Finite Group Databasebeta

← #534237

Subgroups — #534237

Order 512.

4642 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2361C211yesmaximal, characteristic
2C2×#2361C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C212yesmaximal, complemented
5C2×C4×#121C211yesmaximal, characteristic
6C22×#389C211yesmaximal, characteristic, complemented
7#14405C212yesmaximal, complemented
8#14402C212yesmaximal, complemented
9#14112C212yesmaximal, complemented
10#14046C211yesmaximal, characteristic, complemented
11#14043C212yesmaximal, complemented
12#14018C211yesmaximal, characteristic, complemented
13#14015C212yesmaximal, complemented
14#14005C211yesmaximal, characteristic, complemented
15#13977C211yesmaximal, characteristic, complemented
16#13975C212yesmaximal, complemented
17#13920C211yesmaximal, characteristic, complemented
18#13910C211yesmaximal, characteristic, complemented
19#13907C211yesmaximal, characteristic, complemented
20#13899C212yesmaximal, complemented
21#13880C211yesmaximal, characteristic, complemented
22#13821C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C22×#121C2211yescharacteristic
25C22×C4×D4C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2212yes—
30C22×C4×D4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2212yes—
33C23×C4⋊C4C2212yes—
34C23×C4⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2361—28no—
37#2361C4116yescomplemented
38D4×C4⋊C4—28no—
39D4×C4⋊C4—216no—
40C4×#121—28no—
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#389—28no—
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#389C2211yescharacteristic
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#388C2212yes—
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#385C2212yes—
65C2×#385C2212yes—
66C2×#385C2212yes—
67C2×#385C2212yes—
68C2×#385C2212yes—
69C2×#385C2212yes—
70C2×#385C2211yescharacteristic
71C2×#385C2212yes—
72C2×#385C2212yes—
73C2×#385C2212yes—
74C2×#385C2211yescharacteristic
75C2×#384C2211yescharacteristic
76C2×#384C2212yes—
77C2×#384C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#380C2212yes—
80C2×#380C2212yes—
81C2×#380C2212yes—
82C2×C4×C4⋊C4C2212yes—
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C4⋊C4C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86C2×C4×C4⋊C4C2211yescharacteristic
87C2×C4×C4⋊C4C2211yescharacteristic
88C2×C4×C22⋊C4C2212yes—
89C2×C4×C22⋊C4C2211yescharacteristic
90C2×C4×C22⋊C4C2211yescharacteristic
91C22×#95C2212yes—
92#1444C2212yes—
93#1444C2212yes—
94#1444C2212yes—
95#1444C2212yes—
96#1444C2212yes—
97#1442C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1436C2211yescharacteristic
109#1436C2212yes—
110#1436C2212yes—
111#1436C2211yescharacteristic
112#1436C2212yes—
113#1436C2211yescharacteristic
114#1436C2212yes—
115#1436C2211yescharacteristic
116C4⋊#95C2212yes—
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121#1434C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2211yescharacteristic
127C4×#95C2211yescharacteristic
128C4×#95C2211yescharacteristic
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C24×C4C2312yes—
133C24×C4C2312yes—
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139C2×#121C2×C418yes—
140C2×#121D418yes—
141C2×#121Q818yes—
142C2×C4×D4—24no—
143C2×C4×D4—28no—
144C2×C4×D4—24no—
145C2×C4×D4—28no—
146C2×C4×D4—28no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—28no—
151C2×C4×D4—28no—
152C2×C4×D4—28no—
153C2×C4×D4—24no—
154C2×C4×D4—42no—
155C2×C4×D4—42no—
156C2×C4×D4—44no—
157C2×C4×D4—44no—
158C2×C4×D4C2×C418yescomplemented
159C2×C4×D4C2×C4116yescomplemented
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—28no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4—28no—
165C22×C4⋊C4—28no—
166C22×C4⋊C4—28no—
167C22×C4⋊C4—24no—
168C22×C4⋊C4—44no—
169C22×C4⋊C4—44no—
170C22×C4⋊C4—42no—
171C22×C4⋊C4C2×C418yescomplemented
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C42—24no—
214C22×C42—24no—
215C22×C42—42no—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#390—24no—
228#390—24no—
229#390C2×C418yescomplemented
230#389—28no—
231#389—24no—
232#389—24no—
233#389—28no—
234#389—24no—
235#389—24no—
236#389—24no—
237#389—24no—
238#389—24no—
239#389—28no—
240#389—28no—
241#389C2×C418yescomplemented
242#389D418yescomplemented
243#388—28no—
244#388—28no—
245#388C2×C4116yescomplemented
246#386—28no—
247#386—28no—
248#386C2×C4116yescomplemented
249#385—28no—
250#385—28no—
251#385—28no—
252#385—28no—
253#385—24no—
254#385—28no—
255#385—28no—
256#385—44no—
257#385—44no—
258#385C2×C4116yescomplemented
259#385D418yescomplemented
260#384—28no—
261#384—24no—
262#384—42no—
263#380—24no—
264#380—28no—
265#380—28no—
266#380—28no—
267C4×C4⋊C4—24no—
268C4×C4⋊C4—24no—
269C4×C4⋊C4—24no—
270C4×C4⋊C4—28no—
271C4×C4⋊C4—42no—
272C4×C4⋊C4C2×C418yescomplemented
273C4×C22⋊C4—24no—
274C4×C22⋊C4—28no—
275C4×C22⋊C4C2×C418yescomplemented
276C2×#95—28no—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2312yes—
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2312yes—
314C25C2412yes—
315C25C2411yescharacteristic
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4C22×C418yes—
325C22×D4C22×C414yes—
326C22×D4C2×D418yes—
327C22×D4C2×D414yes—
328C22×D4C2×Q818yes—
329C22×D4C2×Q814yes—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—24no—
335C23×C4—22no—
336C23×C4—24no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—24no—
340C23×C4—22no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—22no—
344C23×C4—24no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—24no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4C22×C418yes—
381C23×C4C22×C418yes—
382C23×C4C22×C414yes—
383C23×C4C2×D414yes—
384C23×C4C2×D414yes—
385C23×C4C2×Q814yes—
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407#121C4⋊C4164yescomplemented
408C4×D4—232no—
409C4×D4—264no—
410C4×D4—416no—
411C4×D4—432no—
412C4×D4—416no—
413C4×D4—432no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—232no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
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—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—432no—
462C2×C4⋊C4—432no—
463C2×C4⋊C4—416no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—41no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4C22×C418yes—
484C2×C4⋊C4C22×C414yes—
485C2×C4⋊C4C22×C418yes—
486C2×C4⋊C4C22×C414yes—
487C2×C4⋊C4C22×C414yes—
488C2×C4⋊C4C2×D418yes—
489C2×C4⋊C4C2×D414yes—
490C2×C4⋊C4C2×D414yes—
491C2×C4⋊C4C2×D414yes—
492C2×C4⋊C4C2×D414yes—
493C2×C4⋊C4C2×D414yes—
494C2×C4⋊C4C2×Q814yes—
495C2×C4⋊C4#4114yes—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
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—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—22no—
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—42no—
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⋊C4C22×C418yes—
531C2×C22⋊C4C22×C418yes—
532C2×C22⋊C4C22×C414yes—
533C2×C22⋊C4C22×C418yes—
534C2×C22⋊C4C22×C418yes—
535C2×C22⋊C4C22×C414yes—
536C2×C22⋊C4C2×D414yes—
537C2×C22⋊C4C2×D418yes—
538C2×C22⋊C4C2×D414yes—
539C2×C22⋊C4C2×Q818yes—
540C2×C22⋊C4#4114yes—
541C2×C42—24no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—24no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—24no—
550C2×C42—22no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—416no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—41no—
570C2×C42—41no—
571C2×C42C22×C414yes—
572C2×C42C22×C418yes—
573C2×C42C22×C414yes—
574C2×C42C2×D414yes—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—22no—
580#95—24no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—41no—
598#95—42no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95C22×C414yes—
606#95C22×C414yes—
607#95C22×C418yes—
608#95C22×C418yes—
609#95C2×D418yes—
610#95C2×D414yes—
611#95C2×D414yes—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24C23×C414yes—
633C24C23×C412yes—
634C24C22×D414yes—
635C24C22×D412yes—
636C24C22×D412yes—
637C24C22×Q814yes—
638C24C22×Q812yes—
639C24C2×#4112yes—
640C24H(5,𝔽2)12yes—
641C242−1+412yes—
642C24C2511yescharacteristic
643C2×D4—216no—
644C2×D4—216no—
645C2×D4—216no—
646C2×D4—216no—
647C2×D4—216no—
648C2×D4—216no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4C2×C4⋊C4132yescomplemented
656C2×D4C2×C4⋊C4116yescomplemented
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—216no—
689C22×C4—28no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—216no—
745C22×C4—216no—
746C22×C4—216no—
747C22×C4—28no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—21no—
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—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—48no—
784C22×C4—48no—
785C22×C4—44no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—84no—
816C22×C4—84no—
817C22×C4—84no—
818C22×C4—84no—
819C22×C4—84no—
820C22×C4—84no—
821C22×C4—84no—
822C22×C4—84no—
823C22×C4—84no—
824C22×C4—84no—
825C22×C4C2×C4⋊C4116yescomplemented
826C22×C4C23×C412yes—
827C22×C4C23×C412yes—
828C22×C4C23×C414yes—
829C22×C4C23×C414yes—
830C22×C4C23×C412yes—
831C22×C4C23×C412yes—
832C22×C4C23×C414yes—
833C22×C4C23×C412yes—
834C22×C4C23×C412yes—
835C22×C4C22×D412yes—
836C22×C4C22×D412yes—
837C22×C4C22×D412yes—
838C22×C4C22×D414yes—
839C22×C4C22×D412yes—
840C22×C4C22×D412yes—
841C22×C4C22×D414yes—
842C22×C4C22×D412yes—
843C22×C4C22×D414yes—
844C22×C4C22×D412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×Q812yes—
850C22×C4C22×Q814yes—
851C22×C4C22×Q812yes—
852C22×C4C2×#4112yes—
853C22×C4C2×#4114yes—
854C22×C4C2×#4112yes—
855C22×C4C2×#4112yes—
856C22×C4H(5,𝔽2)12yes—
857C22×C4H(5,𝔽2)12yes—
858C22×C42−1+412yes—
859C22×C42−1+412yes—
860C4⋊C4—216no—
861C4⋊C4—28no—
862C4⋊C4—216no—
863C4⋊C4—28no—
864C4⋊C4—216no—
865C4⋊C4—28no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—84no—
882C4⋊C4—84no—
883C4⋊C4—84no—
884C4⋊C4C2×C4⋊C4116yescomplemented
885C4⋊C4C4×D4116yescomplemented
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—216no—
889C22⋊C4—216no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—84no—
899C22⋊C4C2×C4⋊C4132yescomplemented
900C22⋊C4C4×D4116yescomplemented
901C42—216no—
902C42—28no—
903C42—28no—
904C42—28no—
905C42—44no—
906C42—44no—
907C42—48no—
908C42—48no—
909C42—44no—
910C42—44no—
911C42—44no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—42no—
959C23—42no—
960C23—42no—
961C23—42no—
962C23—42no—
963C23—42no—
964C23—42no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—42no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23C22×C4⋊C418yes—
975C23C22×C4⋊C414yes—
976C23C2×C4×D414yes—
977C23#52014yes—
978C23D4214yes—
979C23#54714yes—
980C23D4×Q814yes—
981C23#55414yes—
982C23C24×C411yescharacteristic
983C23C23×D411yescharacteristic
984C23C23×D411yescharacteristic
985C23C23×D411yescharacteristic
986C23C23×Q811yescharacteristic
987C23C22×#4111yescharacteristic
988C23C22×#4111yescharacteristic
989C23C2×H(5,𝔽2)11yescharacteristic
990C23C2×H(5,𝔽2)11yescharacteristic
991C23C2×H(5,𝔽2)11yescharacteristic
992C23C2×2−1+411yescharacteristic
993C23C2×2−1+411yescharacteristic
994C23C2×2−1+411yescharacteristic
995C23#58511yescharacteristic
996C23#58511yescharacteristic
997D4—264no—
998D4—232no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—232no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—432no—
1064C2×C4—432no—
1065C2×C4—416no—
1066C2×C4—416no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—42no—
1071C2×C4—42no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—41no—
1078C2×C4—42no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—42no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—42no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—42no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—816no—
1139C2×C4—816no—
1140C2×C4—816no—
1141C2×C4C22×C4⋊C414yes—
1142C2×C4C22×C4⋊C418yes—
1143C2×C4C22×C4⋊C414yes—
1144C2×C4C2×C4×D414yes—
1145C2×C4C2×C4×D418yes—
1146C2×C4C2×C4×D414yes—
1147C2×C4C2×C4×D414yes—
1148C2×C4#52014yes—
1149C2×C4D4214yes—
1150C2×C4D4214yes—
1151C2×C4#54714yes—
1152C2×C4D4×Q814yes—
1153C2×C4#55414yes—
1154C22—24no—
1155C22—24no—
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—24no—
1160C22—24no—
1161C22—24no—
1162C22—24no—
1163C22—24no—
1164C22—24no—
1165C22—24no—
1166C22—24no—
1167C22—24no—
1168C22—28no—
1169C22—28no—
1170C22—28no—
1171C22—44no—
1172C22—44no—
1173C22—44no—
1174C22—44no—
1175C22—44no—
1176C22—44no—
1177C22—44no—
1178C22—44no—
1179C22—44no—
1180C22—44no—
1181C22—44no—
1182C22—44no—
1183C22D4×C4⋊C418yescomplemented
1184C22C23×C4⋊C411yescharacteristic
1185C22C22×C4×D411yescharacteristic
1186C22C22×C4×D411yescharacteristic
1187C22C2×#52011yescharacteristic
1188C22C2×#52011yescharacteristic
1189C22C4×H(5,𝔽2)11yescharacteristic
1190C22C4×2−1+411yescharacteristic
1191C22C2×D4211yescharacteristic
1192C22C2×D4211yescharacteristic
1193C22C2×D4211yescharacteristic
1194C22C2×#54711yescharacteristic
1195C22C2×#54711yescharacteristic
1196C22C2×D4×Q811yescharacteristic
1197C22C2×D4×Q811yescharacteristic
1198C22D4×#4111yescharacteristic
1199C22D4×#4111yescharacteristic
1200C22C2×#55411yescharacteristic
1201C22C2×#55411yescharacteristic
1202C22#348111yescharacteristic
1203C22#348611yescharacteristic
1204C22#348811yescharacteristic
1205C22#348811yescharacteristic
1206C22#348911yescharacteristic
1207C22#349611yescharacteristic
1208C22#349911yescharacteristic
1209C22#350311yescharacteristic
1210C22#350411yescharacteristic
1211C22#351511yescharacteristic
1212C22#351611yescharacteristic
1213C22#352011yescharacteristic
1214C22#352211yescharacteristic
1215C22#353711yescharacteristic
1216C22#354111yescharacteristic
1217C22#355211yescharacteristic
1218C22#355911yescharacteristic
1219C4—24no—
1220C4—24no—
1221C4—28no—
1222C4—24no—
1223C4—28no—
1224C4—24no—
1225C4—44no—
1226C4—42no—
1227C4—42no—
1228C4—44no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—42no—
1234C4—82no—
1235C4—82no—
1236C4—81no—
1237C4—81no—
1238C4—82no—
1239C4D4×C4⋊C418yescomplemented
1240C2—28no—
1241C2—48no—
1242C2C2×D4×C4⋊C411yescharacteristic
1243C2C2×D4×C4⋊C411yescharacteristic
1244C2C4×D4211yescharacteristic
1245C2#3425011yescharacteristic
1246C2#3429411yescharacteristic
1247C2#3430811yescharacteristic
1248C2#3446111yescharacteristic
1249C2#5899711yescharacteristic
1250C2#5900211yescharacteristic
1251C2#5906211yescharacteristic
1252C2#5911211yescharacteristic
1253C2#5912711yescharacteristic
1254C2#5915511yescharacteristic
1255C2#5945411yescharacteristic
1256C2#5983111yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×D4×C4⋊C4C2semidirect
4. C2×D4×C4⋊C4C2semidirect
6. C22×#389C2semidirect
7. #14405C2semidirect
8. #14402C2semidirect
9. #14112C2semidirect
10. #14046C2semidirect
11. #14043C2semidirect
12. #14018C2semidirect
13. #14015C2semidirect
14. #14005C2semidirect
15. #13977C2semidirect
16. #13975C2semidirect
17. #13920C2semidirect
18. #13910C2semidirect
19. #13907C2semidirect
20. #13899C2semidirect
21. #13880C2semidirect
22. #13821C2semidirect
23. C4×#385C2semidirect
37. #2361C4semidirect
158. C2×C4×D4C2×C4semidirect
159. C2×C4×D4C2×C4semidirect
171. C22×C4⋊C4C2×C4semidirect
229. #390C2×C4semidirect
241. #389C2×C4semidirect
242. #389D4semidirect
245. #388C2×C4semidirect
248. #386C2×C4semidirect
258. #385C2×C4semidirect
259. #385D4semidirect
272. C4×C4⋊C4C2×C4semidirect
275. C4×C22⋊C4C2×C4semidirect
407. #121C4⋊C4semidirect
655. C2×D4C2×C4⋊C4semidirect
656. C2×D4C2×C4⋊C4semidirect
825. C22×C4C2×C4⋊C4semidirect
884. C4⋊C4C2×C4⋊C4semidirect
885. C4⋊C4C4×D4semidirect
899. C22⋊C4C2×C4⋊C4semidirect
900. C22⋊C4C4×D4semidirect
1183. C22D4×C4⋊C4semidirect
1239. C4D4×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23612
C2×D4×C4⋊C42
C2×C4×#1212
C22×#3892
#144052
#144022
#141122
#140462
#140432
#140182
#140152
#140052
#139772
#139752
#139202
#139102
#139072
#138992
#138802
#138212
C4×#3852