Finite Group Databasebeta

← #1260342

Subgroups — #1260342

Order 512.

4028 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2670C212yesmaximal, complemented
2C2×#2547C211yesmaximal, characteristic, complemented
3C2×#2491C211yesmaximal, characteristic, complemented
4C2×#2617C211yesmaximal, characteristic, complemented
5C2×#2358C211yesmaximal, characteristic, complemented
6#16810C211yesmaximal, characteristic, complemented
7#16506C211yesmaximal, characteristic, complemented
8#16500C211yesmaximal, characteristic, complemented
9#16401C211yesmaximal, characteristic, complemented
10#15631C212yesmaximal, complemented
11#15314C212yesmaximal, complemented
12#15307C212yesmaximal, complemented
13#15303C212yesmaximal, complemented
14#15160C211yesmaximal, characteristic, complemented
15#15147C211yesmaximal, characteristic, complemented
16#14820C211yesmaximal, characteristic, complemented
17#14815C211yesmaximal, characteristic, complemented
18#14811C211yesmaximal, characteristic, complemented
19#14732C212yesmaximal, complemented
20#14725C212yesmaximal, complemented
21#14421C212yesmaximal, complemented
22#14225C211yesmaximal, characteristic, complemented
23#13891C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic, complemented
25C22×#124C2212yes—
26C22×#124C2212yes—
27C22×#121C2211yescharacteristic
28C22×#120C2212yes—
29C22×#120C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2670—216no—
35#2617—28no—
36#2547—28no—
37#2491—28no—
38C2×#397C2211yescharacteristic
39C2×#397C2211yescharacteristic
40C2×#397C2211yescharacteristic
41C2×#397C2211yescharacteristic
42C2×#397C2211yescharacteristic, complemented
43C2×#397C2211yescharacteristic, complemented
44C2×#396C2212yescomplemented
45C2×#394C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#393C2212yes—
52C2×#393C2212yescomplemented
53C2×#392C2211yescharacteristic
54C2×#392C2212yes—
55C2×#392C2212yes—
56C2×#392C2212yes—
57C2×#392C2211yescharacteristic
58C2×#392C2211yescharacteristic, complemented
59#2358—28no—
60C2×#391C2212yescomplemented
61C2×#390C2212yes—
62C2×#390C2211yescharacteristic
63C2×#390C2212yes—
64C2×#390C2211yescharacteristic, complemented
65C2×#390C2211yescharacteristic, complemented
66C2×#388C2211yescharacteristic
67C2×#388C2212yes—
68C2×#388C2211yescharacteristic
69C2×#388C2212yes—
70C2×#388C2212yescomplemented
71C2×#386C2211yescharacteristic
72C2×#386C2211yescharacteristic
73C2×#386C2211yescharacteristic
74C2×#386C2212yes—
75C2×#386C2212yes—
76C2×#386C2212yes—
77C2×#386C2212yescomplemented
78C2×#385C2211yescharacteristic
79C2×#385C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×#380C2211yescharacteristic
82C2×#380C2212yes—
83C2×#380C2212yescomplemented
84C2×#379C2212yes—
85C2×C4×C4⋊C4C2211yescharacteristic, complemented
86C2×C4×C4⋊C4C2211yescharacteristic, complemented
87C2×C4×C22⋊C4C2211yescharacteristic
88C2×C4×C22⋊C4C2211yescharacteristic
89#1446C2212yescomplemented
90#1445C2211yescharacteristic, complemented
91#1445C2211yescharacteristic, complemented
92#1444C2211yescharacteristic, complemented
93#1444C2212yescomplemented
94#1441C2212yescomplemented
95#1441C2212yescomplemented
96#1440C2212yes—
97#1440C2212yes—
98#1440C2212yes—
99#1440C2212yes—
100#1440C2212yescomplemented
101#1440C2212yescomplemented
102#1439C2211yescharacteristic
103#1439C2212yes—
104#1439C2212yes—
105#1439C2211yescharacteristic
106#1439C2212yescomplemented
107#1439C2211yescharacteristic, complemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1438C2212yes—
112#1438C2212yes—
113#1438C2211yescharacteristic, complemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120C4⋊#95C2211yescharacteristic, complemented
121C4⋊#95C2212yescomplemented
122#1434C2211yescharacteristic, complemented
123#1434C2211yescharacteristic, complemented
124#1434C2212yescomplemented
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C26C2311yescharacteristic
129C23×Q8C2312yes—
130C23×D4C2312yes—
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C2×C4⋊Q8—24no—
144C2×C4⋊Q8—24no—
145C2×C4⋊Q8—42no—
146C2×#124—28no—
147C2×#124—28no—
148C2×#124—28no—
149C2×#124—28no—
150C2×#124—28no—
151C2×#124—44no—
152C2×#121—24no—
153C2×#121—24no—
154C2×#121—42no—
155C2×#120—28no—
156C2×#120—24no—
157C2×#120—28no—
158C2×#120—24no—
159C2×#120—44no—
160C2×#120D418yescomplemented
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—42no—
165C2×C4×D4—44no—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—42no—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223#397—24no—
224#397—24no—
225#397—24no—
226#397—24no—
227#397—42no—
228#397D418yescomplemented
229#396—44no—
230#394—28no—
231#394—28no—
232#394—28no—
233#394—28no—
234#394—28no—
235#394—44no—
236#393—28no—
237#393—28no—
238#392—28no—
239#392—28no—
240#392—28no—
241#392—24no—
242#392—24no—
243#392—42no—
244#391—28no—
245#390—28no—
246#390—28no—
247#390—24no—
248#390—24no—
249#390—24no—
250#388—28no—
251#388—28no—
252#388—24no—
253#388—24no—
254#388—28no—
255#386—24no—
256#386—24no—
257#386—24no—
258#386—28no—
259#386—44no—
260#386—44no—
261#386—44no—
262#385—24no—
263#385—24no—
264#380—24no—
265#380—28no—
266#380—24no—
267#380—28no—
268#379—28no—
269C4×C4⋊C4—24no—
270C4×C4⋊C4—24no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4D418yescomplemented
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—42no—
310C25—41no—
311C25—42no—
312C25—41no—
313C25—42no—
314C25—42no—
315C25C2×D414yes—
316C25C2412yes—
317C25C2411yescharacteristic
318C25C2411yescharacteristic
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C22×Q8—24no—
322C22×Q8—24no—
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8—42no—
326C22×Q8—42no—
327C22×Q8—42no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—41no—
350C22×D4—42no—
351C22×D4—41no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4C2×D414yes—
376C22×D4C2×D414yes—
377C22×D4C2×D414yes—
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—24no—
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—42no—
391C23×C4—41no—
392C23×C4—41no—
393C23×C4—41no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—41no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4C2×D414yes—
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C4⋊Q8—416no—
422#124—432no—
423#124—432no—
424#121—416no—
425#120—232no—
426#120—432no—
427C4×D4—416no—
428C4×D4—416no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4C2×D414yes—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
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—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—416no—
519C2×C22⋊C4—416no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
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—42no—
537C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
556C2×C22⋊C4C2×D414yes—
557C2×C22⋊C4C2×D418yes—
558C2×C22⋊C4C2×D414yes—
559C2×C22⋊C4C2×D414yes—
560C2×C22⋊C4C2×D414yes—
561C2×C22⋊C4C2×D414yes—
562C2×C22⋊C4#4114yes—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—24no—
567C2×C42—24no—
568C2×C42—24no—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—42no—
572C2×C42—42no—
573C2×C42—42no—
574C2×C42C2×D414yes—
575C2×C42C2×D414yes—
576#95—22no—
577#95—22no—
578#95—24no—
579#95—22no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—22no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95C2×D414yes—
605#95C2×D414yes—
606#95C2×D414yes—
607#95C2×D418yes—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—28no—
645C24—28no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—48no—
662C24—44no—
663C24—48no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—48no—
671C24—82no—
672C24—84no—
673C24—82no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24C22×D412yes—
683C24C22×D412yes—
684C24C22×D412yes—
685C24C22×D412yes—
686C24C22×D412yes—
687C24C22×D412yes—
688C24C2×#4112yes—
689C24H(5,𝔽2)12yes—
690C24C2511yescharacteristic
691C2×Q8—48no—
692C2×Q8—48no—
693C2×Q8—48no—
694C2×Q8—48no—
695C2×Q8—84no—
696C2×Q8—84no—
697C2×Q8—84no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—44no—
725C2×D4—82no—
726C2×D4—82no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
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—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—48no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—82no—
851C22×C4—82no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—82no—
857C22×C4—84no—
858C22×C4—82no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×D414yes—
867C22×C4C22×D414yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C2×#4112yes—
876C22×C4C2×#4112yes—
877C22×C4H(5,𝔽2)14yes—
878C22×C4H(5,𝔽2)12yes—
879C4⋊C4—28no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—84no—
887C4⋊C4—82no—
888C4⋊C4—84no—
889C4⋊C4—84no—
890C22⋊C4—216no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—82no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4#121116yes—
926C42—28no—
927C42—44no—
928C42—48no—
929C42—44no—
930C42—48no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—22no—
941C23—24no—
942C23—22no—
943C23—24no—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—24no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—416no—
968C23—416no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—42no—
973C23—41no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—42no—
998C23—41no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—41no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—41no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—816no—
1059C23—88no—
1060C23—816no—
1061C23—816no—
1062C23—88no—
1063C23—816no—
1064C23—88no—
1065C23—88no—
1066C23—88no—
1067C23C2×#12114yes—
1068C23D4214yes—
1069C23C23×D411yescharacteristic
1070C23C23×D411yescharacteristic
1071C23C23×D411yescharacteristic
1072C23C22×#4111yescharacteristic
1073C23C2×H(5,𝔽2)12yes—
1074C23C2×H(5,𝔽2)11yescharacteristic
1075C23C2×H(5,𝔽2)11yescharacteristic
1076C23#58512yes—
1077C23#58511yescharacteristic
1078C23#58512yes—
1079C23#58512yes—
1080Q8—816no—
1081D4—416no—
1082D4—416no—
1083D4—88no—
1084D4—88no—
1085D4—816no—
1086D4—816no—
1087D4—816no—
1088D4—816no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
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—88no—
1192C2×C4—88no—
1193C2×C4—88no—
1194C2×C4—88no—
1195C2×C4—88no—
1196C2×C4C2×#12114yes—
1197C2×C4C2×#12114yes—
1198C2×C4#53514yes—
1199C2×C4D4214yes—
1200C22—24no—
1201C22—28no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—44no—
1221C22—44no—
1222C22—42no—
1223C22—42no—
1224C22—44no—
1225C22—44no—
1226C22—42no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—832no—
1233C22—82no—
1234C22—82no—
1235C22—81no—
1236C22—81no—
1237C22—82no—
1238C22—82no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22C22×#12111yescharacteristic
1261C22C2×#53511yescharacteristic
1262C22#344911yescharacteristic
1263C22C2×D4211yescharacteristic
1264C22C2×D4211yescharacteristic
1265C22D4×#4111yescharacteristic
1266C22#348512yes—
1267C22#348511yescharacteristic
1268C22#348812yes—
1269C22#348811yescharacteristic
1270C22#349612yes—
1271C22#349611yescharacteristic
1272C22#350011yescharacteristic
1273C22#350012yes—
1274C22#350612yes—
1275C22#351911yescharacteristic
1276C22#352112yes—
1277C22#353312yes—
1278C22#354012yes—
1279C22#354212yes—
1280C22#354512yes—
1281C22#355812yes—
1282C22#356812yes—
1283C4—24no—
1284C4—24no—
1285C4—24no—
1286C4—24no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—81no—
1294C4—81no—
1295C4—82no—
1296C4—82no—
1297C4—82no—
1298C4—81no—
1299C4—82no—
1300C4—82no—
1301C2—44no—
1302C2—44no—
1303C2—82no—
1304C2—82no—
1305C2—162no—
1306C2#3516511yescharacteristic
1307C2#3600911yescharacteristic
1308C2D4×#12111yescharacteristic
1309C2#3767711yescharacteristic
1310C2#3933311yescharacteristic
1311C2#4194611yescharacteristic
1312C2#4267711yescharacteristic
1313C2#4390412yes—
1314C2#4418212yes—
1315C2#4785212yes—
1316C2#4865812yes—
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×#2670C2semidirect
2. C2×#2547C2semidirect
3. C2×#2491C2semidirect
4. C2×#2617C2semidirect
5. C2×#2358C2semidirect
6. #16810C2semidirect
7. #16506C2semidirect
8. #16500C2semidirect
9. #16401C2semidirect
10. #15631C2semidirect
11. #15314C2semidirect
12. #15307C2semidirect
13. #15303C2semidirect
14. #15160C2semidirect
15. #15147C2semidirect
16. #14820C2semidirect
17. #14815C2semidirect
18. #14811C2semidirect
19. #14732C2semidirect
20. #14725C2semidirect
21. #14421C2semidirect
22. #14225C2semidirect
23. #13891C2semidirect
24. C22×C4⋊Q8C22semidirect
42. C2×#397C22semidirect
43. C2×#397C22semidirect
44. C2×#396C22semidirect
52. C2×#393C22semidirect
58. C2×#392C22semidirect
60. C2×#391C22semidirect
64. C2×#390C22semidirect
65. C2×#390C22semidirect
70. C2×#388C22semidirect
77. C2×#386C22semidirect
83. C2×#380C22semidirect
85. C2×C4×C4⋊C4C22semidirect
86. C2×C4×C4⋊C4C22semidirect
89. #1446C22semidirect
90. #1445C22semidirect
91. #1445C22semidirect
92. #1444C22semidirect
93. #1444C22semidirect
94. #1441C22semidirect
95. #1441C22semidirect
100. #1440C22semidirect
101. #1440C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
122. #1434C22semidirect
123. #1434C22semidirect
124. #1434C22semidirect
160. C2×#120D4semidirect
228. #397D4semidirect
272. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26702
C2×#25472
C2×#24912
C2×#26172
C2×#23582
#168102
#165062
#165002
#164012
#156312
#153142
#153072
#153032
#151602
#151472
#148202
#148152
#148112
#147322
#147252
#144212
#142252
#138912