Finite Group Databasebeta

← #1393474

Subgroups — #1393474

Order 512.

4482 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2417C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C22×#399C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic
5#17071C211yesmaximal, characteristic, complemented
6#16814C211yesmaximal, characteristic, complemented
7#16600C211yesmaximal, characteristic, complemented
8#16555C212yesmaximal, complemented
9#16521C212yesmaximal, complemented
10#16398C211yesmaximal, characteristic, complemented
11#16323C212yesmaximal, complemented
12#16298C212yesmaximal, complemented
13#15161C211yesmaximal, characteristic, complemented
14#14777C211yesmaximal, characteristic, complemented
15#14759C211yesmaximal, characteristic, complemented
16#14734C211yesmaximal, characteristic, complemented
17#14729C212yesmaximal, complemented
18#14726C212yesmaximal, complemented
19#14717C211yesmaximal, characteristic, complemented
20#14317C211yesmaximal, characteristic, complemented
21#14015C212yesmaximal, complemented
22#13899C211yesmaximal, characteristic, complemented
23#13867C212yesmaximal
24C24×D4C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic, complemented
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic, complemented
30C23×C4⋊C4C2212yescomplemented
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2212yes—
34#2626—28no—
35#2417—28no—
36C2×#399—28no—
37C2×#399C2211yescharacteristic
38C2×#399C2212yes—
39C2×#399C2211yescharacteristic
40C2×#399C2211yescharacteristic, complemented
41C2×#399C2212yescomplemented
42C2×#399C2211yescharacteristic, complemented
43C2×#399C2211yescharacteristic, complemented
44C2×#399C2211yescharacteristic, complemented
45C2×#398C2212yescomplemented
46C2×#396C2212yes—
47C2×#396C2212yescomplemented
48C2×#396C2212yescomplemented
49C2×#396C2212yescomplemented
50C2×#396C2212yescomplemented
51C2×#393C2211yescharacteristic
52C2×#393C2211yescharacteristic, complemented
53C2×#393C2211yescharacteristic, complemented
54D4×C22⋊C4—28no—
55C2×#391C2211yescharacteristic, complemented
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic, complemented
59C2×#386C2211yescharacteristic
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#385C2212yescomplemented
70C2×#385C2212yescomplemented
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic, complemented
73C2×#380C2211yescharacteristic, complemented
74C2×#380C2212yescomplemented
75C2×#379C2212yes—
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2212yes—
79C2×#379C2212yes—
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2211yescharacteristic, complemented
82#1446C2211yescharacteristic, complemented
83#1445C2211yescharacteristic, complemented
84#1445C2211yescharacteristic, complemented
85#1444C2212yescomplemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1442C2211yescharacteristic, complemented
89#1442C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1439C2212yes—
96#1439C2212yes—
97#1439C2211yescharacteristic
98#1439C2212yes—
99#1439C2212yes—
100#1439C2211yescharacteristic, complemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2211yescharacteristic, complemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119C4⋊#95C2211yescharacteristic, complemented
120#1434C2211yescharacteristic, complemented
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic, complemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4Q818yescomplemented
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—44no—
150C2×C22⋊Q8—42no—
151C2×C4×D4—24no—
152C2×C4×D4—44no—
153C2×C4×D4—44no—
154C2×C4×D4D418yes—
155C22×C4⋊C4—24no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4—28no—
158C22×C4⋊C4—42no—
159C22×C4⋊C4—44no—
160C22×C4⋊C4—44no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
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—28no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223#399—24no—
224#399—24no—
225#399—28no—
226#399—24no—
227#399—28no—
228#399—24no—
229#399—42no—
230#399D418yescomplemented
231#398—28no—
232#396—28no—
233#396—28no—
234#396—28no—
235#396—44no—
236#396—44no—
237#393—24no—
238#393—24no—
239#393—42no—
240#391—24no—
241#390—24no—
242#390—24no—
243#389—24no—
244#386—28no—
245#386—28no—
246#386—24no—
247#386—24no—
248#386—24no—
249#386—24no—
250#386—44no—
251#386—44no—
252#385—28no—
253#385—44no—
254#385—44no—
255#385—44no—
256#380—24no—
257#380—24no—
258#380—28no—
259#380—24no—
260#379—24no—
261#379—24no—
262#379—28no—
263#379—44no—
264#379—44no—
265C4×C22⋊C4—24no—
266C2×#95—24no—
267C2×#95C2312yes—
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
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—22no—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—24no—
306C25—24no—
307C25—22no—
308C25—22no—
309C25—41no—
310C25—42no—
311C25—41no—
312C25—42no—
313C25—42no—
314C25—41no—
315C25—42no—
316C25—41no—
317C25—42no—
318C25—42no—
319C25C2×Q814yes—
320C25C2×Q814yes—
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—42no—
330C22×Q8—42no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—232no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—432no—
347C22×D4—416no—
348C22×D4—416no—
349C22×D4—432no—
350C22×D4C2×D414yes—
351C22×D4C2×Q814yes—
352C22×D4C2×Q814yes—
353C22×D4C2×Q814yes—
354C22×D4C2×Q814yes—
355C22×D4#4114yes—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—24no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—41no—
383C23×C4—41no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4C2×D414yes—
393C23×C4C2×D414yes—
394C23×C4C2×Q814yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C22⋊Q8—416no—
414C22⋊Q8—416no—
415C4×D4—416no—
416C4×D4—416no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—416no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—432no—
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⋊C4C2×D414yes—
465C2×C4⋊C4C2×D414yescomplemented
466C2×C4⋊C4C2×D418yescomplemented
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
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—22no—
486C2×C22⋊C4—22no—
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—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—416no—
517C2×C22⋊C4—416no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—432no—
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⋊C4C2×D414yes—
561C2×C22⋊C4C2×D414yes—
562C2×C22⋊C4C2×D418yes—
563C2×C22⋊C4C2×D414yes—
564C2×C42—22no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42C2×D414yes—
568#95—24no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—24no—
573#95—22no—
574#95—22no—
575#95—24no—
576#95—22no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
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#95C2×D414yescomplemented
600C24—21no—
601C24—21no—
602C24—22no—
603C24—21no—
604C24—21no—
605C24—22no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—22no—
610C24—21no—
611C24—22no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—21no—
618C24—21no—
619C24—22no—
620C24—21no—
621C24—22no—
622C24—28no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—28no—
644C24—28no—
645C24—216no—
646C24—28no—
647C24—48no—
648C24—48no—
649C24—44no—
650C24—44no—
651C24—48no—
652C24—44no—
653C24—48no—
654C24—44no—
655C24—44no—
656C24—48no—
657C24—44no—
658C24—44no—
659C24—48no—
660C24—48no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—48no—
667C24—44no—
668C24—44no—
669C24—48no—
670C24—82no—
671C24—82no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—82no—
679C24—84no—
680C24—82no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C22×Q812yes—
692C24C22×Q812yes—
693C24C22×Q812yes—
694C24C22×Q812yes—
695C24C22×Q812yes—
696C24C2×#4112yes—
697C24C2×#4112yes—
698C24H(5,𝔽2)14yes—
699C24H(5,𝔽2)14yes—
700C242−1+412yes—
701C24C2511yescharacteristic
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—84no—
706C2×Q8—84no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—216no—
710C2×D4—216no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—48no—
720C2×D4—4128no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—48no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4C22⋊Q8116yes—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—216no—
733C22×C4—28no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
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—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
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—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—82no—
854C22×C4—82no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D414yes—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4C22×D414yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×Q812yes—
869C22×C4C22×Q812yes—
870C22×C4C2×#4112yes—
871C22×C4H(5,𝔽2)14yes—
872C22×C4H(5,𝔽2)12yes—
873C4⋊C4—28no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—84no—
886C4⋊C4—84no—
887C4⋊C4—84no—
888C4⋊C4—84no—
889C4⋊C4—84no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—84no—
912C22⋊C4—82no—
913C22⋊C4—82no—
914C22⋊C4—84no—
915C22⋊C4—82no—
916C22⋊C4—82no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C42—44no—
925C42—44no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—22no—
931C23—24no—
932C23—22no—
933C23—22no—
934C23—24no—
935C23—22no—
936C23—24no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—24no—
964C23—22no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—22no—
976C23—24no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—432no—
981C23—416no—
982C23—416no—
983C23—416no—
984C23—41no—
985C23—41no—
986C23—42no—
987C23—42no—
988C23—41no—
989C23—42no—
990C23—41no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—416no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—41no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
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—816no—
1040C23—88no—
1041C23—816no—
1042C23—88no—
1043C23—88no—
1044C23—88no—
1045C23—816no—
1046C23—816no—
1047C23—88no—
1048C23—88no—
1049C23—816no—
1050C23—88no—
1051C23—88no—
1052C23—816no—
1053C23—816no—
1054C23—88no—
1055C23—88no—
1056C23C2×C22⋊Q814yes—
1057C23C2×C22⋊Q814yes—
1058C23#53414yes—
1059C23#53514yes—
1060C23#53818yes—
1061C23#54318yes—
1062C23D4×Q814yes—
1063C23C23×D411yescharacteristic
1064C23C23×D411yescharacteristic
1065C23C23×Q811yescharacteristic
1066C23C22×#4111yescharacteristic
1067C23C2×H(5,𝔽2)12yes—
1068C23C2×H(5,𝔽2)12yes—
1069C23C2×H(5,𝔽2)11yescharacteristic
1070C23C2×H(5,𝔽2)12yes—
1071C23C2×2−1+411yescharacteristic
1072C23#58511yescharacteristic
1073C23#58512yes—
1074Q8—88no—
1075D4—232no—
1076D4—416no—
1077D4—416no—
1078D4—416no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—416no—
1110C2×C4—416no—
1111C2×C4—432no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
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—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
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—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—88no—
1187C2×C4—816no—
1188C2×C4—88no—
1189C2×C4—88no—
1190C2×C4C2×C22⋊Q814yes—
1191C2×C4D4214yes—
1192C22—24no—
1193C22—24no—
1194C22—28no—
1195C22—28no—
1196C22—28no—
1197C22—28no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—28no—
1203C22—24no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—832no—
1235C22—832no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22#262618yescomplemented
1249C22C22×C22⋊Q811yescharacteristic
1250C22C2×#53411yescharacteristic
1251C22C2×#53511yescharacteristic
1252C22C2×#53812yes—
1253C22C2×#54312yes—
1254C22C2×D4211yescharacteristic
1255C22C2×D4×Q811yescharacteristic
1256C22D4×#4111yescharacteristic
1257C22#348412yes—
1258C22#348511yescharacteristic
1259C22#348812yes—
1260C22#348911yescharacteristic
1261C22#349811yescharacteristic
1262C22#350112yes—
1263C22#350111yescharacteristic
1264C22#351312yes—
1265C22#352011yescharacteristic
1266C22#353312yes—
1267C22#353412yes—
1268C22#353412yes—
1269C22#353512yes—
1270C22#353612yes—
1271C22#354312yes—
1272C4—24no—
1273C4—24no—
1274C4—42no—
1275C4—42no—
1276C4—44no—
1277C4—42no—
1278C4—44no—
1279C4—44no—
1280C4—42no—
1281C4—42no—
1282C4—82no—
1283C4—81no—
1284C4—81no—
1285C4—82no—
1286C4—82no—
1287C4—82no—
1288C4—81no—
1289C4—82no—
1290C2—28no—
1291C2—44no—
1292C2—44no—
1293C2—82no—
1294C2—82no—
1295C2C2×#262611yescharacteristic
1296C2#3583611yescharacteristic
1297C2D4×C22⋊Q811yescharacteristic
1298C2#3764611yescharacteristic
1299C2#3767411yescharacteristic
1300C2#3768412yes—
1301C2#3771312yes—
1302C2#4061212yes—
1303C2#4081712yes—
1304C2#4140711yescharacteristic
1305C2#4195211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2417C2semidirect
2. C2×#2626C2semidirect
3. C22×#399C2semidirect
5. #17071C2semidirect
6. #16814C2semidirect
7. #16600C2semidirect
8. #16555C2semidirect
9. #16521C2semidirect
10. #16398C2semidirect
11. #16323C2semidirect
12. #16298C2semidirect
13. #15161C2semidirect
14. #14777C2semidirect
15. #14759C2semidirect
16. #14734C2semidirect
17. #14729C2semidirect
18. #14726C2semidirect
19. #14717C2semidirect
20. #14317C2semidirect
21. #14015C2semidirect
22. #13899C2semidirect
25. C22×C22⋊Q8C22semidirect
26. C22×C22⋊Q8C22semidirect
29. C23×C4⋊C4C22semidirect
30. C23×C4⋊C4C22semidirect
40. C2×#399C22semidirect
41. C2×#399C22semidirect
42. C2×#399C22semidirect
43. C2×#399C22semidirect
44. C2×#399C22semidirect
45. C2×#398C22semidirect
47. C2×#396C22semidirect
48. C2×#396C22semidirect
49. C2×#396C22semidirect
50. C2×#396C22semidirect
52. C2×#393C22semidirect
53. C2×#393C22semidirect
55. C2×#391C22semidirect
58. C2×#389C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
72. C2×#380C22semidirect
73. C2×#380C22semidirect
74. C2×#380C22semidirect
81. C22×#95C22semidirect
82. #1446C22semidirect
83. #1445C22semidirect
84. #1445C22semidirect
85. #1444C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
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
117. #1436C22semidirect
118. #1436C22semidirect
119. C4⋊#95C22semidirect
120. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
134. C23×D4Q8semidirect
230. #399D4semidirect
465. C2×C4⋊C4C2×D4semidirect
466. C2×C4⋊C4C2×D4semidirect
599. #95C2×D4semidirect
1248. C22#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#24172
C2×#26262
C22×#3992
C2×D4×C22⋊C42
#170712
#168142
#166002
#165552
#165212
#163982
#163232
#162982
#151612
#147772
#147592
#147342
#147292
#147262
#147172
#143172
#140152
#138992
#138672