Finite Group Databasebeta

← #533182

Subgroups — #533182

Order 512.

4130 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic
2C2×#2361C211yesmaximal, characteristic, complemented
3C2×#2360C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5C2×C4×#121C211yesmaximal, characteristic, complemented
6#14529C212yesmaximal, complemented
7#14429C212yesmaximal, complemented
8#14207C212yesmaximal, complemented
9#14178C212yesmaximal, complemented
10#14171C212yesmaximal, complemented
11#14034C212yesmaximal, complemented
12#14027C211yesmaximal, characteristic, complemented
13#14026C211yesmaximal, characteristic, complemented
14#14018C212yesmaximal, complemented
15#13998C211yesmaximal, characteristic, complemented
16#13998C211yesmaximal, characteristic, complemented
17#13997C211yesmaximal, characteristic, complemented
18#13997C211yesmaximal, characteristic, complemented
19#13872C211yesmaximal, characteristic, complemented
20#13821C211yesmaximal, characteristic, complemented
21#13820C212yesmaximal, complemented
22#13818C211yesmaximal, characteristic, complemented
23C4×#386C211yesmaximal, characteristic, complemented
24C22×#124C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×C4×D4C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2540C4116yescomplemented
37C2×#399C2212yes—
38C2×#392C2212yes—
39#2361—28no—
40#2360—28no—
41C4×C22⋊Q8—28no—
42C4×#121—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2212yes—
50C2×#390C2211yescharacteristic
51C2×#390C2212yes—
52C2×#390C2212yes—
53C2×#389C2212yes—
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#388C2212yes—
59C2×#388C2212yes—
60C2×#387C2212yes—
61C2×#387C2212yes—
62C2×#386C2212yes—
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#385C2212yes—
68C2×#385C2212yes—
69C2×#385C2212yes—
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2212yes—
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2212yes—
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2212yes—
84C2×C4×C22⋊C4C2212yes—
85C2×C4×C22⋊C4C2211yescharacteristic
86#1445C2212yes—
87#1445C2212yes—
88#1441C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1437C2212yes—
101#1437C2212yes—
102#1437C2211yescharacteristic
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2211yescharacteristic
107#1437C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2211yescharacteristic
111#1436C2212yes—
112#1436C2212yes—
113#1436C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2212yes—
117C4⋊#95C2212yes—
118C4⋊#95C2212yes—
119#1434C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yes—
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C4×#95C2212yes—
128C23×Q8C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#124—42no—
140C2×#124—42no—
141C2×#124C2×C418yescomplemented
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8C2×C418yescomplemented
147C2×C22⋊Q8C2×C418yescomplemented
148C2×#121—24no—
149C2×#121—24no—
150C2×#121—24no—
151C2×#121—24no—
152C2×#121C2×C418yescomplemented
153C2×#121C2×C418yescomplemented
154C2×C4×Q8—24no—
155C2×C4×Q8—24no—
156C2×C4×Q8—42no—
157C2×C4×D4—28no—
158C2×C4×D4—24no—
159C2×C4×D4—28no—
160C2×C4×D4—28no—
161C2×C4×D4—24no—
162C2×C4×D4—42no—
163C2×C4×D4—42no—
164C2×C4×D4—42no—
165C2×C4×D4—44no—
166C2×C4×D4—44no—
167C2×C4×D4—44no—
168C2×C4×D4C2×C418yescomplemented
169C22×C4⋊C4—24no—
170C22×C4⋊C4—24no—
171C22×C4⋊C4—42no—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
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×C42—24no—
212C22×C42—24no—
213C22×C42—42no—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2312yes—
226C22×C42C2312yes—
227#399C2×C4116yescomplemented
228#392C2×C4116yescomplemented
229#391—24no—
230#391—24no—
231#391—42no—
232#390—24no—
233#390—28no—
234#390—24no—
235#390—42no—
236#390—44no—
237#390C2×C4116yescomplemented
238#390C2×C4116yescomplemented
239#389—28no—
240#389—24no—
241#389—24no—
242#389D418yescomplemented
243#389D418yescomplemented
244#388—28no—
245#388—28no—
246#387—28no—
247#387—28no—
248#386—24no—
249#386—24no—
250#386—28no—
251#386—28no—
252#386—44no—
253#385—28no—
254#385—28no—
255#385—28no—
256#380—24no—
257#380—24no—
258#380—42no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—24no—
262C4×C4⋊C4—28no—
263C4×C4⋊C4—24no—
264C4×C4⋊C4—44no—
265C4×C4⋊C4C2×C418yescomplemented
266C4×C22⋊C4—24no—
267C4×C22⋊C4—24no—
268C4×C22⋊C4—28no—
269C4×C22⋊C4—28no—
270C4×C22⋊C4—28no—
271C4×C22⋊C4—42no—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C25C2412yes—
309C25C2411yescharacteristic
310C25C2411yescharacteristic
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8C22×C414yes—
318C22×D4—24no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4C22×C414yes—
343C22×D4C22×C414yes—
344C22×D4C22×C418yes—
345C22×D4C22×C418yes—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—41no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4C22×C414yes—
387C23×C4C22×C414yes—
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408#124—416no—
409C22⋊Q8—232no—
410C22⋊Q8—232no—
411#121—232no—
412#121—232no—
413C4×Q8—416no—
414C4×D4—416no—
415C4×D4—416no—
416C4×D4—432no—
417C4×D4—432no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—416no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4C22×C418yes—
452C2×C4⋊C4C22×C418yes—
453C2×C4⋊C4C22×C414yes—
454C2×C4⋊C4C22×C414yes—
455C2×C4⋊C4C22×C414yes—
456C2×C4⋊C4C2×D414yes—
457C2×C4⋊C4C2×D414yes—
458C2×C4⋊C4C2×D418yes—
459C2×C4⋊C4C2×D418yes—
460C2×C4⋊C4C2×D414yes—
461C2×C4⋊C4C2×D414yes—
462C2×C4⋊C4#4114yes—
463C2×C4⋊C4#4114yes—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C22×C418yes—
530C2×C22⋊C4C22×C414yes—
531C2×C22⋊C4C22×C414yes—
532C2×C22⋊C4C22×C418yes—
533C2×C22⋊C4C22×C418yes—
534C2×C22⋊C4#4114yes—
535C2×C22⋊C4#4114yes—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—24no—
543C2×C42—24no—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—22no—
547C2×C42—24no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—24no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—24no—
557C2×C42—24no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—24no—
561C2×C42—416no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42—41no—
567C2×C42—41no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42C22×C414yes—
573C2×C42C22×C418yes—
574C2×C42C2×D414yes—
575C2×C42C2×D414yes—
576#95—24no—
577#95—22no—
578#95—22no—
579#95—24no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—41no—
599#95—42no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95C22×C418yes—
610#95C2×D418yes—
611#95C2×D418yes—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24C23×C414yes—
651C24C23×C412yes—
652C24C23×C412yes—
653C24C2×#4112yes—
654C24C2×#4112yes—
655C24H(5,𝔽2)12yes—
656C242−1+412yes—
657C24C2511yescharacteristic
658C2×Q8—28no—
659C2×Q8—28no—
660C2×Q8—28no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×D4—216no—
666C2×D4—28no—
667C2×D4—216no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—44no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—28no—
710C22×C4—28no—
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—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4C23×C412yes—
846C22×C4C23×C412yes—
847C22×C4C23×C414yes—
848C22×C4C23×C412yes—
849C22×C4C23×C412yes—
850C22×C4C23×C414yes—
851C22×C4C23×C414yes—
852C22×C4C23×C412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D414yes—
855C22×C4C22×D414yes—
856C22×C4C22×D412yes—
857C22×C4C22×D414yes—
858C22×C4C22×D414yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C22×D412yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4112yes—
865C22×C4C2×#4114yes—
866C22×C4C2×#4114yes—
867C22×C4C2×#4112yes—
868C22×C4C2×#4112yes—
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4H(5,𝔽2)12yes—
872C22×C4H(5,𝔽2)12yes—
873C22×C4H(5,𝔽2)12yes—
874C22×C42−1+412yes—
875C4⋊C4—216no—
876C4⋊C4—216no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—216no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—84no—
888C4⋊C4C4×D4116yescomplemented
889C4⋊C4C4×D4116yescomplemented
890C22⋊C4—216no—
891C22⋊C4—216no—
892C22⋊C4—216no—
893C22⋊C4—216no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C22⋊C4—84no—
914C42—28no—
915C42—28no—
916C42—28no—
917C42—48no—
918C42—48no—
919C42—44no—
920C42—44no—
921C42—48no—
922C42—48no—
923C42—48no—
924C42—44no—
925C42—44no—
926C42—84no—
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—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
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—
1030C23C4×#4114yes—
1031C23#52014yes—
1032C23C24×C411yescharacteristic
1033C23C23×D411yescharacteristic
1034C23C23×D411yescharacteristic
1035C23C22×#4111yescharacteristic
1036C23C22×#4111yescharacteristic
1037C23C22×#4111yescharacteristic
1038C23C22×#4111yescharacteristic
1039C23C2×H(5,𝔽2)11yescharacteristic
1040C23C2×H(5,𝔽2)11yescharacteristic
1041C23C2×H(5,𝔽2)11yescharacteristic
1042C23C2×H(5,𝔽2)11yescharacteristic
1043C23C2×2−1+411yescharacteristic
1044C23C2×2−1+411yescharacteristic
1045C23#58511yescharacteristic
1046C23#58511yescharacteristic
1047Q8—416no—
1048D4—432no—
1049D4—432no—
1050D4—416no—
1051D4—416no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—416no—
1110C2×C4—416no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—416no—
1156C2×C4—416no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—816no—
1186C2×C4—816no—
1187C2×C4C2×C4×D418yes—
1188C2×C4C2×C4×D418yes—
1189C2×C4C2×C4×D414yes—
1190C2×C4C2×C4×D414yes—
1191C2×C4#51814yes—
1192C2×C4D4214yes—
1193C2×C4#54614yes—
1194C2×C4#54814yes—
1195C2×C4#55014yes—
1196C2×C4#55014yes—
1197C2×C4#55914yes—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—82no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22C22×C4×D411yescharacteristic
1244C22C22×C4×D411yescharacteristic
1245C22C2×C4×#4111yescharacteristic
1246C22C2×#51811yescharacteristic
1247C22C2×#52011yescharacteristic
1248C22C4×H(5,𝔽2)11yescharacteristic
1249C22C4×2−1+411yescharacteristic
1250C22C2×D4211yescharacteristic
1251C22C2×#54611yescharacteristic
1252C22C2×#54811yescharacteristic
1253C22C2×#55011yescharacteristic
1254C22C2×#55011yescharacteristic
1255C22D4×#4111yescharacteristic
1256C22D4×#4111yescharacteristic
1257C22#347511yescharacteristic
1258C22C2×#55911yescharacteristic
1259C22#348011yescharacteristic
1260C22#348111yescharacteristic
1261C22#348211yescharacteristic
1262C22#348411yescharacteristic
1263C22#348611yescharacteristic
1264C22#348811yescharacteristic
1265C22#348911yescharacteristic
1266C22#351311yescharacteristic
1267C22#351611yescharacteristic
1268C22#351911yescharacteristic
1269C22#351911yescharacteristic
1270C22#352011yescharacteristic
1271C22#352011yescharacteristic
1272C22#352011yescharacteristic
1273C22#352211yescharacteristic
1274C22#354111yescharacteristic
1275C22#354211yescharacteristic
1276C22#354811yescharacteristic
1277C22#355111yescharacteristic
1278C4—28no—
1279C4—24no—
1280C4—24no—
1281C4—28no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—44no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—82no—
1294C4—81no—
1295C4—82no—
1296C4—81no—
1297C4#236618yes—
1298C2—44no—
1299C2—44no—
1300C2—84no—
1301C2C2×#236611yescharacteristic
1302C2C4×#54611yescharacteristic
1303C2C4×#54811yescharacteristic
1304C2#3423311yescharacteristic
1305C2#3428811yescharacteristic
1306C2#3429411yescharacteristic
1307C2#3441411yescharacteristic
1308C2#5900411yescharacteristic
1309C2#5900511yescharacteristic
1310C2#5904011yescharacteristic
1311C2#5905711yescharacteristic
1312C2#5905811yescharacteristic
1313C2#5905911yescharacteristic
1314C2#5959211yescharacteristic
1315C2#5963411yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2540C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2361C2semidirect
3. C2×#2360C2semidirect
4. C2×C4×C22⋊Q8C2semidirect
5. C2×C4×#121C2semidirect
6. #14529C2semidirect
7. #14429C2semidirect
8. #14207C2semidirect
9. #14178C2semidirect
10. #14171C2semidirect
11. #14034C2semidirect
12. #14027C2semidirect
13. #14026C2semidirect
14. #14018C2semidirect
15. #13998C2semidirect
16. #13998C2semidirect
17. #13997C2semidirect
18. #13997C2semidirect
19. #13872C2semidirect
20. #13821C2semidirect
21. #13820C2semidirect
22. #13818C2semidirect
23. C4×#386C2semidirect
36. #2540C4semidirect
141. C2×#124C2×C4semidirect
146. C2×C22⋊Q8C2×C4semidirect
147. C2×C22⋊Q8C2×C4semidirect
152. C2×#121C2×C4semidirect
153. C2×#121C2×C4semidirect
168. C2×C4×D4C2×C4semidirect
227. #399C2×C4semidirect
228. #392C2×C4semidirect
237. #390C2×C4semidirect
238. #390C2×C4semidirect
242. #389D4semidirect
243. #389D4semidirect
265. C4×C4⋊C4C2×C4semidirect
888. C4⋊C4C4×D4semidirect
889. C4⋊C4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25402
C2×#23612
C2×#23602
C2×C4×C22⋊Q82
C2×C4×#1212
#145292
#144292
#142072
#141782
#141712
#140342
#140272
#140262
#140182
#139982
#139972
#138722
#138212
#138202
#138182
C4×#3862