Finite Group Databasebeta

← #917945

Subgroups — #917945

Order 512.

4058 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic, complemented
2C2×#2416C211yesmaximal, characteristic, complemented
3C2×#2618C211yesmaximal, characteristic, complemented
4C22×#399C211yesmaximal, characteristic, complemented
5#17136C212yesmaximal, complemented
6#17101C212yesmaximal, complemented
7#16555C212yesmaximal, complemented
8#16531C212yesmaximal, complemented
9#16508C212yesmaximal, complemented
10#16276C212yesmaximal, complemented
11#15776C212yesmaximal, complemented
12#15335C212yesmaximal, complemented
13#14926C211yesmaximal, characteristic, complemented
14#14911C211yesmaximal, characteristic, complemented
15#14725C211yesmaximal, characteristic, complemented
16#14719C211yesmaximal, characteristic, complemented
17#14716C211yesmaximal, characteristic, complemented
18#14716C211yesmaximal, characteristic, complemented
19#14256C211yesmaximal, characteristic, complemented
20#14019C211yesmaximal, characteristic, complemented
21#13968C211yesmaximal, characteristic, complemented
22#13967C211yesmaximal, characteristic, complemented
23#13882C211yesmaximal, characteristic, complemented
24C22×#123C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#121C2211yescharacteristic, complemented
31C22×#120C2211yescharacteristic
32C22×#120C2211yescharacteristic
33C22×#120C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C22⋊C4C2211yescharacteristic
41#2618—28no—
42#2539—28no—
43#2416—28no—
44C2×#399—28no—
45C2×#399C2212yes—
46C2×#399C2212yes—
47C2×#399C2212yes—
48C2×#399C2212yes—
49C2×#399C2212yes—
50C2×#398C2212yescomplemented
51C2×#396C2211yescharacteristic, complemented
52C2×#396C2211yescharacteristic, complemented
53C2×#396C2212yescomplemented
54C2×#396C2212yescomplemented
55C2×#394C2212yes—
56C2×#394C2211yescharacteristic, complemented
57C2×#394C2211yescharacteristic, complemented
58C2×#394C2212yescomplemented
59C2×#394C2212yescomplemented
60C2×#392C2212yes—
61C2×#392C2212yes—
62C2×#392C2212yes—
63C2×#390C2212yes—
64C2×#390C2212yes—
65C2×#390C2211yescharacteristic, complemented
66C2×#389C2211yescharacteristic, complemented
67C2×#388C2212yescomplemented
68C2×#387C2212yescomplemented
69C2×#386C2211yescharacteristic
70C2×#386C2211yescharacteristic
71C2×#386C2211yescharacteristic
72C2×#386C2211yescharacteristic
73C2×#386C2211yescharacteristic
74C2×#386C2211yescharacteristic
75C2×#386C2211yescharacteristic
76C2×#386C2211yescharacteristic
77C2×#386C2212yes—
78C2×#381C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2211yescharacteristic, complemented
81C2×#379C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C22×#95C2211yescharacteristic
84#1445C2212yescomplemented
85#1444C2212yescomplemented
86#1442C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1440C2212yes—
93#1440C2212yescomplemented
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yescomplemented
116#1437C2212yes—
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C2×#123—24no—
145C2×#123—24no—
146C2×#123—24no—
147C2×#123—42no—
148C2×#123—42no—
149C2×#123—42no—
150C2×#123—42no—
151C2×#123—42no—
152C2×#123D418yescomplemented
153C2×#121—24no—
154C2×#121—24no—
155C2×#121—24no—
156C2×#121—24no—
157C2×#121—24no—
158C2×#121—24no—
159C2×#121—44no—
160C2×#121—42no—
161C2×#121—42no—
162C2×#121—42no—
163C2×#121—42no—
164C2×#120—24no—
165C2×#120—24no—
166C2×#120—24no—
167C2×#120—42no—
168C2×#120—42no—
169C2×#120—42no—
170C2×#120—42no—
171C2×#120—42no—
172C2×#120—42no—
173C2×C4×D4—24no—
174C2×C4×D4—42no—
175C2×C4×D4—42no—
176C22×C4⋊C4—24no—
177C22×C4⋊C4—24no—
178C22×C4⋊C4—24no—
179C22×C4⋊C4—44no—
180C22×C4⋊C4—44no—
181C22×C4⋊C4—42no—
182C22×C4⋊C4D418yescomplemented
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C22⋊C4—24no—
200C22×C22⋊C4—24no—
201C22×C22⋊C4—24no—
202C22×C22⋊C4—24no—
203C22×C22⋊C4—44no—
204C22×C22⋊C4—44no—
205C22×C22⋊C4—42no—
206C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C42C2311yescharacteristic
243C22×C42C2312yes—
244#399—28no—
245#399—28no—
246#399—28no—
247#399—28no—
248#399—28no—
249#398—28no—
250#396—28no—
251#396—24no—
252#396—24no—
253#396—28no—
254#394—24no—
255#394—24no—
256#394—28no—
257#394—44no—
258#394—44no—
259#392—28no—
260#392—44no—
261#392—44no—
262#390—24no—
263#390—28no—
264#390—28no—
265#389—24no—
266#388—44no—
267#387—44no—
268#386—24no—
269#386—24no—
270#386—24no—
271#386—24no—
272#386—24no—
273#386—44no—
274#386—42no—
275#386—42no—
276#386—42no—
277#381—42no—
278#380—24no—
279#380—24no—
280#379—42no—
281C4×C22⋊C4—24no—
282C2×#95—24no—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C25—22no—
312C25—24no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C25C2411yescharacteristic
325C25C2412yes—
326C25C2411yescharacteristic
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—41no—
366C22×D4—41no—
367C22×D4—41no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—41no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4C2×D414yes—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—41no—
415C23×C4—41no—
416C23×C4—42no—
417C23×C4C2×D414yes—
418C23×C4C2×D414yes—
419C23×C4C2×D414yes—
420C23×C4C2×D414yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439#123—416no—
440#123—416no—
441#123—416no—
442#121—416no—
443#121—416no—
444#121—416no—
445#121—416no—
446#120—416no—
447#120—416no—
448#120—416no—
449C4×D4—416no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—416no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—416no—
489C2×C4⋊C4—416no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4C2×D414yes—
493C2×C4⋊C4C2×D414yes—
494C2×C4⋊C4C2×D414yes—
495C2×C4⋊C4C2×D414yes—
496C2×C4⋊C4C2×D418yes—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
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—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—416no—
581C2×C22⋊C4—416no—
582C2×C22⋊C4—416no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4C2×D414yes—
602C2×C22⋊C4C2×D418yes—
603C2×C22⋊C4#4114yes—
604C2×C42—22no—
605C2×C42—24no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42—42no—
609C2×C42—42no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—22no—
614#95—22no—
615#95—24no—
616#95—22no—
617#95—22no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—28no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—22no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—22no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—22no—
680C24—22no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24C22×D412yes—
712C24C22×D412yes—
713C24C22×D412yes—
714C24C2×#4112yes—
715C24H(5,𝔽2)12yes—
716C24H(5,𝔽2)12yes—
717C24H(5,𝔽2)12yes—
718C24H(5,𝔽2)12yes—
719C242−1+414yes—
720C24C2511yescharacteristic
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—82no—
758C2×D4—82no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4—84no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—28no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
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×C4C22×D414yes—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C22×D414yes—
921C22×C4C22×D412yes—
922C22×C4C2×#4114yes—
923C22×C4H(5,𝔽2)14yes—
924C22×C4H(5,𝔽2)14yes—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—48no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—48no—
940C4⋊C4—84no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—48no—
968C22⋊C4—82no—
969C22⋊C4—82no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C22⋊C4—84no—
973C22⋊C4—84no—
974C22⋊C4—84no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C42—44no—
978C42—84no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—416no—
1008C23—416no—
1009C23—416no—
1010C23—42no—
1011C23—42no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—41no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—41no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
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—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—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—41no—
1085C23—41no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—88no—
1107C23—88no—
1108C23—88no—
1109C23—88no—
1110C23#53414yes—
1111C23#53514yes—
1112C23#54014yes—
1113C23D4214yes—
1114C23#54614yes—
1115C23#55014yes—
1116C23#56014yes—
1117C23C23×D411yescharacteristic
1118C23C23×D411yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C2×H(5,𝔽2)11yescharacteristic
1121C23C2×H(5,𝔽2)11yescharacteristic
1122C23C2×H(5,𝔽2)12yes—
1123C23C2×H(5,𝔽2)11yescharacteristic
1124C23C2×H(5,𝔽2)11yescharacteristic
1125C23C2×H(5,𝔽2)12yes—
1126C23C2×2−1+412yes—
1127C23#58512yes—
1128D4—416no—
1129D4—88no—
1130D4—816no—
1131D4—88no—
1132D4—88no—
1133D4—816no—
1134D4—816no—
1135D4—88no—
1136D4—88no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—416no—
1172C2×C4—416no—
1173C2×C4—416no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—42no—
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—41no—
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—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—88no—
1250C2×C4—88no—
1251C2×C4—88no—
1252C2×C4—88no—
1253C2×C4#53414yes—
1254C22—24no—
1255C22—24no—
1256C22—28no—
1257C22—24no—
1258C22—28no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—28no—
1263C22—28no—
1264C22—42no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—42no—
1269C22—44no—
1270C22—42no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—832no—
1277C22—81no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—81no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—81no—
1287C22—82no—
1288C22—81no—
1289C22—82no—
1290C22—82no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—82no—
1296C22—82no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—82no—
1302C22—82no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—82no—
1310C22—82no—
1311C22—82no—
1312C22—82no—
1313C22#267318yes—
1314C22C2×#53411yescharacteristic
1315C22C2×#53411yescharacteristic
1316C22C2×#53511yescharacteristic
1317C22#344911yescharacteristic
1318C22C2×#54011yescharacteristic
1319C22C2×D4211yescharacteristic
1320C22C2×#54611yescharacteristic
1321C22C2×#55011yescharacteristic
1322C22#348411yescharacteristic
1323C22#348611yescharacteristic
1324C22#348912yes—
1325C22#349812yes—
1326C22#351312yes—
1327C22#352012yes—
1328C22C2×#56011yescharacteristic
1329C22#353412yes—
1330C22#353412yes—
1331C22#353412yes—
1332C22#353512yes—
1333C22#353612yes—
1334C22#353612yes—
1335C22#353612yes—
1336C22#354312yes—
1337C4—24no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—44no—
1346C4—44no—
1347C4—44no—
1348C4—81no—
1349C4—82no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—82no—
1354C4—82no—
1355C2—28no—
1356C2—82no—
1357C2—84no—
1358C2—161no—
1359C2—161no—
1360C2#3670711yescharacteristic
1361C2#3744011yescharacteristic
1362C2#3765311yescharacteristic
1363C2#3912811yescharacteristic
1364C2#3913311yescharacteristic
1365C2#3933611yescharacteristic
1366C2#4084612yes—
1367C2#4195212yes—
1368C2#4402212yes—
1369C2C2×#267311yescharacteristic
1370C2#5254812yes—
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×#2539C2semidirect
2. C2×#2416C2semidirect
3. C2×#2618C2semidirect
4. C22×#399C2semidirect
5. #17136C2semidirect
6. #17101C2semidirect
7. #16555C2semidirect
8. #16531C2semidirect
9. #16508C2semidirect
10. #16276C2semidirect
11. #15776C2semidirect
12. #15335C2semidirect
13. #14926C2semidirect
14. #14911C2semidirect
15. #14725C2semidirect
16. #14719C2semidirect
17. #14716C2semidirect
18. #14716C2semidirect
19. #14256C2semidirect
20. #14019C2semidirect
21. #13968C2semidirect
22. #13967C2semidirect
23. #13882C2semidirect
30. C22×#121C22semidirect
50. C2×#398C22semidirect
51. C2×#396C22semidirect
52. C2×#396C22semidirect
53. C2×#396C22semidirect
54. C2×#396C22semidirect
56. C2×#394C22semidirect
57. C2×#394C22semidirect
58. C2×#394C22semidirect
59. C2×#394C22semidirect
65. C2×#390C22semidirect
66. C2×#389C22semidirect
67. C2×#388C22semidirect
68. C2×#387C22semidirect
80. C2×#380C22semidirect
84. #1445C22semidirect
85. #1444C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
93. #1440C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
115. #1438C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
126. C22⋊#95C22semidirect
152. C2×#123D4semidirect
182. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25392
C2×#24162
C2×#26182
C22×#3992
#171362
#171012
#165552
#165312
#165082
#162762
#157762
#153352
#149262
#149112
#147252
#147192
#147162
#142562
#140192
#139682
#139672
#138822