Finite Group Databasebeta

← #695618

Subgroups — #695618

Order 512.

4578 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2534C211yesmaximal, characteristic, complemented
2C2×#2483C211yesmaximal, characteristic, complemented
3C22×#394C211yesmaximal, characteristic, complemented
4C2×#2358C211yesmaximal, characteristic, complemented
5#16534C212yesmaximal, complemented
6#16274C212yesmaximal, complemented
7#15660C212yesmaximal, complemented
8#15496C212yesmaximal, complemented
9#15403C212yesmaximal, complemented
10#15301C212yesmaximal, complemented
11#14920C211yesmaximal, characteristic, complemented
12#14918C211yesmaximal, characteristic, complemented
13#14911C211yesmaximal, characteristic, complemented
14#14750C212yesmaximal, complemented
15#14730C212yesmaximal, complemented
16#14715C211yesmaximal, characteristic
17#14256C211yesmaximal, characteristic, complemented
18#14016C211yesmaximal, characteristic, complemented
19#13995C211yesmaximal, characteristic, complemented
20#13991C211yesmaximal, characteristic, complemented
21#13873C211yesmaximal, characteristic, complemented
22#13867C211yesmaximal, characteristic, complemented
23#13776C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#120C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic, complemented
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2534—28no—
37#2483—28no—
38C2×#397C2212yescomplemented
39C2×#397C2212yescomplemented
40C2×#396C2212yescomplemented
41C2×#394—28no—
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yescomplemented
47C2×#392C2212yes—
48C2×#392C2212yes—
49#2358—28no—
50C2×#390C2211yescharacteristic, complemented
51C2×#390C2212yescomplemented
52C2×#388C2212yescomplemented
53C2×#388C2211yescharacteristic, complemented
54C2×#388C2211yescharacteristic, complemented
55C2×#388C2212yescomplemented
56C2×#388C2212yescomplemented
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2211yescharacteristic
62C2×#386C2212yescomplemented
63C2×#386C2211yescharacteristic, complemented
64C2×#386C2211yescharacteristic, complemented
65C2×#385C2211yescharacteristic
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2212yescomplemented
69C2×#385C2211yescharacteristic, complemented
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#381C2211yescharacteristic
73C2×#381C2212yescomplemented
74C2×#380C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic, complemented
83C22×#95C2211yescharacteristic
84#1445C2212yescomplemented
85#1442C2212yescomplemented
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#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—42no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C2×#123—24no—
149C2×#123—24no—
150C2×#123—42no—
151C2×#120—24no—
152C2×#120—24no—
153C2×#120—24no—
154C2×#120—24no—
155C2×#120—24no—
156C2×#120—42no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—42no—
161C2×C4×D4—44no—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4—42no—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—42no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4D418yescomplemented
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229#397—28no—
230#397—28no—
231#396—28no—
232#394—28no—
233#394—28no—
234#394—28no—
235#394—28no—
236#394—28no—
237#392—44no—
238#392—44no—
239#390—24no—
240#390—44no—
241#388—24no—
242#388—24no—
243#388—28no—
244#388—44no—
245#388—44no—
246#386—24no—
247#386—24no—
248#386—24no—
249#386—24no—
250#386—28no—
251#386—44no—
252#386—42no—
253#386—44no—
254#385—24no—
255#385—24no—
256#385—24no—
257#385—24no—
258#385—28no—
259#381—24no—
260#381—24no—
261#381—28no—
262#381D418yescomplemented
263#380—24no—
264#379—24no—
265#379—24no—
266#379—24no—
267#379—42no—
268#379—42no—
269C4×C22⋊C4—24no—
270C4×C22⋊C4—24no—
271C4×C22⋊C4—42no—
272C2×#95—24no—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
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—
305C25—22no—
306C25—24no—
307C25—24no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25C2×D414yes—
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2412yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
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—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—416no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—432no—
371C22×D4—416no—
372C22×D4—416no—
373C22×D4—432no—
374C22×D4#4114yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
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—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—41no—
403C23×C4—41no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—41no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4C2×D414yes—
414C23×C4C2×D414yes—
415C23×C4C2×D414yes—
416C23×C4#4114yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435#123—416no—
436#120—232no—
437#120—416no—
438C4×D4—416no—
439C4×D4—416no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—416no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
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—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
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—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
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—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—416no—
529C2×C22⋊C4—416no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—416no—
548C2×C22⋊C4—416no—
549C2×C22⋊C4—416no—
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—42no—
561C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
573C2×C22⋊C4C2×D414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4C2×D414yes—
577C2×C22⋊C4C2×D414yes—
578C2×C22⋊C4#4114yes—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—41no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—42no—
589#95—24no—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95C2×D418yescomplemented
620#95C2×D418yescomplemented
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—28no—
635C24—28no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—21no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—28no—
671C24—28no—
672C24—28no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C2×#4112yes—
719C24C2×#4112yes—
720C24C2×#4112yes—
721C24C2×#4112yes—
722C24H(5,𝔽2)14yes—
723C24H(5,𝔽2)14yes—
724C24H(5,𝔽2)12yes—
725C24H(5,𝔽2)12yes—
726C24C2511yescharacteristic
727C2×D4—28no—
728C2×D4—216no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—4128no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—48no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—82no—
761C2×D4—82no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—22no—
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—22no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—82no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—82no—
892C22×C4—82no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4—84no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4—84no—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D414yes—
906C22×C4C22×D414yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C2×#4112yes—
911C22×C4C2×#4112yes—
912C22×C4C2×#4114yes—
913C22×C4C2×#4112yes—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—82no—
920C4⋊C4—84no—
921C4⋊C4—84no—
922C4⋊C4—84no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—82no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C42—44no—
962C42—44no—
963C42—82no—
964C42—84no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—24no—
1002C23—22no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—416no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
1030C23—41no—
1031C23—42no—
1032C23—41no—
1033C23—42no—
1034C23—41no—
1035C23—42no—
1036C23—41no—
1037C23—42no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—41no—
1045C23—42no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—42no—
1050C23—416no—
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—42no—
1064C23—42no—
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—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—88no—
1092C23—88no—
1093C23—88no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23—816no—
1102C23—88no—
1103C23—88no—
1104C23—88no—
1105C23—88no—
1106C23#52514yes—
1107C23#53214yes—
1108C23#53414yes—
1109C23#54014yes—
1110C23D4214yes—
1111C23#54614yes—
1112C23#54614yes—
1113C23#55314yes—
1114C23C23×D411yescharacteristic
1115C23C23×D411yescharacteristic
1116C23C22×#4111yescharacteristic
1117C23C22×#4111yescharacteristic
1118C23C22×#4111yescharacteristic
1119C23C2×H(5,𝔽2)12yes—
1120C23C2×H(5,𝔽2)11yescharacteristic
1121C23C2×H(5,𝔽2)11yescharacteristic
1122C23C2×H(5,𝔽2)12yes—
1123C23#58512yes—
1124C23#58512yes—
1125D4—416no—
1126D4—432no—
1127D4—432no—
1128D4—416no—
1129D4—88no—
1130D4—816no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—416no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—416no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
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—88no—
1240C2×C4—88no—
1241C2×C4—88no—
1242C2×C4—88no—
1243C2×C4—88no—
1244C2×C4—88no—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—28no—
1250C22—28no—
1251C22—28no—
1252C22—24no—
1253C22—28no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—44no—
1262C22—44no—
1263C22—42no—
1264C22—44no—
1265C22—44no—
1266C22—42no—
1267C22—44no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—44no—
1272C22—42no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—44no—
1283C22—42no—
1284C22—42no—
1285C22—832no—
1286C22—832no—
1287C22—81no—
1288C22—82no—
1289C22—81no—
1290C22—81no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—81no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22#246418yes—
1306C22C2×#52511yescharacteristic
1307C22C2×#53211yescharacteristic
1308C22C2×#53411yescharacteristic
1309C22#344911yescharacteristic
1310C22C2×#54011yescharacteristic
1311C22C2×D4211yescharacteristic
1312C22C2×#54611yescharacteristic
1313C22C2×#54611yescharacteristic
1314C22C2×#55311yescharacteristic
1315C22#348411yescharacteristic
1316C22#348511yescharacteristic
1317C22#348812yes—
1318C22#348812yes—
1319C22#349012yes—
1320C22#351012yes—
1321C22#351312yes—
1322C22#351312yes—
1323C22#351312yes—
1324C22#351312yes—
1325C22#353212yes—
1326C22#353412yes—
1327C22#353412yes—
1328C22#354512yes—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—44no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—81no—
1342C4—82no—
1343C4—81no—
1344C4—82no—
1345C4—82no—
1346C4—82no—
1347C2—28no—
1348C2—44no—
1349C2—82no—
1350C2—82no—
1351C2—84no—
1352C2C2×#246411yescharacteristic
1353C2#3506211yescharacteristic
1354C2#3535411yescharacteristic
1355C2#3573212yes—
1356C2#3764611yescharacteristic
1357C2#3765211yescharacteristic
1358C2#3783211yescharacteristic
1359C2#3946111yescharacteristic
1360C2#4081012yes—
1361C2#4308412yes—
1362C2#4400112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2534C2semidirect
2. C2×#2483C2semidirect
3. C22×#394C2semidirect
4. C2×#2358C2semidirect
5. #16534C2semidirect
6. #16274C2semidirect
7. #15660C2semidirect
8. #15496C2semidirect
9. #15403C2semidirect
10. #15301C2semidirect
11. #14920C2semidirect
12. #14918C2semidirect
13. #14911C2semidirect
14. #14750C2semidirect
15. #14730C2semidirect
17. #14256C2semidirect
18. #14016C2semidirect
19. #13995C2semidirect
20. #13991C2semidirect
21. #13873C2semidirect
22. #13867C2semidirect
23. #13776C2semidirect
29. C22×C4×D4C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
40. C2×#396C22semidirect
46. C2×#394C22semidirect
50. C2×#390C22semidirect
51. C2×#390C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
62. C2×#386C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
73. C2×#381C22semidirect
82. C2×C4×C22⋊C4C22semidirect
84. #1445C22semidirect
85. #1442C22semidirect
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
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
126. C22⋊#95C22semidirect
186. C22×C22⋊C4D4semidirect
262. #381D4semidirect
619. #95C2×D4semidirect
620. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25342
C2×#24832
C22×#3942
C2×#23582
#165342
#162742
#156602
#154962
#154032
#153012
#149202
#149182
#149112
#147502
#147302
#147152
#142562
#140162
#139952
#139912
#138732
#138672
#137762