Finite Group Databasebeta

← #704634

Subgroups — #704634

Order 512.

4591 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic, complemented
2C2×#2472C211yesmaximal, characteristic, complemented
3C2×#2410C211yesmaximal, characteristic
4C22×#394C211yesmaximal, characteristic, complemented
5#16861C212yesmaximal, complemented
6#16372C212yesmaximal, complemented
7#15643C212yesmaximal, complemented
8#15473C212yesmaximal, complemented
9#15319C212yesmaximal, complemented
10#15317C212yesmaximal, complemented
11#15130C212yesmaximal, complemented
12#15091C211yesmaximal, characteristic, complemented
13#14817C212yesmaximal, complemented
14#14724C211yesmaximal, characteristic, complemented
15#14718C211yesmaximal, characteristic, complemented
16#14717C211yesmaximal, characteristic, complemented
17#14259C211yesmaximal, characteristic, complemented
18#13995C211yesmaximal, characteristic, complemented
19#13995C211yesmaximal, characteristic, complemented
20#13991C211yesmaximal, characteristic, complemented
21#13877C211yesmaximal, characteristic, complemented
22C22⋊C42C211yesmaximal, characteristic, complemented
23#13782C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic, complemented
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2212yes—
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2502—28no—
37#2472—28no—
38#2410—28no—
39C2×#398C2212yescomplemented
40C2×#398C2212yescomplemented
41C2×#397C2211yescharacteristic, complemented
42C2×#394—28no—
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2211yescharacteristic, complemented
51C2×#394C2211yescharacteristic, complemented
52C2×#394C2212yescomplemented
53C2×#393C2211yescharacteristic, complemented
54C2×#393C2212yescomplemented
55C2×#392C2212yes—
56C2×#391C2212yescomplemented
57C2×#390C2211yescharacteristic, complemented
58C2×#390C2212yescomplemented
59C2×#390C2212yescomplemented
60C2×#388C2211yescharacteristic, complemented
61C2×#388C2211yescharacteristic, complemented
62C2×#388C2212yescomplemented
63C2×#386C2212yes—
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#384C2212yescomplemented
75C2×#380C2212yescomplemented
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2212yescomplemented
85C22×#95C2211yescharacteristic
86#1443C2212yescomplemented
87#1442C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
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×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4—44no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×#124—24no—
148C2×#124—44no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—42no—
152C2×#121—28no—
153C2×#121—44no—
154C2×#121—44no—
155C2×#120—24no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—42no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—42no—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4D418yescomplemented
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C42C2312yes—
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229#398—28no—
230#398—28no—
231#397—24no—
232#394—28no—
233#394—28no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—24no—
238#394—24no—
239#394—44no—
240#394—44no—
241#394—44no—
242#393—24no—
243#393—44no—
244#392—28no—
245#391—28no—
246#390—24no—
247#390—44no—
248#390—44no—
249#388—24no—
250#388—24no—
251#388—44no—
252#386—24no—
253#386—24no—
254#386—24no—
255#386—24no—
256#386—28no—
257#386—42no—
258#385—24no—
259#385—24no—
260#385—24no—
261#385—24no—
262#385D418yes—
263#384—28no—
264#380—44no—
265#379—24no—
266#379—24no—
267#379—24no—
268#379—24no—
269#379—42no—
270C4×C22⋊C4—24no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—44no—
274C2×#95—24no—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
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—
305C25—22no—
306C25—24no—
307C25—24no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25C2×D414yes—
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2412yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—24no—
335C22×Q8—41no—
336C22×Q8—42no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—416no—
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×D4—432no—
377C22×D4—416no—
378C22×D4—416no—
379C22×D4—432no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4C2×D414yes—
410C23×C4C2×D414yes—
411C23×C4C2×D414yes—
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430#124—416no—
431C22⋊Q8—416no—
432#121—432no—
433#120—416no—
434#120—416no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
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—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—416no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4C2×D418yes—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
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—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
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—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—416no—
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—41no—
539C2×C22⋊C4—41no—
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—416no—
547C2×C22⋊C4—416no—
548C2×C22⋊C4—416no—
549C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4#4114yes—
577C2×C22⋊C4#4114yes—
578C2×C22⋊C4#4114yes—
579C2×C42—22no—
580C2×C42—24no—
581C2×C42—24no—
582C2×C42—22no—
583C2×C42—24no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—42no—
589#95—24no—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95C2×D418yes—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—21no—
629C24—22no—
630C24—21no—
631C24—22no—
632C24—28no—
633C24—28no—
634C24—22no—
635C24—21no—
636C24—22no—
637C24—21no—
638C24—21no—
639C24—21no—
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—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—28no—
659C24—28no—
660C24—28no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24C22×D412yes—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C2×#4112yes—
718C24C2×#4112yes—
719C24C2×#4112yes—
720C24H(5,𝔽2)14yes—
721C24H(5,𝔽2)14yes—
722C24H(5,𝔽2)12yes—
723C242−1+412yes—
724C24C2511yescharacteristic
725C2×Q8—44no—
726C2×Q8—48no—
727C2×Q8—44no—
728C2×Q8—82no—
729C2×Q8—84no—
730C2×D4—216no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
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—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—48no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—82no—
766C2×D4—82no—
767C2×D4—84no—
768C2×D4—84no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
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—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
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—21no—
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—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—48no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D414yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D414yes—
902C22×C4C22×D412yes—
903C22×C4C2×#4114yes—
904C22×C4C2×#4114yes—
905C22×C4C2×#4114yes—
906C22×C4H(5,𝔽2)14yes—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—84no—
914C4⋊C4—84no—
915C4⋊C4—84no—
916C4⋊C4—84no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—82no—
946C22⋊C4—82no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—82no—
952C22⋊C4—82no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4#124116yescomplemented
957C42—48no—
958C42—44no—
959C42—84no—
960C42—82no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
1007C23—416no—
1008C23—416no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
1030C23—42no—
1031C23—41no—
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—416no—
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—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—42no—
1074C23—41no—
1075C23—41no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—88no—
1088C23—88no—
1089C23—88no—
1090C23—816no—
1091C23—816no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—88no—
1099C23—88no—
1100C23—88no—
1101C23—88no—
1102C23C2×#12414yes—
1103C23#53214yes—
1104C23#53514yes—
1105C23#54214yes—
1106C23D4214yes—
1107C23#54714yes—
1108C23#54814yes—
1109C23#55514yes—
1110C23C23×D411yescharacteristic
1111C23C23×D411yescharacteristic
1112C23C22×#4111yescharacteristic
1113C23C22×#4111yescharacteristic
1114C23C22×#4111yescharacteristic
1115C23C2×H(5,𝔽2)12yes—
1116C23C2×H(5,𝔽2)12yes—
1117C23C2×H(5,𝔽2)11yescharacteristic
1118C23C2×H(5,𝔽2)12yes—
1119C23C2×2−1+411yescharacteristic
1120C23#58512yes—
1121Q8—88no—
1122D4—432no—
1123D4—432no—
1124D4—816no—
1125D4—88no—
1126D4—88no—
1127D4—88no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—416no—
1158C2×C4—416no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—42no—
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—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
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—816no—
1235C2×C4—88no—
1236C2×C4—88no—
1237C2×C4—88no—
1238C2×C4C2×#12418yes—
1239C2×C4#53414yes—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—28no—
1245C22—24no—
1246C22—28no—
1247C22—28no—
1248C22—24no—
1249C22—28no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—42no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—44no—
1262C22—42no—
1263C22—42no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—44no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—44no—
1274C22—42no—
1275C22—832no—
1276C22—832no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—82no—
1294C22—81no—
1295C22—82no—
1296C22—82no—
1297C22—81no—
1298C22—82no—
1299C22—81no—
1300C22#249118yes—
1301C22C22×#12411yescharacteristic
1302C22C2×#53211yescharacteristic
1303C22C2×#53411yescharacteristic
1304C22C2×#53511yescharacteristic
1305C22C2×#54211yescharacteristic
1306C22C2×D4211yescharacteristic
1307C22C2×#54711yescharacteristic
1308C22C2×#54811yescharacteristic
1309C22C2×#55511yescharacteristic
1310C22#348411yescharacteristic
1311C22#348412yes—
1312C22#348511yescharacteristic
1313C22#348812yes—
1314C22#351312yes—
1315C22#351312yes—
1316C22#351312yes—
1317C22#351912yes—
1318C22#351912yes—
1319C22#351912yes—
1320C22#353212yes—
1321C22#353412yes—
1322C22#353512yes—
1323C22#353612yes—
1324C4—24no—
1325C4—28no—
1326C4—42no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—81no—
1334C4—82no—
1335C4—81no—
1336C4—82no—
1337C4—81no—
1338C4—82no—
1339C4—81no—
1340C4—82no—
1341C4—81no—
1342C2—28no—
1343C2—44no—
1344C2—84no—
1345C2—82no—
1346C2—161no—
1347C2C2×#249111yescharacteristic
1348C2#3507811yescharacteristic
1349C2#3539411yescharacteristic
1350C2#3590312yes—
1351C2#3764511yescharacteristic
1352C2#3764611yescharacteristic
1353C2#3803911yescharacteristic
1354C2#3891611yescharacteristic
1355C2#4078512yes—
1356C2#4310312yes—
1357C2#4319812yes—
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×#2502C2semidirect
2. C2×#2472C2semidirect
4. C22×#394C2semidirect
5. #16861C2semidirect
6. #16372C2semidirect
7. #15643C2semidirect
8. #15473C2semidirect
9. #15319C2semidirect
10. #15317C2semidirect
11. #15130C2semidirect
12. #15091C2semidirect
13. #14817C2semidirect
14. #14724C2semidirect
15. #14718C2semidirect
16. #14717C2semidirect
17. #14259C2semidirect
18. #13995C2semidirect
19. #13995C2semidirect
20. #13991C2semidirect
21. #13877C2semidirect
22. C22⋊C42C2semidirect
23. #13782C2semidirect
25. C22×#124C22semidirect
39. C2×#398C22semidirect
40. C2×#398C22semidirect
41. C2×#397C22semidirect
50. C2×#394C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
53. C2×#393C22semidirect
54. C2×#393C22semidirect
56. C2×#391C22semidirect
57. C2×#390C22semidirect
58. C2×#390C22semidirect
59. C2×#390C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
62. C2×#388C22semidirect
74. C2×#384C22semidirect
75. C2×#380C22semidirect
84. C2×C4×C22⋊C4C22semidirect
86. #1443C22semidirect
87. #1442C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. C4⋊#95C22semidirect
118. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
184. C22×C22⋊C4D4semidirect
956. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#24722
C2×#24102
C22×#3942
#168612
#163722
#156432
#154732
#153192
#153172
#151302
#150912
#148172
#147242
#147182
#147172
#142592
#139952
#139912
#138772
C22⋊C422
#137822