Finite Group Databasebeta

← #4306643

Subgroups — #4306643

Order 512.

5328 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2359C211yesmaximal, characteristic, complemented
2C2×#2358C212yesmaximal, complemented
3C2×#2342C212yesmaximal, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#15250C211yesmaximal, characteristic, complemented
6#15084C211yesmaximal, characteristic, complemented
7#14985C212yesmaximal, complemented
8#14985C212yesmaximal, complemented
9#14977C212yesmaximal, complemented
10#14977C211yesmaximal, characteristic, complemented
11#14936C211yesmaximal, characteristic, complemented
12#14911C212yesmaximal, complemented
13#14900C211yesmaximal, characteristic, complemented
14#14836C211yesmaximal, characteristic, complemented
15#14807C211yesmaximal, characteristic, complemented
16#14796C211yesmaximal, characteristic, complemented
17#14796C212yesmaximal, complemented
18#14734C212yesmaximal, complemented
19#14715C211yesmaximal, characteristic
20C4×#392C211yesmaximal, characteristic, complemented
21#13847C211yesmaximal, characteristic, complemented
22C2×#1438C211yesmaximal, characteristic, complemented
23#13809C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#120C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yescomplemented
31C22×#117C2211yescharacteristic
32C23×C22⋊C4C2212yes—
33C23×C22⋊C4C2212yes—
34C23×C22⋊C4C2212yes—
35C2×#399C2212yescomplemented
36C2×#399C2211yescharacteristic, complemented
37C2×#399C2212yescomplemented
38C2×#392C2211yescharacteristic
39C2×#392C2211yescharacteristic
40C2×#392C2212yes—
41#2359—28no—
42#2358—216no—
43#2342—216no—
44D4×C22⋊C4—28no—
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2212yescomplemented
48C2×#389C2211yescharacteristic, complemented
49C2×#388C2212yescomplemented
50C2×#388C2211yescharacteristic, complemented
51C2×#388C2212yescomplemented
52C2×#388C2212yescomplemented
53C2×#388C2212yescomplemented
54C2×#388C2212yescomplemented
55C2×#388C2212yescomplemented
56C2×#388C2211yescharacteristic, complemented
57C2×#387C2211yescharacteristic, complemented
58C2×#387C2211yescharacteristic, complemented
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2212yescomplemented
64C2×#386C2212yescomplemented
65C2×#385C2212yes—
66C2×#385C2211yescharacteristic
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#385C2212yescomplemented
70C2×#385C2211yescharacteristic, complemented
71C2×#381C2212yes—
72C2×#380C2211yescharacteristic
73C2×#380C2212yes—
74C2×#379C2212yes—
75C2×#379C2212yes—
76C2×C4×C4⋊C4C2211yescharacteristic, complemented
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2212yes—
79C2×C4×C22⋊C4C2212yescomplemented
80C2×C4×C22⋊C4C2212yescomplemented
81C2×C4×C22⋊C4C2212yescomplemented
82C2×C4×C22⋊C4C2211yescharacteristic, complemented
83C2×#376C2211yescharacteristic, complemented
84C22×#95C2211yescharacteristic
85C22×#95C2211yescharacteristic
86#1445C2211yescharacteristic, complemented
87#1445C2211yescharacteristic, complemented
88#1445C2212yescomplemented
89#1445C2212yescomplemented
90#1445C2211yescharacteristic, complemented
91#1445C2212yescomplemented
92#1444C2211yescharacteristic, complemented
93#1444C2211yescharacteristic, complemented
94#1444C2211yescharacteristic, complemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2211yescharacteristic, complemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1438C2211yescharacteristic
108#1438C2211yescharacteristic
109#1438C2212yes—
110#1438C2211yescharacteristic
111#1438C2212yes—
112#1438C2211yescharacteristic
113#1438C2211yescharacteristic
114#1438C2212yes—
115#1438C2211yescharacteristic
116#1438C2212yescomplemented
117#1438C2212yescomplemented
118#1438C2212yescomplemented
119#1438C2212yescomplemented
120#1434C2212yescomplemented
121#1434C2211yescharacteristic, complemented
122#1434C2212yescomplemented
123#1434C2211yescharacteristic, complemented
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×D4—28no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—42no—
132C23×D4—44no—
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C2×#123—24no—
147C2×#123—24no—
148C2×#123—24no—
149C2×#120—28no—
150C2×#120—28no—
151C2×#120—28no—
152C2×C4×D4—24no—
153C2×C4×D4—28no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—28no—
158C2×C4×D4—42no—
159C2×C4×D4—44no—
160C2×C4×D4—44no—
161C2×C4×D4—44no—
162C2×#117—28no—
163C2×#117—24no—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C22⋊C4—28no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—28no—
180C22×C22⋊C4—28no—
181C22×C22⋊C4—28no—
182C22×C22⋊C4—28no—
183C22×C22⋊C4—28no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2312yes—
225#399—42no—
226#399—44no—
227#399—44no—
228#392—24no—
229#392—42no—
230#392—44no—
231#390—24no—
232#390—24no—
233#390—28no—
234#389—24no—
235#388—24no—
236#388—28no—
237#388—28no—
238#388—28no—
239#388—24no—
240#388—28no—
241#388—28no—
242#388—28no—
243#387—24no—
244#387—24no—
245#386—28no—
246#386—24no—
247#386—28no—
248#386—28no—
249#386—28no—
250#386—28no—
251#385—28no—
252#385—24no—
253#385—24no—
254#385—28no—
255#385—28no—
256#385—28no—
257#381—28no—
258#380—24no—
259#380—28no—
260#379—28no—
261#379—28no—
262C4×C4⋊C4—24no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—28no—
265C4×C22⋊C4—28no—
266C4×C22⋊C4—28no—
267C4×C22⋊C4D418yescomplemented
268C4×C22⋊C4D4116yescomplemented
269#376—42no—
270C2×#95—24no—
271C2×#95—42no—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
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×#95C2311yescharacteristic
303C2×#95C2312yes—
304C2×#95C2312yes—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—24no—
309C25—24no—
310C25—24no—
311C25—24no—
312C25—24no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25#4118yes—
320C25C2412yes—
321C25C2411yescharacteristic
322C25C2412yes—
323C25C2411yescharacteristic
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—232no—
327C22×D4—24no—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—416no—
351C22×D4—42no—
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—432no—
361C22×D4—416no—
362C22×D4—432no—
363C22×D4#4114yes—
364C22×D4#4114yes—
365C23×C4—24no—
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—22no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—41no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—41no—
402C23×C4—42no—
403C23×C4C2×D414yes—
404C23×C4C2×D418yes—
405C23×C4#4114yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425#123—232no—
426#120—264no—
427C4×D4—416no—
428C4×D4—432no—
429C4×D4—416no—
430C4×D4—416no—
431#117—416no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C22⋊C4—264no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
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—24no—
480C2×C22⋊C4—24no—
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—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
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—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
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—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—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—432no—
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—432no—
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⋊C4C2×D418yes—
558C2×C22⋊C4C2×D414yes—
559C2×C22⋊C4C2×D414yes—
560C2×C22⋊C4C2×D418yes—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—24no—
565C2×C42—24no—
566C2×C42—22no—
567C2×C42—24no—
568C2×C42—22no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—42no—
573C2×C42—42no—
574C2×C42C2×D414yes—
575C2×C42C2×D414yes—
576C2×C42C2×D418yescomplemented
577C2×C42C2×D418yescomplemented
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—22no—
588#95—24no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95C2×D414yes—
608#95C2×D414yes—
609#95C2×D418yescomplemented
610#95C2×D418yescomplemented
611C24—21no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—216no—
630C24—22no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—22no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—21no—
654C24—216no—
655C24—216no—
656C24—216no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24C22×D412yes—
689C24C22×D414yes—
690C24C2×#4114yes—
691C24C2×#4112yes—
692C24C2×#4114yes—
693C24C2×#4114yes—
694C24C2×#4112yes—
695C24C2×#4114yes—
696C24C2×#4112yes—
697C24H(5,𝔽2)14yes—
698C24C2511yescharacteristic
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—216no—
702C2×D4—216no—
703C2×D4—216no—
704C2×D4—28no—
705C2×D4—216no—
706C2×D4—216no—
707C2×D4—28no—
708C2×D4—216no—
709C2×D4—28no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—4128no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—44no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—216no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—216no—
802C22×C4—28no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—48no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—44no—
854C22×C4—82no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—82no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4C22×D412yes—
869C22×C4C22×D414yes—
870C22×C4C22×D414yes—
871C22×C4C22×D414yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D414yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D414yes—
878C22×C4C22×D414yes—
879C22×C4C22×D412yes—
880C22×C4C2×#4112yes—
881C22×C4C2×#4112yes—
882C22×C4C2×#4112yes—
883C22×C4C2×#4112yes—
884C22×C4H(5,𝔽2)12yes—
885C22×C4H(5,𝔽2)12yes—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—82no—
896C4⋊C4—84no—
897C4⋊C4—84no—
898C4⋊C4—84no—
899C22⋊C4—216no—
900C22⋊C4—216no—
901C22⋊C4—216no—
902C22⋊C4—216no—
903C22⋊C4—216no—
904C22⋊C4—216no—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—216no—
909C22⋊C4—28no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—84no—
925C22⋊C4—82no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4#127116yes—
931C42—28no—
932C42—44no—
933C42—48no—
934C42—48no—
935C42—44no—
936C42—44no—
937C42—44no—
938C23—22no—
939C23—24no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—22no—
952C23—24no—
953C23—22no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—432no—
987C23—432no—
988C23—432no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—432no—
1006C23—41no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
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—41no—
1045C23—42no—
1046C23—42no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—816no—
1053C23—816no—
1054C23—816no—
1055C23—816no—
1056C23—816no—
1057C23—816no—
1058C23—816no—
1059C23—816no—
1060C23—816no—
1061C23—816no—
1062C23—816no—
1063C23#52514yes—
1064C23#52518yes—
1065C23#52518yes—
1066C23#52514yes—
1067C23C2×#12714yes—
1068C23#55118yes—
1069C23C23×D411yescharacteristic
1070C23C23×D412yes—
1071C23C22×#4112yes—
1072C23C22×#4111yescharacteristic
1073C23C22×#4111yescharacteristic
1074C23C22×#4111yescharacteristic
1075C23C2×H(5,𝔽2)11yescharacteristic
1076C23C2×H(5,𝔽2)12yes—
1077C23C2×H(5,𝔽2)11yescharacteristic
1078C23#58512yes—
1079C23#58511yescharacteristic
1080D4—232no—
1081D4—416no—
1082D4—432no—
1083D4—432no—
1084D4—416no—
1085D4—816no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—416no—
1128C2×C4—416no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—88no—
1195C2×C4—816no—
1196C2×C4—816no—
1197C2×C4—816no—
1198C2×C4—88no—
1199C2×C4C2×#12714yes—
1200C2×C4C2×#12714yes—
1201C2×C4#54614yes—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—28no—
1206C22—28no—
1207C22—28no—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—28no—
1212C22—28no—
1213C22—28no—
1214C22—28no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—42no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—44no—
1239C22—864no—
1240C22—82no—
1241C22—81no—
1242C22—81no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—81no—
1251C22—82no—
1252C22—81no—
1253C22—82no—
1254C22#239718yes—
1255C22C2×#52511yescharacteristic
1256C22C2×#52511yescharacteristic
1257C22C2×#52512yes—
1258C22C2×#52512yes—
1259C22C22×#12711yescharacteristic
1260C22C2×#54611yescharacteristic
1261C22D4×#4112yes—
1262C22C2×#55112yes—
1263C22#347511yescharacteristic
1264C22#348111yescharacteristic
1265C22#348411yescharacteristic
1266C22#348412yes—
1267C22#348811yescharacteristic
1268C22#348812yes—
1269C22#349012yes—
1270C22#349112yes—
1271C22#349412yes—
1272C22#349612yes—
1273C22#350011yescharacteristic
1274C22#350512yes—
1275C22#350811yescharacteristic
1276C22#351312yes—
1277C22#351411yescharacteristic
1278C4—24no—
1279C4—24no—
1280C4—24no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—42no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—81no—
1293C4—82no—
1294C4—81no—
1295C4—81no—
1296C4—82no—
1297C2—28no—
1298C2—48no—
1299C2—82no—
1300C2—84no—
1301C2C2×#239711yescharacteristic
1302C2#3568112yes—
1303C2#3572911yescharacteristic
1304C2#3575311yescharacteristic
1305C2#3576212yes—
1306C2#3592111yescharacteristic
1307C2#3615811yescharacteristic
1308C2#3622012yes—
1309C2#3622212yes—
1310C2#3626011yescharacteristic
1311C2#3636011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2359C2semidirect
2. C2×#2358C2semidirect
3. C2×#2342C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #15250C2semidirect
6. #15084C2semidirect
7. #14985C2semidirect
8. #14985C2semidirect
9. #14977C2semidirect
10. #14977C2semidirect
11. #14936C2semidirect
12. #14911C2semidirect
13. #14900C2semidirect
14. #14836C2semidirect
15. #14807C2semidirect
16. #14796C2semidirect
17. #14796C2semidirect
18. #14734C2semidirect
20. C4×#392C2semidirect
21. #13847C2semidirect
22. C2×#1438C2semidirect
23. #13809C2semidirect
30. C22×C4×D4C22semidirect
35. C2×#399C22semidirect
36. C2×#399C22semidirect
37. C2×#399C22semidirect
47. C2×#390C22semidirect
48. C2×#389C22semidirect
49. C2×#388C22semidirect
50. C2×#388C22semidirect
51. C2×#388C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#387C22semidirect
58. C2×#387C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
76. C2×C4×C4⋊C4C22semidirect
79. C2×C4×C22⋊C4C22semidirect
80. C2×C4×C22⋊C4C22semidirect
81. C2×C4×C22⋊C4C22semidirect
82. C2×C4×C22⋊C4C22semidirect
83. C2×#376C22semidirect
86. #1445C22semidirect
87. #1445C22semidirect
88. #1445C22semidirect
89. #1445C22semidirect
90. #1445C22semidirect
91. #1445C22semidirect
92. #1444C22semidirect
93. #1444C22semidirect
94. #1444C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
116. #1438C22semidirect
117. #1438C22semidirect
118. #1438C22semidirect
119. #1438C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
123. #1434C22semidirect
126. C4×#95C22semidirect
267. C4×C22⋊C4D4semidirect
268. C4×C22⋊C4D4semidirect
576. C2×C42C2×D4semidirect
577. C2×C42C2×D4semidirect
609. #95C2×D4semidirect
610. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23592
C2×#23582
C2×#23422
C2×D4×C22⋊C42
#152502
#150842
#149852
#149772
#149362
#149112
#149002
#148362
#148072
#147962
#147342
#147152
C4×#3922
#138472
C2×#14382
#138092