Finite Group Databasebeta

← #519658

Subgroups — #519658

Order 512.

4280 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic
2C2×#2367C211yesmaximal, characteristic, complemented
3C2×#2363C211yesmaximal, characteristic, complemented
4C2×#2362C211yesmaximal, characteristic, complemented
5C2×#2361C211yesmaximal, characteristic, complemented
6C2×#2360C211yesmaximal, characteristic, complemented
7C2×#2352C211yesmaximal, characteristic, complemented
8#14708C211yesmaximal, characteristic, complemented
9#14700C212yesmaximal, complemented
10#14231C212yesmaximal, complemented
11#14230C212yesmaximal, complemented
12#14228C212yesmaximal, complemented
13#14189C212yesmaximal, complemented
14#14084C212yesmaximal, complemented
15#14084C212yesmaximal, complemented
16#13998C211yesmaximal, characteristic, complemented
17#13998C211yesmaximal, characteristic, complemented
18#13997C211yesmaximal, characteristic, complemented
19#13997C211yesmaximal, characteristic, complemented
20#13954C211yesmaximal, characteristic, complemented
21C4×#390C212yesmaximal, complemented
22C4×#390C211yesmaximal, characteristic, complemented
23C42×C4⋊C4C211yesmaximal, characteristic, complemented
24C22×#124C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35#2540C4116yescomplemented
36C2×#399C2212yes—
37C2×#392C2212yes—
38#2367—28no—
39#2363—28no—
40#2362—28no—
41#2361—28no—
42#2360—28no—
43#2352—28no—
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2212yes—
54C2×#390C2212yes—
55C2×#390C2212yes—
56C2×#390C2212yes—
57C2×#389C2212yes—
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#388C2212yes—
63C2×#388C2212yes—
64C2×#388C2212yes—
65C2×#388C2212yes—
66C2×#388C2212yes—
67C2×#388C2212yes—
68C2×#388C2212yes—
69C2×#387C2212yes—
70C2×#387C2212yes—
71C2×#387C2212yes—
72C2×#386C2212yes—
73C2×#386C2212yes—
74C2×#386C2212yes—
75C2×#385C2212yes—
76C2×#385C2212yes—
77C2×#385C2212yes—
78C2×#382C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×C4×C4⋊C4C2212yes—
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C4⋊C4C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86C2×C4×C4⋊C4C2211yescharacteristic
87C2×C4×C4⋊C4C2211yescharacteristic
88C2×C4×C4⋊C4C2211yescharacteristic
89C2×C4×C22⋊C4C2212yes—
90C2×C4×C22⋊C4C2212yes—
91C2×C4×C22⋊C4C2212yes—
92C2×C4×C22⋊C4C2211yescharacteristic
93C2×C4×C22⋊C4C2211yescharacteristic
94C2×C4×C22⋊C4C2211yescharacteristic
95C2×C4×C22⋊C4C2212yes—
96C2×C4×C22⋊C4C2211yescharacteristic
97C2×C43C2211yescharacteristic
98C2×C43C2212yes—
99#1445C2212yes—
100#1445C2212yes—
101#1444C2212yes—
102#1444C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1437C2212yes—
110#1437C2211yescharacteristic
111#1437C2211yescharacteristic
112#1437C2211yescharacteristic
113#1437C2212yes—
114#1437C2212yes—
115#1437C2212yes—
116#1437C2212yes—
117#1437C2212yes—
118#1437C2212yes—
119#1437C2212yes—
120#1437C2211yescharacteristic
121C4⋊#95C2212yes—
122C4⋊#95C2212yes—
123C4⋊#95C2212yes—
124C4⋊#95C2211yescharacteristic
125C4⋊#95C2212yes—
126C4⋊#95C2211yescharacteristic
127C4×#95C2212yes—
128C4×#95C2212yes—
129C4×#95C2212yes—
130C23×Q8C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2312yes—
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#124—24no—
140C2×#124—24no—
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×C418yes—
153C2×#121C2×C418yescomplemented
154C2×C4×Q8—24no—
155C2×C4×Q8—24no—
156C2×C4×Q8—24no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—28no—
161C2×C4×D4—24no—
162C2×C4×D4—28no—
163C2×C4×D4—24no—
164C2×C4×D4—44no—
165C2×C4×D4C2×C418yescomplemented
166C2×#117—24no—
167C2×#117—24no—
168C2×#117—24no—
169C22×C4⋊C4—24no—
170C22×C4⋊C4—24no—
171C22×C4⋊C4—24no—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229C22×C42C2312yes—
230C22×C42C2312yes—
231C22×C42C2311yescharacteristic
232#399C2×C4116yescomplemented
233#392C2×C4116yescomplemented
234#391—24no—
235#391—24no—
236#391—24no—
237#390—24no—
238#390—24no—
239#390—24no—
240#390—28no—
241#390—24no—
242#390—24no—
243#390—28no—
244#390—44no—
245#390C2×C4116yescomplemented
246#390C2×C4116yescomplemented
247#389—24no—
248#389—24no—
249#389—24no—
250#389—24no—
251#389—28no—
252#388—28no—
253#388—28no—
254#388—28no—
255#388—28no—
256#388—28no—
257#388—28no—
258#388—28no—
259#387—28no—
260#387—28no—
261#387—28no—
262#386—28no—
263#386—28no—
264#386—28no—
265#385—28no—
266#385—28no—
267#385—28no—
268#382—24no—
269#380—24no—
270#380—24no—
271C4×C4⋊C4—24no—
272C4×C4⋊C4—24no—
273C4×C4⋊C4—28no—
274C4×C4⋊C4—24no—
275C4×C4⋊C4C2×C418yescomplemented
276C4×C4⋊C4D418yescomplemented
277C4×C4⋊C4D418yescomplemented
278C4×C4⋊C4D418yescomplemented
279C4×C22⋊C4—28no—
280C4×C22⋊C4—24no—
281C4×C22⋊C4—28no—
282C4×C22⋊C4—24no—
283C4×C22⋊C4—24no—
284C4×C22⋊C4—28no—
285C4×C22⋊C4—24no—
286C4×C22⋊C4—28no—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C43—24no—
318C43—44no—
319C25C2411yescharacteristic
320C25C2412yes—
321C25C2411yescharacteristic
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8C22×C414yes—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—42no—
346C22×D4—41no—
347C22×D4—42no—
348C22×D4—41no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4C22×C414yes—
354C22×D4C22×C414yes—
355C22×D4C22×C418yes—
356C22×D4C22×C418yes—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4C22×C414yes—
384C23×C4C22×C414yes—
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405#124—232no—
406C22⋊Q8—232no—
407C22⋊Q8—232no—
408#121—232no—
409#121—232no—
410C4×Q8—416no—
411C4×D4—232no—
412C4×D4—432no—
413C4×D4—416no—
414#117—416no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—416no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4C22×C414yes—
455C2×C4⋊C4C22×C418yes—
456C2×C4⋊C4C22×C418yes—
457C2×C4⋊C4C22×C414yes—
458C2×C4⋊C4C22×C414yes—
459C2×C4⋊C4C2×D414yes—
460C2×C4⋊C4C2×D414yes—
461C2×C4⋊C4C2×D414yes—
462C2×C4⋊C4C2×D414yes—
463C2×C4⋊C4C2×D414yes—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4#4114yes—
466C2×C4⋊C4#4114yes—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—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—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
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—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4C22×C414yes—
536C2×C22⋊C4C22×C414yes—
537C2×C22⋊C4C22×C418yes—
538C2×C22⋊C4C22×C418yes—
539C2×C22⋊C4C22×C418yes—
540C2×C22⋊C4C22×C418yes—
541C2×C22⋊C4C22×C418yes—
542C2×C22⋊C4C22×C418yes—
543C2×C22⋊C4#4114yes—
544C2×C22⋊C4#4114yes—
545C2×C42—24no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—24no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—24no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—24no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—41no—
583C2×C42—41no—
584C2×C42—42no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42C22×C418yes—
588C2×C42C22×C414yes—
589C2×C42C2×D418yes—
590C2×C42C2×D414yes—
591C2×C42C2×D414yes—
592C2×C42C2×D418yes—
593C2×C42C2×D418yes—
594C2×C42C2×D414yes—
595C2×C42#4114yes—
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—22no—
605#95—22no—
606#95—24no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—22no—
612#95—24no—
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#95C22×C418yes—
623#95C2×D418yes—
624#95C2×D418yes—
625#95C2×D418yes—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—21no—
657C24—22no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—21no—
666C24C23×C414yes—
667C24C23×C412yes—
668C24C23×C412yes—
669C24C2×#4112yes—
670C24C2×#4112yes—
671C24C2511yescharacteristic
672C2×Q8—28no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×D4—216no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—216no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—216no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—84no—
704C2×D4—84no—
705C2×D4—84no—
706C2×D4—84no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
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—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
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—21no—
782C22×C4—21no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4C23×C414yes—
840C22×C4C23×C412yes—
841C22×C4C23×C412yes—
842C22×C4C23×C412yes—
843C22×C4C23×C414yes—
844C22×C4C23×C414yes—
845C22×C4C23×C412yes—
846C22×C4C23×C412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×D414yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D414yes—
853C22×C4C22×D414yes—
854C22×C4C22×D414yes—
855C22×C4C22×D414yes—
856C22×C4C22×D414yes—
857C22×C4C22×D412yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4114yes—
865C22×C4C2×#4114yes—
866C22×C4C2×#4112yes—
867C22×C4C2×#4112yes—
868C22×C4C2×#4112yes—
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4H(5,𝔽2)12yes—
874C22×C42−1+412yes—
875C4⋊C4—28no—
876C4⋊C4—216no—
877C4⋊C4—216no—
878C4⋊C4—28no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—84no—
888C4⋊C4—84no—
889C4⋊C4C4×D4116yes—
890C4⋊C4C4×D4116yescomplemented
891C4⋊C4#127116yes—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—216no—
895C22⋊C4—216no—
896C22⋊C4—216no—
897C22⋊C4—216no—
898C22⋊C4—216no—
899C22⋊C4—216no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C42—28no—
919C42—28no—
920C42—28no—
921C42—216no—
922C42—48no—
923C42—48no—
924C42—48no—
925C42—44no—
926C42—44no—
927C42—48no—
928C42—48no—
929C42—44no—
930C42—48no—
931C42—44no—
932C42—48no—
933C42—44no—
934C42C4×D4116yescomplemented
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—24no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—24no—
961C23—22no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—22no—
966C23—24no—
967C23—41no—
968C23—41no—
969C23—41no—
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—42no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—42no—
996C23—41no—
997C23—41no—
998C23—42no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—41no—
1004C23—41no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—42no—
1010C23—41no—
1011C23—42no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—42no—
1018C23—41no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—41no—
1038C23—42no—
1039C23C4×#4114yes—
1040C23C24×C411yescharacteristic
1041C23C23×D411yescharacteristic
1042C23C23×D411yescharacteristic
1043C23C23×D411yescharacteristic
1044C23C22×#4111yescharacteristic
1045C23C22×#4111yescharacteristic
1046C23C22×#4111yescharacteristic
1047C23C22×#4111yescharacteristic
1048C23C22×#4111yescharacteristic
1049C23C2×H(5,𝔽2)11yescharacteristic
1050C23C2×2−1+411yescharacteristic
1051C23#58511yescharacteristic
1052C23#58511yescharacteristic
1053C23#58511yescharacteristic
1054C23#58511yescharacteristic
1055Q8—416no—
1056D4—416no—
1057D4—432no—
1058D4—416no—
1059D4—816no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—416no—
1159C2×C4—416no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—816no—
1189C2×C4—816no—
1190C2×C4C2×C4×D414yes—
1191C2×C4C2×C4×D414yes—
1192C2×C4C2×C4×D418yes—
1193C2×C4C2×C4×D418yes—
1194C2×C4C2×C4×D414yes—
1195C2×C4C2×C4×D414yes—
1196C2×C4C2×C4×D414yes—
1197C2×C4C2×#12718yes—
1198C2×C4C2×#12714yes—
1199C2×C4#53214yes—
1200C2×C4#53214yes—
1201C2×C4#53214yes—
1202C2×C4#54614yes—
1203C2×C4#54814yes—
1204C22—24no—
1205C22—24no—
1206C22—24no—
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—44no—
1221C22—42no—
1222C22—44no—
1223C22—42no—
1224C22—44no—
1225C22—44no—
1226C22—42no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—44no—
1233C22—81no—
1234C22—82no—
1235C22—81no—
1236C22—82no—
1237C22—81no—
1238C22—82no—
1239C22—81no—
1240C22—82no—
1241C22—82no—
1242C22—81no—
1243C22—81no—
1244C22—82no—
1245C22—81no—
1246C22—82no—
1247C22—81no—
1248C22—82no—
1249C22C22×C4×D411yescharacteristic
1250C22C22×C4×D411yescharacteristic
1251C22C22×C4×D411yescharacteristic
1252C22C2×C4×#4111yescharacteristic
1253C22#342811yescharacteristic
1254C22C4×H(5,𝔽2)11yescharacteristic
1255C22C4×2−1+411yescharacteristic
1256C22C22×#12711yescharacteristic
1257C22C2×#53211yescharacteristic
1258C22C2×#53211yescharacteristic
1259C22C2×#53211yescharacteristic
1260C22C2×#54611yescharacteristic
1261C22C2×#54811yescharacteristic
1262C22D4×#4111yescharacteristic
1263C22D4×#4111yescharacteristic
1264C22D4×#4111yescharacteristic
1265C22D4×#4111yescharacteristic
1266C22#347511yescharacteristic
1267C22#347511yescharacteristic
1268C22#347511yescharacteristic
1269C22#348011yescharacteristic
1270C22#348111yescharacteristic
1271C22#348211yescharacteristic
1272C22#349211yescharacteristic
1273C22#349311yescharacteristic
1274C22#349611yescharacteristic
1275C22#349611yescharacteristic
1276C22#349711yescharacteristic
1277C22#349711yescharacteristic
1278C22#350011yescharacteristic
1279C22#350011yescharacteristic
1280C22#351311yescharacteristic
1281C22#351611yescharacteristic
1282C22#352111yescharacteristic
1283C22#352411yescharacteristic
1284C4—28no—
1285C4—24no—
1286C4—24no—
1287C4—28no—
1288C4—28no—
1289C4—24no—
1290C4—24no—
1291C4—42no—
1292C4—42no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—44no—
1299C4—81no—
1300C4—82no—
1301C4—81no—
1302C4—82no—
1303C4C4×#12718yes—
1304C2—44no—
1305C2—82no—
1306C2—84no—
1307C2C2×C4×#12711yescharacteristic
1308C2#3413611yescharacteristic
1309C2C4×#54611yescharacteristic
1310C2C4×#54811yescharacteristic
1311C2#3427411yescharacteristic
1312C2#3430911yescharacteristic
1313C2#3431211yescharacteristic
1314C2#3626011yescharacteristic
1315C2#3626811yescharacteristic
1316C2#3626911yescharacteristic
1317C2#3642411yescharacteristic
1318C2#3646511yescharacteristic
1319C2#3647011yescharacteristic
1320C2#3647111yescharacteristic
1321C2#3651811yescharacteristic
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×#2367C2semidirect
3. C2×#2363C2semidirect
4. C2×#2362C2semidirect
5. C2×#2361C2semidirect
6. C2×#2360C2semidirect
7. C2×#2352C2semidirect
8. #14708C2semidirect
9. #14700C2semidirect
10. #14231C2semidirect
11. #14230C2semidirect
12. #14228C2semidirect
13. #14189C2semidirect
14. #14084C2semidirect
15. #14084C2semidirect
16. #13998C2semidirect
17. #13998C2semidirect
18. #13997C2semidirect
19. #13997C2semidirect
20. #13954C2semidirect
21. C4×#390C2semidirect
22. C4×#390C2semidirect
23. C42×C4⋊C4C2semidirect
35. #2540C4semidirect
141. C2×#124C2×C4semidirect
146. C2×C22⋊Q8C2×C4semidirect
147. C2×C22⋊Q8C2×C4semidirect
153. C2×#121C2×C4semidirect
165. C2×C4×D4C2×C4semidirect
232. #399C2×C4semidirect
233. #392C2×C4semidirect
245. #390C2×C4semidirect
246. #390C2×C4semidirect
275. C4×C4⋊C4C2×C4semidirect
276. C4×C4⋊C4D4semidirect
277. C4×C4⋊C4D4semidirect
278. C4×C4⋊C4D4semidirect
890. C4⋊C4C4×D4semidirect
934. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25402
C2×#23672
C2×#23632
C2×#23622
C2×#23612
C2×#23602
C2×#23522
#147082
#147002
#142312
#142302
#142282
#141892
#140842
#139982
#139972
#139542
C4×#3902
C42×C4⋊C42