Finite Group Databasebeta

← #648081

Subgroups — #648081

Order 512.

4690 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×#2447C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4C22×#390C211yesmaximal, characteristic
5#15702C212yesmaximal, complemented
6#15502C212yesmaximal, complemented
7#15497C212yesmaximal, complemented
8#15300C212yesmaximal, complemented
9#15226C211yesmaximal, characteristic, complemented
10#15217C211yesmaximal, characteristic, complemented
11#15147C211yesmaximal, characteristic, complemented
12#15138C211yesmaximal, characteristic, complemented
13#14820C212yesmaximal, complemented
14#14820C212yesmaximal, complemented
15#14702C211yesmaximal, characteristic, complemented
16#14139C211yesmaximal, characteristic, complemented
17#14027C211yesmaximal, characteristic, complemented
18#14018C211yesmaximal, characteristic, complemented
19#13916C211yesmaximal, characteristic, complemented
20#13907C211yesmaximal, characteristic, complemented
21#13877C212yesmaximal, complemented
22#13869C212yesmaximal, complemented
23C4×#380C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32C23×C22⋊C4C2212yes—
33C23×C22⋊C4C2212yes—
34C23×C42C2211yescharacteristic
35#2447—28no—
36#2435—28no—
37C2×#397C2212yescomplemented
38C2×#397C2212yescomplemented
39C2×#397C2212yescomplemented
40C2×#397C2212yescomplemented
41C2×#394C2212yes—
42C2×#394C2212yes—
43D4×C22⋊C4—28no—
44C2×#391C2211yescharacteristic, complemented
45C2×#391C2211yescharacteristic, complemented
46C2×#391C2211yescharacteristic, complemented
47C2×#391C2211yescharacteristic, complemented
48C2×#390—28no—
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2212yes—
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2212yes—
58C2×#390C2211yescharacteristic
59C2×#389C2211yescharacteristic, complemented
60C2×#389C2211yescharacteristic, complemented
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#385C2212yescomplemented
64C2×#385C2212yescomplemented
65C2×#381C2212yescomplemented
66C2×#381C2212yescomplemented
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2212yes—
71C2×#379C2212yes—
72C2×#379C2212yes—
73C2×#379C2212yes—
74C2×C4×C4⋊C4C2211yescharacteristic, complemented
75C2×C4×C4⋊C4C2211yescharacteristic, complemented
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78#1441C2212yescomplemented
79#1441C2212yescomplemented
80#1441C2212yescomplemented
81#1441C2212yescomplemented
82#1440C2212yescomplemented
83#1440C2212yescomplemented
84#1440C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1440C2212yescomplemented
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104C4⋊#95C2211yescharacteristic, complemented
105C4⋊#95C2211yescharacteristic, complemented
106C4⋊#95C2211yescharacteristic, complemented
107C4⋊#95C2211yescharacteristic, complemented
108C4⋊#95C2211yescharacteristic, complemented
109C4⋊#95C2211yescharacteristic, complemented
110C4⋊#95C2211yescharacteristic, complemented
111C4⋊#95C2211yescharacteristic, complemented
112#1434C2211yescharacteristic, complemented
113#1434C2211yescharacteristic, complemented
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2212yes—
116C22⋊#95C2212yes—
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—42no—
134C23×D4—42no—
135C23×D4D418yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C2×#124—24no—
146C2×#124—24no—
147C2×#124—24no—
148C2×#124—24no—
149C2×#124—42no—
150C2×#124—42no—
151C2×C22⋊Q8—24no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—42no—
159C2×C4×D4—42no—
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—42no—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C22⋊C4—28no—
177C22×C22⋊C4—28no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—28no—
180C22×C22⋊C4—28no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
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×C42—24no—
214C22×C42—24no—
215C22×C42—42no—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224#397—28no—
225#397—28no—
226#397—44no—
227#397—44no—
228#394—28no—
229#394—28no—
230#391—24no—
231#391—24no—
232#391—42no—
233#391—42no—
234#390—24no—
235#390—24no—
236#390—24no—
237#390—24no—
238#390—24no—
239#390—24no—
240#390—28no—
241#390—28no—
242#390—24no—
243#390D418yes—
244#389—24no—
245#389—42no—
246#386—28no—
247#386—28no—
248#385—28no—
249#385—44no—
250#381—28no—
251#381—44no—
252#380—24no—
253#380—24no—
254#380—24no—
255#380—44no—
256#379—28no—
257#379—28no—
258#379—28no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—42no—
261C4×C22⋊C4—24no—
262C4×C22⋊C4—24no—
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C25—24no—
303C25—24no—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—24no—
309C25—24no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25C2×D418yes—
317C25C2412yes—
318C25C2412yes—
319C25C2411yescharacteristic
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—232no—
330C22×D4—232no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—416no—
344C22×D4—416no—
345C22×D4—416no—
346C22×D4—416no—
347C22×D4—416no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4C2×D414yes—
351C22×D4C2×D418yes—
352C22×D4C2×D414yes—
353C22×D4C2×D414yes—
354C22×D4#4114yes—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—41no—
379C23×C4—41no—
380C23×C4—41no—
381C23×C4—41no—
382C23×C4—42no—
383C23×C4—42no—
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×C4—42no—
393C23×C4C2×D414yes—
394C23×C4#4114yes—
395C23×C4#4114yes—
396C23×C4#4114yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417#124—416no—
418#124—416no—
419C22⋊Q8—416no—
420C4×D4—416no—
421C4×D4—416no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
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—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—416no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4C2×D414yes—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
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—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
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—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
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—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—432no—
516C2×C22⋊C4—432no—
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—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—432no—
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⋊C4C2×D418yes—
547C2×C22⋊C4C2×D418yes—
548C2×C22⋊C4#4114yes—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—416no—
571C2×C42—41no—
572C2×C42—41no—
573C2×C42C2×D414yes—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—24no—
592#95—24no—
593#95—22no—
594#95—41no—
595#95—41no—
596#95—42no—
597#95—42no—
598#95—41no—
599#95—41no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
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—216no—
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—216no—
649C24—216no—
650C24—216no—
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—48no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24C22×D414yes—
683C24C22×D414yes—
684C24C22×D414yes—
685C24C22×D412yes—
686C24C2×#4114yes—
687C24C2×#4112yes—
688C24C2×#4112yes—
689C24C2×#4112yes—
690C24C2×#4112yes—
691C24H(5,𝔽2)12yes—
692C242−1+412yes—
693C24C2511yescharacteristic
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×D4—216no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—4128no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4#121116yes—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—28no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
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—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4#123116yes—
886C22×C4C22×D412yes—
887C22×C4C22×D414yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C2×#4112yes—
893C22×C4C2×#4112yes—
894C22×C4C2×#4112yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4C2×#4112yes—
900C22×C4C2×#4112yes—
901C22×C4H(5,𝔽2)12yes—
902C22×C4H(5,𝔽2)12yes—
903C22×C4H(5,𝔽2)12yes—
904C22×C4H(5,𝔽2)12yes—
905C4⋊C4—28no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—84no—
917C4⋊C4—84no—
918C22⋊C4—28no—
919C22⋊C4—216no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C42—28no—
947C42—44no—
948C42—44no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—44no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—432no—
1008C23—432no—
1009C23—432no—
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—432no—
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—816no—
1056C23—816no—
1057C23—816no—
1058C23—816no—
1059C23—816no—
1060C23—816no—
1061C23—816no—
1062C23—816no—
1063C23—816no—
1064C23—816no—
1065C23—816no—
1066C23C2×#12118yes—
1067C23C2×#12314yes—
1068C23#52914yes—
1069C23#54214yes—
1070C23#54614yes—
1071C23#54714yes—
1072C23#55614yes—
1073C23#55914yes—
1074C23C23×D411yescharacteristic
1075C23C23×D411yescharacteristic
1076C23C22×#4111yescharacteristic
1077C23C22×#4111yescharacteristic
1078C23C22×#4111yescharacteristic
1079C23C22×#4111yescharacteristic
1080C23C22×#4111yescharacteristic
1081C23C2×H(5,𝔽2)11yescharacteristic
1082C23C2×H(5,𝔽2)11yescharacteristic
1083C23C2×H(5,𝔽2)11yescharacteristic
1084C23C2×H(5,𝔽2)11yescharacteristic
1085C23C2×H(5,𝔽2)11yescharacteristic
1086C23C2×2−1+411yescharacteristic
1087C23#58511yescharacteristic
1088C23#58511yescharacteristic
1089Q8—88no—
1090D4—232no—
1091D4—432no—
1092D4—416no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—232no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—416no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—816no—
1228C2×C4—816no—
1229C2×C4—816no—
1230C2×C4C2×#12114yes—
1231C2×C4C2×#12314yes—
1232C2×C4C2×#12314yes—
1233C2×C4#53414yes—
1234C2×C4#54614yes—
1235C2×C4#54614yes—
1236C2×C4#54614yes—
1237C2×C4#55114yes—
1238C2×C4#55114yes—
1239C22—24no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—28no—
1254C22—28no—
1255C22—28no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—864no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22#244718yescomplemented
1285C22C22×#12111yescharacteristic
1286C22C22×#12311yescharacteristic
1287C22C2×#52911yescharacteristic
1288C22C2×#53411yescharacteristic
1289C22C2×#54211yescharacteristic
1290C22C2×#54611yescharacteristic
1291C22C2×#54611yescharacteristic
1292C22C2×#54611yescharacteristic
1293C22C2×#54611yescharacteristic
1294C22C2×#54711yescharacteristic
1295C22D4×#4111yescharacteristic
1296C22C2×#55111yescharacteristic
1297C22C2×#55111yescharacteristic
1298C22C2×#55611yescharacteristic
1299C22#347511yescharacteristic
1300C22C2×#55911yescharacteristic
1301C22#348111yescharacteristic
1302C22#348411yescharacteristic
1303C22#348911yescharacteristic
1304C22#349411yescharacteristic
1305C22#349411yescharacteristic
1306C22#349611yescharacteristic
1307C22#349611yescharacteristic
1308C22#350511yescharacteristic
1309C22#350811yescharacteristic
1310C22#350811yescharacteristic
1311C22#351011yescharacteristic
1312C22#351311yescharacteristic
1313C22#351411yescharacteristic
1314C22#351911yescharacteristic
1315C22#352011yescharacteristic
1316C22#353611yescharacteristic
1317C22#354211yescharacteristic
1318C22#354311yescharacteristic
1319C22#356111yescharacteristic
1320C4—24no—
1321C4—24no—
1322C4—44no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—82no—
1329C4—81no—
1330C4—82no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—82no—
1336C4—81no—
1337C4—82no—
1338C4—82no—
1339C4#241218yes—
1340C2—28no—
1341C2—48no—
1342C2—84no—
1343C2C2×#241211yescharacteristic
1344C2C2×#244711yescharacteristic
1345C2#3554111yescharacteristic
1346C2#3610711yescharacteristic
1347C2#3615311yescharacteristic
1348C2#3621411yescharacteristic
1349C2#3629311yescharacteristic
1350C2#3766411yescharacteristic
1351C2#3805411yescharacteristic
1352C2#3894911yescharacteristic
1353C2#3948611yescharacteristic
1354C2#5914311yescharacteristic
1355C2#5914811yescharacteristic
1356C2#5942411yescharacteristic
1357C2#5986211yescharacteristic
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×#2447C2semidirect
5. #15702C2semidirect
6. #15502C2semidirect
7. #15497C2semidirect
8. #15300C2semidirect
9. #15226C2semidirect
10. #15217C2semidirect
11. #15147C2semidirect
12. #15138C2semidirect
13. #14820C2semidirect
14. #14820C2semidirect
15. #14702C2semidirect
16. #14139C2semidirect
17. #14027C2semidirect
18. #14018C2semidirect
19. #13916C2semidirect
20. #13907C2semidirect
21. #13877C2semidirect
22. #13869C2semidirect
23. C4×#380C2semidirect
37. C2×#397C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
40. C2×#397C22semidirect
44. C2×#391C22semidirect
45. C2×#391C22semidirect
46. C2×#391C22semidirect
47. C2×#391C22semidirect
59. C2×#389C22semidirect
60. C2×#389C22semidirect
63. C2×#385C22semidirect
64. C2×#385C22semidirect
65. C2×#381C22semidirect
66. C2×#381C22semidirect
74. C2×C4×C4⋊C4C22semidirect
75. C2×C4×C4⋊C4C22semidirect
78. #1441C22semidirect
79. #1441C22semidirect
80. #1441C22semidirect
81. #1441C22semidirect
82. #1440C22semidirect
83. #1440C22semidirect
84. #1440C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1440C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. C4⋊#95C22semidirect
105. C4⋊#95C22semidirect
106. C4⋊#95C22semidirect
107. C4⋊#95C22semidirect
108. C4⋊#95C22semidirect
109. C4⋊#95C22semidirect
110. C4⋊#95C22semidirect
111. C4⋊#95C22semidirect
112. #1434C22semidirect
113. #1434C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
1284. C22#2447semidirect

Maximal subgroups

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

subgroupindex
C2×#24472
C2×#24352
C2×D4×C22⋊C42
C22×#3902
#157022
#155022
#154972
#153002
#152262
#152172
#151472
#151382
#148202
#147022
#141392
#140272
#140182
#139162
#139072
#138772
#138692
C4×#3802