422311yescharacteristic
1284C2#3424511yescharacteristic
1285C2#3437011yescharacteristic
1286C2#3439111yescharacteristic
1287C2#3986011yescharacteristic
1288C2#3986311yescharacteristic
1289C2#3988411yescharacteristic
1290C2#3988711yescharacteristic
1291C2#3990811yescharacteristic
1292C2#3991111yescharacteristic
1293C2#3993211yescharacteristic
1294C2#3993511yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2362C2semidirect
4. #14384C2semidirect
5. #14383C2semidirect
8. #14269C2semidirect
9. #14138C2semidirect
10. #14129C2semidirect
11. #14075C2semidirect
12. #14067C2semidirect
13. #13997C2semidirect
14. #13997C2semidirect
15. #13994C2semidirect
16. #13993C2semidirect
17. #13974C2semidirect
18. #13973C2semidirect
19. #13969C2semidirect
20. #13969C2semidirect
21. #13801C2semidirect
22. #13789C2semidirect
28. C22×C4×Q8C22semidirect
31. #2848C4semidirect
33. C2×#391C22semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
36. C2×#389C22semidirect
37. C2×#389C22semidirect
38. C2×#389C22semidirect
43. C2×#387C22semidirect
60. C2×C4×C4⋊C4C22semidirect
61. C2×C4×C4⋊C4C22semidirect
62. C2×C4×C4⋊C4C22semidirect
63. C2×C4×C4⋊C4C22semidirect
72. #1445C22semidirect
73. #1445C22semidirect
74. #1443C22semidirect
75. #1443C22semidirect
76. #1442C22semidirect
77. #1442C22semidirect
78. #1441C22semidirect
79. #1441C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. #1436C22semidirect
108. C4⋊#95C22semidirect
109. C4⋊#95C22semidirect
110. C4⋊#95C22semidirect
111. C4⋊#95C22semidirect
112. C4⋊#95C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
118. #1434C22semidirect
125. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#23622
C2×#22802
#143842
#143832
#143662
#143652
#142692
#141382
#141292
#140752
#140672
#139972
#139942
#139932
#139742
#139732
#139692
#138012
#137892
C4×#3792