Finite Group Databasebeta

← #2735964

Subgroups — #2735964

Order 512.

4400 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2816C211yesmaximal, characteristic, complemented
2C2×#2408C211yesmaximal, characteristic
3C2×#2449C211yesmaximal, characteristic, complemented
4C22×#394C211yesmaximal, characteristic, complemented
5#17101C212yesmaximal, complemented
6#17092C212yesmaximal, complemented
7#17088C212yesmaximal, complemented
8#17084C212yesmaximal, complemented
9#17011C211yesmaximal, characteristic, complemented
10#16811C211yesmaximal, characteristic, complemented
11#16800C211yesmaximal, characteristic, complemented
12#16501C211yesmaximal, characteristic, complemented
13#16259C211yesmaximal, characteristic, complemented
14#16253C211yesmaximal, characteristic, complemented
15#14821C211yesmaximal, characteristic, complemented
16#14766C211yesmaximal, characteristic, complemented
17#14734C212yesmaximal, complemented
18#14725C212yesmaximal, complemented
19#14724C211yesmaximal, characteristic, complemented
20#14718C212yesmaximal, complemented
21#14717C212yesmaximal, complemented
22#14624C211yesmaximal, characteristic, complemented
23#13894C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C22⋊C4C2212yes—
33C23×C22⋊C4C2212yes—
34#2816—28no—
35#2449—28no—
36#2408—28no—
37C2×#399C2212yescomplemented
38C2×#399C2211yescharacteristic, complemented
39C2×#399C2212yescomplemented
40C2×#398C2211yescharacteristic, complemented
41C2×#398C2211yescharacteristic, complemented
42C2×#398C2211yescharacteristic, complemented
43C2×#398C2211yescharacteristic, complemented
44C2×#396C2211yescharacteristic, complemented
45C2×#395C2211yescharacteristic, complemented
46C2×#394—28no—
47C2×#394C2211yescharacteristic
48C2×#394C2212yes—
49C2×#394C2211yescharacteristic
50C2×#394C2211yescharacteristic
51C2×#394C2211yescharacteristic
52C2×#394C2212yes—
53C2×#394C2212yes—
54C2×#394C2211yescharacteristic
55C2×#394C2212yes—
56C2×#394C2211yescharacteristic
57C2×#394C2212yescomplemented
58C2×#394C2212yescomplemented
59C2×#394C2212yescomplemented
60C2×#394C2212yescomplemented
61C2×#393C2212yescomplemented
62C2×#393C2212yescomplemented
63C2×#392C2212yes—
64C2×#390C2211yescharacteristic
65C2×#390C2211yescharacteristic
66C2×#389C2211yescharacteristic, complemented
67C2×#387C2211yescharacteristic, complemented
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2212yes—
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2212yes—
74C2×#385C2211yescharacteristic, complemented
75C2×#381C2211yescharacteristic, complemented
76C2×#380C2211yescharacteristic
77C2×#380C2212yes—
78C2×#379C2212yes—
79C2×#379C2212yes—
80C2×#379C2212yes—
81C22×#95C2211yescharacteristic
82#1445C2212yescomplemented
83#1445C2211yescharacteristic, complemented
84#1444C2211yescharacteristic, complemented
85#1442C2212yescomplemented
86#1441C2211yescharacteristic, complemented
87#1441C2211yescharacteristic, complemented
88#1441C2211yescharacteristic, complemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2211yescharacteristic
114#1438C2211yescharacteristic
115#1438C2212yes—
116#1438C2212yescomplemented
117#1438C2212yescomplemented
118#1438C2212yescomplemented
119#1438C2212yescomplemented
120#1434C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—42no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—44no—
149C2×C22⋊Q8—42no—
150C2×#121—24no—
151C2×#121—24no—
152C2×#121—24no—
153C2×#121—44no—
154C2×#121—42no—
155C2×#120—28no—
156C2×#120—44no—
157C2×#120—44no—
158C2×C4×D4—44no—
159C2×C4×D4D418yes—
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—42no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C22⋊C4—28no—
182C22×C22⋊C4—28no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C42C2311yescharacteristic
222#399—28no—
223#399—24no—
224#399—44no—
225#398—24no—
226#398—24no—
227#398—24no—
228#398—42no—
229#396—24no—
230#395—24no—
231#394—24no—
232#394—24no—
233#394—24no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—28no—
238#394—28no—
239#394—24no—
240#394—42no—
241#394—44no—
242#394—44no—
243#394—44no—
244#394D418yescomplemented
245#393—28no—
246#393—44no—
247#392—28no—
248#390—24no—
249#390—24no—
250#389—24no—
251#387—24no—
252#386—24no—
253#386—24no—
254#386—44no—
255#385—24no—
256#385—24no—
257#385—24no—
258#385—44no—
259#381—24no—
260#380—24no—
261#380—44no—
262#379—28no—
263#379—44no—
264#379—44no—
265C2×#95—24no—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C25—24no—
300C25—24no—
301C25—24no—
302C25—24no—
303C25—24no—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25C2412yes—
315C25C2411yescharacteristic
316C25C2412yes—
317C25C2411yescharacteristic
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—42no—
321C22×Q8—41no—
322C22×Q8—42no—
323C22×D4—24no—
324C22×D4—22no—
325C22×D4—22no—
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—22no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—416no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—416no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—416no—
360C22×D4—432no—
361C22×D4—432no—
362C22×D4C2×D414yes—
363C22×D4C2×D414yes—
364C23×C4—22no—
365C23×C4—24no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—41no—
382C23×C4—41no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—41no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4C2×D414yes—
392C23×C4C2×D414yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C22⋊Q8—416no—
413C22⋊Q8—416no—
414#121—416no—
415#121—416no—
416#120—432no—
417C4×D4—416no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
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—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—416no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—41no—
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×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×D414yes—
466C2×C4⋊C4C2×D414yes—
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—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
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—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
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—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
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—24no—
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—41no—
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—41no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—432no—
532C2×C22⋊C4—432no—
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⋊C4C2×D414yes—
564C2×C22⋊C4C2×D418yes—
565C2×C22⋊C4C2×D418yes—
566C2×C22⋊C4C2×D414yes—
567C2×C42—42no—
568C2×C42C2×D414yes—
569#95—24no—
570#95—22no—
571#95—24no—
572#95—24no—
573#95—22no—
574#95—22no—
575#95—22no—
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—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95C2×D414yes—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—22no—
606C24—21no—
607C24—22no—
608C24—216no—
609C24—21no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
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—84no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24C22×D414yes—
682C24C22×D412yes—
683C24C22×D412yes—
684C24H(5,𝔽2)14yes—
685C24H(5,𝔽2)14yes—
686C24H(5,𝔽2)12yes—
687C24H(5,𝔽2)12yes—
688C242−1+414yes—
689C24C2511yescharacteristic
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—84no—
693C2×Q8—82no—
694C2×Q8—84no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—4128no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—84no—
723C2×D4—84no—
724C2×D4—84no—
725C2×D4—84no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
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—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
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—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—48no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—82no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4C22×D412yes—
864C22×C4C22×D414yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4H(5,𝔽2)12yes—
873C22×C4H(5,𝔽2)12yes—
874C4⋊C4—28no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—84no—
888C4⋊C4—82no—
889C4⋊C4—84no—
890C4⋊C4—84no—
891C4⋊C4—84no—
892C22⋊C4—28no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—84no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C22⋊C4—82no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C42—44no—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—22no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—432no—
967C23—432no—
968C23—432no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—42no—
982C23—41no—
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—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—816no—
1042C23—816no—
1043C23—816no—
1044C23—816no—
1045C23—816no—
1046C23—816no—
1047C23—816no—
1048C23—816no—
1049C23—816no—
1050C23—816no—
1051C23—816no—
1052C23—816no—
1053C23#53414yes—
1054C23#53514yes—
1055C23#53614yes—
1056C23#56218yes—
1057C23#56218yes—
1058C23C23×D411yescharacteristic
1059C23C23×D411yescharacteristic
1060C23C2×H(5,𝔽2)12yes—
1061C23C2×H(5,𝔽2)11yescharacteristic
1062C23C2×H(5,𝔽2)11yescharacteristic
1063C23C2×H(5,𝔽2)11yescharacteristic
1064C23C2×H(5,𝔽2)12yes—
1065C23C2×H(5,𝔽2)11yescharacteristic
1066C23C2×2−1+412yes—
1067C23#58511yescharacteristic
1068C23#58512yes—
1069Q8—88no—
1070D4—416no—
1071D4—416no—
1072D4—432no—
1073D4—416no—
1074D4—816no—
1075D4—816no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—416no—
1104C2×C4—416no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—42no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
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—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—88no—
1191C2×C4—88no—
1192C2×C4—816no—
1193C2×C4D4214yes—
1194C22—24no—
1195C22—24no—
1196C22—24no—
1197C22—24no—
1198C22—28no—
1199C22—28no—
1200C22—28no—
1201C22—24no—
1202C22—28no—
1203C22—24no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—44no—
1209C22—42no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—864no—
1226C22—82no—
1227C22—82no—
1228C22—82no—
1229C22—82no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—82no—
1234C22—82no—
1235C22—82no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22#281618yescomplemented
1247C22C2×#53411yescharacteristic
1248C22C2×#53511yescharacteristic
1249C22C2×#53611yescharacteristic
1250C22C2×D4211yescharacteristic
1251C22#348411yescharacteristic
1252C22#348412yes—
1253C22#348411yescharacteristic
1254C22#348811yescharacteristic
1255C22#348811yescharacteristic
1256C22#348912yes—
1257C22#350011yescharacteristic
1258C22C2×#56212yes—
1259C22C2×#56212yes—
1260C22#353212yes—
1261C22#353312yes—
1262C22#353412yes—
1263C22#353412yes—
1264C22#353512yes—
1265C22#353612yes—
1266C22#353711yescharacteristic
1267C22#354211yescharacteristic
1268C22#354212yes—
1269C22#356112yes—
1270C4—24no—
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—44no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—82no—
1283C4—81no—
1284C4—82no—
1285C4—82no—
1286C4—82no—
1287C4—82no—
1288C4—81no—
1289C2—28no—
1290C2—82no—
1291C2—84no—
1292C2—84no—
1293C2C2×#281611yescharacteristic
1294C2#3764411yescharacteristic
1295C2#3765011yescharacteristic
1296C2#3767611yescharacteristic
1297C2#4049411yescharacteristic
1298C2#4059211yescharacteristic
1299C2#4193311yescharacteristic
1300C2#4544312yes—
1301C2#4545412yes—
1302C2#5231112yes—
1303C2#5237312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2408C2
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×#2816C2semidirect
3. C2×#2449C2semidirect
4. C22×#394C2semidirect
5. #17101C2semidirect
6. #17092C2semidirect
7. #17088C2semidirect
8. #17084C2semidirect
9. #17011C2semidirect
10. #16811C2semidirect
11. #16800C2semidirect
12. #16501C2semidirect
13. #16259C2semidirect
14. #16253C2semidirect
15. #14821C2semidirect
16. #14766C2semidirect
17. #14734C2semidirect
18. #14725C2semidirect
19. #14724C2semidirect
20. #14718C2semidirect
21. #14717C2semidirect
22. #14624C2semidirect
23. #13894C2semidirect
26. C22×C22⋊Q8C22semidirect
37. C2×#399C22semidirect
38. C2×#399C22semidirect
39. C2×#399C22semidirect
40. C2×#398C22semidirect
41. C2×#398C22semidirect
42. C2×#398C22semidirect
43. C2×#398C22semidirect
44. C2×#396C22semidirect
45. C2×#395C22semidirect
57. C2×#394C22semidirect
58. C2×#394C22semidirect
59. C2×#394C22semidirect
60. C2×#394C22semidirect
61. C2×#393C22semidirect
62. C2×#393C22semidirect
66. C2×#389C22semidirect
67. C2×#387C22semidirect
74. C2×#385C22semidirect
75. C2×#381C22semidirect
82. #1445C22semidirect
83. #1445C22semidirect
84. #1444C22semidirect
85. #1442C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
116. #1438C22semidirect
117. #1438C22semidirect
118. #1438C22semidirect
119. #1438C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
126. C22⋊#95C22semidirect
244. #394D4semidirect
1246. C22#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#28162
C2×#24082
C2×#24492
C22×#3942
#171012
#170922
#170882
#170842
#170112
#168112
#168002
#165012
#162592
#162532
#148212
#147662
#147342
#147252
#147242
#147182
#147172
#146242
#138942