Finite Group Databasebeta

← #720066

Subgroups — #720066

Order 512.

4808 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2433C211yesmaximal, characteristic
2C2×#2472C212yesmaximal, complemented
3C2×#2329C211yesmaximal, characteristic, complemented
4#16888C211yesmaximal, characteristic, complemented
5#16887C211yesmaximal, characteristic, complemented
6#16503C211yesmaximal, characteristic, complemented
7#16503C211yesmaximal, characteristic, complemented
8#15640C212yesmaximal, complemented
9#15617C212yesmaximal, complemented
10#15428C212yesmaximal, complemented
11#15317C212yesmaximal, complemented
12#15227C211yesmaximal, characteristic, complemented
13#15140C211yesmaximal, characteristic, complemented
14#14982C211yesmaximal, characteristic, complemented
15#14982C211yesmaximal, characteristic, complemented
16#14725C212yesmaximal, complemented
17#14718C212yesmaximal, complemented
18#14271C211yesmaximal, characteristic, complemented
19#14152C211yesmaximal, characteristic, complemented
20#13995C212yesmaximal, complemented
21#13902C211yesmaximal, characteristic, complemented
22C2×#1438C211yesmaximal, characteristic, complemented
23#13802C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#124C2212yescomplemented
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#120C2212yes—
31C22×#120C2212yes—
32C23×C22⋊C4C2212yes—
33C23×C22⋊C4C2212yes—
34#2472—216no—
35#2433—28no—
36C2×#397C2212yescomplemented
37C2×#394C2212yescomplemented
38C2×#394C2212yescomplemented
39C2×#394C2212yescomplemented
40C2×#394C2212yescomplemented
41C2×#394C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#393C2212yescomplemented
44C2×#392C2212yes—
45C2×#392C2212yes—
46#2329—28no—
47C2×#391C2211yescharacteristic, complemented
48C2×#391C2211yescharacteristic, complemented
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2212yes—
52C2×#390C2212yes—
53C2×#390C2212yescomplemented
54C2×#390C2212yescomplemented
55C2×#390C2212yescomplemented
56C2×#389C2211yescharacteristic, complemented
57C2×#389C2211yescharacteristic, complemented
58C2×#388C2212yescomplemented
59C2×#388C2212yescomplemented
60C2×#387C2211yescharacteristic, complemented
61C2×#387C2211yescharacteristic, complemented
62C2×#387C2211yescharacteristic, complemented
63C2×#387C2211yescharacteristic, complemented
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#379C2212yes—
73C2×#379C2212yes—
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2212yes—
76C2×C4×C22⋊C4C2211yescharacteristic
77C22×#95C2211yescharacteristic
78C22×#95C2211yescharacteristic
79#1445C2211yescharacteristic, complemented
80#1445C2211yescharacteristic, complemented
81#1445C2211yescharacteristic, complemented
82#1445C2211yescharacteristic, complemented
83#1440C2212yescomplemented
84#1440C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1438C2212yes—
96#1438C2211yescharacteristic
97#1438C2212yes—
98#1438C2211yescharacteristic
99#1438C2211yescharacteristic
100#1438C2211yescharacteristic
101#1438C2211yescharacteristic
102#1438C2211yescharacteristic
103#1438C2211yescharacteristic
104#1438C2211yescharacteristic
105#1438C2212yescomplemented
106#1438C2212yescomplemented
107#1438C2211yescharacteristic, complemented
108#1438C2211yescharacteristic, complemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2211yescharacteristic, complemented
112#1438C2211yescharacteristic, complemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121#1434C2211yescharacteristic, complemented
122#1434C2211yescharacteristic, complemented
123C22⋊#95C2212yes—
124C4×#95C2211yescharacteristic, complemented
125C4×#95C2211yescharacteristic, complemented
126C26C2312yes—
127C23×Q8C2311yescharacteristic
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—44no—
132C23×D4—44no—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C2×#127—24no—
147C2×#127—24no—
148C2×#127—44no—
149C2×#127—44no—
150C2×#124—28no—
151C2×#124—44no—
152C2×#124—44no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8D418yescomplemented
156C2×#121—24no—
157C2×#121—24no—
158C2×#121—24no—
159C2×#120—28no—
160C2×#120—28no—
161C2×#120—28no—
162C2×#120—28no—
163C2×#120—44no—
164C2×#120—44no—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C22⋊C4—28no—
177C22×C22⋊C4—44no—
178C22×C22⋊C4—44no—
179C22×C22⋊C4—44no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222#397—28no—
223#394—28no—
224#394—28no—
225#394—44no—
226#394—44no—
227#394—44no—
228#394—44no—
229#393—28no—
230#392—28no—
231#392—28no—
232#391—24no—
233#391—24no—
234#390—28no—
235#390—24no—
236#390—24no—
237#390—44no—
238#390—44no—
239#390—44no—
240#390—44no—
241#389—24no—
242#389—24no—
243#388—28no—
244#388—28no—
245#387—24no—
246#387—24no—
247#387—24no—
248#387—24no—
249#386—28no—
250#386—28no—
251#386—44no—
252#386—44no—
253#385—24no—
254#385—24no—
255#380—24no—
256#380—24no—
257#379—28no—
258#379—44no—
259C4×C22⋊C4—24no—
260C4×C22⋊C4—28no—
261C4×C22⋊C4D418yes—
262C2×#95—24no—
263C2×#95—24no—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C25—24no—
298C25—24no—
299C25—24no—
300C25—24no—
301C25—24no—
302C25—24no—
303C25—24no—
304C25—24no—
305C25—24no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25C2412yes—
313C25C2412yes—
314C25C2412yes—
315C25C2411yescharacteristic
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—42no—
319C22×Q8—42no—
320C22×Q8C2×D414yescomplemented
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
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—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
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—42no—
377C22×D4—42no—
378C22×D4—416no—
379C22×D4—416no—
380C22×D4—432no—
381C22×D4—432no—
382C22×D4—416no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4C2×D414yes—
402C23×C4C2×D414yes—
403C23×C4#4114yes—
404C23×C4#4114yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424#127—416no—
425#127—416no—
426#124—432no—
427C22⋊Q8—232no—
428#121—416no—
429#120—432no—
430#120—432no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
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—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
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⋊C4C2×D414yescomplemented
456C2×C4⋊C4C2×D414yescomplemented
457C2×C4⋊C4C2×D414yescomplemented
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
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—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—432no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
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—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
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—432no—
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⋊C4C2×D414yes—
558C2×C22⋊C4C2×D414yes—
559C2×C22⋊C4C2×D414yes—
560C2×C22⋊C4C2×D414yes—
561C2×C22⋊C4#4114yes—
562C2×C42—24no—
563C2×C42—24no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—24no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—42no—
573C2×C42—42no—
574C2×C42C2×D414yes—
575C2×C42C2×D414yes—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—22no—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—24no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95C2×D414yes—
608#95C2×D414yes—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—216no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
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—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
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—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24C22×D412yes—
692C24C22×D412yes—
693C24C2×#4112yes—
694C24C2×#4112yes—
695C24C2×#4112yes—
696C24H(5,𝔽2)14yes—
697C24H(5,𝔽2)14yes—
698C24H(5,𝔽2)12yes—
699C24H(5,𝔽2)12yes—
700C24C2511yescharacteristic
701C2×Q8—28no—
702C2×Q8—48no—
703C2×Q8—82no—
704C2×Q8—82no—
705C2×Q8—84no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—216no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—4128no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
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—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—28no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
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—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
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—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—82no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—82no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—82no—
869C22×C4—82no—
870C22×C4—84no—
871C22×C4#124116yescomplemented
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C2×#4112yes—
885C22×C4C2×#4112yes—
886C22×C4C2×#4112yes—
887C22×C4C2×#4112yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4112yes—
890C22×C4H(5,𝔽2)14yes—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—44no—
895C4⋊C4—82no—
896C4⋊C4—84no—
897C4⋊C4—82no—
898C4⋊C4—82no—
899C4⋊C4—82no—
900C4⋊C4—82no—
901C4⋊C4—82no—
902C22⋊C4—216no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4#121116yes—
936C42—44no—
937C42—44no—
938C42—48no—
939C42—82no—
940C42—82no—
941C42—84no—
942C23—24no—
943C23—24no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—432no—
973C23—432no—
974C23—432no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
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—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23—816no—
1075C23—816no—
1076C23—816no—
1077C23—816no—
1078C23C2×#12114yes—
1079C23C2×#12414yes—
1080C23#53514yes—
1081C23#55014yes—
1082C23#55014yes—
1083C23#55914yes—
1084C23#55914yes—
1085C23C23×D411yescharacteristic
1086C23C23×D411yescharacteristic
1087C23C22×#4111yescharacteristic
1088C23C22×#4111yescharacteristic
1089C23C22×#4111yescharacteristic
1090C23C2×H(5,𝔽2)11yescharacteristic
1091C23C2×H(5,𝔽2)11yescharacteristic
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)12yes—
1094C23C2×H(5,𝔽2)12yes—
1095C23#58512yes—
1096Q8—88no—
1097D4—432no—
1098D4—416no—
1099D4—416no—
1100D4—816no—
1101D4—816no—
1102D4—88no—
1103D4—816no—
1104D4—816no—
1105D4—816no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—416no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—88no—
1209C2×C4—816no—
1210C2×C4—88no—
1211C2×C4C2×#12114yes—
1212C2×C4C2×#12114yes—
1213C2×C4C2×#12414yes—
1214C2×C4C2×#12414yes—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—28no—
1219C22—28no—
1220C22—24no—
1221C22—28no—
1222C22—24no—
1223C22—28no—
1224C22—24no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—864no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22#254818yes—
1272C22C22×#12111yescharacteristic
1273C22C22×#12411yescharacteristic
1274C22C2×#53511yescharacteristic
1275C22#346012yes—
1276C22C2×#55011yescharacteristic
1277C22C2×#55011yescharacteristic
1278C22C2×#55911yescharacteristic
1279C22C2×#55911yescharacteristic
1280C22#348411yescharacteristic
1281C22#348411yescharacteristic
1282C22#348412yes—
1283C22#348812yes—
1284C22#349012yes—
1285C22#349012yes—
1286C22#349412yes—
1287C22#349811yescharacteristic
1288C22#350011yescharacteristic
1289C22#351312yes—
1290C22#351912yes—
1291C22#353212yes—
1292C22#353412yes—
1293C22#353412yes—
1294C22#353712yes—
1295C4—24no—
1296C4—24no—
1297C4—24no—
1298C4—24no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—82no—
1311C4—82no—
1312C4—82no—
1313C4—82no—
1314C2—28no—
1315C2—84no—
1316C2—84no—
1317C2—162no—
1318C2C2×#254811yescharacteristic
1319C2#3526411yescharacteristic
1320C2#3536711yescharacteristic
1321C2#3569111yescharacteristic
1322C2#3572811yescharacteristic
1323C2#3776912yes—
1324C2#3926412yes—
1325C2#4049011yescharacteristic
1326C2#4049411yescharacteristic
1327C2#4309912yes—
1328C2#4317812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2433C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2472C2semidirect
3. C2×#2329C2semidirect
4. #16888C2semidirect
5. #16887C2semidirect
6. #16503C2semidirect
7. #16503C2semidirect
8. #15640C2semidirect
9. #15617C2semidirect
10. #15428C2semidirect
11. #15317C2semidirect
12. #15227C2semidirect
13. #15140C2semidirect
14. #14982C2semidirect
15. #14982C2semidirect
16. #14725C2semidirect
17. #14718C2semidirect
18. #14271C2semidirect
19. #14152C2semidirect
20. #13995C2semidirect
21. #13902C2semidirect
22. C2×#1438C2semidirect
23. #13802C2semidirect
27. C22×#124C22semidirect
36. C2×#397C22semidirect
37. C2×#394C22semidirect
38. C2×#394C22semidirect
39. C2×#394C22semidirect
40. C2×#394C22semidirect
41. C2×#394C22semidirect
42. C2×#394C22semidirect
43. C2×#393C22semidirect
47. C2×#391C22semidirect
48. C2×#391C22semidirect
53. C2×#390C22semidirect
54. C2×#390C22semidirect
55. C2×#390C22semidirect
56. C2×#389C22semidirect
57. C2×#389C22semidirect
58. C2×#388C22semidirect
59. C2×#388C22semidirect
60. C2×#387C22semidirect
61. C2×#387C22semidirect
62. C2×#387C22semidirect
63. C2×#387C22semidirect
79. #1445C22semidirect
80. #1445C22semidirect
81. #1445C22semidirect
82. #1445C22semidirect
83. #1440C22semidirect
84. #1440C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
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. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
124. C4×#95C22semidirect
125. C4×#95C22semidirect
155. C2×C22⋊Q8D4semidirect
320. C22×Q8C2×D4semidirect
455. C2×C4⋊C4C2×D4semidirect
456. C2×C4⋊C4C2×D4semidirect
457. C2×C4⋊C4C2×D4semidirect
871. C22×C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#24332
C2×#24722
C2×#23292
#168882
#168872
#165032
#156402
#156172
#154282
#153172
#152272
#151402
#149822
#147252
#147182
#142712
#141522
#139952
#139022
C2×#14382
#138022