Finite Group Databasebeta

← #617436

Subgroups — #617436

Order 512.

4278 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic, complemented
2C2×#2539C211yesmaximal, characteristic, complemented
3C2×#2534C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic, complemented
5C2×#2617C211yesmaximal, characteristic, complemented
6C22×#388C211yesmaximal, characteristic, complemented
7#15666C212yesmaximal, complemented
8#15655C212yesmaximal, complemented
9#15617C212yesmaximal, complemented
10#15615C212yesmaximal, complemented
11#15423C212yesmaximal, complemented
12#15394C212yesmaximal, complemented
13#15351C212yesmaximal, complemented
14#15320C212yesmaximal, complemented
15#14927C211yesmaximal, characteristic, complemented
16#14926C211yesmaximal, characteristic, complemented
17#14725C211yesmaximal, characteristic, complemented
18#14716C211yesmaximal, characteristic, complemented
19#14706C211yesmaximal, characteristic, complemented
20#14271C211yesmaximal, characteristic, complemented
21#14255C211yesmaximal, characteristic, complemented
22#13907C211yesmaximal, characteristic, complemented
23#13784C211yesmaximal, 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×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C42C2211yescharacteristic
40#2854—28no—
41#2617—28no—
42#2539—28no—
43#2534—28no—
44#2416—28no—
45C2×#399C2212yes—
46C2×#397C2212yes—
47C2×#396C2212yes—
48C2×#396C2211yescharacteristic, complemented
49C2×#396C2211yescharacteristic, complemented
50C2×#394C2212yes—
51C2×#394C2212yes—
52C2×#394C2212yes—
53C2×#394C2212yes—
54C2×#394C2211yescharacteristic, complemented
55C2×#394C2211yescharacteristic, complemented
56C2×#392C2212yes—
57C2×#392C2212yes—
58C2×#392C2212yes—
59C2×#390C2212yes—
60C2×#390C2212yes—
61C2×#390C2212yescomplemented
62C2×#390C2211yescharacteristic, complemented
63C2×#389C2212yescomplemented
64C2×#389C2211yescharacteristic, complemented
65C2×#389C2212yescomplemented
66C2×#388—28no—
67C2×#388C2212yes—
68C2×#388C2212yes—
69C2×#388C2212yes—
70C2×#388C2212yes—
71C2×#388C2212yes—
72C2×#388C2212yescomplemented
73C2×#388C2212yescomplemented
74C2×#386C2212yes—
75C2×#386C2211yescharacteristic
76C2×#386C2211yescharacteristic
77C2×#386C2211yescharacteristic
78C2×#386C2211yescharacteristic
79C2×#386C2211yescharacteristic
80C2×#386C2211yescharacteristic
81C2×#386C2211yescharacteristic
82C2×#386C2211yescharacteristic
83C2×#381C2211yescharacteristic
84C2×#380C2211yescharacteristic
85C2×#380C2211yescharacteristic
86C2×#380C2211yescharacteristic
87C2×#380C2211yescharacteristic, complemented
88C2×#379C2211yescharacteristic
89C2×C4×C22⋊C4C2211yescharacteristic
90C22×#95C2211yescharacteristic
91C22×#95C2211yescharacteristic
92#1445C2212yescomplemented
93#1444C2212yescomplemented
94#1442C2212yescomplemented
95#1441C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1440C2212yes—
99#1440C2212yes—
100#1440C2212yes—
101#1440C2212yescomplemented
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122C4⋊#95C2212yescomplemented
123#1434C2212yescomplemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C2×#123—24no—
147C2×#123—24no—
148C2×#123—24no—
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—42no—
153C2×#123—42no—
154C2×#123—42no—
155C2×#121—24no—
156C2×#121—24no—
157C2×#121—24no—
158C2×#121—24no—
159C2×#121—24no—
160C2×#121—24no—
161C2×#121—24no—
162C2×#121—24no—
163C2×#121—44no—
164C2×#121—42no—
165C2×#121—42no—
166C2×#120—24no—
167C2×#120—24no—
168C2×#120—24no—
169C2×#120—24no—
170C2×#120—24no—
171C2×#120—24no—
172C2×#120—42no—
173C2×#120—42no—
174C2×#120—42no—
175C2×C4×D4—24no—
176C2×C4×D4—24no—
177C2×C4×D4—24no—
178C22×C4⋊C4—44no—
179C22×C4⋊C4D418yescomplemented
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C22⋊C4—24no—
195C22×C22⋊C4—24no—
196C22×C22⋊C4—24no—
197C22×C22⋊C4—24no—
198C22×C22⋊C4—24no—
199C22×C22⋊C4—44no—
200C22×C22⋊C4—42no—
201C22×C22⋊C4D418yescomplemented
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C42—24no—
239C22×C42—24no—
240C22×C42—42no—
241C22×C42C2311yescharacteristic
242C22×C42C2312yes—
243C22×C42C2312yes—
244C22×C42C2312yes—
245#399—28no—
246#397—28no—
247#396—24no—
248#396—24no—
249#396—28no—
250#394—24no—
251#394—24no—
252#394—28no—
253#394—28no—
254#394—28no—
255#394—44no—
256#392—28no—
257#392—28no—
258#392—44no—
259#390—24no—
260#390—28no—
261#390—28no—
262#390—28no—
263#389—24no—
264#389—28no—
265#389—44no—
266#388—28no—
267#388—28no—
268#388—28no—
269#388—28no—
270#388—28no—
271#388—28no—
272#388—28no—
273#386—24no—
274#386—24no—
275#386—24no—
276#386—24no—
277#386—28no—
278#386—24no—
279#386—42no—
280#386—42no—
281#386D418yescomplemented
282#381—24no—
283#380—24no—
284#380—24no—
285#380—24no—
286#380—24no—
287#379—24no—
288C4×C22⋊C4—24no—
289C2×#95—24no—
290C2×#95—24no—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25C2×D414yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2412yes—
333C25C2411yescharacteristic
334C25C2411yescharacteristic
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—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—24no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—42no—
374C22×D4—41no—
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×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4C2×D414yes—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4C2×D414yes—
423C23×C4C2×D414yes—
424C23×C4C2×D414yes—
425C23×C4C2×D414yes—
426C23×C4C2×D414yes—
427C23×C4C2×D414yes—
428C23×C4#4114yes—
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2412yes—
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447#123—416no—
448#123—416no—
449#123—416no—
450#121—416no—
451#121—416no—
452#121—416no—
453#121—416no—
454#120—416no—
455#120—416no—
456#120—416no—
457C4×D4—416no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—416no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4C2×D414yes—
494C2×C4⋊C4C2×D414yes—
495C2×C4⋊C4C2×D414yes—
496C2×C4⋊C4C2×D414yes—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—232no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—416no—
584C2×C22⋊C4—416no—
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⋊C4C2×D418yes—
600C2×C22⋊C4C2×D418yes—
601C2×C22⋊C4C2×D414yes—
602C2×C22⋊C4C2×D418yes—
603C2×C22⋊C4#4114yes—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42—24no—
609C2×C42—24no—
610C2×C42—22no—
611C2×C42—24no—
612C2×C42—42no—
613C2×C42—42no—
614C2×C42—416no—
615C2×C42—42no—
616C2×C42—42no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—22no—
624#95—22no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—22no—
631#95—22no—
632#95—24no—
633#95—24no—
634#95—24no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95—42no—
642#95—42no—
643#95—42no—
644#95C2×D418yes—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—28no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—21no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—28no—
675C24—28no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—21no—
688C24—21no—
689C24—22no—
690C24—21no—
691C24—21no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—48no—
699C24—48no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—48no—
705C24—48no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24C22×D414yes—
719C24C22×D412yes—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C22×D412yes—
723C24C2×#4112yes—
724C24C2×#4112yes—
725C24H(5,𝔽2)12yes—
726C24H(5,𝔽2)12yes—
727C24C2511yescharacteristic
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
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—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—82no—
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—
778C2×D4—84no—
779C2×D4—84no—
780C2×D4—84no—
781C2×D4—84no—
782C2×D4—84no—
783C2×D4—84no—
784C2×D4—84no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
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—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—28no—
840C22×C4—28no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—48no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—84no—
910C22×C4—84no—
911C22×C4—84no—
912C22×C4—84no—
913C22×C4—84no—
914C22×C4—84no—
915C22×C4#121116yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D414yes—
919C22×C4C22×D414yes—
920C22×C4C22×D414yes—
921C22×C4C22×D412yes—
922C22×C4C22×D412yes—
923C22×C4C22×D412yes—
924C22×C4C22×D412yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D412yes—
928C22×C4C2×#4114yes—
929C22×C4C2×#4112yes—
930C22×C4C2×#4112yes—
931C22×C4H(5,𝔽2)14yes—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—48no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—84no—
945C4⋊C4—84no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—216no—
949C22⋊C4—216no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—82no—
976C22⋊C4—82no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C22⋊C4—84no—
982C42—48no—
983C42—48no—
984C42—44no—
985C42—84no—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—22no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—22no—
1007C23—22no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—416no—
1015C23—416no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—41no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—416no—
1024C23—41no—
1025C23—42no—
1026C23—42no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—41no—
1035C23—42no—
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—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—42no—
1072C23—42no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—42no—
1084C23—41no—
1085C23—41no—
1086C23—42no—
1087C23—41no—
1088C23—41no—
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—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—816no—
1110C23—816no—
1111C23—88no—
1112C23—88no—
1113C23—816no—
1114C23—816no—
1115C23—88no—
1116C23—88no—
1117C23C2×#12114yes—
1118C23#53214yes—
1119C23#54014yes—
1120C23D4214yes—
1121C23D4214yes—
1122C23#54614yes—
1123C23#55014yes—
1124C23C23×D411yescharacteristic
1125C23C23×D411yescharacteristic
1126C23C23×D411yescharacteristic
1127C23C22×#4111yescharacteristic
1128C23C22×#4111yescharacteristic
1129C23C2×H(5,𝔽2)12yes—
1130C23C2×H(5,𝔽2)11yescharacteristic
1131C23C2×H(5,𝔽2)11yescharacteristic
1132C23#58512yes—
1133C23#58512yes—
1134C23#58512yes—
1135D4—416no—
1136D4—88no—
1137D4—88no—
1138D4—88no—
1139D4—816no—
1140D4—816no—
1141D4—816no—
1142D4—88no—
1143D4—88no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—416no—
1181C2×C4—416no—
1182C2×C4—416no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—416no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
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—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—42no—
1238C2×C4—41no—
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—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—88no—
1256C2×C4—88no—
1257C2×C4—88no—
1258C2×C4C2×#12114yes—
1259C2×C4C2×#12114yes—
1260C2×C4#53414yes—
1261C22—24no—
1262C22—24no—
1263C22—28no—
1264C22—24no—
1265C22—28no—
1266C22—28no—
1267C22—24no—
1268C22—28no—
1269C22—24no—
1270C22—24no—
1271C22—42no—
1272C22—42no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—832no—
1284C22—82no—
1285C22—82no—
1286C22—81no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—81no—
1293C22—82no—
1294C22—81no—
1295C22—82no—
1296C22—81no—
1297C22—82no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—82no—
1303C22—82no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—82no—
1312C22—81no—
1313C22—81no—
1314C22—82no—
1315C22—82no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22#242818yes—
1321C22C22×#12111yescharacteristic
1322C22C2×#53211yescharacteristic
1323C22C2×#53411yescharacteristic
1324C22#344911yescharacteristic
1325C22#344912yes—
1326C22C2×#54011yescharacteristic
1327C22C2×D4211yescharacteristic
1328C22C2×D4211yescharacteristic
1329C22C2×#54611yescharacteristic
1330C22C2×#55011yescharacteristic
1331C22#348511yescharacteristic
1332C22#348512yes—
1333C22#348711yescharacteristic
1334C22#348812yes—
1335C22#349312yes—
1336C22#349612yes—
1337C22#350512yes—
1338C22#351412yes—
1339C22#352112yes—
1340C22#353312yes—
1341C22#353412yes—
1342C22#355812yes—
1343C22#356012yes—
1344C4—24no—
1345C4—24no—
1346C4—24no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—44no—
1352C4—44no—
1353C4—42no—
1354C4—44no—
1355C4—82no—
1356C4—82no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—82no—
1362C2—28no—
1363C2—82no—
1364C2—84no—
1365C2—161no—
1366C2—161no—
1367C2C2×#242811yescharacteristic
1368C2#3500011yescharacteristic
1369C2#3515011yescharacteristic
1370C2#3546512yes—
1371C2#3698712yes—
1372C2#3764611yescharacteristic
1373C2#3765511yescharacteristic
1374C2#3767812yes—
1375C2#3808612yes—
1376C2#3912911yescharacteristic
1377C2#3913511yescharacteristic
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×#2854C2semidirect
2. C2×#2539C2semidirect
3. C2×#2534C2semidirect
4. C2×#2416C2semidirect
5. C2×#2617C2semidirect
6. C22×#388C2semidirect
7. #15666C2semidirect
8. #15655C2semidirect
9. #15617C2semidirect
10. #15615C2semidirect
11. #15423C2semidirect
12. #15394C2semidirect
13. #15351C2semidirect
14. #15320C2semidirect
15. #14927C2semidirect
16. #14926C2semidirect
17. #14725C2semidirect
18. #14716C2semidirect
19. #14706C2semidirect
20. #14271C2semidirect
21. #14255C2semidirect
22. #13907C2semidirect
23. #13784C2semidirect
30. C22×#121C22semidirect
48. C2×#396C22semidirect
49. C2×#396C22semidirect
54. C2×#394C22semidirect
55. C2×#394C22semidirect
61. C2×#390C22semidirect
62. C2×#390C22semidirect
63. C2×#389C22semidirect
64. C2×#389C22semidirect
65. C2×#389C22semidirect
72. C2×#388C22semidirect
73. C2×#388C22semidirect
87. C2×#380C22semidirect
92. #1445C22semidirect
93. #1444C22semidirect
94. #1442C22semidirect
95. #1441C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
101. #1440C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. C4⋊#95C22semidirect
123. #1434C22semidirect
128. C22⋊#95C22semidirect
179. C22×C4⋊C4D4semidirect
201. C22×C22⋊C4D4semidirect
281. #386D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#25392
C2×#25342
C2×#24162
C2×#26172
C22×#3882
#156662
#156552
#156172
#156152
#154232
#153942
#153512
#153202
#149272
#149262
#147252
#147162
#147062
#142712
#142552
#139072
#137842