Finite Group Databasebeta

← #1085248

Subgroups — #1085248

Order 512.

2462 conjugacy classes of subgroups.

The subgroup lattice has 1431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2552C211yesmaximal, characteristic, complemented
2C2×#2475C211yesmaximal, characteristic
3C2×#2462C211yesmaximal, characteristic, complemented
4C2×#2323C211yesmaximal, characteristic
5#17062C211yesmaximal, characteristic
6#16349C211yesmaximal, characteristic, complemented
7#16293C211yesmaximal, characteristic, complemented
8#15970C211yesmaximal, characteristic
9#15880C211yesmaximal, characteristic
10#15848C211yesmaximal, characteristic, complemented
11#15583C211yesmaximal, characteristic
12#15517C211yesmaximal, characteristic, complemented
13#15441C211yesmaximal, characteristic
14#15434C211yesmaximal, characteristic, complemented
15#15430C211yesmaximal, characteristic
16#15430C211yesmaximal, characteristic
17#15422C211yesmaximal, characteristic
18#15388C211yesmaximal, characteristic, complemented
19#15306C211yesmaximal, characteristic
20#15151C211yesmaximal, characteristic, complemented
21#15093C211yesmaximal, characteristic
22#14907C211yesmaximal, characteristic
23#14880C211yesmaximal, characteristic, complemented
24#14816C211yesmaximal, characteristic, complemented
25#14804C211yesmaximal, characteristic, complemented
26#14548C211yesmaximal, characteristic, complemented
27#14529C211yesmaximal, characteristic
28#14443C211yesmaximal, characteristic, complemented
29#14194C211yesmaximal, characteristic
30#14191C211yesmaximal, characteristic, complemented
31#14069C211yesmaximal, characteristic, complemented
32C22×#125C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C22×#117C2211yescharacteristic
37#2552—28no—
38#2475—28no—
39#2462—28no—
40C2×#400C2211yescharacteristic
41C2×#399C2211yescharacteristic
42C2×#399C2211yescharacteristic
43C2×#398C2211yescharacteristic
44C2×#398C2211yescharacteristic
45C2×#398C2211yescharacteristic
46C2×#398C2211yescharacteristic
47C2×#398C2211yescharacteristic
48C2×#398C2211yescharacteristic
49C2×#398C2211yescharacteristic
50C2×#398C2211yescharacteristic
51C2×#398C2211yescharacteristic
52C2×#398C2211yescharacteristic
53C2×#398C2211yescharacteristic
54C2×#398C2211yescharacteristic
55C2×#397C2211yescharacteristic
56C2×#397C2211yescharacteristic
57C2×#396C2211yescharacteristic
58C2×#395C2211yescharacteristic
59C2×#395C2211yescharacteristic
60C2×#395C2211yescharacteristic
61C2×#395C2211yescharacteristic
62#2323—28no—
63C2×#391C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#389C2211yescharacteristic
66C2×#389C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#389C2211yescharacteristic
69C2×#389C2211yescharacteristic
70C2×#389C2211yescharacteristic
71C2×#389C2211yescharacteristic
72C2×#389C2211yescharacteristic
73C2×#388C2211yescharacteristic
74C2×#388C2211yescharacteristic
75C2×#388C2211yescharacteristic
76C2×#388C2211yescharacteristic
77C2×#388C2211yescharacteristic
78C2×#388C2211yescharacteristic
79C2×#387C2211yescharacteristic
80C2×#387C2211yescharacteristic
81C2×#387C2211yescharacteristic
82C2×#387C2211yescharacteristic
83C2×#387C2211yescharacteristic
84C2×#387C2211yescharacteristic
85C2×#387C2211yescharacteristic
86C2×#387C2211yescharacteristic
87C2×#387C2211yescharacteristic
88C2×#387C2211yescharacteristic
89C2×#385C2211yescharacteristic
90C2×#385C2211yescharacteristic
91C2×#385C2211yescharacteristic
92C2×#385C2211yescharacteristic
93C2×#384C2211yescharacteristic
94C2×#384C2211yescharacteristic
95C2×#384C2211yescharacteristic
96C2×#380C2211yescharacteristic
97C2×C4×C4⋊C4C2211yescharacteristic
98C2×C4×C4⋊C4C2211yescharacteristic
99C2×C4×C4⋊C4C2211yescharacteristic
100C2×C4×C4⋊C4C2211yescharacteristic
101C2×C4×C4⋊C4C2211yescharacteristic
102#1445C2211yescharacteristic
103#1445C2211yescharacteristic
104#1445C2211yescharacteristic
105#1445C2211yescharacteristic
106#1445C2211yescharacteristic
107#1445C2211yescharacteristic
108#1445C2211yescharacteristic
109#1445C2211yescharacteristic
110#1445C2211yescharacteristic
111#1444C2211yescharacteristic
112#1444C2211yescharacteristic
113#1444C2211yescharacteristic
114#1444C2211yescharacteristic
115#1444C2211yescharacteristic
116#1444C2211yescharacteristic
117#1444C2211yescharacteristic
118#1444C2211yescharacteristic
119#1443C2211yescharacteristic
120#1443C2211yescharacteristic
121#1443C2211yescharacteristic
122#1443C2211yescharacteristic
123#1443C2211yescharacteristic
124#1442C2211yescharacteristic
125#1442C2211yescharacteristic
126#1442C2211yescharacteristic
127#1442C2211yescharacteristic
128#1442C2211yescharacteristic
129#1442C2211yescharacteristic
130#1442C2211yescharacteristic
131#1441C2211yescharacteristic
132#1441C2211yescharacteristic
133#1441C2211yescharacteristic
134#1441C2211yescharacteristic
135#1441C2211yescharacteristic
136#1441C2211yescharacteristic
137#1441C2211yescharacteristic
138#1441C2211yescharacteristic
139#1441C2211yescharacteristic
140#1441C2211yescharacteristic
141#1441C2211yescharacteristic
142#1441C2211yescharacteristic
143#1441C2211yescharacteristic
144#1441C2211yescharacteristic
145#1440C2211yescharacteristic
146#1440C2211yescharacteristic
147#1439C2211yescharacteristic
148#1439C2211yescharacteristic
149#1439C2211yescharacteristic
150#1439C2211yescharacteristic
151#1439C2211yescharacteristic
152#1439C2211yescharacteristic
153#1439C2211yescharacteristic
154#1439C2211yescharacteristic
155#1439C2211yescharacteristic
156#1439C2211yescharacteristic
157#1439C2211yescharacteristic
158#1437C2211yescharacteristic
159#1437C2211yescharacteristic
160#1437C2211yescharacteristic
161#1437C2211yescharacteristic
162#1436C2211yescharacteristic
163#1436C2211yescharacteristic
164#1436C2211yescharacteristic
165#1436C2211yescharacteristic
166#1436C2211yescharacteristic
167#1436C2211yescharacteristic
168#1436C2211yescharacteristic
169#1436C2211yescharacteristic
170#1436C2211yescharacteristic
171#1436C2211yescharacteristic
172#1436C2211yescharacteristic
173#1436C2211yescharacteristic
174#1436C2211yescharacteristic
175#1436C2211yescharacteristic
176#1436C2211yescharacteristic
177#1436C2211yescharacteristic
178#1436C2211yescharacteristic
179#1436C2211yescharacteristic
180#1436C2211yescharacteristic
181#1436C2211yescharacteristic
182C4⋊#95C2211yescharacteristic
183C4⋊#95C2211yescharacteristic
184C4⋊#95C2211yescharacteristic
185C4⋊#95C2211yescharacteristic
186#1434C2211yescharacteristic
187#1434C2211yescharacteristic
188#1434C2211yescharacteristic
189#1434C2211yescharacteristic
190#1434C2211yescharacteristic
191C23×Q8C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C2×#125—24no—
194C2×#125—24no—
195C2×#125—24no—
196C2×#125—24no—
197C2×#125—42no—
198C2×#125—42no—
199C2×C22⋊Q8—24no—
200C2×C22⋊Q8—24no—
201C2×C22⋊Q8—24no—
202C2×C4×Q8—24no—
203C2×C4×Q8—24no—
204C2×C4×Q8—42no—
205C2×#117—24no—
206C2×#117—24no—
207C2×#117—42no—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4C2311yescharacteristic
252C22×C22⋊C4C2311yescharacteristic
253C22×C22⋊C4C2311yescharacteristic
254C22×C22⋊C4C2311yescharacteristic
255C22×C22⋊C4C2311yescharacteristic
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2311yescharacteristic
259C22×C22⋊C4C2311yescharacteristic
260C22×C22⋊C4C2311yescharacteristic
261C22×C22⋊C4C2311yescharacteristic
262C22×C22⋊C4C2311yescharacteristic
263C22×C22⋊C4C2311yescharacteristic
264C22×C22⋊C4C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277#400—24no—
278#399—24no—
279#399—24no—
280#398—24no—
281#398—24no—
282#398—24no—
283#398—24no—
284#398—24no—
285#398—24no—
286#398—24no—
287#398—24no—
288#398—24no—
289#398—42no—
290#398—42no—
291#398—42no—
292#397—24no—
293#397—42no—
294#396—24no—
295#395—24no—
296#395—24no—
297#395—42no—
298#395—42no—
299#391—24no—
300#389—24no—
301#389—24no—
302#389—24no—
303#389—24no—
304#389—24no—
305#389—24no—
306#389—24no—
307#389—24no—
308#389D418yes—
309#388—24no—
310#388—24no—
311#388—24no—
312#388—24no—
313#388—24no—
314#388—24no—
315#387—24no—
316#387—24no—
317#387—24no—
318#387—24no—
319#387—24no—
320#387—24no—
321#387—24no—
322#387—24no—
323#387—24no—
324#387D418yes—
325#385—24no—
326#385—24no—
327#385—42no—
328#385—42no—
329#384—24no—
330#384—24no—
331#384—24no—
332#380—24no—
333C4×C4⋊C4—24no—
334C4×C4⋊C4—24no—
335C4×C4⋊C4—24no—
336C4×C4⋊C4—24no—
337C4×C4⋊C4—24no—
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2311yescharacteristic
353C2×#95C2311yescharacteristic
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2311yescharacteristic
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C2×#95C2311yescharacteristic
370C2×#95C2311yescharacteristic
371C2×#95C2311yescharacteristic
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C2×#95C2311yescharacteristic
377C2×#95C2311yescharacteristic
378C2×#95C2311yescharacteristic
379C2×#95C2311yescharacteristic
380C2×#95C2311yescharacteristic
381C2×#95C2311yescharacteristic
382C2×#95C2311yescharacteristic
383C2×#95C2311yescharacteristic
384C2×#95C2311yescharacteristic
385C2×#95C2311yescharacteristic
386C2×#95C2311yescharacteristic
387C2×#95C2311yescharacteristic
388C2×#95C2311yescharacteristic
389C2×#95C2311yescharacteristic
390C2×#95C2311yescharacteristic
391C2×#95C2311yescharacteristic
392C2×#95C2311yescharacteristic
393C2×#95C2311yescharacteristic
394C2×#95C2311yescharacteristic
395C2×#95C2311yescharacteristic
396C2×#95C2311yescharacteristic
397C2×#95C2311yescharacteristic
398C2×#95C2311yescharacteristic
399C2×#95C2311yescharacteristic
400C2×#95C2311yescharacteristic
401C2×#95C2311yescharacteristic
402C2×#95C2311yescharacteristic
403C2×#95C2311yescharacteristic
404C2×#95C2311yescharacteristic
405C2×#95C2311yescharacteristic
406C2×#95C2311yescharacteristic
407C2×#95C2311yescharacteristic
408C2×#95C2311yescharacteristic
409C2×#95C2311yescharacteristic
410C2×#95C2311yescharacteristic
411C2×#95C2311yescharacteristic
412C2×#95C2311yescharacteristic
413C2×#95C2311yescharacteristic
414C2×#95C2311yescharacteristic
415C2×#95C2311yescharacteristic
416C2×#95C2311yescharacteristic
417C2×#95C2311yescharacteristic
418C2×#95C2311yescharacteristic
419C2×#95C2311yescharacteristic
420C2×#95C2311yescharacteristic
421C2×#95C2311yescharacteristic
422C25C2411yescharacteristic
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—41no—
429C22×Q8—41no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—41no—
436C23×C4—41no—
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467#125—416no—
468#125—416no—
469C22⋊Q8—232no—
470C4×Q8—416no—
471#117—416no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4C2×D414yes—
595C2×C4⋊C4C2×D414yes—
596C2×C4⋊C4C2×D414yes—
597C2×C4⋊C4C2×D414yes—
598C2×C4⋊C4C2×D414yes—
599C2×C4⋊C4C2×D414yes—
600C2×C4⋊C4#4114yes—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4—41no—
629C2×C22⋊C4—41no—
630C2×C22⋊C4—41no—
631C2×C22⋊C4—41no—
632C2×C22⋊C4—41no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4—41no—
637C2×C22⋊C4—41no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4#4114yes—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—22no—
652C2×C42—22no—
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—22no—
658C2×C42—22no—
659C2×C42—22no—
660C2×C42—22no—
661C2×C42—22no—
662C2×C42—22no—
663C2×C42—22no—
664C2×C42—41no—
665C2×C42—41no—
666C2×C42—41no—
667C2×C42—41no—
668C2×C42—41no—
669C2×C42—41no—
670C2×C42—41no—
671C2×C42—41no—
672C2×C42—41no—
673C2×C42—41no—
674C2×C42—41no—
675C2×C42—41no—
676C2×C42—41no—
677C2×C42C2×D414yes—
678C2×C42C2×D414yes—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—22no—
693#95—22no—
694#95—22no—
695#95—22no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—22no—
710#95—22no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—41no—
733#95—41no—
734#95—41no—
735#95—41no—
736#95—41no—
737#95—41no—
738#95—41no—
739#95—41no—
740#95—41no—
741#95—41no—
742#95—41no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95—41no—
752#95—41no—
753#95—41no—
754#95—41no—
755#95—41no—
756#95—41no—
757#95C2×D414yes—
758#95C2×D414yes—
759#95C2×D414yes—
760#95C2×D414yes—
761#95C2×D414yes—
762#95C2×D414yes—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24C2×#4112yes—
778C24C2511yescharacteristic
779C2×Q8—28no—
780C2×Q8—44no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—44no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—28no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4C22×D412yes—
977C22×C4C22×D412yes—
978C22×C4C22×D412yes—
979C22×C4C22×D412yes—
980C22×C4C22×D412yes—
981C22×C4C22×D412yes—
982C22×C4C22×D412yes—
983C22×C4C22×D412yes—
984C22×C4C22×D412yes—
985C22×C4C22×D412yes—
986C22×C4C22×D412yes—
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C2×#4112yes—
991C22×C4C2×#4112yes—
992C22×C4C2×#4112yes—
993C22×C4C2×#4112yes—
994C22×C4C2×#4112yes—
995C22×C4H(5,𝔽2)12yes—
996C22×C4H(5,𝔽2)12yes—
997C22×C42−1+412yes—
998C22×C42−1+412yes—
999C22×C42−1+412yes—
1000C22×C42−1+412yes—
1001C22×C42−1+412yes—
1002C22×C42−1+412yes—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—82no—
1037C4⋊C4—82no—
1038C4⋊C4—82no—
1039C4⋊C4—82no—
1040C4⋊C4—82no—
1041C4⋊C4—82no—
1042C4⋊C4—82no—
1043C4⋊C4—82no—
1044C4⋊C4—82no—
1045C4⋊C4—82no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—82no—
1057C22⋊C4—82no—
1058C22⋊C4—82no—
1059C22⋊C4—82no—
1060C42—28no—
1061C42—28no—
1062C42—44no—
1063C42—44no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—44no—
1071C42—82no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23C23×D411yescharacteristic
1108C23C23×D411yescharacteristic
1109C23C22×#4111yescharacteristic
1110C23C22×#4111yescharacteristic
1111C23C2×H(5,𝔽2)11yescharacteristic
1112C23C2×H(5,𝔽2)11yescharacteristic
1113C23C2×2−1+411yescharacteristic
1114C23C2×2−1+411yescharacteristic
1115C23C2×2−1+411yescharacteristic
1116C23C2×2−1+411yescharacteristic
1117C23C2×2−1+411yescharacteristic
1118C23C2×2−1+411yescharacteristic
1119C23#58511yescharacteristic
1120C23#58511yescharacteristic
1121C23#58511yescharacteristic
1122Q8—416no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—416no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4#52514yes—
1331C2×C4#53614yes—
1332C2×C4D4214yes—
1333C2×C4#55014yes—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22C2×#52511yescharacteristic
1350C22C2×#53611yescharacteristic
1351C22C2×D4211yescharacteristic
1352C22C2×#55011yescharacteristic
1353C22D4×#4111yescharacteristic
1354C22#348511yescharacteristic
1355C22#348611yescharacteristic
1356C22#348611yescharacteristic
1357C22#348811yescharacteristic
1358C22#348911yescharacteristic
1359C22#348911yescharacteristic
1360C22#349911yescharacteristic
1361C22#349911yescharacteristic
1362C22#350611yescharacteristic
1363C22#350911yescharacteristic
1364C22#350911yescharacteristic
1365C22#351511yescharacteristic
1366C22#351511yescharacteristic
1367C22#351511yescharacteristic
1368C22#351511yescharacteristic
1369C22#351911yescharacteristic
1370C22#352311yescharacteristic
1371C22#352311yescharacteristic
1372C22#353811yescharacteristic
1373C22#354111yescharacteristic
1374C22#355211yescharacteristic
1375C22#355211yescharacteristic
1376C22#355211yescharacteristic
1377C22#355411yescharacteristic
1378C22#355511yescharacteristic
1379C22#355911yescharacteristic
1380C22#355911yescharacteristic
1381C22#356311yescharacteristic
1382C22#356411yescharacteristic
1383C22#356511yescharacteristic
1384C4—24no—
1385C4—24no—
1386C4—24no—
1387C4—24no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C2—82no—
1415C2#3545311yescharacteristic
1416C2#3574911yescharacteristic
1417C2#3610111yescharacteristic
1418C2#3767511yescharacteristic
1419C2#3913911yescharacteristic
1420C2#3989011yescharacteristic
1421C2#4444711yescharacteristic
1422C2#4484911yescharacteristic
1423C2#4521711yescharacteristic
1424C2#4669211yescharacteristic
1425C2#4679511yescharacteristic
1426C2#4771711yescharacteristic
1427C2#5017611yescharacteristic
1428C2#5140711yescharacteristic
1429C2#5171611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2552C2semidirect
3. C2×#2462C2semidirect
6. #16349C2semidirect
7. #16293C2semidirect
10. #15848C2semidirect
12. #15517C2semidirect
14. #15434C2semidirect
18. #15388C2semidirect
20. #15151C2semidirect
23. #14880C2semidirect
24. #14816C2semidirect
25. #14804C2semidirect
26. #14548C2semidirect
28. #14443C2semidirect
30. #14191C2semidirect
31. #14069C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25522
C2×#24752
C2×#24622
C2×#23232
#170622
#163492
#162932
#159702
#158802
#158482
#155832
#155172
#154412
#154342
#154302
#154222
#153882
#153062
#151512
#150932
#149072
#148802
#148162
#148042
#145482
#145292
#144432
#141942
#141912
#140692