Finite Group Databasebeta

← #848407

Subgroups — #848407

Order 512.

3846 conjugacy classes of subgroups.

The subgroup lattice has 1335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2416C211yesmaximal, characteristic, complemented
2C22×#388C211yesmaximal, characteristic, complemented
3#16497C212yesmaximal, complemented
4#16341C212yesmaximal, complemented
5#16087C212yesmaximal, complemented
6#15607C212yesmaximal, complemented
7#15428C212yesmaximal, complemented
8#15320C212yesmaximal, complemented
9#14945C211yesmaximal, characteristic, complemented
10#14913C211yesmaximal, characteristic, complemented
11#14725C211yesmaximal, characteristic, complemented
12#14716C211yesmaximal, characteristic, complemented
13#14716C211yesmaximal, characteristic, complemented
14#14716C211yesmaximal, characteristic, complemented
15#14698C211yesmaximal, characteristic, complemented
16#14696C211yesmaximal, characteristic, complemented
17#14567C212yesmaximal, complemented
18#14415C212yesmaximal, complemented
19#14152C211yesmaximal, characteristic, complemented
20#14016C211yesmaximal, characteristic, complemented
21#13995C211yesmaximal, characteristic, complemented
22#13967C211yesmaximal, characteristic, complemented
23#13882C211yesmaximal, characteristic, complemented
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic, complemented
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C42C2211yescharacteristic
37#2416—28no—
38C2×#396C2211yescharacteristic, complemented
39C2×#396C2211yescharacteristic, complemented
40C2×#394C2212yes—
41C2×#394C2211yescharacteristic, complemented
42C2×#394C2211yescharacteristic, complemented
43C2×#392C2212yes—
44C2×#392C2212yes—
45C2×#392C2212yes—
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic, complemented
48C2×#390C2212yescomplemented
49C2×#389C2211yescharacteristic, complemented
50C2×#388—28no—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#388C2212yes—
55C2×#388C2212yescomplemented
56C2×#387C2212yescomplemented
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic, complemented
72C2×#379C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C22×#95C2211yescharacteristic
75C22×#95C2211yescharacteristic
76#1445C2212yescomplemented
77#1445C2212yescomplemented
78#1443C2212yescomplemented
79#1443C2212yescomplemented
80#1442C2212yescomplemented
81#1442C2212yescomplemented
82#1441C2212yescomplemented
83#1440C2212yes—
84#1440C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1440C2212yescomplemented
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yescomplemented
95#1438C2212yes—
96#1438C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yescomplemented
105#1438C2212yescomplemented
106#1437C2212yes—
107#1437C2212yes—
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116C4⋊#95C2212yescomplemented
117#1434C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C26C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C2×#121—24no—
143C2×#121—24no—
144C2×#121—24no—
145C2×#121—24no—
146C2×#121—24no—
147C2×#121—24no—
148C2×#121—44no—
149C2×#121—42no—
150C2×#121—42no—
151C2×#121—42no—
152C2×#121—42no—
153C2×#120—24no—
154C2×#120—24no—
155C2×#120—42no—
156C2×#120—42no—
157C2×#120—42no—
158C2×#120—42no—
159C2×#120—42no—
160C2×#120—42no—
161C2×#120—42no—
162C2×C4×D4—24no—
163C2×C4×D4—42no—
164C2×C4×D4—42no—
165C22×C4⋊C4—44no—
166C22×C4⋊C4D418yescomplemented
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C22⋊C4—24no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C42—24no—
220C22×C42—44no—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225#396—24no—
226#396—24no—
227#394—24no—
228#394—24no—
229#394—44no—
230#392—28no—
231#392—44no—
232#392—44no—
233#390—24no—
234#390—44no—
235#390—44no—
236#389—24no—
237#388—28no—
238#388—28no—
239#388—28no—
240#388—28no—
241#388—44no—
242#387—44no—
243#386—24no—
244#386—24no—
245#386—24no—
246#386—28no—
247#386—24no—
248#386—42no—
249#386—42no—
250#386—42no—
251#386—42no—
252#386—42no—
253#386—42no—
254#386—42no—
255#385—42no—
256#380—24no—
257#380—42no—
258#379—42no—
259C4×C22⋊C4—42no—
260C2×#95—24no—
261C2×#95—24no—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
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—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C25—22no—
295C25—24no—
296C25—22no—
297C25—22no—
298C25—22no—
299C25—22no—
300C25—22no—
301C25—22no—
302C25—42no—
303C25—42no—
304C25—42no—
305C25C2411yescharacteristic
306C25C2411yescharacteristic
307C25C2412yes—
308C25C2411yescharacteristic
309C25C2411yescharacteristic
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4—42no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4#4114yes—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—41no—
396C23×C4—41no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4C2×D414yes—
400C23×C4C2×D414yes—
401C23×C4C2×D414yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420#121—416no—
421#121—416no—
422#121—416no—
423#121—416no—
424#120—416no—
425#120—416no—
426#120—416no—
427C4×D4—416no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—416no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4C2×D414yes—
452C2×C4⋊C4C2×D414yes—
453C2×C4⋊C4C2×D414yes—
454C2×C4⋊C4C2×D414yes—
455C2×C22⋊C4—232no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
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—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—416no—
534C2×C22⋊C4—416no—
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⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4#4118yes—
561C2×C22⋊C4#4114yes—
562C2×C42—22no—
563C2×C42—24no—
564C2×C42—24no—
565C2×C42—24no—
566C2×C42—24no—
567C2×C42—41no—
568C2×C42—41no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—416no—
572C2×C42—42no—
573C2×C42—42no—
574C2×C42—42no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—28no—
612C24—22no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—21no—
625C24—22no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—22no—
657C24—22no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24C22×D412yes—
681C24C2×#4114yes—
682C24C2×#4112yes—
683C24C2×#4112yes—
684C24C2×#4112yes—
685C24H(5,𝔽2)12yes—
686C24H(5,𝔽2)12yes—
687C24H(5,𝔽2)12yes—
688C24H(5,𝔽2)12yes—
689C24C2511yescharacteristic
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—82no—
725C2×D4—84no—
726C2×D4—84no—
727C2×D4—84no—
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—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
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—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
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—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C2×#4114yes—
887C22×C4C2×#4114yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4114yes—
890C22×C4H(5,𝔽2)14yes—
891C22×C4H(5,𝔽2)14yes—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—84no—
901C4⋊C4—84no—
902C22⋊C4—216no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—82no—
927C22⋊C4—82no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C42—48no—
939C42—48no—
940C42—44no—
941C42—84no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—416no—
971C23—416no—
972C23—416no—
973C23—41no—
974C23—42no—
975C23—41no—
976C23—41no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—42no—
982C23—41no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—41no—
990C23—41no—
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—41no—
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—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—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
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—41no—
1056C23—41no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—88no—
1070C23—88no—
1071C23—88no—
1072C23—88no—
1073C23#53514yes—
1074C23#53814yes—
1075C23#53814yes—
1076C23#54614yes—
1077C23#55014yes—
1078C23#55314yes—
1079C23#56014yes—
1080C23C23×D411yescharacteristic
1081C23C22×#4112yes—
1082C23C22×#4111yescharacteristic
1083C23C22×#4111yescharacteristic
1084C23C2×H(5,𝔽2)12yes—
1085C23C2×H(5,𝔽2)11yescharacteristic
1086C23C2×H(5,𝔽2)11yescharacteristic
1087C23C2×H(5,𝔽2)11yescharacteristic
1088C23C2×H(5,𝔽2)11yescharacteristic
1089C23C2×H(5,𝔽2)12yes—
1090C23#58512yes—
1091D4—416no—
1092D4—88no—
1093D4—88no—
1094D4—88no—
1095D4—816no—
1096D4—816no—
1097D4—816no—
1098D4—88no—
1099D4—88no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—416no—
1133C2×C4—416no—
1134C2×C4—416no—
1135C2×C4—416no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—41no—
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—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
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—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—88no—
1213C2×C4—88no—
1214C2×C4—88no—
1215C2×C4#52514yes—
1216C2×C4#53414yes—
1217C22—24no—
1218C22—28no—
1219C22—28no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—28no—
1224C22—24no—
1225C22—28no—
1226C22—24no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—42no—
1233C22—44no—
1234C22—42no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—832no—
1240C22—81no—
1241C22—82no—
1242C22—82no—
1243C22—81no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—81no—
1250C22—82no—
1251C22—82no—
1252C22—81no—
1253C22—82no—
1254C22—81no—
1255C22—81no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—82no—
1267C22—82no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—82no—
1273C22—82no—
1274C22—81no—
1275C22—81no—
1276C22#271418yes—
1277C22C2×#52511yescharacteristic
1278C22C2×#53411yescharacteristic
1279C22C2×#53511yescharacteristic
1280C22C2×#53811yescharacteristic
1281C22C2×#53811yescharacteristic
1282C22C2×#54611yescharacteristic
1283C22C2×#55011yescharacteristic
1284C22C2×#55311yescharacteristic
1285C22#347512yes—
1286C22#348112yes—
1287C22#348411yescharacteristic
1288C22#348711yescharacteristic
1289C22#349412yes—
1290C22#351412yes—
1291C22#351912yes—
1292C22#351912yes—
1293C22#351912yes—
1294C22#351912yes—
1295C22C2×#56011yescharacteristic
1296C22#353412yes—
1297C22#353412yes—
1298C22#353712yes—
1299C22#355812yes—
1300C4—24no—
1301C4—24no—
1302C4—42no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C4—81no—
1311C4—82no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—82no—
1316C4—82no—
1317C4—82no—
1318C2—28no—
1319C2—82no—
1320C2—84no—
1321C2—161no—
1322C2—161no—
1323C2#3507611yescharacteristic
1324C2#3642611yescharacteristic
1325C2#3652911yescharacteristic
1326C2#3671011yescharacteristic
1327C2#3802011yescharacteristic
1328C2#3817412yes—
1329C2#3853712yes—
1330C2#3913511yescharacteristic
1331C2#4603812yes—
1332C2C2×#271411yescharacteristic
1333C2#5968712yes—
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×#2416C2semidirect
2. C22×#388C2semidirect
3. #16497C2semidirect
4. #16341C2semidirect
5. #16087C2semidirect
6. #15607C2semidirect
7. #15428C2semidirect
8. #15320C2semidirect
9. #14945C2semidirect
10. #14913C2semidirect
11. #14725C2semidirect
12. #14716C2semidirect
13. #14716C2semidirect
14. #14716C2semidirect
15. #14698C2semidirect
16. #14696C2semidirect
17. #14567C2semidirect
18. #14415C2semidirect
19. #14152C2semidirect
20. #14016C2semidirect
21. #13995C2semidirect
22. #13967C2semidirect
23. #13882C2semidirect
27. C22×#121C22semidirect
38. C2×#396C22semidirect
39. C2×#396C22semidirect
41. C2×#394C22semidirect
42. C2×#394C22semidirect
47. C2×#390C22semidirect
48. C2×#390C22semidirect
49. C2×#389C22semidirect
55. C2×#388C22semidirect
56. C2×#387C22semidirect
71. C2×#380C22semidirect
76. #1445C22semidirect
77. #1445C22semidirect
78. #1443C22semidirect
79. #1443C22semidirect
80. #1442C22semidirect
81. #1442C22semidirect
82. #1441C22semidirect
84. #1440C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1440C22semidirect
94. #1439C22semidirect
104. #1438C22semidirect
105. #1438C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. C4⋊#95C22semidirect
117. #1434C22semidirect
124. C22⋊#95C22semidirect
166. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24162
C22×#3882
#164972
#163412
#160872
#156072
#154282
#153202
#149452
#149132
#147252
#147162
#146982
#146962
#145672
#144152
#141522
#140162
#139952
#139672
#138822