Finite Group Databasebeta

← #846880

Subgroups — #846880

Order 512.

4770 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×#2579C211yesmaximal, characteristic, complemented
2C2×#2418C211yesmaximal, characteristic, complemented
3C2×#2410C211yesmaximal, characteristic
4C22×#390C211yesmaximal, characteristic, complemented
5#16371C212yesmaximal, complemented
6#16290C212yesmaximal, complemented
7#15505C212yesmaximal, complemented
8#15370C212yesmaximal, complemented
9#15346C212yesmaximal, complemented
10#15316C212yesmaximal, complemented
11#15092C211yesmaximal, characteristic, complemented
12#14734C211yesmaximal, characteristic, complemented
13#14726C211yesmaximal, characteristic, complemented
14#14725C211yesmaximal, characteristic, complemented
15#14724C211yesmaximal, characteristic, complemented
16#14718C211yesmaximal, characteristic, complemented
17#14697C211yesmaximal, characteristic, complemented
18#14696C211yesmaximal, characteristic, complemented
19#14573C212yesmaximal, complemented
20#14361C212yesmaximal, complemented
21#13967C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13877C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic, complemented
26C22×#121C2212yes—
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C42C2211yescharacteristic
37#2579—28no—
38#2418—28no—
39#2410—28no—
40C2×#399C2211yescharacteristic, complemented
41C2×#399C2212yescomplemented
42C2×#398C2212yescomplemented
43C2×#397C2211yescharacteristic, complemented
44C2×#396C2212yescomplemented
45C2×#396C2212yescomplemented
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2211yescharacteristic, complemented
50C2×#394C2211yescharacteristic, complemented
51C2×#394C2212yescomplemented
52C2×#394C2212yescomplemented
53C2×#392C2212yes—
54C2×#390—28no—
55C2×#390C2212yes—
56C2×#390C2212yes—
57C2×#390C2212yes—
58C2×#390C2212yes—
59C2×#389C2212yescomplemented
60C2×#388C2211yescharacteristic, complemented
61C2×#388C2211yescharacteristic, complemented
62C2×#388C2212yescomplemented
63C2×#387C2212yescomplemented
64C2×#386C2211yescharacteristic
65C2×#386C2212yes—
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic, complemented
70C2×#386C2212yescomplemented
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2211yescharacteristic
76C2×#385C2211yescharacteristic
77C2×#385C2212yescomplemented
78C2×#385C2212yescomplemented
79C2×#380C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×#380C2211yescharacteristic
82C2×#380C2212yescomplemented
83C2×#379C2211yescharacteristic
84C2×#379C2211yescharacteristic
85C2×#379C2211yescharacteristic
86C2×#379C2211yescharacteristic
87C2×#379C2211yescharacteristic
88#1444C2212yescomplemented
89#1444C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117C4⋊#95C2212yescomplemented
118#1434C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—28no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—42no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×#123—24no—
148C2×#123—44no—
149C2×#121—28no—
150C2×#121—28no—
151C2×#121—44no—
152C2×#120—24no—
153C2×#120—24no—
154C2×#120—24no—
155C2×#120—24no—
156C2×#120—42no—
157C2×#120—42no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—42no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—42no—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4D418yescomplemented
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C42—24no—
229C22×C42—44no—
230C22×C42C2312yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233#399—24no—
234#399—44no—
235#398—28no—
236#397—24no—
237#396—28no—
238#396—44no—
239#394—28no—
240#394—24no—
241#394—24no—
242#394—28no—
243#394—44no—
244#394—44no—
245#394—44no—
246#392—28no—
247#390—28no—
248#390—28no—
249#390—28no—
250#390—28no—
251#389—44no—
252#388—24no—
253#388—24no—
254#388—44no—
255#387—28no—
256#386—24no—
257#386—24no—
258#386—24no—
259#386—28no—
260#386—44no—
261#386—42no—
262#386D418yes—
263#385—24no—
264#385—24no—
265#385—24no—
266#385—24no—
267#385—28no—
268#385—44no—
269#385—42no—
270#385—42no—
271#380—24no—
272#380—24no—
273#380—24no—
274#380—44no—
275#379—24no—
276#379—24no—
277#379—42no—
278#379—42no—
279#379—42no—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C25—22no—
309C25—24no—
310C25—24no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25C2×D414yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2412yes—
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C22×D4—232no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—432no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—416no—
365C22×D4—416no—
366C22×D4—432no—
367C22×D4—42no—
368C22×D4—41no—
369C22×D4—41no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4C2×D414yes—
377C22×D4#4118yes—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—24no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—41no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4C2×D414yes—
413C23×C4C2×D414yes—
414C23×C4C2×D414yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433#123—416no—
434#121—432no—
435#120—416no—
436#120—416no—
437C4×D4—416no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—416no—
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—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
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—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
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—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—22no—
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—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—416no—
539C2×C22⋊C4—416no—
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—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—416no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—416no—
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—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4C2×D414yes—
583C2×C22⋊C4C2×D414yes—
584C2×C22⋊C4C2×D414yes—
585C2×C22⋊C4C2×D418yes—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D414yes—
588C2×C22⋊C4#4114yes—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—24no—
592C2×C42—24no—
593C2×C42—24no—
594C2×C42—24no—
595C2×C42—41no—
596C2×C42—42no—
597C2×C42—42no—
598C2×C42—416no—
599#95—24no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—22no—
604#95—24no—
605#95—24no—
606#95—22no—
607#95—24no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—24no—
612#95—24no—
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#95—42no—
626#95C2×D418yes—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—28no—
641C24—28no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—22no—
663C24—21no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—21no—
668C24—22no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—28no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
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—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C22×D412yes—
723C24C22×D412yes—
724C24C22×D412yes—
725C24C2×#4114yes—
726C24C2×#4114yes—
727C24C2×#4112yes—
728C24H(5,𝔽2)12yes—
729C24H(5,𝔽2)12yes—
730C242−1+412yes—
731C242−1+412yes—
732C24C2511yescharacteristic
733C2×D4—216no—
734C2×D4—216no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—216no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—4128no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—48no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—82no—
767C2×D4—82no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—216no—
775C22×C4—28no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—216no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—22no—
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—21no—
810C22×C4—21no—
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—21no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
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—21no—
850C22×C4—21no—
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—21no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—44no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—82no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4—84no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D414yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D414yes—
910C22×C4C2×#4114yes—
911C22×C4C2×#4114yes—
912C22×C4H(5,𝔽2)14yes—
913C22×C4H(5,𝔽2)14yes—
914C22×C4H(5,𝔽2)14yes—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—82no—
924C4⋊C4—82no—
925C4⋊C4—84no—
926C4⋊C4—84no—
927C4⋊C4—84no—
928C4⋊C4—84no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—216no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—82no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—82no—
960C22⋊C4—82no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C22⋊C4—84no—
968C42—48no—
969C42—48no—
970C42—44no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—22no—
1000C23—24no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—416no—
1019C23—416no—
1020C23—416no—
1021C23—416no—
1022C23—416no—
1023C23—416no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—41no—
1035C23—416no—
1036C23—42no—
1037C23—41no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
1041C23—42no—
1042C23—41no—
1043C23—41no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—41no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—41no—
1057C23—41no—
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—41no—
1079C23—42no—
1080C23—41no—
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—42no—
1096C23—42no—
1097C23—88no—
1098C23—88no—
1099C23—88no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23—88no—
1109C23—88no—
1110C23—88no—
1111C23—88no—
1112C23#52514yes—
1113C23#53614yes—
1114C23#53714yes—
1115C23#54214yes—
1116C23D4214yes—
1117C23#54614yes—
1118C23#54714yes—
1119C23#56214yes—
1120C23C23×D411yescharacteristic
1121C23C23×D411yescharacteristic
1122C23C22×#4112yes—
1123C23C22×#4111yescharacteristic
1124C23C2×H(5,𝔽2)12yes—
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×H(5,𝔽2)11yescharacteristic
1127C23C2×H(5,𝔽2)12yes—
1128C23C2×H(5,𝔽2)12yes—
1129C23C2×2−1+411yescharacteristic
1130C23C2×2−1+411yescharacteristic
1131D4—432no—
1132D4—432no—
1133D4—416no—
1134D4—816no—
1135D4—88no—
1136D4—88no—
1137C2×C4—232no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—416no—
1170C2×C4—416no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
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—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
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—88no—
1245C2×C4—816no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C2×C4#53414yes—
1249C2×C4#54618yes—
1250C22—24no—
1251C22—24no—
1252C22—28no—
1253C22—28no—
1254C22—24no—
1255C22—24no—
1256C22—28no—
1257C22—24no—
1258C22—28no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—42no—
1289C22—44no—
1290C22—832no—
1291C22—832no—
1292C22—81no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—81no—
1299C22—82no—
1300C22—82no—
1301C22—81no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—81no—
1310C22#267218yes—
1311C22C2×#52511yescharacteristic
1312C22C2×#53411yescharacteristic
1313C22C2×#53611yescharacteristic
1314C22C2×#53711yescharacteristic
1315C22C2×#54211yescharacteristic
1316C22C2×D4211yescharacteristic
1317C22C2×#54612yes—
1318C22C2×#54611yescharacteristic
1319C22C2×#54711yescharacteristic
1320C22#348112yes—
1321C22#348411yescharacteristic
1322C22#348411yescharacteristic
1323C22#349012yes—
1324C22#349812yes—
1325C22#351912yes—
1326C22#351912yes—
1327C22#352012yes—
1328C22#352012yes—
1329C22C2×#56211yescharacteristic
1330C22#353612yes—
1331C22#353612yes—
1332C22#353712yes—
1333C22#354312yes—
1334C4—28no—
1335C4—24no—
1336C4—44no—
1337C4—44no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—82no—
1347C4—82no—
1348C4—81no—
1349C4—82no—
1350C4—81no—
1351C4—81no—
1352C2—28no—
1353C2—44no—
1354C2—82no—
1355C2—84no—
1356C2—82no—
1357C2#3507711yescharacteristic
1358C2#3609811yescharacteristic
1359C2#3631711yescharacteristic
1360C2#3670611yescharacteristic
1361C2#3803611yescharacteristic
1362C2#3807812yes—
1363C2#3856612yes—
1364C2#3933611yescharacteristic
1365C2#4608812yes—
1366C2C2×#267211yescharacteristic
1367C2#5940812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2410C2
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×#2579C2semidirect
2. C2×#2418C2semidirect
4. C22×#390C2semidirect
5. #16371C2semidirect
6. #16290C2semidirect
7. #15505C2semidirect
8. #15370C2semidirect
9. #15346C2semidirect
10. #15316C2semidirect
11. #15092C2semidirect
12. #14734C2semidirect
13. #14726C2semidirect
14. #14725C2semidirect
15. #14724C2semidirect
16. #14718C2semidirect
17. #14697C2semidirect
18. #14696C2semidirect
19. #14573C2semidirect
20. #14361C2semidirect
21. #13967C2semidirect
22. #13877C2semidirect
23. #13877C2semidirect
25. C22×#123C22semidirect
40. C2×#399C22semidirect
41. C2×#399C22semidirect
42. C2×#398C22semidirect
43. C2×#397C22semidirect
44. C2×#396C22semidirect
45. C2×#396C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
59. C2×#389C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
62. C2×#388C22semidirect
63. C2×#387C22semidirect
69. C2×#386C22semidirect
70. C2×#386C22semidirect
77. C2×#385C22semidirect
78. C2×#385C22semidirect
82. C2×#380C22semidirect
88. #1444C22semidirect
89. #1444C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. C4⋊#95C22semidirect
118. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
188. C22×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25792
C2×#24182
C2×#24102
C22×#3902
#163712
#162902
#155052
#153702
#153462
#153162
#150922
#147342
#147262
#147252
#147242
#147182
#146972
#146962
#145732
#143612
#139672
#138772