Finite Group Databasebeta

← #647845

Subgroups — #647845

Order 512.

4580 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2534C211yesmaximal, characteristic, complemented
2C2×#2406C211yesmaximal, characteristic, complemented
3C2×#2404C211yesmaximal, characteristic
4C2×#2339C211yesmaximal, characteristic, complemented
5C2×C4×#123C211yesmaximal, characteristic, complemented
6C22×#388C211yesmaximal, characteristic, complemented
7#15452C212yesmaximal, complemented
8#15427C212yesmaximal, complemented
9#15418C212yesmaximal, complemented
10#15411C212yesmaximal, complemented
11#15073C211yesmaximal, characteristic, complemented
12#14921C211yesmaximal, characteristic, complemented
13#14918C211yesmaximal, characteristic, complemented
14#14911C211yesmaximal, characteristic, complemented
15#14789C212yesmaximal, complemented
16#14751C212yesmaximal, complemented
17#14706C211yesmaximal, characteristic, complemented
18#14140C212yesmaximal, complemented
19#14036C212yesmaximal, complemented
20#14016C211yesmaximal, characteristic, complemented
21#13995C211yesmaximal, characteristic, complemented
22#13967C211yesmaximal, characteristic, complemented
23#13874C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2534—28no—
37#2406—28no—
38#2404—28no—
39C2×#396C2212yes—
40C2×#395C2212yescomplemented
41C2×#394C2212yes—
42C2×#394C2212yescomplemented
43C2×#393C2212yes—
44C2×#392C2212yes—
45#2339—28no—
46C4×#123—28no—
47C2×#391C2211yescharacteristic, complemented
48C2×#391C2211yescharacteristic, complemented
49C2×#390C2212yes—
50C2×#388—28no—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#388C2212yescomplemented
57C2×#387C2212yescomplemented
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2211yescharacteristic
62C2×#386C2212yes—
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2212yes—
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic, complemented
69C2×#386C2211yescharacteristic, complemented
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2212yescomplemented
73C2×#385C2212yescomplemented
74C2×#381C2211yescharacteristic
75C2×#381C2211yescharacteristic
76C2×#381C2211yescharacteristic
77C2×#381C2211yescharacteristic
78C2×#381C2211yescharacteristic
79C2×#381C2211yescharacteristic, complemented
80C2×#380C2211yescharacteristic
81C2×#380C2211yescharacteristic, complemented
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×C4×C4⋊C4C2212yescomplemented
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic, complemented
87C2×C4×C22⋊C4C2212yescomplemented
88C22×#95C2211yescharacteristic
89C22×#95C2211yescharacteristic
90C22×#95C2211yescharacteristic, complemented
91#1443C2212yescomplemented
92#1443C2212yescomplemented
93#1442C2212yescomplemented
94#1442C2212yescomplemented
95#1442C2212yescomplemented
96#1442C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1440C2212yes—
101#1440C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1437C2212yes—
116#1437C2212yes—
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122#1436C2212yescomplemented
123#1434C2212yescomplemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—24no—
134C22×#41—24no—
135C22×#41—42no—
136C22×#41—42no—
137C23×Q8C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C23×D4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C2×#123—24no—
154C2×#123—24no—
155C2×#123—24no—
156C2×#123—24no—
157C2×#123—42no—
158C2×#123D418yescomplemented
159C2×#120—24no—
160C2×#120—24no—
161C2×#120—24no—
162C2×#120—24no—
163C2×#120—24no—
164C2×#120—42no—
165C2×C4×D4—24no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—24no—
169C2×C4×D4—42no—
170C2×C4×D4—42no—
171C22×C4⋊C4—24no—
172C22×C4⋊C4—24no—
173C22×C4⋊C4—42no—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—28no—
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⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C42—24no—
222C22×C42—24no—
223C22×C42—42no—
224C22×C42C2312yes—
225C22×C42C2312yes—
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229#396—28no—
230#395—28no—
231#394—28no—
232#394—28no—
233#393—28no—
234#392—28no—
235#391—24no—
236#391—24no—
237#390—28no—
238#388—28no—
239#388—28no—
240#388—28no—
241#388—28no—
242#388—28no—
243#388—28no—
244#387—28no—
245#386—24no—
246#386—24no—
247#386—24no—
248#386—24no—
249#386—28no—
250#386—24no—
251#386—28no—
252#386—28no—
253#386—24no—
254#386—24no—
255#386—28no—
256#386D418yes—
257#385—24no—
258#385—28no—
259#385—28no—
260#385—42no—
261#381—24no—
262#381—24no—
263#381—24no—
264#381—24no—
265#381—24no—
266#381—24no—
267#380—24no—
268#380—24no—
269#379—24no—
270#379—42no—
271C4×C4⋊C4—28no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—28no—
274C4×C22⋊C4—24no—
275C2×#95—24no—
276C2×#95—24no—
277C2×#95D418yescomplemented
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C25—22no—
317C25—24no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25C2412yes—
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C2×#41—232no—
332C2×#41—416no—
333C2×#41—416no—
334C2×#41—416no—
335C2×#41—416no—
336C2×#41—416no—
337C2×#41—416no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—41no—
344C22×Q8—41no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—24no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4C2×D414yes—
377C22×D4C2×D414yes—
378C22×D4#4114yes—
379C22×D4#4114yes—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—24no—
404C23×C4—24no—
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—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—24no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—41no—
423C23×C4—41no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4C2×D414yes—
434C23×C4C2×D414yes—
435C23×C4C2×D414yes—
436C23×C4C2×D414yes—
437C23×C4C2×D414yes—
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457#123—232no—
458#123—416no—
459#120—416no—
460#120—416no—
461C4×D4—416no—
462C4×D4—416no—
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—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—416no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4C2×D418yes—
491C2×C22⋊C4—232no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
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—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—24no—
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—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—416no—
563C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
576C2×C22⋊C4C2×D414yes—
577C2×C22⋊C4C2×D418yes—
578C2×C22⋊C4C2×D418yes—
579C2×C22⋊C4#4118yescomplemented
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—24no—
585C2×C42—24no—
586C2×C42—24no—
587C2×C42—24no—
588C2×C42—24no—
589C2×C42—24no—
590C2×C42—41no—
591C2×C42—41no—
592C2×C42—42no—
593C2×C42—42no—
594C2×C42—42no—
595C2×C42—416no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—24no—
600#95—24no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—24no—
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—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95C2×D414yes—
630#95C2×D414yes—
631#95C2×D414yes—
632#95C2×D414yes—
633#95C2×D418yes—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—28no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—21no—
651C24—22no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—21no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24C22×D412yes—
694C24C22×D412yes—
695C24C22×D412yes—
696C24C22×D412yes—
697C24C22×D412yes—
698C24C2×#4114yes—
699C24C2×#4112yes—
700C24C2×#4112yes—
701C24C2×#4112yes—
702C24C2×#4112yes—
703C24H(5,𝔽2)12yes—
704C24H(5,𝔽2)12yes—
705C24C2511yescharacteristic
706#41—4128no—
707C2×Q8—28no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—44no—
711C2×Q8—44no—
712C2×Q8—44no—
713C2×Q8—44no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4#121116yes—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
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—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—48no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—48no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—82no—
902C22×C4—84no—
903C22×C4—82no—
904C22×C4—84no—
905C22×C4—84no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4C22×D414yes—
909C22×C4C22×D414yes—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913C22×C4C22×D412yes—
914C22×C4C22×D414yes—
915C22×C4C22×D414yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C2×#4114yes—
921C22×C4C2×#4112yes—
922C22×C4C2×#4112yes—
923C22×C4C2×#4114yes—
924C4⋊C4—216no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—84no—
932C4⋊C4—84no—
933C22⋊C4—216no—
934C22⋊C4—28no—
935C22⋊C4—216no—
936C22⋊C4—28no—
937C22⋊C4—216no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—82no—
958C22⋊C4—82no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C42—48no—
964C42—48no—
965C42—48no—
966C42—44no—
967C42—44no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—24no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—416no—
1009C23—416no—
1010C23—416no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—41no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—41no—
1026C23—42no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—41no—
1032C23—41no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—41no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—88no—
1072C23—88no—
1073C23—88no—
1074C23—88no—
1075C23C2×#12114yes—
1076C23C2×#12114yes—
1077C23#52514yes—
1078C23#53814yes—
1079C23D4214yes—
1080C23D4214yes—
1081C23#54614yes—
1082C23#54614yes—
1083C23C23×D411yescharacteristic
1084C23C23×D411yescharacteristic
1085C23C23×D411yescharacteristic
1086C23C22×#4111yescharacteristic
1087C23C22×#4111yescharacteristic
1088C23C22×#4112yes—
1089C23C2×H(5,𝔽2)11yescharacteristic
1090C23C2×H(5,𝔽2)11yescharacteristic
1091C23#58512yes—
1092C23#58512yes—
1093C23#58512yes—
1094Q8—416no—
1095D4—232no—
1096D4—416no—
1097D4—416no—
1098D4—816no—
1099D4—816no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—416no—
1144C2×C4—416no—
1145C2×C4—416no—
1146C2×C4—416no—
1147C2×C4—416no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—416no—
1153C2×C4—416no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
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—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—88no—
1223C2×C4—88no—
1224C2×C4—88no—
1225C2×C4C2×#12114yes—
1226C2×C4#52514yes—
1227C22—28no—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—24no—
1232C22—28no—
1233C22—24no—
1234C22—28no—
1235C22—28no—
1236C22—24no—
1237C22—24no—
1238C22—28no—
1239C22—44no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—44no—
1246C22—44no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—44no—
1255C22—42no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—832no—
1261C22—82no—
1262C22—82no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—81no—
1274C22—82no—
1275C22#242418yes—
1276C22C22×#12111yescharacteristic
1277C22C2×#52511yescharacteristic
1278C22C2×#52511yescharacteristic
1279C22#344911yescharacteristic
1280C22C2×#53811yescharacteristic
1281C22C2×D4211yescharacteristic
1282C22C2×D4211yescharacteristic
1283C22C2×#54611yescharacteristic
1284C22C2×#54611yescharacteristic
1285C22D4×#4112yes—
1286C22D4×#4112yes—
1287C22#347512yes—
1288C22#347512yes—
1289C22#348511yescharacteristic
1290C22#348512yes—
1291C22#348711yescharacteristic
1292C22#350012yes—
1293C22#351312yes—
1294C22#351312yes—
1295C22#352112yes—
1296C22#352112yes—
1297C22#353312yes—
1298C22#354512yes—
1299C4—24no—
1300C4—24no—
1301C4—42no—
1302C4—44no—
1303C4—44no—
1304C4—44no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—44no—
1310C4—42no—
1311C4—42no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—82no—
1316C4—82no—
1317C4—81no—
1318C2—28no—
1319C2—44no—
1320C2—82no—
1321C2—84no—
1322C2C2×#242411yescharacteristic
1323C2#3487511yescharacteristic
1324C2#3545411yescharacteristic
1325C2#3609911yescharacteristic
1326C2#3610211yescharacteristic
1327C2#3621812yes—
1328C2#3765511yescharacteristic
1329C2#3814412yes—
1330C2#3933311yescharacteristic
1331C2#5903212yes—
1332C2#5980512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2404C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#2534C2semidirect
2. C2×#2406C2semidirect
4. C2×#2339C2semidirect
5. C2×C4×#123C2semidirect
6. C22×#388C2semidirect
7. #15452C2semidirect
8. #15427C2semidirect
9. #15418C2semidirect
10. #15411C2semidirect
11. #15073C2semidirect
12. #14921C2semidirect
13. #14918C2semidirect
14. #14911C2semidirect
15. #14789C2semidirect
16. #14751C2semidirect
17. #14706C2semidirect
18. #14140C2semidirect
19. #14036C2semidirect
20. #14016C2semidirect
21. #13995C2semidirect
22. #13967C2semidirect
23. #13874C2semidirect
40. C2×#395C22semidirect
42. C2×#394C22semidirect
47. C2×#391C22semidirect
48. C2×#391C22semidirect
56. C2×#388C22semidirect
57. C2×#387C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
72. C2×#385C22semidirect
73. C2×#385C22semidirect
79. C2×#381C22semidirect
81. C2×#380C22semidirect
84. C2×C4×C4⋊C4C22semidirect
86. C2×C4×C22⋊C4C22semidirect
87. C2×C4×C22⋊C4C22semidirect
90. C22×#95C22semidirect
91. #1443C22semidirect
92. #1443C22semidirect
93. #1442C22semidirect
94. #1442C22semidirect
95. #1442C22semidirect
96. #1442C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
123. #1434C22semidirect
128. C22⋊#95C22semidirect
158. C2×#123D4semidirect
277. C2×#95D4semidirect
579. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25342
C2×#24062
C2×#24042
C2×#23392
C2×C4×#1232
C22×#3882
#154522
#154272
#154182
#154112
#150732
#149212
#149182
#149112
#147892
#147512
#147062
#141402
#140362
#140162
#139952
#139672
#138742