Finite Group Databasebeta

← #522676

Subgroups — #522676

Order 512.

5548 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2613C211yesmaximal, characteristic
2C2×#2359C211yesmaximal, characteristic, complemented
3C2×#2321C211yesmaximal, characteristic, complemented
4C2×#2309C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6#14694C211yesmaximal, characteristic, complemented
7#14573C212yesmaximal, complemented
8#14523C212yesmaximal, complemented
9#14521C212yesmaximal, complemented
10#14519C212yesmaximal, complemented
11#14262C211yesmaximal, characteristic, complemented
12#14228C212yesmaximal, complemented
13#14207C212yesmaximal, complemented
14#14205C212yesmaximal, complemented
15#14201C212yesmaximal, complemented
16#14135C211yesmaximal, characteristic, complemented
17#14128C211yesmaximal, characteristic, complemented
18#13995C211yesmaximal, characteristic, complemented
19#13991C211yesmaximal, characteristic, complemented
20#13971C211yesmaximal, characteristic, complemented
21#13967C211yesmaximal, characteristic, complemented
22#13799C211yesmaximal, characteristic, complemented
23C4×#379C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2613C4116yescomplemented
36C2×#394C2212yes—
37C2×#394C2212yes—
38C2×#392C2212yes—
39C2×#392C2212yes—
40#2359—28no—
41#2321—28no—
42#2309—28no—
43C2×#390C2212yes—
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2212yescomplemented
48C2×#390C2212yescomplemented
49C2×#389C2211yescharacteristic, complemented
50C2×#388C2212yescomplemented
51C2×#388C2212yescomplemented
52C2×#388C2211yescharacteristic, complemented
53C2×#388C2211yescharacteristic, complemented
54C2×#388C2212yescomplemented
55C2×#388C2212yescomplemented
56C2×#387C2211yescharacteristic, complemented
57C2×#387C2211yescharacteristic, complemented
58C2×#386—28no—
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2211yescharacteristic
66C2×#386C2212yescomplemented
67C2×#386C2212yescomplemented
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic, complemented
74C2×#381C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic, complemented
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic, complemented
86C2×C4×C22⋊C4C2212yescomplemented
87C2×C4×C22⋊C4C2212yescomplemented
88C22×#95C2211yescharacteristic
89C22×#95C2211yescharacteristic
90#1444C2212yescomplemented
91#1442C2212yescomplemented
92#1441C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1438C2212yescomplemented
105#1438C2212yescomplemented
106#1437C2212yescomplemented
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1434C2212yescomplemented
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C4×#95C2212yescomplemented
128C26C2311yescharacteristic
129C26C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—42no—
135C23×D4—42no—
136C23×D4C2×C418yescomplemented
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4—24no—
143C24×C4—24no—
144C24×C4—44no—
145C24×C4—44no—
146C24×C4—42no—
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C2×#123—24no—
156C2×#123—24no—
157C2×#123C2×C418yescomplemented
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—42no—
161C2×#120—42no—
162C2×#120C2×C418yes—
163C2×#120C2×C418yescomplemented
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×C4×D4—42no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117—24no—
170C2×#117—24no—
171C2×#117—42no—
172C2×#117—42no—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—24no—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—44no—
188C22×C22⋊C4—44no—
189C22×C22⋊C4—42no—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2312yes—
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2311yescharacteristic
229C22×C42C2312yes—
230C22×C42C2312yes—
231C22×C42C2311yescharacteristic
232#394C2×C4116yescomplemented
233#394C2×C4116yescomplemented
234#392C2×C4116yescomplemented
235#392C2×C4116yescomplemented
236#390—28no—
237#390—28no—
238#390—28no—
239#390—28no—
240#390—28no—
241#390—44no—
242#389—24no—
243#388—28no—
244#388—28no—
245#388—24no—
246#388—24no—
247#388—44no—
248#388—44no—
249#387—24no—
250#387—24no—
251#386—24no—
252#386—24no—
253#386—28no—
254#386—28no—
255#386—28no—
256#386—28no—
257#386—28no—
258#386—44no—
259#386—44no—
260#386—44no—
261#386—42no—
262#385—24no—
263#385—24no—
264#385—24no—
265#385—42no—
266#381C2×C418yescomplemented
267#379—24no—
268#379—24no—
269#379—24no—
270#379C2×C418yescomplemented
271#379C2×C418yescomplemented
272#379D418yescomplemented
273C4×C4⋊C4—24no—
274C4×C22⋊C4—24no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4—24no—
277C4×C22⋊C4—44no—
278C4×C22⋊C4—44no—
279C4×C22⋊C4—42no—
280C2×#95—24no—
281C2×#95D418yescomplemented
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25—42no—
331C25—42no—
332C25C22×C414yes—
333C25C22×C414yes—
334C25C2×D414yes—
335C25#4114yes—
336C25C2412yes—
337C25C2411yescharacteristic
338C25C2412yes—
339C25C2411yescharacteristic
340C22×D4—232no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—232no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—416no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—416no—
364C22×D4—416no—
365C22×D4—416no—
366C22×D4—416no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4C22×C414yes—
378C22×D4C22×C418yes—
379C22×D4C22×C418yes—
380C22×D4C22×C418yes—
381C22×D4C22×C418yescomplemented
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—41no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—416no—
424C23×C4—416no—
425C23×C4—432no—
426C23×C4—416no—
427C23×C4—432no—
428C23×C4C22×C414yes—
429C23×C4C2×D414yes—
430C23×C4C2×D414yes—
431C23×C4C2×D414yes—
432C23×C4#4114yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452#123—232no—
453#120—232no—
454#120—416no—
455C4×D4—416no—
456#117—416no—
457#117—416no—
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—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4C22×C414yescomplemented
485C2×C4⋊C4C22×C414yescomplemented
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
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—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
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—41no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—416no—
555C2×C22⋊C4—416no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4C22×C414yes—
575C2×C22⋊C4C22×C418yes—
576C2×C22⋊C4C22×C414yes—
577C2×C22⋊C4C22×C414yes—
578C2×C22⋊C4C22×C418yes—
579C2×C22⋊C4C22×C418yes—
580C2×C22⋊C4C22×C414yescomplemented
581C2×C22⋊C4C22×C414yescomplemented
582C2×C22⋊C4C22×C418yescomplemented
583C2×C22⋊C4C22×C418yescomplemented
584C2×C22⋊C4C22×C418yescomplemented
585C2×C22⋊C4C2×D414yes—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D418yes—
588C2×C22⋊C4C2×D418yes—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—24no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—24no—
598C2×C42—24no—
599C2×C42—22no—
600C2×C42—24no—
601C2×C42—24no—
602C2×C42—42no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—42no—
607C2×C42—42no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42—42no—
611#95—24no—
612#95—24no—
613#95—22no—
614#95—22no—
615#95—24no—
616#95—22no—
617#95—22no—
618#95—24no—
619#95—22no—
620#95—22no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95C22×C418yescomplemented
638#95C22×C418yescomplemented
639#95C2×D414yes—
640#95C2×D414yes—
641#95C2×D414yes—
642#95C2×D414yes—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—28no—
648C24—28no—
649C24—28no—
650C24—28no—
651C24—28no—
652C24—28no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—28no—
666C24—21no—
667C24—22no—
668C24—22no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—28no—
691C24—28no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—44no—
701C24—44no—
702C24—48no—
703C24—44no—
704C24—48no—
705C24—44no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—44no—
711C24—44no—
712C24—44no—
713C24—48no—
714C24—44no—
715C24—48no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24—44no—
720C24—84no—
721C24—84no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24—84no—
728C24C4×D4116yes—
729C24C23×C414yes—
730C24C23×C412yes—
731C24C23×C414yes—
732C24C23×C412yes—
733C24C22×D414yes—
734C24C22×D412yes—
735C24C22×D412yes—
736C24C2×#4114yes—
737C24C2×#4112yes—
738C24C2×#4112yes—
739C24H(5,𝔽2)12yes—
740C24H(5,𝔽2)12yes—
741C24C2511yescharacteristic
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—216no—
745C2×D4—216no—
746C2×D4—28no—
747C2×D4—216no—
748C2×D4—216no—
749C2×D4—216no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—4128no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4—84no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—28no—
796C22×C4—216no—
797C22×C4—28no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—28no—
857C22×C4—28no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—44no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—48no—
903C22×C4—4128no—
904C22×C4—48no—
905C22×C4—44no—
906C22×C4—48no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—82no—
911C22×C4—84no—
912C22×C4—84no—
913C22×C4—84no—
914C22×C4—84no—
915C22×C4—84no—
916C22×C4—84no—
917C22×C4C4×D4116yes—
918C22×C4C23×C414yes—
919C22×C4C23×C414yes—
920C22×C4C23×C412yes—
921C22×C4C23×C412yes—
922C22×C4C23×C412yes—
923C22×C4C23×C412yes—
924C22×C4C23×C412yes—
925C22×C4C22×D412yes—
926C22×C4C22×D414yes—
927C22×C4C22×D412yes—
928C22×C4C22×D412yes—
929C22×C4C22×D412yes—
930C22×C4C22×D412yes—
931C22×C4C22×D412yes—
932C22×C4C22×D412yes—
933C22×C4C22×D412yes—
934C22×C4C2×#4112yes—
935C22×C4C2×#4112yes—
936C22×C4H(5,𝔽2)14yes—
937C22×C4H(5,𝔽2)14yes—
938C4⋊C4—28no—
939C4⋊C4—28no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—48no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—82no—
946C4⋊C4—84no—
947C4⋊C4—84no—
948C22⋊C4—216no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—82no—
974C22⋊C4—84no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C22⋊C4—84no—
982C42—44no—
983C42—44no—
984C42—48no—
985C42—44no—
986C42—44no—
987C42—82no—
988C42—84no—
989C42—84no—
990C23—24no—
991C23—24no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—22no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—232no—
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—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—22no—
1026C23—22no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—22no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—432no—
1038C23—416no—
1039C23—432no—
1040C23—416no—
1041C23—432no—
1042C23—432no—
1043C23—416no—
1044C23—416no—
1045C23—416no—
1046C23—416no—
1047C23—416no—
1048C23—416no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—416no—
1066C23—42no—
1067C23—41no—
1068C23—41no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—41no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—41no—
1079C23—42no—
1080C23—41no—
1081C23—42no—
1082C23—41no—
1083C23—41no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—816no—
1113C23—816no—
1114C23—816no—
1115C23—816no—
1116C23—88no—
1117C23—88no—
1118C23—88no—
1119C23—88no—
1120C23C2×C4×D418yes—
1121C23C2×C4×D414yes—
1122C23C2×C4×D414yes—
1123C23#51814yes—
1124C23D4214yes—
1125C23#54614yes—
1126C23#54614yes—
1127C23#55114yes—
1128C23C24×C411yescharacteristic
1129C23C23×D411yescharacteristic
1130C23C23×D411yescharacteristic
1131C23C22×#4111yescharacteristic
1132C23C22×#4111yescharacteristic
1133C23C2×H(5,𝔽2)11yescharacteristic
1134C23C2×H(5,𝔽2)11yescharacteristic
1135C23C2×H(5,𝔽2)12yes—
1136C23C2×H(5,𝔽2)12yes—
1137C23#58512yes—
1138C23#58512yes—
1139D4—432no—
1140D4—432no—
1141D4—416no—
1142D4—816no—
1143D4—816no—
1144C2×C4—232no—
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—24no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—416no—
1194C2×C4—432no—
1195C2×C4—416no—
1196C2×C4—432no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—42no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—88no—
1260C2×C4—88no—
1261C2×C4—88no—
1262C2×C4C2×C4×D414yes—
1263C2×C4C2×C4×D414yes—
1264C2×C4#53514yes—
1265C22—28no—
1266C22—24no—
1267C22—28no—
1268C22—28no—
1269C22—24no—
1270C22—24no—
1271C22—24no—
1272C22—24no—
1273C22—24no—
1274C22—28no—
1275C22—28no—
1276C22—28no—
1277C22—28no—
1278C22—464no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—42no—
1292C22—44no—
1293C22—44no—
1294C22—42no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—42no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—832no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—81no—
1311C22—82no—
1312C22—81no—
1313C22—82no—
1314C22—81no—
1315C22—82no—
1316C22—81no—
1317C22—82no—
1318C22#235818yes—
1319C22C22×C4×D411yescharacteristic
1320C22C22×C4×D411yescharacteristic
1321C22C2×#51811yescharacteristic
1322C22C4×H(5,𝔽2)12yes—
1323C22C4×H(5,𝔽2)12yes—
1324C22C2×#53511yescharacteristic
1325C22#344911yescharacteristic
1326C22#346012yes—
1327C22C2×D4211yescharacteristic
1328C22C2×#54611yescharacteristic
1329C22C2×#54611yescharacteristic
1330C22C2×#55111yescharacteristic
1331C22#348411yescharacteristic
1332C22#348711yescharacteristic
1333C22#349012yes—
1334C22#349112yes—
1335C22#349612yes—
1336C22#349612yes—
1337C22#350612yes—
1338C22#353212yes—
1339C22#353312yes—
1340C22#354212yes—
1341C22#354212yes—
1342C4—24no—
1343C4—24no—
1344C4—24no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—42no—
1356C4—44no—
1357C4—82no—
1358C4—81no—
1359C4—81no—
1360C4—82no—
1361C2—28no—
1362C2—48no—
1363C2—82no—
1364C2—84no—
1365C2C4×#53511yescharacteristic
1366C2C2×#235811yescharacteristic
1367C2#3426511yescharacteristic
1368C2#3427312yes—
1369C2#3440712yes—
1370C2#3783311yescharacteristic
1371C2#3784311yescharacteristic
1372C2#3796512yes—
1373C2#3933211yescharacteristic
1374C2#3933911yescharacteristic
1375C2#3942912yes—
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
2. C2×#2359C2semidirect
3. C2×#2321C2semidirect
4. C2×#2309C2semidirect
5. C22×#386C2semidirect
6. #14694C2semidirect
7. #14573C2semidirect
8. #14523C2semidirect
9. #14521C2semidirect
10. #14519C2semidirect
11. #14262C2semidirect
12. #14228C2semidirect
13. #14207C2semidirect
14. #14205C2semidirect
15. #14201C2semidirect
16. #14135C2semidirect
17. #14128C2semidirect
18. #13995C2semidirect
19. #13991C2semidirect
20. #13971C2semidirect
21. #13967C2semidirect
22. #13799C2semidirect
23. C4×#379C2semidirect
35. #2613C4semidirect
47. C2×#390C22semidirect
48. C2×#390C22semidirect
49. C2×#389C22semidirect
50. C2×#388C22semidirect
51. C2×#388C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#387C22semidirect
57. C2×#387C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
73. C2×#385C22semidirect
81. C2×C4×C4⋊C4C22semidirect
85. C2×C4×C22⋊C4C22semidirect
86. C2×C4×C22⋊C4C22semidirect
87. C2×C4×C22⋊C4C22semidirect
90. #1444C22semidirect
91. #1442C22semidirect
92. #1441C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1438C22semidirect
105. #1438C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
127. C4×#95C22semidirect
136. C23×D4C2×C4semidirect
157. C2×#123C2×C4semidirect
163. C2×#120C2×C4semidirect
232. #394C2×C4semidirect
233. #394C2×C4semidirect
234. #392C2×C4semidirect
235. #392C2×C4semidirect
266. #381C2×C4semidirect
270. #379C2×C4semidirect
271. #379C2×C4semidirect
272. #379D4semidirect
281. C2×#95D4semidirect
381. C22×D4C22×C4semidirect
484. C2×C4⋊C4C22×C4semidirect
485. C2×C4⋊C4C22×C4semidirect
580. C2×C22⋊C4C22×C4semidirect
581. C2×C22⋊C4C22×C4semidirect
582. C2×C22⋊C4C22×C4semidirect
583. C2×C22⋊C4C22×C4semidirect
584. C2×C22⋊C4C22×C4semidirect
637. #95C22×C4semidirect
638. #95C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26132
C2×#23592
C2×#23212
C2×#23092
C22×#3862
#146942
#145732
#145232
#145212
#145192
#142622
#142282
#142072
#142052
#142012
#141352
#141282
#139952
#139912
#139712
#139672
#137992
C4×#3792