Finite Group Databasebeta

← #528265

Subgroups — #528265

Order 512.

2438 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2713C211yesmaximal, characteristic
2C2×#2336C211yesmaximal, characteristic
3C2×C4×C4⋊Q8C211yesmaximal, characteristic
4#14704C211yesmaximal, characteristic
5#14538C211yesmaximal, characteristic
6#14524C211yesmaximal, characteristic
7#14432C211yesmaximal, characteristic
8#14420C211yesmaximal, characteristic
9#14414C211yesmaximal, characteristic
10#14414C211yesmaximal, characteristic
11#14380C211yesmaximal, characteristic
12#14326C211yesmaximal, characteristic
13#14314C211yesmaximal, characteristic
14#14221C211yesmaximal, characteristic
15#14217C211yesmaximal, characteristic
16#14208C211yesmaximal, characteristic
17#14192C211yesmaximal, characteristic
18#14180C211yesmaximal, characteristic
19#14179C211yesmaximal, characteristic
20#14174C211yesmaximal, characteristic
21#14174C211yesmaximal, characteristic
22#14113C211yesmaximal, characteristic
23#14097C211yesmaximal, characteristic
24#14060C211yesmaximal, characteristic
25#14055C211yesmaximal, characteristic
26#14033C211yesmaximal, characteristic
27#13989C211yesmaximal, characteristic
28#13817C211yesmaximal, characteristic
29#13817C211yesmaximal, characteristic
30#13790C211yesmaximal, characteristic
31C4×#387C211yesmaximal, characteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#2713C4116yescomplemented
37C2×#400C2211yescharacteristic
38C2×#400C2211yescharacteristic
39C2×#398C2211yescharacteristic
40C2×#398C2211yescharacteristic
41C2×#395C2211yescharacteristic
42C2×#395C2211yescharacteristic
43#2336—28no—
44C4×C4⋊Q8—28no—
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#387C2211yescharacteristic
58C2×#387C2211yescharacteristic
59C2×#387C2211yescharacteristic
60C2×#387C2211yescharacteristic
61C2×#387C2211yescharacteristic
62C2×#387C2211yescharacteristic
63C2×#387C2211yescharacteristic
64C2×#387C2211yescharacteristic
65C2×#387C2211yescharacteristic
66C2×#387C2211yescharacteristic
67C2×#387C2211yescharacteristic
68C2×#387C2211yescharacteristic
69C2×#387C2211yescharacteristic
70C2×#387C2211yescharacteristic
71C2×#387C2211yescharacteristic
72C2×#387C2211yescharacteristic
73C2×#384C2211yescharacteristic
74C2×#383C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C4⋊C4C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C4⋊C4C2211yescharacteristic
85C2×C43C2211yescharacteristic
86#1446C2211yescharacteristic
87#1446C2211yescharacteristic
88#1445C2211yescharacteristic
89#1445C2211yescharacteristic
90#1445C2211yescharacteristic
91#1445C2211yescharacteristic
92#1443C2211yescharacteristic
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#1441C2211yescharacteristic
109#1441C2211yescharacteristic
110#1441C2211yescharacteristic
111#1441C2211yescharacteristic
112#1441C2211yescharacteristic
113#1441C2211yescharacteristic
114#1441C2211yescharacteristic
115#1441C2211yescharacteristic
116#1441C2211yescharacteristic
117#1441C2211yescharacteristic
118#1441C2211yescharacteristic
119#1441C2211yescharacteristic
120#1436C2211yescharacteristic
121#1436C2211yescharacteristic
122#1436C2211yescharacteristic
123#1436C2211yescharacteristic
124#1436C2211yescharacteristic
125#1436C2211yescharacteristic
126#1436C2211yescharacteristic
127#1436C2211yescharacteristic
128#1436C2211yescharacteristic
129#1436C2211yescharacteristic
130#1436C2211yescharacteristic
131#1436C2211yescharacteristic
132#1436C2211yescharacteristic
133#1436C2211yescharacteristic
134#1436C2211yescharacteristic
135#1436C2211yescharacteristic
136#1436C2211yescharacteristic
137#1436C2211yescharacteristic
138#1436C2211yescharacteristic
139#1436C2211yescharacteristic
140#1436C2211yescharacteristic
141#1436C2211yescharacteristic
142#1436C2211yescharacteristic
143#1436C2211yescharacteristic
144#1436C2211yescharacteristic
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
164C4⋊#95C2211yescharacteristic
165C4⋊#95C2211yescharacteristic
166C4⋊#95C2211yescharacteristic
167#1434C2211yescharacteristic
168#1434C2211yescharacteristic
169#1434C2211yescharacteristic
170#1434C2211yescharacteristic
171#1434C2211yescharacteristic
172#1434C2211yescharacteristic
173#1434C2211yescharacteristic
174#1434C2211yescharacteristic
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
189C4×#95C2211yescharacteristic
190C23×Q8C2311yescharacteristic
191C23×Q8C2311yescharacteristic
192C2×C4⋊Q8—24no—
193C2×C4⋊Q8—24no—
194C2×C4⋊Q8C2×C418yes—
195C2×#125—24no—
196C2×#125—24no—
197C2×#125C2×C418yes—
198C2×C4×Q8—24no—
199C2×C4×Q8—24no—
200C2×C4×Q8—24no—
201C2×C4×Q8—24no—
202C2×C4×Q8—42no—
203C2×C4×Q8—42no—
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×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
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
257#400C2×C418yes—
258#400C2×C418yes—
259#398C2×C418yes—
260#398C2×C418yes—
261#395C2×C418yes—
262#395C2×C418yes—
263#391—24no—
264#391—24no—
265#391—24no—
266#391—24no—
267#391C2×C418yes—
268#391C2×C418yes—
269#389—24no—
270#389—24no—
271#389—24no—
272#389—24no—
273#389C2×C418yes—
274#389D418yes—
275#387—24no—
276#387—24no—
277#387—24no—
278#387—24no—
279#387—24no—
280#387—24no—
281#387—24no—
282#387—24no—
283#387—24no—
284#387—24no—
285#387—42no—
286#387—42no—
287#387C2×C418yes—
288#387C2×C418yes—
289#387C2×C418yes—
290#387C2×C418yes—
291#384—24no—
292#383—24no—
293C4×C4⋊C4—24no—
294C4×C4⋊C4—24no—
295C4×C4⋊C4—24no—
296C4×C4⋊C4—24no—
297C4×C4⋊C4—24no—
298C4×C4⋊C4—24no—
299C4×C4⋊C4—24no—
300C4×C4⋊C4—24no—
301C4×C4⋊C4—42no—
302C4×C4⋊C4—42no—
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
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
396C2×#95C2311yescharacteristic
397C2×#95C2311yescharacteristic
398C2×#95C2311yescharacteristic
399C2×#95C2311yescharacteristic
400C2×#95C2311yescharacteristic
401C2×#95C2311yescharacteristic
402C2×#95C2311yescharacteristic
403C43—24no—
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—22no—
410C22×Q8—22no—
411C22×Q8—22no—
412C22×Q8—41no—
413C22×Q8—41no—
414C22×Q8—41no—
415C22×Q8—41no—
416C22×Q8C22×C414yes—
417C22×Q8C22×C414yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C4⋊Q8—232no—
450#125—232no—
451C4×Q8—416no—
452C4×Q8—416no—
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—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—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⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4C22×C414yes—
525C2×C4⋊C4C22×C414yes—
526C2×C4⋊C4C22×C414yes—
527C2×C4⋊C4C22×C414yes—
528C2×C4⋊C4C22×C414yes—
529C2×C4⋊C4C22×C414yes—
530C2×C4⋊C4C22×C414yes—
531C2×C4⋊C4C22×C414yes—
532C2×C4⋊C4C22×C414yes—
533C2×C4⋊C4C22×C414yes—
534C2×C4⋊C4C22×C414yes—
535C2×C4⋊C4C22×C414yes—
536C2×C4⋊C4C22×C414yes—
537C2×C4⋊C4C22×C414yes—
538C2×C4⋊C4C2×D414yes—
539C2×C4⋊C4C2×D414yes—
540C2×C4⋊C4C2×D414yes—
541C2×C4⋊C4C2×D414yes—
542C2×C4⋊C4#4114yes—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
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—41no—
580C2×C42—41no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—41no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—41no—
589C2×C42—41no—
590C2×C42—41no—
591C2×C42—41no—
592C2×C42—41no—
593C2×C42—41no—
594C2×C42—41no—
595C2×C42—41no—
596C2×C42—41no—
597C2×C42—41no—
598C2×C42—41no—
599C2×C42—41no—
600C2×C42—41no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42C22×C414yes—
608C2×C42C22×C414yes—
609C2×C42C22×C414yes—
610C2×C42C2×D414yes—
611C2×C42#4114yes—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
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—41no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95—41no—
667#95—41no—
668#95—41no—
669#95—41no—
670#95—41no—
671#95—41no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95—41no—
676#95—41no—
677#95—41no—
678#95—41no—
679#95—41no—
680#95—41no—
681#95—41no—
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#95C22×C414yes—
694#95C22×C414yes—
695#95C22×C414yes—
696#95C22×C414yes—
697#95C22×C414yes—
698#95C22×C414yes—
699#95C22×C414yes—
700#95C22×C414yes—
701#95C22×C414yes—
702#95C22×C414yes—
703#95C22×C414yes—
704#95C22×C414yes—
705#95C22×C414yes—
706#95C22×C414yes—
707#95C22×C414yes—
708#95C22×C414yes—
709#95C2×D414yes—
710#95C2×D414yes—
711#95#4114yes—
712C24C2511yescharacteristic
713C2×Q8—28no—
714C2×Q8—28no—
715C2×Q8—28no—
716C2×Q8—28no—
717C2×Q8—44no—
718C2×Q8—44no—
719C2×Q8—44no—
720C2×Q8—44no—
721C2×Q8—44no—
722C2×Q8—44no—
723C2×Q8—44no—
724C2×Q8—44no—
725C2×Q8—44no—
726C2×Q8—44no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—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×C4C23×C412yes—
908C22×C4C23×C412yes—
909C22×C4C23×C412yes—
910C22×C4C23×C412yes—
911C22×C4C23×C412yes—
912C22×C4C23×C412yes—
913C22×C4C23×C412yes—
914C22×C4C23×C412yes—
915C22×C4C23×C412yes—
916C22×C4C23×C412yes—
917C22×C4C23×C412yes—
918C22×C4C23×C412yes—
919C22×C4C23×C412yes—
920C22×C4C23×C412yes—
921C22×C4C23×C412yes—
922C22×C4C22×D412yes—
923C22×C4C22×D412yes—
924C22×C4C22×D412yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D412yes—
928C22×C4C22×D412yes—
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—
942C22×C42−1+412yes—
943C22×C42−1+412yes—
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—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
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—44no—
970C4⋊C4—44no—
971C4⋊C4—82no—
972C4⋊C4—82no—
973C4⋊C4C4×D4116yes—
974C42—28no—
975C42—28no—
976C42—28no—
977C42—28no—
978C42—28no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—44no—
983C42—44no—
984C42—44no—
985C42—44no—
986C42—44no—
987C42—44no—
988C42—44no—
989C42—44no—
990C42—44no—
991C42—82no—
992C42—82no—
993C42—82no—
994C42—82no—
995C42—82no—
996C42—82no—
997C23C24×C411yescharacteristic
998C23C23×D411yescharacteristic
999C23C22×#4111yescharacteristic
1000C23C22×#4111yescharacteristic
1001C23C22×#4111yescharacteristic
1002C23C2×H(5,𝔽2)11yescharacteristic
1003C23C2×2−1+411yescharacteristic
1004C23C2×2−1+411yescharacteristic
1005C23C2×2−1+411yescharacteristic
1006C23C2×2−1+411yescharacteristic
1007C23C2×2−1+411yescharacteristic
1008C23#58511yescharacteristic
1009C23#58511yescharacteristic
1010C23#58511yescharacteristic
1011C23#58511yescharacteristic
1012Q8—416no—
1013Q8—416no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
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—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
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—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
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—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×C4C2×C4×D414yes—
1225C2×C4C2×C4×D414yes—
1226C2×C4C2×C4×D414yes—
1227C2×C4C4×#4114yes—
1228C2×C4#51914yes—
1229C2×C4#54114yes—
1230C2×C4#54614yes—
1231C22C22×C4×D411yescharacteristic
1232C22C2×C4×#4111yescharacteristic
1233C22C2×#51911yescharacteristic
1234C22C4×H(5,𝔽2)11yescharacteristic
1235C22C4×2−1+411yescharacteristic
1236C22C4×2−1+411yescharacteristic
1237C22C4×2−1+411yescharacteristic
1238C22C2×#54111yescharacteristic
1239C22#345511yescharacteristic
1240C22#346111yescharacteristic
1241C22#346111yescharacteristic
1242C22C2×#54611yescharacteristic
1243C22D4×#4111yescharacteristic
1244C22#347511yescharacteristic
1245C22#348111yescharacteristic
1246C22#348511yescharacteristic
1247C22#348611yescharacteristic
1248C22#348611yescharacteristic
1249C22#348911yescharacteristic
1250C22#350711yescharacteristic
1251C22#350711yescharacteristic
1252C22#350711yescharacteristic
1253C22#350911yescharacteristic
1254C22#351511yescharacteristic
1255C22#351611yescharacteristic
1256C22#352311yescharacteristic
1257C22#352311yescharacteristic
1258C22#355211yescharacteristic
1259C22#355211yescharacteristic
1260C22#355511yescharacteristic
1261C22#355711yescharacteristic
1262C22#355911yescharacteristic
1263C22#356011yescharacteristic
1264C22#356411yescharacteristic
1265C22#356511yescharacteristic
1266C4—24no—
1267C4—24no—
1268C4—24no—
1269C4—24no—
1270C4—24no—
1271C4—24no—
1272C4—24no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C2C4×#54111yescharacteristic
1298C2C4×#54611yescharacteristic
1299C2#3426611yescharacteristic
1300C2#3429111yescharacteristic
1301C2#3432811yescharacteristic
1302C2#3443411yescharacteristic
1303C2#3452511yescharacteristic
1304C2#3769511yescharacteristic
1305C2#3769811yescharacteristic
1306C2#3781111yescharacteristic
1307C2#3782111yescharacteristic
1308C2#3999311yescharacteristic
1309C2#3999911yescharacteristic
1310C2#4042911yescharacteristic
1311C2#4043911yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC24C25
commutatorC23C24×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
36. #2713C4semidirect

Maximal subgroups

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

subgroupindex
C2×#27132
C2×#23362
C2×C4×C4⋊Q82
#147042
#145382
#145242
#144322
#144202
#144142
#143802
#143262
#143142
#142212
#142172
#142082
#141922
#141802
#141792
#141742
#141132
#140972
#140602
#140552
#140332
#139892
#138172
#137902
C4×#3872