Finite Group Databasebeta

← #686983

Subgroups — #686983

Order 512.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2413C211yesmaximal, characteristic, complemented
2C2×#2405C211yesmaximal, characteristic
3C2×#2405C211yesmaximal, characteristic
4C22×#397C211yesmaximal, characteristic, complemented
5C2×#2342C211yesmaximal, characteristic, complemented
6C2×#2308C211yesmaximal, characteristic
7#16286C212yesmaximal, complemented
8#16285C212yesmaximal, complemented
9#15398C212yesmaximal, complemented
10#15298C212yesmaximal, complemented
11#15297C212yesmaximal, complemented
12#15282C212yesmaximal, complemented
13#15069C211yesmaximal, characteristic, complemented
14#14927C211yesmaximal, characteristic, complemented
15#14921C211yesmaximal, characteristic, complemented
16#14912C211yesmaximal, characteristic, complemented
17#14802C212yesmaximal, complemented
18#14741C212yesmaximal, complemented
19#14262C211yesmaximal, characteristic, complemented
20#14135C211yesmaximal, characteristic, complemented
21#14020C211yesmaximal, characteristic, complemented
22#13996C211yesmaximal, characteristic, complemented
23#13869C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#117C2211yescharacteristic, complemented
30C23×C4⋊C4C2211yescharacteristic, complemented
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2413—28no—
36#2405—28no—
37#2405—28no—
38C2×#398C2212yescomplemented
39C2×#397—28no—
40C2×#397C2212yes—
41C2×#397C2212yes—
42C2×#397C2212yescomplemented
43C2×#397C2212yescomplemented
44C2×#396C2212yescomplemented
45C2×#394C2211yescharacteristic
46C2×#394C2212yes—
47C2×#394C2211yescharacteristic
48C2×#394C2211yescharacteristic
49C2×#394C2212yes—
50C2×#394C2211yescharacteristic
51#2342—28no—
52#2308—28no—
53C2×#389C2212yescomplemented
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#388C2212yescomplemented
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2212yes—
69C2×#385C2211yescharacteristic
70C2×#385C2212yescomplemented
71C2×#385C2211yescharacteristic, complemented
72C2×#385C2211yescharacteristic, complemented
73C2×#381C2212yes—
74C2×#381C2211yescharacteristic, complemented
75C2×#381C2211yescharacteristic, complemented
76C2×#381C2211yescharacteristic, complemented
77C2×#380C2211yescharacteristic, complemented
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2212yes—
81C2×#379C2211yescharacteristic
82C2×#379C2212yes—
83C2×#379C2211yescharacteristic
84C2×C4×C22⋊C4C2212yescomplemented
85C2×C4×C22⋊C4C2211yescharacteristic, complemented
86C22×#95C2211yescharacteristic, complemented
87C22×#95C2211yescharacteristic, complemented
88C22×#95C2211yescharacteristic, complemented
89#1445C2212yescomplemented
90#1444C2212yescomplemented
91#1444C2212yescomplemented
92#1443C2212yescomplemented
93#1443C2212yescomplemented
94#1442C2212yescomplemented
95#1442C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1440C2212yes—
101#1440C2212yes—
102#1440C2212yescomplemented
103#1440C2212yescomplemented
104#1440C2212yescomplemented
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1439C2212yescomplemented
115#1439C2212yescomplemented
116#1439C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1436C2212yescomplemented
121C4⋊#95C2212yescomplemented
122#1434C2212yescomplemented
123C22⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic, complemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C22⋊#95C2211yescharacteristic, complemented
128C22⋊#95C2211yescharacteristic, complemented
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—24no—
135C23×D4—24no—
136C23×D4—42no—
137C23×D4—42no—
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C23×D4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—24no—
153C2×#123—24no—
154C2×#123—24no—
155C2×#123—24no—
156C2×#123—24no—
157C2×#123—24no—
158C2×#123—42no—
159C2×#123—42no—
160C2×#123—42no—
161C2×#123—42no—
162C2×#117—24no—
163C2×#117—24no—
164C2×#117—42no—
165C22×C4⋊C4—24no—
166C22×C4⋊C4—24no—
167C22×C4⋊C4—42no—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—24no—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—24no—
188C22×C22⋊C4—24no—
189C22×C22⋊C4—42no—
190C22×C22⋊C4—42no—
191C22×C22⋊C4D418yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C42C2312yes—
230C22×C42C2312yes—
231#398—28no—
232#397—28no—
233#397—28no—
234#397—28no—
235#397—28no—
236#396—28no—
237#394—28no—
238#394—28no—
239#394—24no—
240#394—24no—
241#394—24no—
242#394—24no—
243#389—28no—
244#388—28no—
245#388—28no—
246#388—28no—
247#386—24no—
248#386—24no—
249#386—24no—
250#386—24no—
251#386—28no—
252#386—24no—
253#386—24no—
254#386—24no—
255#386—28no—
256#386D418yes—
257#385—24no—
258#385—28no—
259#385—28no—
260#385—24no—
261#385—24no—
262#385—42no—
263#381—24no—
264#381—24no—
265#381—28no—
266#381—42no—
267#380—24no—
268#379—24no—
269#379—28no—
270#379—28no—
271#379—24no—
272#379—24no—
273#379D418yes—
274C4×C22⋊C4—28no—
275C4×C22⋊C4—24no—
276C2×#95—24no—
277C2×#95—24no—
278C2×#95—24no—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
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×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—41no—
323C25—41no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25—42no—
331C25—42no—
332C25C2×D414yes—
333C25C2×D414yes—
334C25#4114yes—
335C25C2411yescharacteristic
336C25C2411yescharacteristic
337C25C2411yescharacteristic
338C25C2411yescharacteristic
339C25C2411yescharacteristic
340C22×D4—232no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4—41no—
367C22×D4—416no—
368C22×D4—416no—
369C22×D4—416no—
370C22×D4—416no—
371C22×D4—416no—
372C22×D4—416no—
373C22×D4C2×D414yes—
374C22×D4#4114yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—41no—
408C23×C4—41no—
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—42no—
419C23×C4—42no—
420C23×C4C2×D414yes—
421C23×C4C2×D414yes—
422C23×C4C2×D414yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441#123—416no—
442#123—416no—
443#123—416no—
444#123—416no—
445#117—416no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—416no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C22⋊C4—232no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
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—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
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—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—416no—
545C2×C22⋊C4—42no—
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—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—416no—
563C2×C22⋊C4—416no—
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⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4C2×D414yes—
581C2×C22⋊C4C2×D414yes—
582C2×C22⋊C4C2×D414yes—
583C2×C22⋊C4C2×D414yes—
584C2×C22⋊C4C2×D414yes—
585C2×C22⋊C4C2×D414yes—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D418yes—
588C2×C22⋊C4C2×D418yes—
589C2×C22⋊C4C2×D418yes—
590C2×C42—24no—
591C2×C42—24no—
592C2×C42—24no—
593C2×C42—42no—
594C2×C42—42no—
595C2×C42—42no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—24no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95C2×D418yes—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—28no—
651C24—28no—
652C24—28no—
653C24—28no—
654C24—28no—
655C24—28no—
656C24—28no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—44no—
686C24—44no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24—48no—
693C24—44no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—82no—
704C24—82no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24#121116yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C22×D412yes—
719C24C22×D412yes—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C22×D412yes—
723C24C22×D412yes—
724C24C2×#4112yes—
725C24C2×#4112yes—
726C24C2×#4112yes—
727C24C2×#4112yes—
728C24C2×#4112yes—
729C24H(5,𝔽2)12yes—
730C24H(5,𝔽2)12yes—
731C24C2511yescharacteristic
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—4128no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
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—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
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—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—28no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—48no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—48no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—84no—
903C22×C4—84no—
904C22×C4—84no—
905C22×C4—84no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4—84no—
909C22×C4—84no—
910C22×C4—84no—
911C22×C4—84no—
912C22×C4—84no—
913C22×C4C22×D412yes—
914C22×C4C22×D412yes—
915C22×C4C22×D414yes—
916C22×C4C22×D414yes—
917C22×C4C22×D412yes—
918C22×C4C22×D414yes—
919C22×C4C22×D414yes—
920C22×C4C22×D412yes—
921C22×C4C22×D412yes—
922C22×C4C2×#4112yes—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—84no—
934C4⋊C4—84no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—82no—
964C22⋊C4—82no—
965C22⋊C4—82no—
966C22⋊C4—82no—
967C22⋊C4—84no—
968C22⋊C4—84no—
969C22⋊C4—82no—
970C22⋊C4—82no—
971C22⋊C4—84no—
972C42—48no—
973C42—84no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—24no—
1012C23—22no—
1013C23—22no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—232no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—416no—
1030C23—416no—
1031C23—416no—
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—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—42no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—42no—
1065C23—42no—
1066C23—41no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—816no—
1085C23—88no—
1086C23—88no—
1087C23—88no—
1088C23—816no—
1089C23—816no—
1090C23—816no—
1091C23—88no—
1092C23—88no—
1093C23—88no—
1094C23—816no—
1095C23—816no—
1096C23—88no—
1097C23—88no—
1098C23—88no—
1099C23—816no—
1100C23—88no—
1101C23—816no—
1102C23C2×#12114yes—
1103C23C2×#12114yes—
1104C23C2×#12114yes—
1105C23#52514yes—
1106C23#53814yes—
1107C23D4214yes—
1108C23D4214yes—
1109C23#54614yes—
1110C23#54614yes—
1111C23C23×D411yescharacteristic
1112C23C23×D411yescharacteristic
1113C23C23×D411yescharacteristic
1114C23C22×#4111yescharacteristic
1115C23C22×#4111yescharacteristic
1116C23C2×H(5,𝔽2)11yescharacteristic
1117C23C2×H(5,𝔽2)11yescharacteristic
1118C23#58512yes—
1119C23#58512yes—
1120C23#58512yes—
1121C23#58512yes—
1122D4—416no—
1123D4—416no—
1124D4—416no—
1125D4—416no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—416no—
1157C2×C4—416no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—416no—
1163C2×C4—42no—
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—42no—
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—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
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—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—88no—
1244C2×C4—816no—
1245C2×C4—88no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C22—28no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—28no—
1255C22—28no—
1256C22—28no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—24no—
1264C22—44no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—42no—
1279C22—42no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—42no—
1290C22—832no—
1291C22—832no—
1292C22—82no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—81no—
1304C22#242418yes—
1305C22C22×#12111yescharacteristic
1306C22C2×#52511yescharacteristic
1307C22#344911yescharacteristic
1308C22#344911yescharacteristic
1309C22C2×#53811yescharacteristic
1310C22C2×D4211yescharacteristic
1311C22C2×D4211yescharacteristic
1312C22C2×#54611yescharacteristic
1313C22C2×#54611yescharacteristic
1314C22#348512yes—
1315C22#348512yes—
1316C22#348511yescharacteristic
1317C22#348512yes—
1318C22#348511yescharacteristic
1319C22#349112yes—
1320C22#349112yes—
1321C22#350012yes—
1322C22#352112yes—
1323C22#352112yes—
1324C22#353312yes—
1325C22#354512yes—
1326C22#356012yes—
1327C22#356012yes—
1328C4—44no—
1329C4—44no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—44no—
1338C4—82no—
1339C4—81no—
1340C4—82no—
1341C4—81no—
1342C4—81no—
1343C4—82no—
1344C4—82no—
1345C4—81no—
1346C2—28no—
1347C2—44no—
1348C2—44no—
1349C2—82no—
1350C2—82no—
1351C2C2×#242411yescharacteristic
1352C2#3508911yescharacteristic
1353C2#3544711yescharacteristic
1354C2#3601012yes—
1355C2#3765411yescharacteristic
1356C2#3803011yescharacteristic
1357C2#3890111yescharacteristic
1358C2#3933311yescharacteristic
1359C2#4142712yes—
1360C2#4349212yes—
1361C2#4352512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2413C2semidirect
4. C22×#397C2semidirect
5. C2×#2342C2semidirect
7. #16286C2semidirect
8. #16285C2semidirect
9. #15398C2semidirect
10. #15298C2semidirect
11. #15297C2semidirect
12. #15282C2semidirect
13. #15069C2semidirect
14. #14927C2semidirect
15. #14921C2semidirect
16. #14912C2semidirect
17. #14802C2semidirect
18. #14741C2semidirect
19. #14262C2semidirect
20. #14135C2semidirect
21. #14020C2semidirect
22. #13996C2semidirect
23. #13869C2semidirect
29. C22×#117C22semidirect
30. C23×C4⋊C4C22semidirect
38. C2×#398C22semidirect
42. C2×#397C22semidirect
43. C2×#397C22semidirect
44. C2×#396C22semidirect
53. C2×#389C22semidirect
56. C2×#388C22semidirect
70. C2×#385C22semidirect
71. C2×#385C22semidirect
72. C2×#385C22semidirect
74. C2×#381C22semidirect
75. C2×#381C22semidirect
76. C2×#381C22semidirect
77. C2×#380C22semidirect
84. C2×C4×C22⋊C4C22semidirect
85. C2×C4×C22⋊C4C22semidirect
86. C22×#95C22semidirect
87. C22×#95C22semidirect
88. C22×#95C22semidirect
89. #1445C22semidirect
90. #1444C22semidirect
91. #1444C22semidirect
92. #1443C22semidirect
93. #1443C22semidirect
94. #1442C22semidirect
95. #1442C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
102. #1440C22semidirect
103. #1440C22semidirect
104. #1440C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1439C22semidirect
115. #1439C22semidirect
116. #1439C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1436C22semidirect
121. C4⋊#95C22semidirect
122. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24132
C2×#24052
C22×#3972
C2×#23422
C2×#23082
#162862
#162852
#153982
#152982
#152972
#152822
#150692
#149272
#149212
#149122
#148022
#147412
#142622
#141352
#140202
#139962
#138692