Finite Group Databasebeta

← #792613

Subgroups — #792613

Order 512.

5732 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×#2610C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic, complemented
3C22×#392C211yesmaximal, characteristic
4C2×#2342C211yesmaximal, characteristic, complemented
5#17022C211yesmaximal, characteristic, complemented
6#16680C211yesmaximal, characteristic, complemented
7#15651C212yesmaximal, complemented
8#15423C212yesmaximal, complemented
9#15307C212yesmaximal, complemented
10#15299C212yesmaximal, complemented
11#14928C211yesmaximal, characteristic, complemented
12#14915C211yesmaximal, characteristic, complemented
13#14900C211yesmaximal, characteristic, complemented
14#14886C211yesmaximal, characteristic, complemented
15#14758C211yesmaximal, characteristic, complemented
16#14724C211yesmaximal, characteristic, complemented
17#14717C211yesmaximal, characteristic, complemented
18#14228C211yesmaximal, characteristic, complemented
19#13991C212yesmaximal, complemented
20#13902C212yesmaximal, complemented
21#13873C212yesmaximal, complemented
22#13867C212yesmaximal, complemented
23#13809C211yesmaximal, characteristic, complemented
24C24×D4C2212yes—
25C24×D4C2211yescharacteristic
26C22×#124C2211yescharacteristic, complemented
27C22×#124C2211yescharacteristic, complemented
28C22×C22⋊Q8C2211yescharacteristic
29C22×#117C2211yescharacteristic, complemented
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32C23×C22⋊C4C2211yescharacteristic
33#2610—28no—
34#2435—28no—
35C2×#395C2211yescharacteristic, complemented
36C2×#394C2212yescomplemented
37C2×#394C2211yescharacteristic, complemented
38C2×#394C2212yescomplemented
39C2×#394C2212yescomplemented
40C2×#394C2211yescharacteristic, complemented
41C2×#393C2211yescharacteristic, complemented
42C2×#393C2211yescharacteristic, complemented
43C2×#392—28no—
44C2×#392C2212yes—
45C2×#392C2211yescharacteristic
46C2×#392C2211yescharacteristic
47C2×#392C2211yescharacteristic
48C2×#392C2212yes—
49C2×#392C2211yescharacteristic
50#2342—28no—
51C2×#390C2211yescharacteristic, complemented
52C2×#390C2212yescomplemented
53C2×#390C2211yescharacteristic, complemented
54C2×#390C2212yescomplemented
55C2×#390C2212yescomplemented
56C2×#390C2212yescomplemented
57C2×#388C2211yescharacteristic, complemented
58C2×#388C2212yescomplemented
59C2×#388C2211yescharacteristic, complemented
60C2×#388C2212yescomplemented
61C2×#388C2211yescharacteristic, complemented
62C2×#388C2211yescharacteristic, complemented
63C2×#388C2212yescomplemented
64C2×#388C2212yescomplemented
65C2×#386C2212yescomplemented
66C2×#386C2212yescomplemented
67C2×#386C2212yescomplemented
68C2×#386C2212yescomplemented
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#381C2211yescharacteristic, complemented
72C2×#380C2212yes—
73C2×#380C2211yescharacteristic, complemented
74C2×#379C2212yes—
75C2×#379C2212yes—
76C2×#379C2211yescharacteristic
77C2×#379C2212yes—
78C2×#379C2212yes—
79C2×#379C2212yes—
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic, complemented
84C2×#376C2211yescharacteristic, complemented
85C22×#95C2211yescharacteristic
86#1446C2211yescharacteristic, complemented
87#1444C2212yescomplemented
88#1444C2211yescharacteristic, complemented
89#1441C2211yescharacteristic, complemented
90#1441C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2211yescharacteristic, complemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2211yescharacteristic, complemented
102#1439C2212yescomplemented
103#1438C2212yescomplemented
104#1438C2212yescomplemented
105#1438C2212yescomplemented
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2211yescharacteristic, complemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2211yescharacteristic, complemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1434C2212yescomplemented
119#1434C2211yescharacteristic, complemented
120#1434C2212yescomplemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—28no—
131C23×D4—28no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—28no—
135C23×D4—42no—
136C23×D4—44no—
137C23×D4—44no—
138C23×D4—44no—
139C23×D4—44no—
140C23×D4—44no—
141C23×D4—44no—
142C23×D4C2311yescharacteristic
143C23×D4C2312yes—
144C23×D4C2312yes—
145C23×D4C2312yes—
146C23×D4C2312yes—
147C23×D4C2312yes—
148C23×D4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2312yes—
153C24×C4C2311yescharacteristic
154C2×#124—24no—
155C2×#124—24no—
156C2×#124—24no—
157C2×#124—42no—
158C2×#124—44no—
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—44no—
161C2×#117—24no—
162C2×#117—24no—
163C2×#117—42no—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—28no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#395—24no—
228#394—24no—
229#394—28no—
230#394—28no—
231#394—42no—
232#394—44no—
233#393—24no—
234#393—42no—
235#392—28no—
236#392—24no—
237#392—24no—
238#392—28no—
239#392—24no—
240#392D418yes—
241#390—28no—
242#390—24no—
243#390—24no—
244#390—44no—
245#390—44no—
246#390—44no—
247#388—28no—
248#388—28no—
249#388—24no—
250#388—24no—
251#388—24no—
252#388—24no—
253#388—44no—
254#388—44no—
255#386—28no—
256#386—44no—
257#386—44no—
258#386—44no—
259#385—24no—
260#385—24no—
261#381—24no—
262#380—24no—
263#380—44no—
264#379—24no—
265#379—28no—
266#379—28no—
267#379—28no—
268#379—44no—
269#379—44no—
270C4×C22⋊C4—28no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4D418yescomplemented
274#376—24no—
275C2×#95—24no—
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C25—24no—
307C25—22no—
308C25—24no—
309C25—22no—
310C25—24no—
311C25—22no—
312C25—22no—
313C25—24no—
314C25—24no—
315C25—24no—
316C25—24no—
317C25—24no—
318C25—24no—
319C25—24no—
320C25—24no—
321C25—41no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—41no—
330C25—42no—
331C25#4114yes—
332C25C2412yes—
333C25C2411yescharacteristic
334C25C2412yes—
335C25C2411yescharacteristic
336C25C2411yescharacteristic
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—42no—
341C22×Q8—42no—
342C22×D4—24no—
343C22×D4—24no—
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—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—22no—
368C22×D4—416no—
369C22×D4—432no—
370C22×D4—42no—
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×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—432no—
388C22×D4—416no—
389C22×D4—432no—
390C22×D4—416no—
391C22×D4—432no—
392C22×D4—432no—
393C22×D4—432no—
394C22×D4—432no—
395C22×D4—432no—
396C22×D4—432no—
397C22×D4C2×D418yes—
398C22×D4C2×D414yes—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—24no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—24no—
416C23×C4—22no—
417C23×C4—41no—
418C23×C4—41no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—41no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4C2×D414yes—
427C23×C4#4118yes—
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446#124—416no—
447#124—416no—
448C22⋊Q8—416no—
449#117—416no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C22⋊C4—232no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
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—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
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—24no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—416no—
538C2×C22⋊C4—432no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—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⋊C4—42no—
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—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4C2×D414yes—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D418yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4#4114yes—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—24no—
595C2×C42—24no—
596C2×C42—24no—
597C2×C42—22no—
598C2×C42—24no—
599C2×C42—41no—
600C2×C42—42no—
601C2×C42—42no—
602C2×C42—42no—
603C2×C42—42no—
604C2×C42C2×D414yescomplemented
605C2×C42C2×D414yescomplemented
606#95—22no—
607#95—24no—
608#95—24no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—22no—
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#95C2×D414yes—
634#95C2×D414yescomplemented
635#95C2×D414yescomplemented
636C24—21no—
637C24—21no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—216no—
651C24—28no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—21no—
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—21no—
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—21no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—28no—
691C24—216no—
692C24—48no—
693C24—44no—
694C24—44no—
695C24—48no—
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—48no—
710C24—44no—
711C24—48no—
712C24—44no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—44no—
718C24—48no—
719C24—44no—
720C24—48no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—82no—
728C24—84no—
729C24—84no—
730C24—84no—
731C24—84no—
732C24—84no—
733C24—82no—
734C24—84no—
735C24—84no—
736C24—84no—
737C24—84no—
738C24—84no—
739C24—84no—
740C24—84no—
741C24—84no—
742C24—84no—
743C24—84no—
744C24—84no—
745C24—84no—
746C24C22×D414yes—
747C24C22×D412yes—
748C24C22×D412yes—
749C24C2×#4112yes—
750C24C2×#4112yes—
751C24C2×#4112yes—
752C24C2×#4112yes—
753C24C2×#4114yes—
754C24H(5,𝔽2)14yes—
755C24H(5,𝔽2)12yes—
756C24H(5,𝔽2)14yes—
757C24C2511yescharacteristic
758C2×Q8—44no—
759C2×Q8—44no—
760C2×Q8—44no—
761C2×Q8—84no—
762C2×Q8—84no—
763C2×D4—28no—
764C2×D4—216no—
765C2×D4—216no—
766C2×D4—216no—
767C2×D4—28no—
768C2×D4—216no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—48no—
797C2×D4—48no—
798C2×D4—48no—
799C2×D4—48no—
800C2×D4—48no—
801C2×D4—48no—
802C2×D4—48no—
803C2×D4—4256no—
804C2×D4—4128no—
805C2×D4—48no—
806C2×D4—48no—
807C2×D4—48no—
808C2×D4—44no—
809C2×D4—48no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—216no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
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—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—28no—
862C22×C4—28no—
863C22×C4—216no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
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—21no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—44no—
908C22×C4—48no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—48no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—44no—
920C22×C4—48no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—82no—
925C22×C4—82no—
926C22×C4—84no—
927C22×C4—84no—
928C22×C4—82no—
929C22×C4—84no—
930C22×C4C22×D412yes—
931C22×C4C22×D412yes—
932C22×C4C22×D412yes—
933C22×C4C22×D412yes—
934C22×C4C22×D412yes—
935C22×C4C22×D412yes—
936C22×C4C22×D412yes—
937C22×C4C22×D412yes—
938C22×C4C22×D414yes—
939C22×C4C2×#4114yes—
940C22×C4C2×#4112yes—
941C22×C4C2×#4112yes—
942C22×C4C2×#4114yes—
943C22×C4H(5,𝔽2)12yes—
944C22×C4H(5,𝔽2)14yes—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—48no—
948C4⋊C4—44no—
949C4⋊C4—84no—
950C4⋊C4—84no—
951C4⋊C4—82no—
952C4⋊C4—82no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—216no—
960C22⋊C4—44no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—44no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C22⋊C4—82no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C22⋊C4—82no—
982C22⋊C4—84no—
983C22⋊C4—84no—
984C22⋊C4—84no—
985C22⋊C4—84no—
986C22⋊C4—84no—
987C22⋊C4—84no—
988C22⋊C4—84no—
989C22⋊C4—84no—
990C22⋊C4—84no—
991C22⋊C4—84no—
992C22⋊C4—84no—
993C42—28no—
994C42—44no—
995C42—44no—
996C42—48no—
997C42—84no—
998C42—82no—
999C23—22no—
1000C23—24no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—22no—
1021C23—24no—
1022C23—24no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—22no—
1027C23—22no—
1028C23—24no—
1029C23—22no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—22no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—22no—
1046C23—24no—
1047C23—24no—
1048C23—432no—
1049C23—416no—
1050C23—432no—
1051C23—432no—
1052C23—432no—
1053C23—41no—
1054C23—41no—
1055C23—42no—
1056C23—41no—
1057C23—42no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—416no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—41no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—41no—
1072C23—41no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—41no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—41no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—41no—
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—41no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—41no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—42no—
1125C23—42no—
1126C23—42no—
1127C23—42no—
1128C23—42no—
1129C23—42no—
1130C23—42no—
1131C23—42no—
1132C23—42no—
1133C23—42no—
1134C23—42no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—88no—
1139C23—816no—
1140C23—816no—
1141C23—88no—
1142C23—88no—
1143C23—816no—
1144C23—88no—
1145C23—816no—
1146C23—816no—
1147C23—816no—
1148C23—816no—
1149C23—816no—
1150C23—816no—
1151C23—816no—
1152C23—816no—
1153C23—88no—
1154C23—816no—
1155C23—816no—
1156C23—816no—
1157C23—816no—
1158C23#52514yes—
1159C23#53214yes—
1160C23#53514yes—
1161C23#54614yes—
1162C23#55118yes—
1163C23#55518yes—
1164C23C23×D411yescharacteristic
1165C23C23×D411yescharacteristic
1166C23C22×#4111yescharacteristic
1167C23C22×#4111yescharacteristic
1168C23C22×#4112yes—
1169C23C2×H(5,𝔽2)12yes—
1170C23C2×H(5,𝔽2)11yescharacteristic
1171C23C2×H(5,𝔽2)11yescharacteristic
1172C23C2×H(5,𝔽2)12yes—
1173C23C2×H(5,𝔽2)12yes—
1174C23#58511yescharacteristic
1175Q8—88no—
1176D4—432no—
1177D4—416no—
1178D4—416no—
1179D4—432no—
1180D4—432no—
1181D4—432no—
1182D4—432no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—416no—
1219C2×C4—432no—
1220C2×C4—416no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—42no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—41no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—41no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—41no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—41no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—41no—
1271C2×C4—42no—
1272C2×C4—41no—
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×C4D4214yes—
1293C2×C4#54618yes—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—28no—
1300C22—28no—
1301C22—28no—
1302C22—28no—
1303C22—24no—
1304C22—24no—
1305C22—28no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—42no—
1315C22—42no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—42no—
1321C22—44no—
1322C22—42no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—44no—
1334C22—832no—
1335C22—864no—
1336C22—82no—
1337C22—81no—
1338C22—81no—
1339C22—82no—
1340C22—82no—
1341C22—82no—
1342C22—81no—
1343C22—82no—
1344C22—82no—
1345C22—82no—
1346C22—82no—
1347C22—82no—
1348C22—82no—
1349C22—82no—
1350C22—82no—
1351C22—82no—
1352C22—82no—
1353C22—82no—
1354C22—82no—
1355C22—82no—
1356C22—82no—
1357C22—81no—
1358C22#261018yescomplemented
1359C22C2×#52511yescharacteristic
1360C22C2×#53211yescharacteristic
1361C22C2×#53511yescharacteristic
1362C22C2×D4211yescharacteristic
1363C22C2×#54611yescharacteristic
1364C22C2×#54612yes—
1365C22D4×#4111yescharacteristic
1366C22C2×#55112yes—
1367C22C2×#55512yes—
1368C22#348411yescharacteristic
1369C22#348412yes—
1370C22#348811yescharacteristic
1371C22#349012yes—
1372C22#349012yes—
1373C22#349412yes—
1374C22#349811yescharacteristic
1375C22#350511yescharacteristic
1376C22#350812yes—
1377C22#351911yescharacteristic
1378C22#351912yes—
1379C22#353212yes—
1380C22#353212yes—
1381C22#354212yes—
1382C4—24no—
1383C4—28no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—81no—
1394C4—82no—
1395C4—81no—
1396C4—82no—
1397C4—82no—
1398C4—82no—
1399C4—81no—
1400C2—28no—
1401C2—44no—
1402C2—82no—
1403C2—84no—
1404C2—84no—
1405C2C2×#261011yescharacteristic
1406C2#3569211yescharacteristic
1407C2#3592211yescharacteristic
1408C2#3609611yescharacteristic
1409C2#3612111yescharacteristic
1410C2#3764511yescharacteristic
1411C2#4193411yescharacteristic
1412C2#4393112yes—
1413C2#4396312yes—
1414C2#5900612yes—
1415C2#5902612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#392C2
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×#2610C2semidirect
2. C2×#2435C2semidirect
4. C2×#2342C2semidirect
5. #17022C2semidirect
6. #16680C2semidirect
7. #15651C2semidirect
8. #15423C2semidirect
9. #15307C2semidirect
10. #15299C2semidirect
11. #14928C2semidirect
12. #14915C2semidirect
13. #14900C2semidirect
14. #14886C2semidirect
15. #14758C2semidirect
16. #14724C2semidirect
17. #14717C2semidirect
18. #14228C2semidirect
19. #13991C2semidirect
20. #13902C2semidirect
21. #13873C2semidirect
22. #13867C2semidirect
23. #13809C2semidirect
26. C22×#124C22semidirect
27. C22×#124C22semidirect
29. C22×#117C22semidirect
35. C2×#395C22semidirect
36. C2×#394C22semidirect
37. C2×#394C22semidirect
38. C2×#394C22semidirect
39. C2×#394C22semidirect
40. C2×#394C22semidirect
41. C2×#393C22semidirect
42. C2×#393C22semidirect
51. C2×#390C22semidirect
52. C2×#390C22semidirect
53. C2×#390C22semidirect
54. C2×#390C22semidirect
55. C2×#390C22semidirect
56. C2×#390C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
59. C2×#388C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
64. C2×#388C22semidirect
65. C2×#386C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
71. C2×#381C22semidirect
73. C2×#380C22semidirect
83. C2×C4×C22⋊C4C22semidirect
84. C2×#376C22semidirect
86. #1446C22semidirect
87. #1444C22semidirect
88. #1444C22semidirect
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. #1438C22semidirect
104. #1438C22semidirect
105. #1438C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1434C22semidirect
119. #1434C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
126. C4×#95C22semidirect
273. C4×C22⋊C4D4semidirect
604. C2×C42C2×D4semidirect
605. C2×C42C2×D4semidirect
634. #95C2×D4semidirect
635. #95C2×D4semidirect
1358. C22#2610semidirect

Maximal subgroups

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

subgroupindex
C2×#26102
C2×#24352
C22×#3922
C2×#23422
#170222
#166802
#156512
#154232
#153072
#152992
#149282
#149152
#149002
#148862
#147582
#147242
#147172
#142282
#139912
#139022
#138732
#138672
#138092