Finite Group Databasebeta

← #845683

Subgroups — #845683

Order 512.

3688 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic, complemented
2C2×C4×#120C211yesmaximal, characteristic
3#16426C212yesmaximal, complemented
4#16255C212yesmaximal
5#16006C212yesmaximal, complemented
6#15998C212yesmaximal, complemented
7#15688C212yesmaximal, complemented
8#15550C212yesmaximal, complemented
9#15220C211yesmaximal, characteristic, complemented
10#15220C211yesmaximal, characteristic, complemented
11#15183C211yesmaximal, characteristic, complemented
12#15181C211yesmaximal, characteristic, complemented
13#15132C211yesmaximal, characteristic, complemented
14#15129C211yesmaximal, characteristic, complemented
15#14680C211yesmaximal, characteristic, complemented
16#14680C211yesmaximal, characteristic, complemented
17#14542C212yesmaximal, complemented
18#14366C212yesmaximal, complemented
19#13974C211yesmaximal, characteristic, complemented
20#13973C211yesmaximal, characteristic, complemented
21#13905C211yesmaximal, characteristic, complemented
22#13871C211yesmaximal, characteristic, complemented
23#13871C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C22×#120C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2211yescharacteristic, complemented
30#2485—28no—
31C2×#397C2212yes—
32C2×#397C2212yescomplemented
33C2×#394C2212yes—
34C2×#394C2212yes—
35C4×#120—28no—
36C2×#389C2211yescharacteristic, complemented
37C2×#389C2211yescharacteristic, complemented
38C2×#389C2211yescharacteristic, complemented
39C2×#389C2211yescharacteristic, complemented
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#387C2212yescomplemented
43C2×#386C2211yescharacteristic
44C2×#386C2211yescharacteristic
45C2×#386C2211yescharacteristic
46C2×#385C2211yescharacteristic
47C2×#385C2211yescharacteristic
48C2×#385C2211yescharacteristic
49C2×#382C2211yescharacteristic, complemented
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic, complemented
63C2×#380C2211yescharacteristic, complemented
64C2×#380C2211yescharacteristic, complemented
65C2×#379C2211yescharacteristic
66C2×#379C2212yes—
67C2×#379C2212yes—
68C2×C4×C4⋊C4C2211yescharacteristic, complemented
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72#1445C2212yescomplemented
73#1445C2212yescomplemented
74#1443C2212yescomplemented
75#1443C2212yescomplemented
76#1443C2212yescomplemented
77#1443C2212yescomplemented
78#1443C2212yescomplemented
79#1442C2212yescomplemented
80#1442C2212yescomplemented
81#1442C2212yescomplemented
82#1441C2212yescomplemented
83#1441C2212yescomplemented
84#1441C2212yescomplemented
85#1440C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yescomplemented
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1437C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111#1436C2212yescomplemented
112C4⋊#95C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118#1434C2212yescomplemented
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C26C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C24×C4—24no—
130C24×C4—24no—
131C24×C4—24no—
132C24×C4—42no—
133C24×C4—42no—
134C24×C4—42no—
135C24×C4—42no—
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C2×#120—24no—
144C2×#120—24no—
145C2×#120—24no—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—42no—
151C2×C4×D4—42no—
152C2×C4×D4—42no—
153C2×C4×D4—42no—
154C2×C4×D4D418yes—
155C2×#117—24no—
156C2×#117—42no—
157C2×#117—42no—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2312yes—
205C22×C42C2312yes—
206#397—28no—
207#397—28no—
208#394—28no—
209#394—44no—
210#389—24no—
211#389—24no—
212#389—42no—
213#389—42no—
214#388—28no—
215#388—44no—
216#387—28no—
217#386—24no—
218#386—24no—
219#386—24no—
220#385—24no—
221#385—24no—
222#385—24no—
223#382—42no—
224#380—24no—
225#380—24no—
226#380—24no—
227#380—24no—
228#380—24no—
229#380—42no—
230#380—42no—
231#380—42no—
232#380—42no—
233#380—42no—
234#380—42no—
235#380—42no—
236#380—42no—
237#380—42no—
238#380—42no—
239#379—28no—
240#379—24no—
241#379—44no—
242C4×C4⋊C4—42no—
243C4×C22⋊C4—24no—
244C4×C22⋊C4—24no—
245C4×C22⋊C4—24no—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2311yescharacteristic
256C2×#95C2311yescharacteristic
257C2×#95C2312yes—
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2312yes—
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—
286C25—22no—
287C25—22no—
288C25—22no—
289C25—22no—
290C25—22no—
291C25—22no—
292C25—41no—
293C25—41no—
294C25—41no—
295C25—41no—
296C25—41no—
297C25—41no—
298C25—41no—
299C25—41no—
300C25#4114yes—
301C25C2411yescharacteristic
302C25C2411yescharacteristic
303C25C2411yescharacteristic
304C25C2411yescharacteristic
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—41no—
318C22×D4—41no—
319C22×D4—41no—
320C22×D4—41no—
321C22×D4—41no—
322C22×D4—41no—
323C22×D4—41no—
324C22×D4—41no—
325C22×D4C2×D414yes—
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—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—41no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4—416no—
372C23×C4—416no—
373C23×C4—416no—
374C23×C4—416no—
375C23×C4—416no—
376C23×C4—416no—
377C23×C4—416no—
378C23×C4C2×D414yes—
379C23×C4C2×D414yes—
380C23×C4#4114yes—
381C23×C4#4114yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401#120—232no—
402C4×D4—416no—
403C4×D4—416no—
404C4×D4—416no—
405#117—416no—
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—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4C2×D414yes—
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—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4C2×D414yes—
533C2×C22⋊C4C2×D414yes—
534C2×C22⋊C4#4114yes—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—24no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—42no—
545C2×C42—42no—
546C2×C42—42no—
547C2×C42—42no—
548C2×C42—42no—
549C2×C42C2×D414yes—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—24no—
557#95—24no—
558#95—24no—
559#95—24no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—24no—
565#95—24no—
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#95—42no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
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—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—28no—
627C24—28no—
628C24—28no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24C22×D412yes—
676C24C22×D412yes—
677C24C2×#4112yes—
678C24C2×#4112yes—
679C24C2×#4112yes—
680C24C2×#4112yes—
681C24C2×#4112yes—
682C24C2×#4112yes—
683C24H(5,𝔽2)12yes—
684C242−1+412yes—
685C24C2511yescharacteristic
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—4128no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C2×#4112yes—
881C22×C4C2×#4112yes—
882C22×C4C2×#4112yes—
883C22×C4C2×#4112yes—
884C22×C4C2×#4112yes—
885C22×C4C2×#4112yes—
886C22×C4H(5,𝔽2)12yes—
887C22×C4H(5,𝔽2)12yes—
888C22×C4H(5,𝔽2)12yes—
889C22×C4H(5,𝔽2)12yes—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—84no—
903C4⋊C4—84no—
904C4⋊C4—84no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C42—28no—
934C42—48no—
935C42—44no—
936C42—44no—
937C42—84no—
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—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—416no—
1000C23—416no—
1001C23—416no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
1007C23—416no—
1008C23—416no—
1009C23—416no—
1010C23—416no—
1011C23—416no—
1012C23—416no—
1013C23—416no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23#52514yes—
1091C23#55214yes—
1092C23#55314yes—
1093C23C23×D411yescharacteristic
1094C23C22×#4111yescharacteristic
1095C23C22×#4111yescharacteristic
1096C23C22×#4111yescharacteristic
1097C23C22×#4111yescharacteristic
1098C23C2×H(5,𝔽2)11yescharacteristic
1099C23C2×H(5,𝔽2)11yescharacteristic
1100C23C2×H(5,𝔽2)11yescharacteristic
1101C23C2×H(5,𝔽2)11yescharacteristic
1102C23C2×H(5,𝔽2)11yescharacteristic
1103C23C2×2−1+411yescharacteristic
1104C23#58511yescharacteristic
1105C23#58511yescharacteristic
1106C23#58511yescharacteristic
1107C23#58511yescharacteristic
1108D4—416no—
1109D4—416no—
1110D4—416no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—416no—
1136C2×C4—416no—
1137C2×C4—416no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—416no—
1171C2×C4—416no—
1172C2×C4—416no—
1173C2×C4—416no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—41no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—41no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—41no—
1244C2×C4#53414yes—
1245C2×C4#53814yes—
1246C2×C4#53814yes—
1247C2×C4#54614yes—
1248C2×C4#54614yes—
1249C2×C4#55114yes—
1250C2×C4#56014yes—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—464no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22C2×#52511yescharacteristic
1313C22C2×#53411yescharacteristic
1314C22#344911yescharacteristic
1315C22C2×#53811yescharacteristic
1316C22C2×#53811yescharacteristic
1317C22C2×#54611yescharacteristic
1318C22C2×#54611yescharacteristic
1319C22C2×#55111yescharacteristic
1320C22C2×#55211yescharacteristic
1321C22C2×#55311yescharacteristic
1322C22#347511yescharacteristic
1323C22#347511yescharacteristic
1324C22#348811yescharacteristic
1325C22#348911yescharacteristic
1326C22#349311yescharacteristic
1327C22#349311yescharacteristic
1328C22#349411yescharacteristic
1329C22#349511yescharacteristic
1330C22#350511yescharacteristic
1331C22#350511yescharacteristic
1332C22#350511yescharacteristic
1333C22#350511yescharacteristic
1334C22#350611yescharacteristic
1335C22#350611yescharacteristic
1336C22#351911yescharacteristic
1337C22#352011yescharacteristic
1338C22C2×#56011yescharacteristic
1339C22#353611yescharacteristic
1340C22#353911yescharacteristic
1341C22#354011yescharacteristic
1342C22#354011yescharacteristic
1343C22#354111yescharacteristic
1344C22#354111yescharacteristic
1345C22#354211yescharacteristic
1346C22#354211yescharacteristic
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—82no—
1356C4—82no—
1357C4—82no—
1358C4—82no—
1359C4—82no—
1360C4—81no—
1361C4—81no—
1362C4—82no—
1363C4—82no—
1364C4—82no—
1365C4#269718yes—
1366C2—44no—
1367C2—44no—
1368C2—44no—
1369C2—82no—
1370C2#3503111yescharacteristic
1371C2#3615611yescharacteristic
1372C2#3615711yescharacteristic
1373C2#3726811yescharacteristic
1374C2#3784411yescharacteristic
1375C2#3784511yescharacteristic
1376C2#3947711yescharacteristic
1377C2#3973311yescharacteristic
1378C2#3991111yescharacteristic
1379C2#3993411yescharacteristic
1380C2#4550811yescharacteristic
1381C2#4564611yescharacteristic
1382C2C2×#269711yescharacteristic
1383C2#5919711yescharacteristic
1384C2#5920011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×#2485C2semidirect
3. #16426C2semidirect
5. #16006C2semidirect
6. #15998C2semidirect
7. #15688C2semidirect
8. #15550C2semidirect
9. #15220C2semidirect
10. #15220C2semidirect
11. #15183C2semidirect
12. #15181C2semidirect
13. #15132C2semidirect
14. #15129C2semidirect
15. #14680C2semidirect
16. #14680C2semidirect
17. #14542C2semidirect
18. #14366C2semidirect
19. #13974C2semidirect
20. #13973C2semidirect
21. #13905C2semidirect
22. #13871C2semidirect
23. #13871C2semidirect
29. C22×#117C22semidirect
32. C2×#397C22semidirect
36. C2×#389C22semidirect
37. C2×#389C22semidirect
38. C2×#389C22semidirect
39. C2×#389C22semidirect
42. C2×#387C22semidirect
49. C2×#382C22semidirect
62. C2×#380C22semidirect
63. C2×#380C22semidirect
64. C2×#380C22semidirect
68. C2×C4×C4⋊C4C22semidirect
72. #1445C22semidirect
73. #1445C22semidirect
74. #1443C22semidirect
75. #1443C22semidirect
76. #1443C22semidirect
77. #1443C22semidirect
78. #1443C22semidirect
79. #1442C22semidirect
80. #1442C22semidirect
81. #1442C22semidirect
82. #1441C22semidirect
83. #1441C22semidirect
84. #1441C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
99. #1439C22semidirect
108. #1437C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. C4⋊#95C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×C4×#1202
#164262
#162552
#160062
#159982
#156882
#155502
#152202
#151832
#151812
#151322
#151292
#146802
#145422
#143662
#139742
#139732
#139052
#138712