Finite Group Databasebeta

← #517599

Subgroups — #517599

Order 512.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#518C211yesmaximal, characteristic, complemented
2C2×#2613C211yesmaximal, characteristic
3C2×#2359C211yesmaximal, characteristic, complemented
4C2×#2358C212yesmaximal, complemented
5#14300C211yesmaximal, characteristic, complemented
6#14299C211yesmaximal, characteristic, complemented
7#14190C211yesmaximal, characteristic, complemented
8#14189C211yesmaximal, characteristic, complemented
9#14187C212yesmaximal, complemented
10#14185C212yesmaximal, complemented
11#14176C211yesmaximal, characteristic, complemented
12#14175C211yesmaximal, characteristic, complemented
13#14173C212yesmaximal, complemented
14#14171C212yesmaximal, complemented
15#14135C211yesmaximal, characteristic, complemented
16#14134C212yesmaximal, complemented
17#14128C211yesmaximal, characteristic, complemented
18#14127C212yesmaximal, complemented
19C4×#394C211yesmaximal, characteristic, complemented
20C4×#392C211yesmaximal, characteristic, complemented
21C2×#1438C211yesmaximal, characteristic, complemented
22#13799C211yesmaximal, characteristic, complemented
23C22⋊C42C212yesmaximal, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#120C2212yes—
27C2×#518—28no—
28C2×#518—216no—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×C4×D4C2212yes—
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×C4×D4C2212yescomplemented
37C22×#117C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C23×C22⋊C4C2212yes—
40C23×C22⋊C4C2212yes—
41C23×C22⋊C4C2212yes—
42C23×C22⋊C4C2212yes—
43#2613C4116yescomplemented
44C2×#394C2211yescharacteristic
45C2×#394C2212yes—
46C2×#394C2211yescharacteristic
47C2×#392C2211yescharacteristic
48C2×#392C2212yes—
49C2×#392C2211yescharacteristic
50#2359—28no—
51#2358—216no—
52C2×#390C2212yescomplemented
53C2×#389C2211yescharacteristic, complemented
54C2×#388C2212yescomplemented
55C2×#388C2212yescomplemented
56C2×#388C2211yescharacteristic, complemented
57C2×#388C2211yescharacteristic, complemented
58C2×#387C2211yescharacteristic, complemented
59C2×#387C2211yescharacteristic, complemented
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2212yescomplemented
63C2×#386C2212yescomplemented
64C2×#386C2212yescomplemented
65C2×#386C2212yescomplemented
66C2×#385C2211yescharacteristic
67C2×#385C2212yes—
68C2×#385C2212yescomplemented
69C2×#385C2211yescharacteristic, complemented
70C2×#385C2212yescomplemented
71C2×#385C2212yescomplemented
72C2×#381C2211yescharacteristic
73C2×#379C2212yes—
74C2×C4×C4⋊C4C2211yescharacteristic, complemented
75C2×C4×C22⋊C4C2212yes—
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic, complemented
78C2×C4×C22⋊C4C2212yescomplemented
79C2×C4×C22⋊C4C2212yescomplemented
80C2×C4×C22⋊C4C2212yescomplemented
81C22×#95C2211yescharacteristic
82C22×#95C2211yescharacteristic
83#1444C2211yescharacteristic, complemented
84#1444C2211yescharacteristic, complemented
85#1442C2211yescharacteristic, complemented
86#1442C2211yescharacteristic, complemented
87#1441C2211yescharacteristic, complemented
88#1441C2211yescharacteristic, complemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2211yescharacteristic, complemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2211yescharacteristic, complemented
97#1438C2211yescharacteristic
98#1438C2212yes—
99#1438C2211yescharacteristic
100#1438C2212yes—
101#1438C2211yescharacteristic
102#1438C2211yescharacteristic
103#1438C2212yescomplemented
104#1438C2212yescomplemented
105#1437C2212yescomplemented
106#1437C2212yescomplemented
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1436C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1434C2211yescharacteristic, complemented
116#1434C2211yescharacteristic, complemented
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C4×#95C2211yescharacteristic, complemented
127C4×#95C2211yescharacteristic, complemented
128C26C2312yes—
129C23×D4—28no—
130C23×D4—28no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4C2×C418yescomplemented
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2312yes—
147C24×C4C2312yes—
148C24×C4C2312yes—
149C2×#123—24no—
150C2×#123—24no—
151C2×#123C2×C418yescomplemented
152C2×#120—28no—
153C2×#120—28no—
154C2×#120C2×C4116yescomplemented
155#518—2128no—
156C2×C4×D4—28no—
157C2×C4×D4—28no—
158C2×C4×D4—28no—
159C2×C4×D4—28no—
160C2×C4×D4—28no—
161C2×C4×D4—28no—
162C2×C4×D4—28no—
163C2×C4×D4—28no—
164C2×C4×D4—28no—
165C2×C4×D4—28no—
166C2×C4×D4—28no—
167C2×C4×D4—28no—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4—24no—
171C2×C4×D4—24no—
172C2×C4×D4—24no—
173C2×C4×D4—44no—
174C2×C4×D4—44no—
175C2×#117—24no—
176C2×#117—28no—
177C2×#117—28no—
178C2×#117D418yescomplemented
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C22⋊C4—28no—
191C22×C22⋊C4—28no—
192C22×C22⋊C4—28no—
193C22×C22⋊C4—28no—
194C22×C22⋊C4—28no—
195C22×C22⋊C4—28no—
196C22×C22⋊C4—28no—
197C22×C22⋊C4—44no—
198C22×C22⋊C4—44no—
199C22×C22⋊C4—44no—
200C22×C22⋊C4—44no—
201C22×C22⋊C4D4116yescomplemented
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2312yes—
239C22×C42C2311yescharacteristic
240#394C2×C418yescomplemented
241#394C2×C4116yescomplemented
242#394C2×C418yescomplemented
243#392C2×C418yescomplemented
244#392C2×C4116yescomplemented
245#392C2×C418yescomplemented
246#390—28no—
247#389—24no—
248#388—24no—
249#388—28no—
250#388—28no—
251#388—24no—
252#387—24no—
253#387—24no—
254#386—28no—
255#386—28no—
256#386—28no—
257#386—24no—
258#386—44no—
259#386—44no—
260#385—28no—
261#385—24no—
262#385—28no—
263#385—24no—
264#385—44no—
265#385—44no—
266#381C2×C418yescomplemented
267#379C2×C4116yescomplemented
268C4×C4⋊C4—24no—
269C4×C22⋊C4—28no—
270C4×C22⋊C4—28no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—44no—
274C4×C22⋊C4—44no—
275C2×#95—24no—
276C2×#95—24no—
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2312yes—
311C25—24no—
312C25—24no—
313C25—24no—
314C25—24no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25C22×C418yes—
324C25C2×D418yes—
325C25#4118yes—
326C25C2411yescharacteristic
327C25C2412yes—
328C25C2412yes—
329C25C2411yescharacteristic
330C22×D4—232no—
331C22×D4—232no—
332C22×D4—264no—
333C22×D4—264no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—232no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4C22×C414yes—
366C22×D4C22×C414yes—
367C22×D4C22×C418yes—
368C22×D4C22×C414yes—
369C22×D4C22×C418yes—
370C22×D4C22×C418yes—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—41no—
408C23×C4—42no—
409C23×C4—41no—
410C23×C4—41no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4C22×C414yes—
422C23×C4C2×D414yes—
423C23×C4C2×D418yes—
424C23×C4C2×D418yes—
425C23×C4#4114yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445#123—232no—
446#120—264no—
447C4×D4—264no—
448C4×D4—264no—
449C4×D4—232no—
450C4×D4—232no—
451C4×D4—232no—
452C4×D4—232no—
453C4×D4—432no—
454C4×D4—416no—
455#117—232no—
456#117—232no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4C22×C414yes—
481C2×C4⋊C4C22×C414yes—
482C2×C4⋊C4C2×D414yes—
483C2×C4⋊C4C2×D414yes—
484C2×C22⋊C4—264no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—264no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—432no—
536C2×C22⋊C4—432no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4C22×C418yes—
559C2×C22⋊C4C22×C418yes—
560C2×C22⋊C4C22×C418yes—
561C2×C22⋊C4C22×C414yes—
562C2×C22⋊C4C22×C414yes—
563C2×C22⋊C4C22×C414yes—
564C2×C22⋊C4C22×C418yes—
565C2×C22⋊C4C22×C418yes—
566C2×C22⋊C4C22×C418yes—
567C2×C22⋊C4C22×C418yes—
568C2×C22⋊C4C2×D414yes—
569C2×C22⋊C4C2×D418yes—
570C2×C22⋊C4C2×D418yes—
571C2×C22⋊C4C2×D418yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D418yes—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—24no—
578C2×C42—24no—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—24no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—24no—
587C2×C42—42no—
588C2×C42—41no—
589C2×C42—42no—
590C2×C42—42no—
591C2×C42—42no—
592C2×C42C2×D414yes—
593C2×C42C2×D414yes—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—24no—
599#95—24no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—22no—
605#95—22no—
606#95—24no—
607#95—24no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—24no—
612#95—22no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95C22×C414yes—
626#95C22×C414yes—
627#95C22×C418yes—
628C24—21no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—216no—
659C24—216no—
660C24—216no—
661C24—216no—
662C24—216no—
663C24—216no—
664C24—21no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—21no—
671C24—21no—
672C24—22no—
673C24—21no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24C4×D4132yescomplemented
703C24C23×C412yes—
704C24C23×C414yes—
705C24C23×C414yes—
706C24C23×C412yes—
707C24C22×D414yes—
708C24C22×D414yes—
709C24C22×D414yes—
710C24C22×D412yes—
711C24C2×#4114yes—
712C24C2×#4114yes—
713C24C2×#4114yes—
714C24C2×#4112yes—
715C24C2511yescharacteristic
716C2×D4—216no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—216no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—216no—
723C2×D4—216no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—2256no—
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—216no—
730C2×D4—216no—
731C2×D4—216no—
732C2×D4—216no—
733C2×D4—28no—
734C2×D4—216no—
735C2×D4—216no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C2×D4—84no—
753C22×C4—216no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—216no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—216no—
828C22×C4—216no—
829C22×C4—216no—
830C22×C4—216no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—82no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—82no—
890C22×C4—82no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4C4×D4116yescomplemented
895C22×C4C23×C414yes—
896C22×C4C23×C414yes—
897C22×C4C23×C412yes—
898C22×C4C23×C412yes—
899C22×C4C23×C412yes—
900C22×C4C23×C412yes—
901C22×C4C23×C412yes—
902C22×C4C22×D414yes—
903C22×C4C22×D412yes—
904C22×C4C22×D414yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D414yes—
909C22×C4C22×D412yes—
910C22×C4C22×D414yes—
911C22×C4C22×D412yes—
912C22×C4C2×#4112yes—
913C22×C4C2×#4112yes—
914C22×C4H(5,𝔽2)14yes—
915C22×C4H(5,𝔽2)12yes—
916C22×C4H(5,𝔽2)12yes—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—84no—
927C4⋊C4—82no—
928C22⋊C4—216no—
929C22⋊C4—216no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—216no—
933C22⋊C4—216no—
934C22⋊C4—216no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—216no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—216no—
941C22⋊C4—216no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C22⋊C4—84no—
956C22⋊C4—82no—
957C22⋊C4#120116yes—
958C42—216no—
959C42—28no—
960C42—28no—
961C42—44no—
962C42—48no—
963C42—44no—
964C42—84no—
965C42—82no—
966C23—22no—
967C23—24no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—264no—
1021C23—22no—
1022C23—24no—
1023C23—22no—
1024C23—24no—
1025C23—22no—
1026C23—432no—
1027C23—432no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—41no—
1061C23—42no—
1062C23—41no—
1063C23—42no—
1064C23—42no—
1065C23—41no—
1066C23—41no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—41no—
1073C23—41no—
1074C23—42no—
1075C23—42no—
1076C23—41no—
1077C23—41no—
1078C23—816no—
1079C23—816no—
1080C23—816no—
1081C23—816no—
1082C23—816no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23—816no—
1087C23—816no—
1088C23—816no—
1089C23—816no—
1090C23C2×C4×D418yes—
1091C23C2×C4×D418yes—
1092C23C2×C4×D418yes—
1093C23C2×C4×D414yes—
1094C23C2×#12014yes—
1095C23#52518yes—
1096C23#52514yes—
1097C23C24×C411yescharacteristic
1098C23C23×D412yes—
1099C23C23×D411yescharacteristic
1100C23C22×#4112yes—
1101C23C22×#4111yescharacteristic
1102C23C2×H(5,𝔽2)11yescharacteristic
1103C23C2×H(5,𝔽2)12yes—
1104C23C2×H(5,𝔽2)11yescharacteristic
1105C23#58511yescharacteristic
1106C23#58512yes—
1107C23#58511yescharacteristic
1108D4—264no—
1109D4—232no—
1110D4—232no—
1111D4—432no—
1112D4—416no—
1113D4—816no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—232no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—816no—
1221C2×C4—816no—
1222C2×C4—88no—
1223C2×C4—816no—
1224C2×C4—816no—
1225C2×C4—88no—
1226C2×C4—816no—
1227C2×C4—88no—
1228C2×C4C2×C4×D414yes—
1229C2×C4C2×C4×D414yes—
1230C2×C4C2×#12014yes—
1231C2×C4C2×#12014yes—
1232C22—24no—
1233C22—28no—
1234C22—24no—
1235C22—24no—
1236C22—28no—
1237C22—24no—
1238C22—28no—
1239C22—24no—
1240C22—28no—
1241C22—24no—
1242C22—28no—
1243C22—28no—
1244C22—28no—
1245C22—28no—
1246C22—28no—
1247C22—28no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—42no—
1274C22—44no—
1275C22—42no—
1276C22—42no—
1277C22—864no—
1278C22—81no—
1279C22—82no—
1280C22—81no—
1281C22—81no—
1282C22—82no—
1283C22—81no—
1284C22C4×#12018yes—
1285C22C22×C4×D412yes—
1286C22C22×C4×D411yescharacteristic
1287C22C4×H(5,𝔽2)11yescharacteristic
1288C22C4×H(5,𝔽2)12yes—
1289C22C4×H(5,𝔽2)11yescharacteristic
1290C22C22×#12011yescharacteristic
1291C22C2×#52512yes—
1292C22C2×#52511yescharacteristic
1293C22#348412yes—
1294C22#348512yes—
1295C22#348811yescharacteristic
1296C22#348811yescharacteristic
1297C22#349012yes—
1298C22#349112yes—
1299C22#349412yes—
1300C22#349612yes—
1301C22#349612yes—
1302C22#349811yescharacteristic
1303C22#350011yescharacteristic
1304C22#350512yes—
1305C22#350512yes—
1306C22#350811yescharacteristic
1307C22#351011yescharacteristic
1308C4—24no—
1309C4—24no—
1310C4—24no—
1311C4—24no—
1312C4—44no—
1313C4—42no—
1314C4—42no—
1315C4—44no—
1316C4—42no—
1317C4—44no—
1318C4—42no—
1319C4—44no—
1320C4—42no—
1321C4—44no—
1322C4—42no—
1323C4—42no—
1324C4—81no—
1325C4—82no—
1326C4—81no—
1327C2—28no—
1328C2—48no—
1329C2—48no—
1330C2—82no—
1331C2C2×C4×#12011yescharacteristic
1332C2#3426412yes—
1333C2#3426911yescharacteristic
1334C2#3427312yes—
1335C2#3427511yescharacteristic
1336C2#3568011yescharacteristic
1337C2#3568112yes—
1338C2#3568311yescharacteristic
1339C2#3575011yescharacteristic
1340C2#3575112yes—
1341C2#3575311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2613C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#518C2semidirect
3. C2×#2359C2semidirect
4. C2×#2358C2semidirect
5. #14300C2semidirect
6. #14299C2semidirect
7. #14190C2semidirect
8. #14189C2semidirect
9. #14187C2semidirect
10. #14185C2semidirect
11. #14176C2semidirect
12. #14175C2semidirect
13. #14173C2semidirect
14. #14171C2semidirect
15. #14135C2semidirect
16. #14134C2semidirect
17. #14128C2semidirect
18. #14127C2semidirect
19. C4×#394C2semidirect
20. C4×#392C2semidirect
21. C2×#1438C2semidirect
22. #13799C2semidirect
23. C22⋊C42C2semidirect
36. C22×C4×D4C22semidirect
43. #2613C4semidirect
52. C2×#390C22semidirect
53. C2×#389C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
58. C2×#387C22semidirect
59. C2×#387C22semidirect
62. C2×#386C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
65. C2×#386C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
71. C2×#385C22semidirect
74. C2×C4×C4⋊C4C22semidirect
77. C2×C4×C22⋊C4C22semidirect
78. C2×C4×C22⋊C4C22semidirect
79. C2×C4×C22⋊C4C22semidirect
80. C2×C4×C22⋊C4C22semidirect
83. #1444C22semidirect
84. #1444C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
103. #1438C22semidirect
104. #1438C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1434C22semidirect
116. #1434C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C4×#95C22semidirect
127. C4×#95C22semidirect
133. C23×D4C2×C4semidirect
151. C2×#123C2×C4semidirect
154. C2×#120C2×C4semidirect
178. C2×#117D4semidirect
201. C22×C22⋊C4D4semidirect
240. #394C2×C4semidirect
241. #394C2×C4semidirect
242. #394C2×C4semidirect
243. #392C2×C4semidirect
244. #392C2×C4semidirect
245. #392C2×C4semidirect
266. #381C2×C4semidirect
267. #379C2×C4semidirect
702. C24C4×D4semidirect
894. C22×C4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5182
C2×#26132
C2×#23592
C2×#23582
#143002
#142992
#141902
#141892
#141872
#141852
#141762
#141752
#141732
#141712
#141352
#141342
#141282
#141272
C4×#3942
C4×#3922
C2×#14382
#137992
C22⋊C422