Finite Group Databasebeta

← #918632

Subgroups — #918632

Order 512.

4655 conjugacy classes of subgroups.

The subgroup lattice has 1417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic, complemented
2C2×#2534C211yesmaximal, characteristic, complemented
3C2×#2444C211yesmaximal, characteristic, complemented
4C22×#394C211yesmaximal, characteristic, complemented
5#17126C212yesmaximal, complemented
6#17083C212yesmaximal, complemented
7#16552C212yesmaximal, complemented
8#16350C212yesmaximal, complemented
9#16284C212yesmaximal, complemented
10#16274C212yesmaximal, complemented
11#15423C212yesmaximal, complemented
12#15299C212yesmaximal, complemented
13#14918C211yesmaximal, characteristic, complemented
14#14911C211yesmaximal, characteristic, complemented
15#14725C211yesmaximal, characteristic, complemented
16#14716C211yesmaximal, characteristic, complemented
17#14715C211yesmaximal, characteristic, complemented
18#14715C211yesmaximal, characteristic, complemented
19#14256C211yesmaximal, characteristic, complemented
20#14256C211yesmaximal, characteristic, complemented
21#13971C211yesmaximal, characteristic, complemented
22#13967C211yesmaximal, characteristic, complemented
23#13883C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×#120C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38#2539—28no—
39#2534—28no—
40#2444—28no—
41C2×#400C2211yescharacteristic, complemented
42C2×#399C2212yescomplemented
43C2×#397C2211yescharacteristic, complemented
44C2×#397C2211yescharacteristic, complemented
45C2×#396C2212yescomplemented
46C2×#394—28no—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#394C2212yescomplemented
52C2×#394C2211yescharacteristic, complemented
53C2×#394C2212yescomplemented
54C2×#392C2212yes—
55C2×#392C2212yes—
56C2×#392C2212yes—
57C2×#392C2212yes—
58C2×#392C2212yescomplemented
59C2×#392C2212yescomplemented
60C2×#390C2212yescomplemented
61C2×#390C2212yescomplemented
62C2×#388C2212yescomplemented
63C2×#388C2211yescharacteristic, complemented
64C2×#388C2212yescomplemented
65C2×#387C2211yescharacteristic, complemented
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2211yescharacteristic
71C2×#386C2212yescomplemented
72C2×#386C2211yescharacteristic, complemented
73C2×#386C2212yescomplemented
74C2×#385C2211yescharacteristic
75C2×#381C2211yescharacteristic
76C2×#381C2211yescharacteristic
77C2×#381C2211yescharacteristic, complemented
78C2×#380C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×#379C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C22×#95C2211yescharacteristic
85#1443C2212yescomplemented
86#1442C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1438C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1434C2212yescomplemented
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—42no—
131C23×D4—42no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C23×D4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—42no—
152C2×#123—42no—
153C2×#123—42no—
154C2×#123D418yescomplemented
155C2×#121—24no—
156C2×#121—24no—
157C2×#121—42no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—24no—
161C2×#120—24no—
162C2×#120—42no—
163C2×#120—42no—
164C2×#120—42no—
165C2×#120—42no—
166C2×#120—42no—
167C2×#120—42no—
168C2×#120—42no—
169C2×#120—42no—
170C2×C4×D4—24no—
171C2×C4×D4—24no—
172C2×C4×D4—42no—
173C22×C4⋊C4—24no—
174C22×C4⋊C4—42no—
175C22×C4⋊C4—42no—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C22⋊C4—24no—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—24no—
188C22×C22⋊C4—24no—
189C22×C22⋊C4—24no—
190C22×C22⋊C4—24no—
191C22×C22⋊C4—44no—
192C22×C22⋊C4—44no—
193C22×C22⋊C4—42no—
194C22×C22⋊C4—42no—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236#400—24no—
237#399—28no—
238#397—24no—
239#397—24no—
240#396—28no—
241#394—28no—
242#394—28no—
243#394—28no—
244#394—28no—
245#394—28no—
246#394—24no—
247#394—44no—
248#392—28no—
249#392—44no—
250#392—44no—
251#392—44no—
252#392—44no—
253#392—44no—
254#390—28no—
255#390—28no—
256#388—28no—
257#388—24no—
258#388—44no—
259#387—24no—
260#386—24no—
261#386—24no—
262#386—24no—
263#386—28no—
264#386—24no—
265#386—44no—
266#386—42no—
267#386—42no—
268#385—24no—
269#381—24no—
270#381—24no—
271#381—42no—
272#380—24no—
273#379—24no—
274#379—24no—
275#379—42no—
276#379—42no—
277C4×C22⋊C4—24no—
278C2×#95D418yescomplemented
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
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×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C25—22no—
312C25—22no—
313C25—24no—
314C25—24no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—22no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25—42no—
331C25—42no—
332C25—42no—
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C25C2412yes—
336C25C2412yes—
337C25C2411yescharacteristic
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—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—24no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—416no—
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—41no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4—42no—
393C22×D4—42no—
394C22×D4—42no—
395C22×D4—42no—
396C22×D4—42no—
397C22×D4—42no—
398C22×D4—42no—
399C22×D4—416no—
400C22×D4—416no—
401C22×D4—432no—
402C22×D4—432no—
403C22×D4C2×D414yes—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—41no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4C2×D414yes—
433C23×C4C2×D414yes—
434C23×C4C2×D414yes—
435C23×C4C2×D414yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454#123—416no—
455#123—416no—
456#121—416no—
457#120—416no—
458#120—416no—
459#120—416no—
460#120—416no—
461C4×D4—416no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—416no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4C2×D418yescomplemented
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
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—24no—
511C2×C22⋊C4—24no—
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—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—22no—
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—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—24no—
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—41no—
558C2×C22⋊C4—42no—
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—42no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—416no—
572C2×C22⋊C4—416no—
573C2×C22⋊C4—416no—
574C2×C22⋊C4—416no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
601C2×C22⋊C4C2×D418yescomplemented
602C2×C22⋊C4#4114yes—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—24no—
606C2×C42—41no—
607C2×C42—42no—
608C2×C42—42no—
609#95—24no—
610#95—24no—
611#95—22no—
612#95—22no—
613#95—24no—
614#95—22no—
615#95—24no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—42no—
622#95—42no—
623#95—42no—
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#95C2×D414yes—
638#95C2×D414yes—
639#95C2×D414yes—
640#95C2×D414yes—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—28no—
646C24—28no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—22no—
660C24—21no—
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—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—21no—
693C24—21no—
694C24—22no—
695C24—22no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—44no—
712C24—44no—
713C24—44no—
714C24—44no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24—44no—
720C24—44no—
721C24—44no—
722C24—44no—
723C24—44no—
724C24—44no—
725C24—44no—
726C24—44no—
727C24—44no—
728C24—84no—
729C24—84no—
730C24—84no—
731C24—84no—
732C24—84no—
733C24—84no—
734C24—84no—
735C24—84no—
736C24—84no—
737C24—84no—
738C24—84no—
739C24—84no—
740C24C22×D412yes—
741C24C22×D412yes—
742C24C22×D412yes—
743C24C2×#4112yes—
744C24H(5,𝔽2)14yes—
745C24H(5,𝔽2)14yes—
746C24H(5,𝔽2)12yes—
747C24H(5,𝔽2)12yes—
748C24H(5,𝔽2)12yes—
749C24H(5,𝔽2)12yes—
750C24C2511yescharacteristic
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—44no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—44no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—4128no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—82no—
791C2×D4—84no—
792C2×D4—84no—
793C2×D4—84no—
794C2×D4—84no—
795C2×D4—84no—
796C2×D4—84no—
797C2×D4—84no—
798C2×D4—84no—
799C2×D4—84no—
800C2×D4—84no—
801C2×D4—84no—
802C2×D4—84no—
803C2×D4—84no—
804C2×D4—84no—
805C2×D4—84no—
806C2×D4—84no—
807C2×D4—84no—
808C2×D4—84no—
809C2×D4—84no—
810C2×D4—84no—
811C2×D4—84no—
812C2×D4—84no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
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—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—28no—
866C22×C4—28no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—48no—
924C22×C4—48no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—82no—
933C22×C4—84no—
934C22×C4—84no—
935C22×C4—84no—
936C22×C4—84no—
937C22×C4—84no—
938C22×C4—84no—
939C22×C4—84no—
940C22×C4—84no—
941C22×C4C22×D412yes—
942C22×C4C22×D412yes—
943C22×C4C22×D414yes—
944C22×C4C22×D414yes—
945C22×C4C22×D412yes—
946C22×C4C22×D412yes—
947C22×C4C22×D412yes—
948C22×C4C22×D412yes—
949C22×C4C22×D412yes—
950C22×C4C2×#4114yes—
951C4⋊C4—48no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—48no—
955C4⋊C4—44no—
956C4⋊C4—48no—
957C4⋊C4—48no—
958C4⋊C4—82no—
959C4⋊C4—84no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—82no—
987C22⋊C4—82no—
988C22⋊C4—82no—
989C22⋊C4—82no—
990C22⋊C4—82no—
991C22⋊C4—84no—
992C22⋊C4—84no—
993C22⋊C4—84no—
994C22⋊C4—84no—
995C22⋊C4—84no—
996C22⋊C4—84no—
997C22⋊C4—84no—
998C22⋊C4—84no—
999C42—44no—
1000C42—84no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—416no—
1037C23—416no—
1038C23—416no—
1039C23—416no—
1040C23—416no—
1041C23—416no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—41no—
1061C23—42no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
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—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—42no—
1127C23—42no—
1128C23—42no—
1129C23—42no—
1130C23—41no—
1131C23—42no—
1132C23—42no—
1133C23—42no—
1134C23—42no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23—816no—
1140C23—816no—
1141C23—816no—
1142C23—816no—
1143C23—816no—
1144C23—816no—
1145C23—816no—
1146C23—816no—
1147C23—88no—
1148C23—88no—
1149C23—88no—
1150C23—88no—
1151C23—88no—
1152C23—88no—
1153C23—88no—
1154C23—88no—
1155C23#53414yes—
1156C23#53514yes—
1157C23#54014yes—
1158C23D4214yes—
1159C23#54614yes—
1160C23#55014yes—
1161C23#56014yes—
1162C23C23×D411yescharacteristic
1163C23C23×D411yescharacteristic
1164C23C22×#4111yescharacteristic
1165C23C2×H(5,𝔽2)11yescharacteristic
1166C23C2×H(5,𝔽2)11yescharacteristic
1167C23C2×H(5,𝔽2)11yescharacteristic
1168C23C2×H(5,𝔽2)11yescharacteristic
1169C23C2×H(5,𝔽2)12yes—
1170C23C2×H(5,𝔽2)12yes—
1171C23#58512yes—
1172C23#58512yes—
1173D4—432no—
1174D4—432no—
1175D4—416no—
1176D4—816no—
1177D4—88no—
1178D4—816no—
1179D4—816no—
1180D4—816no—
1181D4—88no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—416no—
1213C2×C4—416no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—41no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
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—41no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—41no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—42no—
1281C2×C4—42no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—88no—
1291C2×C4—88no—
1292C2×C4—88no—
1293C2×C4—88no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—28no—
1298C22—28no—
1299C22—24no—
1300C22—24no—
1301C22—28no—
1302C22—24no—
1303C22—28no—
1304C22—42no—
1305C22—42no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—832no—
1324C22—832no—
1325C22—82no—
1326C22—82no—
1327C22—81no—
1328C22—82no—
1329C22—82no—
1330C22—82no—
1331C22—82no—
1332C22—82no—
1333C22—82no—
1334C22—82no—
1335C22—82no—
1336C22—81no—
1337C22—81no—
1338C22—82no—
1339C22—82no—
1340C22—82no—
1341C22—82no—
1342C22—81no—
1343C22—82no—
1344C22—82no—
1345C22—82no—
1346C22—82no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—82no—
1351C22—82no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—82no—
1356C22—81no—
1357C22—82no—
1358C22#267318yes—
1359C22C2×#53411yescharacteristic
1360C22C2×#53511yescharacteristic
1361C22#344911yescharacteristic
1362C22#344911yescharacteristic
1363C22C2×#54011yescharacteristic
1364C22C2×D4211yescharacteristic
1365C22C2×#54611yescharacteristic
1366C22C2×#55011yescharacteristic
1367C22#348411yescharacteristic
1368C22#348411yescharacteristic
1369C22#348812yes—
1370C22#348812yes—
1371C22#351312yes—
1372C22#351312yes—
1373C22C2×#56011yescharacteristic
1374C22#353212yes—
1375C22#353212yes—
1376C22#353412yes—
1377C22#353412yes—
1378C22#353412yes—
1379C22#353412yes—
1380C22#354512yes—
1381C22#354512yes—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—42no—
1390C4—44no—
1391C4—44no—
1392C4—81no—
1393C4—81no—
1394C4—82no—
1395C4—82no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—82no—
1400C2—28no—
1401C2—82no—
1402C2—84no—
1403C2—84no—
1404C2—161no—
1405C2#3670311yescharacteristic
1406C2#3760611yescharacteristic
1407C2#3765211yescharacteristic
1408C2#3765211yescharacteristic
1409C2#3912811yescharacteristic
1410C2#3912811yescharacteristic
1411C2#4081012yes—
1412C2#4198112yes—
1413C2#4400112yes—
1414C2C2×#267311yescharacteristic
1415C2#5232012yes—
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×#2534C2semidirect
3. C2×#2444C2semidirect
4. C22×#394C2semidirect
5. #17126C2semidirect
6. #17083C2semidirect
7. #16552C2semidirect
8. #16350C2semidirect
9. #16284C2semidirect
10. #16274C2semidirect
11. #15423C2semidirect
12. #15299C2semidirect
13. #14918C2semidirect
14. #14911C2semidirect
15. #14725C2semidirect
16. #14716C2semidirect
17. #14715C2semidirect
18. #14715C2semidirect
19. #14256C2semidirect
20. #14256C2semidirect
21. #13971C2semidirect
22. #13967C2semidirect
23. #13883C2semidirect
41. C2×#400C22semidirect
42. C2×#399C22semidirect
43. C2×#397C22semidirect
44. C2×#397C22semidirect
45. C2×#396C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
53. C2×#394C22semidirect
58. C2×#392C22semidirect
59. C2×#392C22semidirect
60. C2×#390C22semidirect
61. C2×#390C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
64. C2×#388C22semidirect
65. C2×#387C22semidirect
71. C2×#386C22semidirect
72. C2×#386C22semidirect
73. C2×#386C22semidirect
77. C2×#381C22semidirect
85. #1443C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1434C22semidirect
154. C2×#123D4semidirect
278. C2×#95D4semidirect
487. C2×C4⋊C4C2×D4semidirect
601. C2×C22⋊C4C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25392
C2×#25342
C2×#24442
C22×#3942
#171262
#170832
#165522
#163502
#162842
#162742
#154232
#152992
#149182
#149112
#147252
#147162
#147152
#142562
#139712
#139672
#138832