Finite Group Databasebeta

← #553718

Subgroups — #553718

Order 512.

3806 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2323C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic
4#14680C211yesmaximal, characteristic
5#14416C212yesmaximal, complemented
6#14408C212yesmaximal, complemented
7#14398C212yesmaximal, complemented
8#14392C212yesmaximal, complemented
9#14384C212yesmaximal, complemented
10#14383C212yesmaximal, complemented
11#14366C212yesmaximal
12#14365C212yesmaximal
13#14264C211yesmaximal, characteristic, complemented
14#14258C211yesmaximal, characteristic, complemented
15#13997C211yesmaximal, characteristic, complemented
16#13997C211yesmaximal, characteristic, complemented
17#13994C211yesmaximal, characteristic, complemented
18#13993C211yesmaximal, characteristic, complemented
19#13974C211yesmaximal, characteristic, complemented
20#13973C211yesmaximal, characteristic, complemented
21#13969C211yesmaximal, characteristic, complemented
22#13969C211yesmaximal, characteristic, complemented
23#13777C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic, complemented
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2848C4116yescomplemented
32#2323—28no—
33C2×#391C2211yescharacteristic, complemented
34C2×#391C2211yescharacteristic, complemented
35C2×#391C2211yescharacteristic, complemented
36C2×#389C2212yescomplemented
37C2×#389C2211yescharacteristic, complemented
38C2×#389C2211yescharacteristic, complemented
39C2×#389C2211yescharacteristic, complemented
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#387C2212yescomplemented
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48#2280—28no—
49C2×#381C2211yescharacteristic
50C2×#381C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#379C2211yescharacteristic
65C2×#379C2211yescharacteristic
66C2×#379C2212yes—
67C2×#379C2212yes—
68C2×C4×C4⋊C4C2211yescharacteristic, complemented
69C2×C4×C4⋊C4C2211yescharacteristic, complemented
70C2×C4×C4⋊C4C2211yescharacteristic, complemented
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75#1445C2212yescomplemented
76#1445C2212yescomplemented
77#1444C2212yescomplemented
78#1443C2212yescomplemented
79#1443C2212yescomplemented
80#1442C2212yescomplemented
81#1442C2212yescomplemented
82#1442C2212yescomplemented
83#1441C2212yescomplemented
84#1441C2212yescomplemented
85#1441C2212yescomplemented
86#1441C2212yescomplemented
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1437C2212yes—
100#1437C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1436C2212yescomplemented
108#1436C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113C4⋊#95C2212yescomplemented
114C4⋊#95C2212yescomplemented
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118C4⋊#95C2211yescharacteristic, complemented
119C4⋊#95C2211yescharacteristic, complemented
120C4⋊#95C2211yescharacteristic, complemented
121#1434C2212yescomplemented
122#1434C2212yescomplemented
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
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⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2312yes—
206C22×C42C2312yes—
207C22×C42C2312yes—
208C22×C42C2312yes—
209#391—24no—
210#391—42no—
211#391—42no—
212#389—28no—
213#389—24no—
214#389—42no—
215#389—42no—
216#388—28no—
217#388—28no—
218#388—44no—
219#388—44no—
220#387—28no—
221#385C2×C4116yes—
222#385C2×C4116yes—
223#385C2×C4116yes—
224#381—24no—
225#381—24no—
226#380—24no—
227#380—24no—
228#380—24no—
229#380—24no—
230#380—24no—
231#380—24no—
232#380—42no—
233#380—42no—
234#380—42no—
235#380—42no—
236#380C2×C418yes—
237#380C2×C418yes—
238#380C2×C418yes—
239#379—24no—
240#379—24no—
241#379—44no—
242#379C2×C4116yes—
243C4×C4⋊C4—24no—
244C4×C4⋊C4—42no—
245C4×C4⋊C4—42no—
246C4×C22⋊C4—24no—
247C4×C22⋊C4—24no—
248C4×C22⋊C4—24no—
249C4×C22⋊C4—24no—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2311yescharacteristic
253C2×#95C2311yescharacteristic
254C2×#95C2312yes—
255C2×#95C2311yescharacteristic
256C2×#95C2311yescharacteristic
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
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×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C25—22no—
292C25—22no—
293C25—22no—
294C25—22no—
295C25—22no—
296C25—22no—
297C25—41no—
298C25—41no—
299C25—41no—
300C25—41no—
301C25—41no—
302C25—41no—
303C25—41no—
304C25—41no—
305C25C22×C414yes—
306C25C2411yescharacteristic
307C25C2411yescharacteristic
308C25C2411yescharacteristic
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8C22×C414yes—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—232no—
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—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—416no—
340C23×C4—416no—
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—41no—
351C23×C4—41no—
352C23×C4—41no—
353C23×C4—416no—
354C23×C4—416no—
355C23×C4—416no—
356C23×C4—416no—
357C23×C4C22×C414yes—
358C23×C4C22×C414yes—
359C23×C4C22×C414yes—
360C23×C4C22×C414yes—
361C23×C4C22×C414yes—
362C23×C4C22×C414yes—
363C23×C4C2×D414yes—
364C23×C4#4114yes—
365C23×C4C2412yes—
366C23×C4C2411yescharacteristic
367C23×C4C2411yescharacteristic
368C23×C4C2412yes—
369C23×C4C2411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C22⋊Q8—232no—
386C22⋊Q8—416no—
387C22⋊Q8—416no—
388C4×Q8—416no—
389#117—416no—
390#117—416no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—24no—
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—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4C22×C414yes—
438C2×C4⋊C4C22×C414yes—
439C2×C4⋊C4C22×C414yes—
440C2×C4⋊C4C22×C418yes—
441C2×C4⋊C4C22×C418yes—
442C2×C4⋊C4C22×C418yes—
443C2×C4⋊C4C2×D414yes—
444C2×C4⋊C4C2×D414yes—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
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—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4—41no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—41no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
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⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4C22×C418yes—
510C2×C22⋊C4C22×C418yes—
511C2×C22⋊C4C22×C418yes—
512C2×C22⋊C4C22×C418yes—
513C2×C22⋊C4C22×C418yes—
514C2×C22⋊C4C22×C418yes—
515C2×C22⋊C4C2×D414yes—
516C2×C22⋊C4C2×D414yes—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—24no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—24no—
529C2×C42—42no—
530C2×C42—42no—
531C2×C42—42no—
532C2×C42—42no—
533C2×C42—42no—
534C2×C42—42no—
535C2×C42—42no—
536C2×C42—42no—
537C2×C42—42no—
538C2×C42—42no—
539C2×C42C2×D414yes—
540C2×C42C2×D414yes—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—24no—
550#95—24no—
551#95—24no—
552#95—24no—
553#95—24no—
554#95—24no—
555#95—42no—
556#95—42no—
557#95—42no—
558#95—42no—
559#95—42no—
560#95—42no—
561#95—42no—
562#95—42no—
563#95—42no—
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#95—42no—
573#95—42no—
574#95—42no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95C22×C418yes—
580#95C22×C418yes—
581#95C22×C418yes—
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—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—28no—
619C24—28no—
620C24—28no—
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—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24C23×C412yes—
654C24C23×C412yes—
655C24C23×C412yes—
656C24C22×D412yes—
657C24C2×#4112yes—
658C24H(5,𝔽2)12yes—
659C242−1+412yes—
660C242−1+412yes—
661C242−1+412yes—
662C24C2511yescharacteristic
663C2×Q8—28no—
664C2×Q8—28no—
665C2×Q8—28no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—44no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
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—4128no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4C4×D4116yes—
833C22×C4C23×C414yes—
834C22×C4C23×C414yes—
835C22×C4C23×C414yes—
836C22×C4C23×C412yes—
837C22×C4C23×C412yes—
838C22×C4C23×C414yes—
839C22×C4C23×C412yes—
840C22×C4C23×C412yes—
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D412yes—
844C22×C4C22×D412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D412yes—
847C22×C4C2×#4112yes—
848C22×C4C2×#4112yes—
849C22×C4H(5,𝔽2)12yes—
850C22×C4H(5,𝔽2)12yes—
851C22×C4H(5,𝔽2)12yes—
852C22×C4H(5,𝔽2)12yes—
853C4⋊C4—28no—
854C4⋊C4—216no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—84no—
869C4⋊C4—84no—
870C4⋊C4—84no—
871C22⋊C4—216no—
872C22⋊C4—216no—
873C22⋊C4—48no—
874C22⋊C4—48no—
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—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—84no—
890C22⋊C4—84no—
891C22⋊C4—84no—
892C22⋊C4—84no—
893C22⋊C4—84no—
894C22⋊C4—84no—
895C42—28no—
896C42—28no—
897C42—48no—
898C42—44no—
899C42—44no—
900C42—84no—
901C42—84no—
902C42—84no—
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—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—416no—
958C23—416no—
959C23—416no—
960C23—416no—
961C23—416no—
962C23—416no—
963C23—416no—
964C23—416no—
965C23—416no—
966C23—416no—
967C23—416no—
968C23—416no—
969C23—416no—
970C23—416no—
971C23—416no—
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—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23C2×C4×D414yes—
1021C23#51914yes—
1022C23#52014yes—
1023C23C24×C411yescharacteristic
1024C23C23×D411yescharacteristic
1025C23C22×#4111yescharacteristic
1026C23C2×H(5,𝔽2)11yescharacteristic
1027C23C2×H(5,𝔽2)11yescharacteristic
1028C23C2×H(5,𝔽2)11yescharacteristic
1029C23C2×H(5,𝔽2)11yescharacteristic
1030C23C2×H(5,𝔽2)11yescharacteristic
1031C23C2×2−1+411yescharacteristic
1032C23C2×2−1+411yescharacteristic
1033C23C2×2−1+411yescharacteristic
1034C23#58511yescharacteristic
1035C23#58511yescharacteristic
1036C23#58511yescharacteristic
1037C23#58511yescharacteristic
1038Q8—416no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—232no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
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—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—416no—
1077C2×C4—416no—
1078C2×C4—416no—
1079C2×C4—42no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—42no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—42no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—41no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—41no—
1119C2×C4—416no—
1120C2×C4—416no—
1121C2×C4—42no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4C2×C4×D414yes—
1178C2×C4C2×C4×D414yes—
1179C2×C4#51814yes—
1180C2×C4#51814yes—
1181C2×C4#53414yes—
1182C2×C4#53514yes—
1183C2×C4#53814yes—
1184C2×C4#53814yes—
1185C22—24no—
1186C22—24no—
1187C22—24no—
1188C22—24no—
1189C22—24no—
1190C22—24no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—464no—
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—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22C22×C4×D411yescharacteristic
1232C22C2×#51811yescharacteristic
1233C22C2×#51811yescharacteristic
1234C22C2×#51911yescharacteristic
1235C22C2×#52011yescharacteristic
1236C22#342811yescharacteristic
1237C22#342811yescharacteristic
1238C22C2×#53411yescharacteristic
1239C22C2×#53511yescharacteristic
1240C22C2×#53811yescharacteristic
1241C22C2×#53811yescharacteristic
1242C22#348811yescharacteristic
1243C22#348911yescharacteristic
1244C22#348911yescharacteristic
1245C22#348911yescharacteristic
1246C22#349411yescharacteristic
1247C22#349511yescharacteristic
1248C22#349511yescharacteristic
1249C22#349511yescharacteristic
1250C22#353611yescharacteristic
1251C22#353611yescharacteristic
1252C22#353811yescharacteristic
1253C22#353811yescharacteristic
1254C22#353911yescharacteristic
1255C22#353911yescharacteristic
1256C22#354011yescharacteristic
1257C22#354011yescharacteristic
1258C22#354111yescharacteristic
1259C22#354111yescharacteristic
1260C22#354111yescharacteristic
1261C22#354111yescharacteristic
1262C22#354111yescharacteristic
1263C22#354111yescharacteristic
1264C22#354211yescharacteristic
1265C22#354211yescharacteristic
1266C4—24no—
1267C4—42no—
1268C4—42no—
1269C4—44no—
1270C4—44no—
1271C4—44no—
1272C4—42no—
1273C4—42no—
1274C4—44no—
1275C4—42no—
1276C4—42no—
1277C4—82no—
1278C4—81no—
1279C4—81no—
1280C4—82no—
1281C4—82no—
1282C4—82no—
1283C4—81no—
1284C4—81no—
1285C4#232118yes—
1286C2—44no—
1287C2—44no—
1288C2—44no—
1289C2C2×#232111yescharacteristic
1290C2#3420211yescharacteristic
1291C2#3420311yescharacteristic
1292C2#3437011yescharacteristic
1293C2#3438011yescharacteristic
1294C2#3439111yescharacteristic
1295C2#3440411yescharacteristic
1296C2#3726811yescharacteristic
1297C2#3727111yescharacteristic
1298C2#3728211yescharacteristic
1299C2#3728511yescharacteristic
1300C2#3737411yescharacteristic
1301C2#3737511yescharacteristic
1302C2#3738011yescharacteristic
1303C2#3738111yescharacteristic
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×#2323C2semidirect
5. #14416C2semidirect
6. #14408C2semidirect
7. #14398C2semidirect
8. #14392C2semidirect
9. #14384C2semidirect
10. #14383C2semidirect
13. #14264C2semidirect
14. #14258C2semidirect
15. #13997C2semidirect
16. #13997C2semidirect
17. #13994C2semidirect
18. #13993C2semidirect
19. #13974C2semidirect
20. #13973C2semidirect
21. #13969C2semidirect
22. #13969C2semidirect
23. #13777C2semidirect
28. C22×C4×Q8C22semidirect
31. #2848C4semidirect
33. C2×#391C22semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
36. C2×#389C22semidirect
37. C2×#389C22semidirect
38. C2×#389C22semidirect
39. C2×#389C22semidirect
44. C2×#387C22semidirect
68. C2×C4×C4⋊C4C22semidirect
69. C2×C4×C4⋊C4C22semidirect
70. C2×C4×C4⋊C4C22semidirect
75. #1445C22semidirect
76. #1445C22semidirect
77. #1444C22semidirect
78. #1443C22semidirect
79. #1443C22semidirect
80. #1442C22semidirect
81. #1442C22semidirect
82. #1442C22semidirect
83. #1441C22semidirect
84. #1441C22semidirect
85. #1441C22semidirect
86. #1441C22semidirect
107. #1436C22semidirect
108. #1436C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
119. C4⋊#95C22semidirect
120. C4⋊#95C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#23232
C2×#22802
#146802
#144162
#144082
#143982
#143922
#143842
#143832
#143662
#143652
#142642
#142582
#139972
#139942
#139932
#139742
#139732
#139692
#137772