Finite Group Databasebeta

← #918943

Subgroups — #918943

Order 512.

5130 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2505C211yesmaximal, characteristic, complemented
2C22×#392C211yesmaximal, characteristic
3#17095C212yesmaximal, complemented
4#17095C212yesmaximal, complemented
5#16809C212yesmaximal, complemented
6#16516C212yesmaximal, complemented
7#16372C212yesmaximal, complemented
8#16289C212yesmaximal, complemented
9#15776C212yesmaximal, complemented
10#15617C212yesmaximal, complemented
11#14734C211yesmaximal, characteristic, complemented
12#14726C211yesmaximal, characteristic, complemented
13#14724C211yesmaximal, characteristic, complemented
14#14724C211yesmaximal, characteristic, complemented
15#14724C211yesmaximal, characteristic, complemented
16#14724C211yesmaximal, characteristic, complemented
17#14262C211yesmaximal, characteristic, complemented
18#14262C211yesmaximal, characteristic, complemented
19#13991C211yesmaximal, characteristic, complemented
20#13971C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic, complemented
22#13902C211yesmaximal, characteristic, complemented
23#13883C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C24×D4C2211yescharacteristic
26C24×D4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30#2505—28no—
31C2×#400C2211yescharacteristic, complemented
32C2×#400C2211yescharacteristic, complemented
33C2×#400C2211yescharacteristic, complemented
34C2×#399C2212yescomplemented
35C2×#398C2211yescharacteristic, complemented
36C2×#396C2212yescomplemented
37C2×#394C2212yescomplemented
38C2×#394C2212yescomplemented
39C2×#394C2212yescomplemented
40C2×#394C2212yescomplemented
41C2×#394C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#394C2212yescomplemented
44C2×#394C2212yescomplemented
45C2×#392—28no—
46C2×#392C2212yes—
47C2×#392C2212yes—
48C2×#392C2212yes—
49C2×#392C2212yes—
50C2×#390C2212yescomplemented
51C2×#390C2212yescomplemented
52C2×#390C2212yescomplemented
53C2×#390C2212yescomplemented
54C2×#389C2211yescharacteristic, complemented
55C2×#388C2212yescomplemented
56C2×#388C2212yescomplemented
57C2×#387C2211yescharacteristic, complemented
58C2×#387C2211yescharacteristic, complemented
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#382C2211yescharacteristic, complemented
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#379C2211yescharacteristic
69C2×#379C2211yescharacteristic
70C2×#379C2211yescharacteristic
71C2×#379C2211yescharacteristic
72C2×#379C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C22×#95C2211yescharacteristic
83#1443C2212yescomplemented
84#1442C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1438C2212yescomplemented
104#1438C2212yescomplemented
105#1438C2212yescomplemented
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1436C2212yescomplemented
118#1434C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C26C2311yescharacteristic
126C26C2311yescharacteristic
127C26C2311yescharacteristic
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—44no—
134C23×D4—44no—
135C23×D4—42no—
136C23×D4—42no—
137C23×D4—42no—
138C23×D4—42no—
139C23×D4—44no—
140C23×D4—44no—
141C23×D4—44no—
142C23×D4—44no—
143C23×D4C2312yes—
144C23×D4C2312yes—
145C23×D4C2312yes—
146C23×D4C2312yes—
147C23×D4C2312yes—
148C23×D4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C22⋊C4—24no—
167C22×C22⋊C4—24no—
168C22×C22⋊C4—24no—
169C22×C22⋊C4—44no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4—42no—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214#400—24no—
215#400—24no—
216#400—24no—
217#399—44no—
218#398—24no—
219#396—44no—
220#394—44no—
221#394—44no—
222#394—44no—
223#394—44no—
224#394—44no—
225#394—44no—
226#394—44no—
227#394—44no—
228#392—28no—
229#392—28no—
230#392—28no—
231#392—28no—
232#390—44no—
233#390—44no—
234#390—44no—
235#390—44no—
236#389—24no—
237#388—44no—
238#388—44no—
239#387—24no—
240#387—24no—
241#385—24no—
242#385—24no—
243#385—24no—
244#385—24no—
245#385—42no—
246#385—42no—
247#382—24no—
248#380—24no—
249#380—42no—
250#379—24no—
251#379—24no—
252#379—24no—
253#379—24no—
254#379—42no—
255#379—42no—
256#379—42no—
257#379—42no—
258#379—42no—
259#379—42no—
260#379—42no—
261#379—42no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4—42no—
264C2×#95D418yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C25—22no—
298C25—22no—
299C25—22no—
300C25—24no—
301C25—24no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25#4114yes—
330C25C2412yes—
331C25C2412yes—
332C25C2412yes—
333C25C2411yescharacteristic
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—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—42no—
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×D4—42no—
366C22×D4—42no—
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—416no—
377C22×D4—416no—
378C22×D4—416no—
379C22×D4—416no—
380C22×D4—416no—
381C22×D4—432no—
382C22×D4—432no—
383C22×D4—416no—
384C22×D4—416no—
385C22×D4—416no—
386C22×D4—416no—
387C22×D4—432no—
388C22×D4—432no—
389C22×D4—432no—
390C22×D4—432no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4C2×D414yes—
409C23×C4C2×D414yes—
410C23×C4C2×D414yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
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—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
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—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—416no—
519C2×C22⋊C4—416no—
520C2×C22⋊C4—416no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
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—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—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⋊C4—42no—
575C2×C22⋊C4#4114yes—
576C2×C42—22no—
577C2×C42—24no—
578C2×C42—22no—
579C2×C42—24no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—42no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—24no—
596#95—24no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95C2×D414yes—
612#95C2×D414yes—
613#95C2×D414yes—
614#95C2×D414yes—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—28no—
620C24—28no—
621C24—28no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
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—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—28no—
665C24—28no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24—84no—
721C24—84no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24—84no—
728C24—84no—
729C24—84no—
730C24C22×D412yes—
731C24C2×#4114yes—
732C24C2×#4112yes—
733C24C2×#4112yes—
734C24H(5,𝔽2)14yes—
735C24H(5,𝔽2)14yes—
736C24H(5,𝔽2)12yes—
737C24H(5,𝔽2)12yes—
738C24H(5,𝔽2)12yes—
739C242−1+412yes—
740C24C2511yescharacteristic
741C2×D4—216no—
742C2×D4—216no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
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—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—4128no—
778C2×D4—4128no—
779C2×D4—4128no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
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—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
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—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—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—21no—
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—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C2×#4112yes—
908C22×C4C2×#4112yes—
909C22×C4H(5,𝔽2)14yes—
910C22×C4H(5,𝔽2)14yes—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—82no—
915C4⋊C4—84no—
916C4⋊C4—82no—
917C4⋊C4—82no—
918C4⋊C4—82no—
919C4⋊C4—82no—
920C4⋊C4—82no—
921C4⋊C4—82no—
922C4⋊C4—84no—
923C4⋊C4—84no—
924C22⋊C4—28no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C42—44no—
963C42—82no—
964C42—84no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
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—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
1007C23—416no—
1008C23—416no—
1009C23—416no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
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—42no—
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—42no—
1066C23—42no—
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—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23—88no—
1108C23—88no—
1109C23—88no—
1110C23—88no—
1111C23—88no—
1112C23—88no—
1113C23—88no—
1114C23—88no—
1115C23—88no—
1116C23—88no—
1117C23—88no—
1118C23—88no—
1119C23#53514yes—
1120C23#53914yes—
1121C23#54014yes—
1122C23#54614yes—
1123C23#54814yes—
1124C23#55314yes—
1125C23#56214yes—
1126C23C23×D411yescharacteristic
1127C23C22×#4111yescharacteristic
1128C23C22×#4111yescharacteristic
1129C23C2×H(5,𝔽2)11yescharacteristic
1130C23C2×H(5,𝔽2)11yescharacteristic
1131C23C2×H(5,𝔽2)12yes—
1132C23C2×H(5,𝔽2)12yes—
1133C23C2×H(5,𝔽2)11yescharacteristic
1134C23C2×H(5,𝔽2)12yes—
1135C23C2×H(5,𝔽2)12yes—
1136C23C2×2−1+411yescharacteristic
1137D4—432no—
1138D4—432no—
1139D4—432no—
1140D4—432no—
1141D4—432no—
1142D4—432no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
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—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—416no—
1168C2×C4—416no—
1169C2×C4—416no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
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—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
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—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
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—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—88no—
1250C2×C4#53514yes—
1251C2×C4#53514yes—
1252C22—28no—
1253C22—28no—
1254C22—24no—
1255C22—28no—
1256C22—28no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—832no—
1284C22—832no—
1285C22—832no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22#271118yes—
1311C22C2×#53511yescharacteristic
1312C22C2×#53511yescharacteristic
1313C22C2×#53511yescharacteristic
1314C22C2×#53911yescharacteristic
1315C22C2×#54011yescharacteristic
1316C22C2×#54611yescharacteristic
1317C22C2×#54811yescharacteristic
1318C22C2×#55311yescharacteristic
1319C22#348411yescharacteristic
1320C22#348411yescharacteristic
1321C22#349012yes—
1322C22#349012yes—
1323C22#351912yes—
1324C22#351912yes—
1325C22C2×#56211yescharacteristic
1326C22#353212yes—
1327C22#353212yes—
1328C22#353212yes—
1329C22#353212yes—
1330C22#353612yes—
1331C22#353612yes—
1332C22#354312yes—
1333C22#354312yes—
1334C4—24no—
1335C4—24no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—82no—
1343C4—82no—
1344C4—82no—
1345C4—81no—
1346C4—81no—
1347C4—82no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—82no—
1353C2—28no—
1354C2—84no—
1355C2—84no—
1356C2—84no—
1357C2#3670311yescharacteristic
1358C2#3761411yescharacteristic
1359C2#3783311yescharacteristic
1360C2#3783311yescharacteristic
1361C2#3912011yescharacteristic
1362C2#3912011yescharacteristic
1363C2#4063812yes—
1364C2#4073012yes—
1365C2#4317312yes—
1366C2C2×#271111yescharacteristic
1367C2#5231612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#392C2
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×#2505C2semidirect
3. #17095C2semidirect
4. #17095C2semidirect
5. #16809C2semidirect
6. #16516C2semidirect
7. #16372C2semidirect
8. #16289C2semidirect
9. #15776C2semidirect
10. #15617C2semidirect
11. #14734C2semidirect
12. #14726C2semidirect
13. #14724C2semidirect
14. #14724C2semidirect
15. #14724C2semidirect
16. #14724C2semidirect
17. #14262C2semidirect
18. #14262C2semidirect
19. #13991C2semidirect
20. #13971C2semidirect
21. #13902C2semidirect
22. #13902C2semidirect
23. #13883C2semidirect
31. C2×#400C22semidirect
32. C2×#400C22semidirect
33. C2×#400C22semidirect
34. C2×#399C22semidirect
35. C2×#398C22semidirect
36. C2×#396C22semidirect
37. C2×#394C22semidirect
38. C2×#394C22semidirect
39. C2×#394C22semidirect
40. C2×#394C22semidirect
41. C2×#394C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
50. C2×#390C22semidirect
51. C2×#390C22semidirect
52. C2×#390C22semidirect
53. C2×#390C22semidirect
54. C2×#389C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#387C22semidirect
58. C2×#387C22semidirect
65. C2×#382C22semidirect
83. #1443C22semidirect
84. #1442C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1438C22semidirect
104. #1438C22semidirect
105. #1438C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1436C22semidirect
118. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25052
C22×#3922
#170952
#168092
#165162
#163722
#162892
#157762
#156172
#147342
#147262
#147242
#142622
#139912
#139712
#139022
#138832