Finite Group Databasebeta

← #1260242

Subgroups — #1260242

Order 512.

4696 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic, complemented
2C2×#2561C211yesmaximal, characteristic, complemented
3C2×#2617C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#16632C211yesmaximal, characteristic, complemented
6#16509C211yesmaximal, characteristic, complemented
7#16500C211yesmaximal, characteristic, complemented
8#16265C211yesmaximal, characteristic, complemented
9#15776C212yesmaximal, complemented
10#15380C212yesmaximal, complemented
11#15299C212yesmaximal, complemented
12#15268C212yesmaximal, complemented
13#15112C211yesmaximal, characteristic, complemented
14#14915C211yesmaximal, characteristic, complemented
15#14762C211yesmaximal, characteristic, complemented
16#14730C212yesmaximal, complemented
17#14717C211yesmaximal, characteristic, complemented
18#14716C211yesmaximal, characteristic, complemented
19#14715C212yesmaximal, complemented
20#14520C212yesmaximal, complemented
21#14358C212yesmaximal, complemented
22#14225C211yesmaximal, characteristic, complemented
23#13890C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic, complemented
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C22×#121C2211yescharacteristic, complemented
29C22×#121C2211yescharacteristic, complemented
30C22×#120C2212yes—
31C22×#120C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2617—28no—
37#2561—28no—
38#2540—28no—
39C2×#399C2212yescomplemented
40C2×#397C2211yescharacteristic
41C2×#397C2211yescharacteristic, complemented
42C2×#397C2211yescharacteristic, complemented
43C2×#396C2212yescomplemented
44C2×#394C2212yes—
45C2×#394C2212yescomplemented
46C2×#394C2212yescomplemented
47C2×#393C2211yescharacteristic
48C2×#393C2211yescharacteristic, complemented
49C2×#393C2211yescharacteristic, complemented
50C2×#392C2211yescharacteristic
51C2×#392C2212yes—
52C2×#392C2212yes—
53C2×#392C2212yes—
54C2×#392C2212yes—
55C2×#392C2211yescharacteristic, complemented
56C2×#392C2211yescharacteristic, complemented
57D4×C22⋊C4—28no—
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2212yescomplemented
61C2×#390C2212yescomplemented
62C2×#390C2212yescomplemented
63C2×#388C2212yes—
64C2×#388C2212yes—
65C2×#388C2212yescomplemented
66C2×#387C2212yescomplemented
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2211yescharacteristic
71C2×#386C2212yes—
72C2×#386C2212yescomplemented
73C2×#386C2212yescomplemented
74C2×#381C2212yescomplemented
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic, complemented
77C2×#379C2211yescharacteristic
78C2×#379C2212yes—
79C2×#379C2211yescharacteristic
80C2×#379C2212yes—
81C2×C4×C4⋊C4C2211yescharacteristic, complemented
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic, complemented
84#1446C2211yescharacteristic, complemented
85#1445C2211yescharacteristic, complemented
86#1444C2211yescharacteristic, complemented
87#1442C2212yescomplemented
88#1442C2212yescomplemented
89#1441C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1439C2212yes—
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic, complemented
96#1439C2211yescharacteristic, complemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2211yescharacteristic, complemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1434C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122#1434C2212yescomplemented
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×D4C2311yescharacteristic
141C23×D4C2312yes—
142C23×D4C2312yes—
143C23×D4C2311yescharacteristic
144C23×D4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×#124—24no—
151C2×#124—44no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—44no—
156C2×C22⋊Q8—42no—
157C2×#121—24no—
158C2×#121—24no—
159C2×#121—24no—
160C2×#121—44no—
161C2×#121—42no—
162C2×#120—28no—
163C2×#120—28no—
164C2×#120—44no—
165C2×#120—44no—
166C2×#120—44no—
167C2×#120—44no—
168C2×C4×D4—24no—
169C2×C4×D4—44no—
170C2×C4×D4—44no—
171C2×C4×D4D418yescomplemented
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229C22×C42C2312yes—
230#399—28no—
231#397—24no—
232#397—24no—
233#397D418yescomplemented
234#396—44no—
235#394—28no—
236#394—28no—
237#394—44no—
238#393—24no—
239#393—24no—
240#393—42no—
241#392—28no—
242#392—28no—
243#392—24no—
244#392—24no—
245#392—44no—
246#392—42no—
247#392—44no—
248#390—24no—
249#390—28no—
250#390—28no—
251#390—24no—
252#390—44no—
253#388—28no—
254#388—28no—
255#388—44no—
256#387—44no—
257#386—24no—
258#386—24no—
259#386—24no—
260#386—24no—
261#386—28no—
262#386—44no—
263#386—44no—
264#381—28no—
265#380—24no—
266#380—24no—
267#379—28no—
268#379—24no—
269#379—24no—
270#379—44no—
271C4×C4⋊C4—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—24no—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
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×#95C2311yescharacteristic
302C2×#95C2312yes—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—24no—
313C25—41no—
314C25—41no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—41no—
319C25—41no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25#4114yes—
325C25C2412yes—
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—42no—
335C22×Q8—42no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—232no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
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—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—22no—
368C22×D4—42no—
369C22×D4—42no—
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—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4—42no—
393C22×D4—42no—
394C22×D4—42no—
395C22×D4—432no—
396C22×D4—432no—
397C22×D4—416no—
398C22×D4—416no—
399C22×D4C2×D414yes—
400C22×D4#4114yes—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—24no—
411C23×C4—22no—
412C23×C4—24no—
413C23×C4—22no—
414C23×C4—42no—
415C23×C4—41no—
416C23×C4—41no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4C2×D414yes—
425C23×C4C2×D414yes—
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443#124—416no—
444C22⋊Q8—416no—
445C22⋊Q8—416no—
446#121—416no—
447#121—416no—
448#120—432no—
449#120—432no—
450C4×D4—416no—
451C4×D4—416no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
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×C4⋊C4C2×D414yes—
472C2×C4⋊C4C2×D414yescomplemented
473C2×C22⋊C4—24no—
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—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
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—22no—
500C2×C22⋊C4—22no—
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—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
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—22no—
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—416no—
532C2×C22⋊C4—416no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
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—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
584C2×C22⋊C4C2×D418yes—
585C2×C22⋊C4C2×D414yes—
586C2×C22⋊C4C2×D414yes—
587C2×C42—24no—
588C2×C42—22no—
589C2×C42—24no—
590C2×C42—24no—
591C2×C42—42no—
592C2×C42—42no—
593C2×C42—42no—
594C2×C42—42no—
595C2×C42—42no—
596C2×C42C2×D414yes—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—22no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95C2×D414yescomplemented
625#95C2×D418yescomplemented
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—21no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—28no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—21no—
670C24—22no—
671C24—22no—
672C24—28no—
673C24—28no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—48no—
690C24—44no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—48no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—48no—
703C24—48no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—48no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—82no—
712C24—82no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—82no—
717C24—82no—
718C24—84no—
719C24—84no—
720C24—84no—
721C24—84no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24—84no—
728C24—84no—
729C24—84no—
730C24—84no—
731C24—84no—
732C24C22×D412yes—
733C24C22×D412yes—
734C24C22×D412yes—
735C24C2×#4112yes—
736C24C2×#4112yes—
737C24C2×#4112yes—
738C24C2×#4112yes—
739C24C2×#4112yes—
740C24H(5,𝔽2)14yes—
741C24H(5,𝔽2)12yes—
742C24C2511yescharacteristic
743C2×Q8—44no—
744C2×Q8—44no—
745C2×Q8—44no—
746C2×Q8—84no—
747C2×Q8—84no—
748C2×D4—216no—
749C2×D4—216no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—44no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—4128no—
771C2×D4—48no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—84no—
787C2×D4—84no—
788C2×D4—84no—
789C2×D4—84no—
790C2×D4—84no—
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—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—28no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—21no—
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—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—21no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—48no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—48no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—48no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—84no—
912C22×C4—84no—
913C22×C4—84no—
914C22×C4—84no—
915C22×C4—84no—
916C22×C4—82no—
917C22×C4—82no—
918C22×C4—84no—
919C22×C4—84no—
920C22×C4C22×D412yes—
921C22×C4C22×D414yes—
922C22×C4C22×D414yes—
923C22×C4C22×D412yes—
924C22×C4C22×D412yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D412yes—
928C22×C4C22×D412yes—
929C22×C4C2×#4112yes—
930C22×C4H(5,𝔽2)14yes—
931C22×C4H(5,𝔽2)14yes—
932C22×C4H(5,𝔽2)12yes—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—48no—
937C4⋊C4—48no—
938C4⋊C4—44no—
939C4⋊C4—84no—
940C4⋊C4—84no—
941C22⋊C4—216no—
942C22⋊C4—28no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—82no—
968C22⋊C4—82no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C22⋊C4—84no—
973C22⋊C4—82no—
974C22⋊C4—82no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C42—28no—
982C42—44no—
983C42—84no—
984C42—84no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—22no—
1014C23—24no—
1015C23—24no—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—22no—
1031C23—24no—
1032C23—22no—
1033C23—416no—
1034C23—416no—
1035C23—416no—
1036C23—416no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—41no—
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—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—42no—
1076C23—41no—
1077C23—41no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—42no—
1087C23—42no—
1088C23—41no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—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—88no—
1137C23—816no—
1138C23—88no—
1139C23—88no—
1140C23—816no—
1141C23—88no—
1142C23—816no—
1143C23—816no—
1144C23—816no—
1145C23—88no—
1146C23—816no—
1147C23—816no—
1148C23—816no—
1149C23—88no—
1150C23—88no—
1151C23—88no—
1152C23—88no—
1153C23—88no—
1154C23#52514yes—
1155C23#53514yes—
1156C23#54614yes—
1157C23C23×D411yescharacteristic
1158C23C23×D411yescharacteristic
1159C23C22×#4111yescharacteristic
1160C23C22×#4111yescharacteristic
1161C23C2×H(5,𝔽2)12yes—
1162C23C2×H(5,𝔽2)12yes—
1163C23C2×H(5,𝔽2)11yescharacteristic
1164C23C2×H(5,𝔽2)11yescharacteristic
1165C23C2×H(5,𝔽2)12yes—
1166C23#58511yescharacteristic
1167C23#58512yes—
1168Q8—88no—
1169D4—232no—
1170D4—416no—
1171D4—416no—
1172D4—416no—
1173D4—88no—
1174D4—816no—
1175D4—816no—
1176D4—816no—
1177D4—816no—
1178D4—816no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—416no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—41no—
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—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—41no—
1245C2×C4—42no—
1246C2×C4—41no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—88no—
1278C2×C4—88no—
1279C2×C4—88no—
1280C2×C4—88no—
1281C2×C4#53414yes—
1282C2×C4D4214yes—
1283C22—24no—
1284C22—24no—
1285C22—24no—
1286C22—24no—
1287C22—24no—
1288C22—28no—
1289C22—24no—
1290C22—24no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—44no—
1308C22—44no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—42no—
1322C22—42no—
1323C22—44no—
1324C22—42no—
1325C22—42no—
1326C22—832no—
1327C22—832no—
1328C22—81no—
1329C22—81no—
1330C22—82no—
1331C22—82no—
1332C22—82no—
1333C22—81no—
1334C22—81no—
1335C22—82no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—82no—
1341C22—82no—
1342C22—82no—
1343C22—82no—
1344C22—82no—
1345C22—82no—
1346C22—82no—
1347C22—82no—
1348C22—82no—
1349C22—82no—
1350C22—82no—
1351C22—82no—
1352C22—82no—
1353C22—82no—
1354C22—82no—
1355C22C2×#52511yescharacteristic
1356C22C2×#53411yescharacteristic
1357C22C2×#53511yescharacteristic
1358C22C2×D4211yescharacteristic
1359C22C2×#54611yescharacteristic
1360C22D4×#4111yescharacteristic
1361C22#348411yescharacteristic
1362C22#348811yescharacteristic
1363C22#348812yes—
1364C22#349012yes—
1365C22#349012yes—
1366C22#349812yes—
1367C22#350011yescharacteristic
1368C22#350511yescharacteristic
1369C22#350512yes—
1370C22#351412yes—
1371C22#351911yescharacteristic
1372C22#353212yes—
1373C22#353412yes—
1374C22#354212yes—
1375C22#354312yes—
1376C22#355112yes—
1377C22#355812yes—
1378C4—24no—
1379C4—24no—
1380C4—44no—
1381C4—42no—
1382C4—44no—
1383C4—44no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—81no—
1389C4—81no—
1390C4—82no—
1391C4—82no—
1392C4—81no—
1393C4—82no—
1394C4—82no—
1395C2—44no—
1396C2—44no—
1397C2—44no—
1398C2—82no—
1399C2—82no—
1400C2—162no—
1401C2#3505011yescharacteristic
1402C2#3570311yescharacteristic
1403C2#3609611yescharacteristic
1404C2#3767711yescharacteristic
1405C2#3933611yescharacteristic
1406C2#4058811yescharacteristic
1407C2#4294211yescharacteristic
1408C2#4393212yes—
1409C2#4413812yes—
1410C2#4798912yes—
1411C2#4868512yes—
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×#2561C2semidirect
3. C2×#2617C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #16632C2semidirect
6. #16509C2semidirect
7. #16500C2semidirect
8. #16265C2semidirect
9. #15776C2semidirect
10. #15380C2semidirect
11. #15299C2semidirect
12. #15268C2semidirect
13. #15112C2semidirect
14. #14915C2semidirect
15. #14762C2semidirect
16. #14730C2semidirect
17. #14717C2semidirect
18. #14716C2semidirect
19. #14715C2semidirect
20. #14520C2semidirect
21. #14358C2semidirect
22. #14225C2semidirect
23. #13890C2semidirect
25. C22×#124C22semidirect
26. C22×C22⋊Q8C22semidirect
27. C22×C22⋊Q8C22semidirect
28. C22×#121C22semidirect
29. C22×#121C22semidirect
39. C2×#399C22semidirect
41. C2×#397C22semidirect
42. C2×#397C22semidirect
43. C2×#396C22semidirect
45. C2×#394C22semidirect
46. C2×#394C22semidirect
48. C2×#393C22semidirect
49. C2×#393C22semidirect
55. C2×#392C22semidirect
56. C2×#392C22semidirect
60. C2×#390C22semidirect
61. C2×#390C22semidirect
62. C2×#390C22semidirect
65. C2×#388C22semidirect
66. C2×#387C22semidirect
72. C2×#386C22semidirect
73. C2×#386C22semidirect
74. C2×#381C22semidirect
76. C2×#380C22semidirect
81. C2×C4×C4⋊C4C22semidirect
83. C2×C4×C22⋊C4C22semidirect
84. #1446C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1442C22semidirect
88. #1442C22semidirect
89. #1441C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
171. C2×C4×D4D4semidirect
233. #397D4semidirect
472. C2×C4⋊C4C2×D4semidirect
624. #95C2×D4semidirect
625. #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×#25612
C2×#26172
C2×D4×C22⋊C42
#166322
#165092
#165002
#162652
#157762
#153802
#152992
#152682
#151122
#149152
#147622
#147302
#147172
#147162
#147152
#145202
#143582
#142252
#138902