Finite Group Databasebeta

← #4867142

Subgroups — #4867142

Order 512.

4050 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2600C211yesmaximal, characteristic, complemented
2C2×#2408C211yesmaximal, characteristic, complemented
3#17091C212yesmaximal, complemented
4#17090C212yesmaximal, complemented
5#17005C211yesmaximal, characteristic, complemented
6#16807C211yesmaximal, characteristic, complemented
7#16664C211yesmaximal, characteristic, complemented
8#16662C211yesmaximal, characteristic, complemented
9#16648C212yesmaximal, complemented
10#16519C211yesmaximal, characteristic, complemented
11#16516C211yesmaximal, characteristic, complemented
12#16361C211yesmaximal, characteristic, complemented
13#16361C211yesmaximal, characteristic, complemented
14#16266C212yesmaximal, complemented
15#16255C212yesmaximal, complemented
16#16249C212yesmaximal, complemented
17#15297C212yesmaximal, complemented
18#15266C212yesmaximal, complemented
19#14724C211yesmaximal, characteristic, complemented
20#14722C211yesmaximal, characteristic, complemented
21#14722C211yesmaximal, characteristic, complemented
22#14715C211yesmaximal, characteristic, complemented
23#14345C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#120C2212yes—
28C22×#120C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic, complemented
31#2600—28no—
32#2408—28no—
33C2×#397C2212yes—
34C2×#397C2211yescharacteristic, complemented
35C2×#396C2212yescomplemented
36C2×#394C2212yes—
37C2×#394C2211yescharacteristic
38C2×#394C2211yescharacteristic
39C2×#394C2212yes—
40C2×#394C2211yescharacteristic
41C2×#394C2212yes—
42C2×#394C2211yescharacteristic, complemented
43C2×#394C2212yescomplemented
44C2×#394C2212yescomplemented
45C2×#394C2212yescomplemented
46C2×#392C2211yescharacteristic
47C2×#392C2212yes—
48C2×#392C2211yescharacteristic
49C2×#392C2211yescharacteristic
50C2×#392C2212yes—
51C2×#392C2212yescomplemented
52C2×#392C2212yescomplemented
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#388C2211yescharacteristic
56C2×#388C2211yescharacteristic, complemented
57C2×#387C2211yescharacteristic, complemented
58C2×#387C2211yescharacteristic, complemented
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yescomplemented
62C2×#386C2212yescomplemented
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic, complemented
65C2×#383C2211yescharacteristic, complemented
66C2×#382C2211yescharacteristic, complemented
67C2×#381C2211yescharacteristic, complemented
68C2×#380C2211yescharacteristic
69C2×#379C2212yes—
70C2×#379C2212yes—
71C2×#379C2212yes—
72C2×#379C2212yes—
73#1445C2212yescomplemented
74#1445C2212yescomplemented
75#1444C2211yescharacteristic, complemented
76#1444C2211yescharacteristic, complemented
77#1443C2212yescomplemented
78#1442C2211yescharacteristic, complemented
79#1442C2211yescharacteristic, complemented
80#1442C2212yescomplemented
81#1441C2211yescharacteristic, complemented
82#1441C2211yescharacteristic, complemented
83#1440C2212yes—
84#1440C2212yes—
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1440C2212yescomplemented
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1439C2212yes—
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2211yescharacteristic, complemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2211yescharacteristic, complemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2211yescharacteristic
109#1438C2211yescharacteristic
110#1438C2211yescharacteristic
111#1438C2211yescharacteristic
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1438C2212yescomplemented
117#1438C2212yescomplemented
118#1438C2212yescomplemented
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic, complemented
125C26C2312yes—
126C23×D4—24no—
127C23×D4—42no—
128C23×D4—42no—
129C23×D4—44no—
130C23×D4—44no—
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C2×#121—24no—
145C2×#121—24no—
146C2×#121—44no—
147C2×#121—44no—
148C2×#120—28no—
149C2×#120—44no—
150C2×#120—44no—
151C2×#120—44no—
152C2×#120—44no—
153C2×#120—44no—
154C2×C4×D4—24no—
155C2×C4×D4—42no—
156C2×C4×D4—42no—
157C2×C4×D4—42no—
158C2×C4×D4—42no—
159C2×C4×D4D418yescomplemented
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211#397—24no—
212#397—44no—
213#396—44no—
214#394—24no—
215#394—28no—
216#394—24no—
217#394—42no—
218#394—42no—
219#394—44no—
220#394—44no—
221#394—44no—
222#394—44no—
223#394—44no—
224#392—24no—
225#392—28no—
226#392—42no—
227#392—42no—
228#392—44no—
229#392—44no—
230#392—44no—
231#390—24no—
232#390—24no—
233#388—24no—
234#388—24no—
235#387—24no—
236#387—24no—
237#386—24no—
238#386—24no—
239#386—44no—
240#386—44no—
241#385—24no—
242#385—24no—
243#383—42no—
244#382—42no—
245#381—24no—
246#380—24no—
247#379—28no—
248#379—44no—
249#379—44no—
250#379—44no—
251C2×#95C2312yes—
252C2×#95C2311yescharacteristic
253C2×#95C2311yescharacteristic
254C2×#95C2311yescharacteristic
255C2×#95C2312yes—
256C2×#95C2311yescharacteristic
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
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—
285C25—24no—
286C25—24no—
287C25—24no—
288C25—24no—
289C25—24no—
290C25—42no—
291C25—42no—
292C25—42no—
293C25—42no—
294C25—42no—
295C25—42no—
296C25—42no—
297C25—42no—
298C25—42no—
299C25—42no—
300C25C2411yescharacteristic
301C25C2412yes—
302C25C2412yes—
303C25C2411yescharacteristic
304C25C2411yescharacteristic
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—22no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—22no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—24no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—41no—
342C22×D4—42no—
343C22×D4—41no—
344C22×D4—416no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—41no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—416no—
368C22×D4—416no—
369C22×D4—432no—
370C22×D4—432no—
371C22×D4C2×D414yes—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—41no—
380C23×C4—41no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4C2×D414yes—
386C23×C4C2×D414yes—
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405#121—416no—
406#121—416no—
407#120—432no—
408#120—432no—
409C4×D4—416no—
410C4×D4—416no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
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—41no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—41no—
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⋊C4C2×D414yes—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
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—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—41no—
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—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
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⋊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⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4C2×D414yes—
547C2×C22⋊C4C2×D414yes—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—41no—
552C2×C42—41no—
553C2×C42C2×D414yes—
554#95—24no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—24no—
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—
588C24—21no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—22no—
594C24—21no—
595C24—22no—
596C24—21no—
597C24—21no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—21no—
608C24—21no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24C22×D412yes—
681C24C22×D412yes—
682C24H(5,𝔽2)14yes—
683C24H(5,𝔽2)14yes—
684C24H(5,𝔽2)12yes—
685C24H(5,𝔽2)14yes—
686C24C2511yescharacteristic
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—44no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—44no—
713C2×D4—4128no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—82no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
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—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
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—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—44no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4—82no—
860C22×C4—82no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4H(5,𝔽2)12yes—
869C22×C4H(5,𝔽2)12yes—
870C22×C4H(5,𝔽2)12yes—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—82no—
878C4⋊C4—84no—
879C4⋊C4—84no—
880C4⋊C4—84no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—44no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C22⋊C4—44no—
897C22⋊C4—82no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C22⋊C4—82no—
903C22⋊C4—82no—
904C22⋊C4—82no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C22⋊C4—84no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C42—28no—
921C42—44no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—42no—
961C23—42no—
962C23—42no—
963C23—42no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—42no—
969C23—42no—
970C23—432no—
971C23—41no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—41no—
977C23—41no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—41no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—41no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—816no—
1062C23—816no—
1063C23—816no—
1064C23—816no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23—816no—
1075C23#53514yes—
1076C23C23×D411yescharacteristic
1077C23C2×H(5,𝔽2)11yescharacteristic
1078C23C2×H(5,𝔽2)11yescharacteristic
1079C23C2×H(5,𝔽2)12yes—
1080C23C2×H(5,𝔽2)12yes—
1081C23C2×H(5,𝔽2)12yes—
1082C23C2×H(5,𝔽2)11yescharacteristic
1083C23C2×H(5,𝔽2)11yescharacteristic
1084C23#58512yes—
1085C23#58511yescharacteristic
1086C23#58511yescharacteristic
1087D4—416no—
1088D4—416no—
1089D4—416no—
1090D4—416no—
1091D4—432no—
1092D4—88no—
1093D4—816no—
1094D4—816no—
1095D4—816no—
1096D4—816no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—416no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
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—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—88no—
1204C2×C4—88no—
1205C2×C4#53414yes—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—42no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—42no—
1230C22—42no—
1231C22—44no—
1232C22—42no—
1233C22—44no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—44no—
1238C22—42no—
1239C22—42no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—864no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—81no—
1248C22—82no—
1249C22—82no—
1250C22—81no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—81no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—81no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22C2×#53411yescharacteristic
1271C22C2×#53511yescharacteristic
1272C22#344911yescharacteristic
1273C22#348411yescharacteristic
1274C22#348411yescharacteristic
1275C22#348811yescharacteristic
1276C22#348811yescharacteristic
1277C22#353212yes—
1278C22#353212yes—
1279C22#353212yes—
1280C22#353312yes—
1281C22#353412yes—
1282C22#353412yes—
1283C22#353412yes—
1284C22#353711yescharacteristic
1285C22#353712yes—
1286C22#354011yescharacteristic
1287C22#354211yescharacteristic
1288C22#354212yes—
1289C22#354212yes—
1290C22#354211yescharacteristic
1291C22#355812yes—
1292C22#356012yes—
1293C4—24no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—82no—
1300C4—81no—
1301C4—81no—
1302C4—82no—
1303C4—82no—
1304C4—82no—
1305C4—81no—
1306C4—81no—
1307C4—82no—
1308C4—81no—
1309C4—81no—
1310C4—82no—
1311C2—44no—
1312C2—82no—
1313C2—82no—
1314C2—84no—
1315C2—84no—
1316C2#3671411yescharacteristic
1317C2#3726911yescharacteristic
1318C2#3744811yescharacteristic
1319C2#4059011yescharacteristic
1320C2#4059411yescharacteristic
1321C2#4060211yescharacteristic
1322C2#4060611yescharacteristic
1323C2#5482212yes—
1324C2#5500712yes—
1325C2#5720912yes—
1326C2#5747412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2600C2semidirect
2. C2×#2408C2semidirect
3. #17091C2semidirect
4. #17090C2semidirect
5. #17005C2semidirect
6. #16807C2semidirect
7. #16664C2semidirect
8. #16662C2semidirect
9. #16648C2semidirect
10. #16519C2semidirect
11. #16516C2semidirect
12. #16361C2semidirect
13. #16361C2semidirect
14. #16266C2semidirect
15. #16255C2semidirect
16. #16249C2semidirect
17. #15297C2semidirect
18. #15266C2semidirect
19. #14724C2semidirect
20. #14722C2semidirect
21. #14722C2semidirect
22. #14715C2semidirect
23. #14345C2semidirect
30. C22×C4×D4C22semidirect
34. C2×#397C22semidirect
35. C2×#396C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
45. C2×#394C22semidirect
51. C2×#392C22semidirect
52. C2×#392C22semidirect
56. C2×#388C22semidirect
57. C2×#387C22semidirect
58. C2×#387C22semidirect
61. C2×#386C22semidirect
62. C2×#386C22semidirect
64. C2×#385C22semidirect
65. C2×#383C22semidirect
66. C2×#382C22semidirect
67. C2×#381C22semidirect
73. #1445C22semidirect
74. #1445C22semidirect
75. #1444C22semidirect
76. #1444C22semidirect
77. #1443C22semidirect
78. #1442C22semidirect
79. #1442C22semidirect
80. #1442C22semidirect
81. #1441C22semidirect
82. #1441C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1440C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1438C22semidirect
117. #1438C22semidirect
118. #1438C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
159. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26002
C2×#24082
#170912
#170902
#170052
#168072
#166642
#166622
#166482
#165192
#165162
#163612
#162662
#162552
#162492
#152972
#152662
#147242
#147222
#147152
#143452