Finite Group Databasebeta

← #1260266

Subgroups — #1260266

Order 512.

4808 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic, complemented
2C2×#2539C211yesmaximal, characteristic, complemented
3C2×#2626C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#16600C211yesmaximal, characteristic, complemented
6#16509C211yesmaximal, characteristic, complemented
7#16508C211yesmaximal, characteristic, complemented
8#16260C211yesmaximal, characteristic, complemented
9#15776C212yesmaximal, complemented
10#15335C212yesmaximal, complemented
11#15272C212yesmaximal, complemented
12#15268C212yesmaximal, complemented
13#15084C211yesmaximal, characteristic, complemented
14#14915C211yesmaximal, characteristic, complemented
15#14765C211yesmaximal, characteristic, complemented
16#14721C212yesmaximal, complemented
17#14717C211yesmaximal, characteristic, complemented
18#14716C211yesmaximal, characteristic, complemented
19#14715C212yesmaximal, complemented
20#14534C212yesmaximal, complemented
21#14358C212yesmaximal, complemented
22#14240C211yesmaximal, characteristic, complemented
23#13890C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic, complemented
26C22×#123C2212yescomplemented
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C22×C22⋊Q8C2211yescharacteristic, complemented
29C22×#121C2211yescharacteristic, complemented
30C22×#121C2211yescharacteristic, complemented
31C22×#120C2212yes—
32C22×#120C2212yes—
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37#2626—28no—
38#2540—28no—
39#2539—28no—
40C2×#399C2211yescharacteristic
41C2×#399C2211yescharacteristic, complemented
42C2×#399C2212yescomplemented
43C2×#399C2211yescharacteristic, complemented
44C2×#396C2212yes—
45C2×#396C2212yescomplemented
46C2×#394C2212yescomplemented
47C2×#394C2212yescomplemented
48C2×#393C2211yescharacteristic
49C2×#393C2211yescharacteristic, complemented
50C2×#393C2211yescharacteristic, complemented
51C2×#392C2211yescharacteristic
52C2×#392C2212yes—
53C2×#392C2212yes—
54C2×#392C2212yes—
55C2×#392C2212yes—
56C2×#392C2211yescharacteristic, complemented
57C2×#392C2211yescharacteristic, complemented
58D4×C22⋊C4—28no—
59C2×#390C2212yes—
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#390C2212yescomplemented
63C2×#390C2212yescomplemented
64C2×#390C2212yescomplemented
65C2×#388C2212yescomplemented
66C2×#388C2212yescomplemented
67C2×#388C2212yescomplemented
68C2×#387C2212yescomplemented
69C2×#386C2211yescharacteristic
70C2×#386C2211yescharacteristic
71C2×#386C2211yescharacteristic
72C2×#386C2211yescharacteristic
73C2×#386C2212yes—
74C2×#386C2212yescomplemented
75C2×#385C2212yescomplemented
76C2×#380C2211yescharacteristic
77C2×#380C2211yescharacteristic, complemented
78C2×#379C2211yescharacteristic
79C2×#379C2212yes—
80C2×#379C2211yescharacteristic
81C2×#379C2212yes—
82C2×C4×C4⋊C4C2211yescharacteristic, complemented
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic, complemented
85#1446C2211yescharacteristic, complemented
86#1445C2211yescharacteristic, complemented
87#1444C2212yescomplemented
88#1442C2211yescharacteristic, complemented
89#1441C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1439C2212yes—
93#1439C2211yescharacteristic
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2211yescharacteristic, complemented
97#1439C2212yescomplemented
98#1439C2211yescharacteristic, complemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2211yescharacteristic, complemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1437C2212yes—
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121#1434C2211yescharacteristic, complemented
122#1434C2211yescharacteristic, complemented
123C22⋊#95C2212yes—
124C22⋊#95C2211yescharacteristic, complemented
125C22⋊#95C2211yescharacteristic, complemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—44no—
134C23×D4—44no—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C23×D4C2312yes—
143C23×D4C2311yescharacteristic
144C23×D4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×#124—24no—
151C2×#124—44no—
152C2×#123—28no—
153C2×#123—44no—
154C2×#123—44no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—44no—
159C2×C22⋊Q8—42no—
160C2×#121—24no—
161C2×#121—24no—
162C2×#121—24no—
163C2×#121—44no—
164C2×#121—42no—
165C2×#120—28no—
166C2×#120—28no—
167C2×#120—44no—
168C2×#120—44no—
169C2×#120—44no—
170C2×#120—44no—
171C2×C4×D4—24no—
172C2×C4×D4—44no—
173C2×C4×D4—44no—
174C2×C4×D4D418yescomplemented
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
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—42no—
190C22×C22⋊C4—42no—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2312yes—
235#399—28no—
236#399—24no—
237#399—24no—
238#399D418yescomplemented
239#396—28no—
240#396—28no—
241#394—44no—
242#394—44no—
243#393—24no—
244#393—24no—
245#393—42no—
246#392—28no—
247#392—28no—
248#392—24no—
249#392—24no—
250#392—44no—
251#392—42no—
252#392—44no—
253#390—24no—
254#390—28no—
255#390—28no—
256#390—28no—
257#390—28no—
258#390—24no—
259#388—44no—
260#388—44no—
261#388—44no—
262#387—44no—
263#386—24no—
264#386—24no—
265#386—24no—
266#386—24no—
267#386—44no—
268#386—44no—
269#385—28no—
270#380—24no—
271#380—24no—
272#379—24no—
273#379—24no—
274#379—28no—
275#379—44no—
276C4×C4⋊C4—24no—
277C4×C22⋊C4—24no—
278C4×C22⋊C4—24no—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—24no—
315C25—22no—
316C25—41no—
317C25—41no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25—41no—
322C25—41no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25#4114yes—
328C25C2412yes—
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—42no—
338C22×Q8—42no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—232no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—22no—
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—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—432no—
399C22×D4—432no—
400C22×D4—416no—
401C22×D4—416no—
402C22×D4C2×D414yes—
403C22×D4#4114yes—
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—24no—
414C23×C4—22no—
415C23×C4—24no—
416C23×C4—22no—
417C23×C4—42no—
418C23×C4—41no—
419C23×C4—41no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4C2×D414yes—
428C23×C4C2×D414yes—
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446#124—416no—
447#123—432no—
448C22⋊Q8—416no—
449C22⋊Q8—416no—
450#121—416no—
451#121—416no—
452#120—432no—
453#120—432no—
454C4×D4—416no—
455C4×D4—416no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4C2×D414yes—
481C2×C4⋊C4C2×D414yescomplemented
482C2×C4⋊C4C2×D418yescomplemented
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
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—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
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—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
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—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—416no—
545C2×C22⋊C4—416no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
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⋊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⋊C4C2×D414yes—
594C2×C22⋊C4C2×D414yes—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4C2×D418yes—
597C2×C42—24no—
598C2×C42—22no—
599C2×C42—24no—
600C2×C42—24no—
601C2×C42—42no—
602C2×C42—42no—
603C2×C42—42no—
604C2×C42—42no—
605C2×C42—42no—
606C2×C42C2×D414yes—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—24no—
615#95—24no—
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×D414yescomplemented
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—28no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—21no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—28no—
681C24—28no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—48no—
698C24—44no—
699C24—48no—
700C24—44no—
701C24—44no—
702C24—48no—
703C24—48no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—44no—
715C24—48no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24—82no—
720C24—84no—
721C24—82no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—82no—
726C24—82no—
727C24—84no—
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—
744C24C2×#4112yes—
745C24C2×#4112yes—
746C24C2×#4112yes—
747C24C2×#4112yes—
748C24H(5,𝔽2)14yes—
749C242−1+412yes—
750C24C2511yescharacteristic
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—84no—
755C2×Q8—84no—
756C2×D4—216no—
757C2×D4—216no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—44no—
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—44no—
781C2×D4—44no—
782C2×D4—4128no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—44no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—44no—
794C2×D4—44no—
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—
813C2×D4—84no—
814C2×D4—84no—
815C2×D4—84no—
816C2×D4—84no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—28no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—22no—
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—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—28no—
868C22×C4—28no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
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—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—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—21no—
905C22×C4—48no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—48no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—48no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—84no—
919C22×C4—84no—
920C22×C4—84no—
921C22×C4—84no—
922C22×C4—84no—
923C22×C4—82no—
924C22×C4—82no—
925C22×C4—84no—
926C22×C4—84no—
927C22×C4C22×D412yes—
928C22×C4C22×D414yes—
929C22×C4C22×D412yes—
930C22×C4C22×D412yes—
931C22×C4C22×D412yes—
932C22×C4C22×D414yes—
933C22×C4C22×D412yes—
934C22×C4C22×D412yes—
935C22×C4C22×D412yes—
936C22×C4C2×#4112yes—
937C22×C4H(5,𝔽2)14yes—
938C22×C4H(5,𝔽2)14yes—
939C22×C4H(5,𝔽2)14yes—
940C22×C4H(5,𝔽2)12yes—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—48no—
945C4⋊C4—48no—
946C4⋊C4—48no—
947C4⋊C4—48no—
948C4⋊C4—44no—
949C4⋊C4—84no—
950C4⋊C4—84no—
951C22⋊C4—216no—
952C22⋊C4—216no—
953C22⋊C4—28no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—44no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—82no—
980C22⋊C4—82no—
981C22⋊C4—84no—
982C22⋊C4—84no—
983C22⋊C4—82no—
984C22⋊C4—82no—
985C22⋊C4—84no—
986C22⋊C4—84no—
987C22⋊C4—84no—
988C22⋊C4—84no—
989C22⋊C4—84no—
990C22⋊C4—84no—
991C42—28no—
992C42—44no—
993C42—84no—
994C42—84no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—22no—
1008C23—24no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—24no—
1026C23—22no—
1027C23—22no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—22no—
1041C23—24no—
1042C23—22no—
1043C23—416no—
1044C23—416no—
1045C23—416no—
1046C23—416no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—42no—
1052C23—41no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
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—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—41no—
1093C23—41no—
1094C23—42no—
1095C23—42no—
1096C23—41no—
1097C23—42no—
1098C23—41no—
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—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
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—42no—
1139C23—42no—
1140C23—42no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—88no—
1147C23—816no—
1148C23—88no—
1149C23—88no—
1150C23—816no—
1151C23—88no—
1152C23—816no—
1153C23—816no—
1154C23—816no—
1155C23—816no—
1156C23—816no—
1157C23—88no—
1158C23—88no—
1159C23—88no—
1160C23—88no—
1161C23—816no—
1162C23—88no—
1163C23—88no—
1164C23#52514yes—
1165C23#53514yes—
1166C23#54814yes—
1167C23C23×D411yescharacteristic
1168C23C23×D411yescharacteristic
1169C23C22×#4111yescharacteristic
1170C23C22×#4111yescharacteristic
1171C23C2×H(5,𝔽2)12yes—
1172C23C2×H(5,𝔽2)12yes—
1173C23C2×H(5,𝔽2)11yescharacteristic
1174C23C2×H(5,𝔽2)12yes—
1175C23C2×H(5,𝔽2)12yes—
1176C23C2×2−1+411yescharacteristic
1177C23#58511yescharacteristic
1178Q8—88no—
1179D4—232no—
1180D4—416no—
1181D4—416no—
1182D4—416no—
1183D4—88no—
1184D4—816no—
1185D4—816no—
1186D4—816no—
1187D4—816no—
1188D4—816no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—416no—
1223C2×C4—42no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
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—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—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—41no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—41no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—42no—
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—88no—
1288C2×C4—88no—
1289C2×C4—88no—
1290C2×C4—88no—
1291C2×C4#53414yes—
1292C2×C4D4214yes—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—28no—
1301C22—42no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—44no—
1325C22—44no—
1326C22—42no—
1327C22—42no—
1328C22—44no—
1329C22—44no—
1330C22—42no—
1331C22—42no—
1332C22—44no—
1333C22—42no—
1334C22—42no—
1335C22—44no—
1336C22—832no—
1337C22—832no—
1338C22—82no—
1339C22—82no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—82no—
1347C22—81no—
1348C22—81no—
1349C22—82no—
1350C22—82no—
1351C22—82no—
1352C22—82no—
1353C22—82no—
1354C22—82no—
1355C22—82no—
1356C22—82no—
1357C22—82no—
1358C22—82no—
1359C22—82no—
1360C22—82no—
1361C22—82no—
1362C22—82no—
1363C22—82no—
1364C22—82no—
1365C22C2×#52511yescharacteristic
1366C22C2×#53411yescharacteristic
1367C22C2×#53511yescharacteristic
1368C22C2×D4211yescharacteristic
1369C22C2×#54811yescharacteristic
1370C22D4×#4111yescharacteristic
1371C22#348412yes—
1372C22#348411yescharacteristic
1373C22#348911yescharacteristic
1374C22#349012yes—
1375C22#349012yes—
1376C22#349012yes—
1377C22#349812yes—
1378C22#349811yescharacteristic
1379C22#350511yescharacteristic
1380C22#351912yes—
1381C22#352011yescharacteristic
1382C22#353612yes—
1383C22#353612yes—
1384C22#354312yes—
1385C22#354312yes—
1386C22#354612yes—
1387C22#355812yes—
1388C4—24no—
1389C4—24no—
1390C4—44no—
1391C4—42no—
1392C4—44no—
1393C4—44no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—44no—
1399C4—82no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—82no—
1404C4—82no—
1405C2—44no—
1406C2—44no—
1407C2—44no—
1408C2—82no—
1409C2—82no—
1410C2—162no—
1411C2#3505011yescharacteristic
1412C2#3569211yescharacteristic
1413C2#3609711yescharacteristic
1414C2#3767411yescharacteristic
1415C2#3933611yescharacteristic
1416C2#4059311yescharacteristic
1417C2#4298811yescharacteristic
1418C2#4300212yes—
1419C2#4301012yes—
1420C2#4958912yes—
1421C2#4993412yes—
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×#2540C2semidirect
2. C2×#2539C2semidirect
3. C2×#2626C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #16600C2semidirect
6. #16509C2semidirect
7. #16508C2semidirect
8. #16260C2semidirect
9. #15776C2semidirect
10. #15335C2semidirect
11. #15272C2semidirect
12. #15268C2semidirect
13. #15084C2semidirect
14. #14915C2semidirect
15. #14765C2semidirect
16. #14721C2semidirect
17. #14717C2semidirect
18. #14716C2semidirect
19. #14715C2semidirect
20. #14534C2semidirect
21. #14358C2semidirect
22. #14240C2semidirect
23. #13890C2semidirect
25. C22×#124C22semidirect
26. C22×#123C22semidirect
27. C22×C22⋊Q8C22semidirect
28. C22×C22⋊Q8C22semidirect
29. C22×#121C22semidirect
30. C22×#121C22semidirect
41. C2×#399C22semidirect
42. C2×#399C22semidirect
43. C2×#399C22semidirect
45. C2×#396C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
49. C2×#393C22semidirect
50. C2×#393C22semidirect
56. C2×#392C22semidirect
57. C2×#392C22semidirect
62. C2×#390C22semidirect
63. C2×#390C22semidirect
64. C2×#390C22semidirect
65. C2×#388C22semidirect
66. C2×#388C22semidirect
67. C2×#388C22semidirect
68. C2×#387C22semidirect
74. C2×#386C22semidirect
75. C2×#385C22semidirect
77. C2×#380C22semidirect
82. C2×C4×C4⋊C4C22semidirect
84. C2×C4×C22⋊C4C22semidirect
85. #1446C22semidirect
86. #1445C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1441C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
174. C2×C4×D4D4semidirect
238. #399D4semidirect
481. C2×C4⋊C4C2×D4semidirect
482. C2×C4⋊C4C2×D4semidirect
633. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25402
C2×#25392
C2×#26262
C2×D4×C22⋊C42
#166002
#165092
#165082
#162602
#157762
#153352
#152722
#152682
#150842
#149152
#147652
#147212
#147172
#147162
#147152
#145342
#143582
#142402
#138902