Finite Group Databasebeta

← #653582

Subgroups — #653582

Order 512.

2193 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2519C211yesmaximal, characteristic
2C2×C4×#125C211yesmaximal, characteristic, complemented
3#16104C211yesmaximal, characteristic, complemented
4#16052C211yesmaximal, characteristic, complemented
5#15894C211yesmaximal, characteristic
6#15846C211yesmaximal, characteristic
7#15792C211yesmaximal, characteristic, complemented
8#15455C211yesmaximal, characteristic
9#15435C211yesmaximal, characteristic, complemented
10#15389C211yesmaximal, characteristic
11#15076C211yesmaximal, characteristic, complemented
12#14931C211yesmaximal, characteristic
13#14929C211yesmaximal, characteristic, complemented
14#14847C211yesmaximal, characteristic, complemented
15#14809C211yesmaximal, characteristic, complemented
16#14805C211yesmaximal, characteristic
17#14793C211yesmaximal, characteristic
18#14792C211yesmaximal, characteristic
19#14711C211yesmaximal, characteristic
20#14206C211yesmaximal, characteristic
21#14206C211yesmaximal, characteristic
22#14125C211yesmaximal, characteristic
23#14111C211yesmaximal, characteristic, complemented
24#14097C211yesmaximal, characteristic, complemented
25#14037C211yesmaximal, characteristic
26#14030C211yesmaximal, characteristic, complemented
27#14014C211yesmaximal, characteristic, complemented
28#14010C211yesmaximal, characteristic
29#13985C211yesmaximal, characteristic, complemented
30#13825C211yesmaximal, characteristic, complemented
31C4×#387C211yesmaximal, characteristic, complemented
32C22×#126C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C22×#125C2211yescharacteristic
35#2519—28no—
36C2×#399C2211yescharacteristic
37C2×#398C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#396C2211yescharacteristic
40C2×#396C2211yescharacteristic
41C2×#396C2211yescharacteristic
42C4×#125—28no—
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#388C2211yescharacteristic
48C2×#388C2211yescharacteristic
49C2×#388C2211yescharacteristic
50C2×#388C2211yescharacteristic
51C2×#388C2211yescharacteristic
52C2×#388C2211yescharacteristic
53C2×#388C2211yescharacteristic
54C2×#388C2211yescharacteristic
55C2×#387C2211yescharacteristic
56C2×#387C2211yescharacteristic
57C2×#387C2211yescharacteristic
58C2×#387C2211yescharacteristic
59C2×#387C2211yescharacteristic
60C2×#387C2211yescharacteristic
61C2×#387C2211yescharacteristic
62C2×#387C2211yescharacteristic
63C2×#387C2211yescharacteristic
64C2×#387C2211yescharacteristic
65C2×#387C2211yescharacteristic
66C2×#387C2211yescharacteristic
67C2×#383C2211yescharacteristic
68C2×#382C2211yescharacteristic
69C2×#382C2211yescharacteristic
70C2×#382C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C43C2211yescharacteristic
81#1445C2211yescharacteristic
82#1445C2211yescharacteristic
83#1445C2211yescharacteristic
84#1444C2211yescharacteristic
85#1444C2211yescharacteristic
86#1444C2211yescharacteristic
87#1444C2211yescharacteristic
88#1444C2211yescharacteristic
89#1444C2211yescharacteristic
90#1444C2211yescharacteristic
91#1444C2211yescharacteristic
92#1444C2211yescharacteristic
93#1443C2211yescharacteristic
94#1443C2211yescharacteristic
95#1443C2211yescharacteristic
96#1443C2211yescharacteristic
97#1443C2211yescharacteristic
98#1442C2211yescharacteristic
99#1442C2211yescharacteristic
100#1442C2211yescharacteristic
101#1442C2211yescharacteristic
102#1442C2211yescharacteristic
103#1442C2211yescharacteristic
104#1442C2211yescharacteristic
105#1442C2211yescharacteristic
106#1442C2211yescharacteristic
107#1442C2211yescharacteristic
108#1442C2211yescharacteristic
109#1442C2211yescharacteristic
110#1441C2211yescharacteristic
111#1441C2211yescharacteristic
112#1441C2211yescharacteristic
113#1441C2211yescharacteristic
114#1441C2211yescharacteristic
115#1441C2211yescharacteristic
116#1441C2211yescharacteristic
117#1441C2211yescharacteristic
118#1441C2211yescharacteristic
119#1441C2211yescharacteristic
120#1441C2211yescharacteristic
121#1441C2211yescharacteristic
122#1441C2211yescharacteristic
123#1440C2211yescharacteristic
124#1440C2211yescharacteristic
125#1440C2211yescharacteristic
126#1440C2211yescharacteristic
127#1439C2211yescharacteristic
128#1439C2211yescharacteristic
129#1439C2211yescharacteristic
130#1439C2211yescharacteristic
131#1439C2211yescharacteristic
132#1439C2211yescharacteristic
133#1439C2211yescharacteristic
134#1439C2211yescharacteristic
135#1437C2211yescharacteristic
136#1437C2211yescharacteristic
137#1437C2211yescharacteristic
138#1437C2211yescharacteristic
139#1437C2211yescharacteristic
140#1437C2211yescharacteristic
141#1437C2211yescharacteristic
142#1437C2211yescharacteristic
143#1437C2211yescharacteristic
144#1437C2211yescharacteristic
145#1436C2211yescharacteristic
146#1436C2211yescharacteristic
147#1436C2211yescharacteristic
148#1436C2211yescharacteristic
149#1436C2211yescharacteristic
150#1436C2211yescharacteristic
151#1436C2211yescharacteristic
152#1436C2211yescharacteristic
153#1436C2211yescharacteristic
154#1436C2211yescharacteristic
155#1436C2211yescharacteristic
156#1436C2211yescharacteristic
157#1436C2211yescharacteristic
158#1436C2211yescharacteristic
159#1436C2211yescharacteristic
160#1436C2211yescharacteristic
161#1436C2211yescharacteristic
162#1436C2211yescharacteristic
163#1436C2211yescharacteristic
164#1436C2211yescharacteristic
165#1436C2211yescharacteristic
166#1436C2211yescharacteristic
167#1436C2211yescharacteristic
168#1436C2211yescharacteristic
169#1436C2211yescharacteristic
170#1436C2211yescharacteristic
171C4⋊#95C2211yescharacteristic
172C4⋊#95C2211yescharacteristic
173C4⋊#95C2211yescharacteristic
174C4⋊#95C2211yescharacteristic
175#1434C2211yescharacteristic
176#1434C2211yescharacteristic
177#1434C2211yescharacteristic
178#1434C2211yescharacteristic
179#1434C2211yescharacteristic
180#1434C2211yescharacteristic
181#1434C2211yescharacteristic
182C4×#95C2211yescharacteristic
183C4×#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C4×#95C2211yescharacteristic
189C2×#126—24no—
190C2×#126—24no—
191C2×#126—42no—
192C2×#125—24no—
193C2×#125—24no—
194C2×#125—24no—
195C2×#125—24no—
196C2×#125—24no—
197C2×#125—42no—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2311yescharacteristic
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263#399—24no—
264#398—24no—
265#398—24no—
266#396—24no—
267#396—24no—
268#396—24no—
269#389—24no—
270#389—24no—
271#389—24no—
272#389—24no—
273#388—24no—
274#388—24no—
275#388—24no—
276#388—24no—
277#388—24no—
278#388—24no—
279#388—24no—
280#388—42no—
281#387—24no—
282#387—24no—
283#387—24no—
284#387—24no—
285#387—24no—
286#387—24no—
287#387—24no—
288#387—24no—
289#387—24no—
290#387—42no—
291#387—42no—
292#387D418yes—
293#383—42no—
294#382—24no—
295#382—24no—
296#382—24no—
297C4×C4⋊C4—24no—
298C4×C4⋊C4—24no—
299C4×C4⋊C4—24no—
300C4×C4⋊C4—24no—
301C4×C4⋊C4—24no—
302C4×C4⋊C4—24no—
303C4×C4⋊C4—24no—
304C4×C4⋊C4—24no—
305C4×C4⋊C4—24no—
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2311yescharacteristic
330C2×#95C2311yescharacteristic
331C2×#95C2311yescharacteristic
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
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
396C43—24no—
397C25C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428#126—416no—
429#125—232no—
430#125—416no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
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—41no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4—41no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4C2×D414yes—
519C2×C4⋊C4C2×D414yes—
520C2×C4⋊C4#4114yes—
521C2×C4⋊C4#4114yes—
522C2×C4⋊C4#4114yes—
523C2×C4⋊C4#4114yes—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—41no—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42—41no—
622C2×C42—41no—
623C2×C42—41no—
624C2×C42—41no—
625C2×C42C2×D414yes—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—22no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95C2×D414yes—
711#95C2×D414yes—
712#95C2×D414yes—
713#95C2×D414yes—
714#95#4114yes—
715#95#4114yes—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24C2511yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
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—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
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—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
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—21no—
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×C4C22×D412yes—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C2×#4112yes—
921C22×C4C2×#4112yes—
922C22×C4C2×#4112yes—
923C22×C4C2×#4112yes—
924C22×C4C2×#4112yes—
925C22×C4C2×#4112yes—
926C22×C4C2×#4112yes—
927C22×C4C2×#4112yes—
928C22×C4C2×#4112yes—
929C22×C4C2×#4112yes—
930C22×C4C2×#4112yes—
931C22×C4C2×#4112yes—
932C22×C4C2×#4112yes—
933C22×C4C2×#4112yes—
934C22×C4C2×#4112yes—
935C22×C4C2×#4112yes—
936C22×C4C2×#4112yes—
937C22×C4C2×#4112yes—
938C22×C4H(5,𝔽2)12yes—
939C22×C42−1+412yes—
940C22×C42−1+412yes—
941C22×C42−1+412yes—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—82no—
970C4⋊C4—82no—
971C4⋊C4—82no—
972C4⋊C4—82no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—82no—
985C22⋊C4—82no—
986C22⋊C4—82no—
987C22⋊C4—82no—
988C42—28no—
989C42—28no—
990C42—28no—
991C42—44no—
992C42—44no—
993C42—44no—
994C42—44no—
995C42—44no—
996C42—44no—
997C42—44no—
998C42—44no—
999C42—44no—
1000C42—44no—
1001C42—44no—
1002C42—44no—
1003C42—44no—
1004C42—44no—
1005C42—82no—
1006C42—82no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23C23×D411yescharacteristic
1043C23C22×#4111yescharacteristic
1044C23C22×#4111yescharacteristic
1045C23C22×#4111yescharacteristic
1046C23C22×#4111yescharacteristic
1047C23C22×#4111yescharacteristic
1048C23C22×#4111yescharacteristic
1049C23C2×H(5,𝔽2)11yescharacteristic
1050C23C2×2−1+411yescharacteristic
1051C23C2×2−1+411yescharacteristic
1052C23C2×2−1+411yescharacteristic
1053C23#58511yescharacteristic
1054C23#58511yescharacteristic
1055C23#58511yescharacteristic
1056C23#58511yescharacteristic
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
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—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
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—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
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#52514yes—
1264C2×C4#54114yes—
1265C2×C4#54614yes—
1266C2×C4#55214yes—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22C2×#52511yescharacteristic
1283C22#344411yescharacteristic
1284C22#344411yescharacteristic
1285C22C2×#54111yescharacteristic
1286C22#346011yescharacteristic
1287C22C2×#54611yescharacteristic
1288C22D4×#4111yescharacteristic
1289C22D4×#4111yescharacteristic
1290C22D4×#4111yescharacteristic
1291C22C2×#55211yescharacteristic
1292C22#347511yescharacteristic
1293C22#348011yescharacteristic
1294C22#348211yescharacteristic
1295C22#348211yescharacteristic
1296C22#348211yescharacteristic
1297C22#348211yescharacteristic
1298C22#348311yescharacteristic
1299C22#348611yescharacteristic
1300C22#348911yescharacteristic
1301C22#349411yescharacteristic
1302C22#350711yescharacteristic
1303C22#351111yescharacteristic
1304C22#351511yescharacteristic
1305C22#351511yescharacteristic
1306C22#351611yescharacteristic
1307C22#351811yescharacteristic
1308C22#352111yescharacteristic
1309C22#352111yescharacteristic
1310C22#352111yescharacteristic
1311C22#352111yescharacteristic
1312C22#352411yescharacteristic
1313C22#355311yescharacteristic
1314C22#355411yescharacteristic
1315C22#355911yescharacteristic
1316C22#356311yescharacteristic
1317C4—24no—
1318C4—24no—
1319C4—24no—
1320C4—24no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C2—161no—
1348C2#3471511yescharacteristic
1349C2#3497311yescharacteristic
1350C2#3549211yescharacteristic
1351C2#3613711yescharacteristic
1352C2#3622711yescharacteristic
1353C2#3623211yescharacteristic
1354C2#3639111yescharacteristic
1355C2#3771911yescharacteristic
1356C2#3887311yescharacteristic
1357C2#4013011yescharacteristic
1358C2#4046711yescharacteristic
1359C2#5908811yescharacteristic
1360C2#5910011yescharacteristic
1361C2#5950511yescharacteristic
1362C2#5953611yescharacteristic
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
2. C2×C4×#125C2semidirect
3. #16104C2semidirect
4. #16052C2semidirect
7. #15792C2semidirect
9. #15435C2semidirect
11. #15076C2semidirect
13. #14929C2semidirect
14. #14847C2semidirect
15. #14809C2semidirect
23. #14111C2semidirect
24. #14097C2semidirect
26. #14030C2semidirect
27. #14014C2semidirect
29. #13985C2semidirect
30. #13825C2semidirect
31. C4×#387C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25192
C2×C4×#1252
#161042
#160522
#158942
#158462
#157922
#154552
#154352
#153892
#150762
#149312
#149292
#148472
#148092
#148052
#147932
#147922
#147112
#142062
#141252
#141112
#140972
#140372
#140302
#140142
#140102
#139852
#138252
C4×#3872