Finite Group Databasebeta

← #518137

Subgroups — #518137

Order 512.

4790 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#551C211yesmaximal, characteristic
2C2×#2343C211yesmaximal, characteristic, complemented
3C2×#2274C211yesmaximal, characteristic, complemented
4#14291C211yesmaximal, characteristic, complemented
5#14288C211yesmaximal, characteristic, complemented
6#14256C211yesmaximal, characteristic, complemented
7#14166C211yesmaximal, characteristic, complemented
8#14153C211yesmaximal, characteristic, complemented
9#14135C211yesmaximal, characteristic, complemented
10#14101C212yesmaximal, complemented
11#14099C212yesmaximal, complemented
12#14095C212yesmaximal, complemented
13#14095C212yesmaximal, complemented
14#14052C212yesmaximal, complemented
15#13995C212yesmaximal
16#13941C211yesmaximal, characteristic, complemented
17#13938C211yesmaximal, characteristic, complemented
18#13868C211yesmaximal, characteristic, complemented
19#13852C211yesmaximal, characteristic, complemented
20#13847C211yesmaximal, characteristic, complemented
21C2×#1439C211yesmaximal, characteristic, complemented
22#13813C212yesmaximal, complemented
23C22⋊C42C212yesmaximal, complemented
24C2×#551—28no—
25C2×#551—28no—
26C2×#551C4116yescomplemented
27C22×#126C2211yescharacteristic
28C22×#126C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#123C2211yescharacteristic
32C22×#123C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×#120C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C22×#117C2211yescharacteristic
40C22×#117C2211yescharacteristic
41C23×C4⋊C4C2211yescharacteristic
42C23×C22⋊C4C2211yescharacteristic
43C23×C22⋊C4C2211yescharacteristic
44C23×C22⋊C4C2212yes—
45#2343—28no—
46C2×#391C2212yescomplemented
47C2×#390C2212yes—
48C2×#390C2212yes—
49C2×#387C2212yescomplemented
50C2×#387C2212yescomplemented
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#385C2212yes—
54C2×#383C2211yescharacteristic, complemented
55C2×#382C2211yescharacteristic, complemented
56C2×#381C2211yescharacteristic
57C2×#379C2212yes—
58#2274—28no—
59C2×C4×C4⋊C4C2212yescomplemented
60C2×C4×C4⋊C4C2212yescomplemented
61C2×C4×C4⋊C4C2211yescharacteristic, complemented
62C2×C4×C4⋊C4C2211yescharacteristic, complemented
63C2×C4×C4⋊C4C2211yescharacteristic, complemented
64C2×C4×C4⋊C4C2211yescharacteristic, complemented
65C2×C4×C4⋊C4C2211yescharacteristic, complemented
66C2×C4×C22⋊C4C2212yes—
67C2×C4×C22⋊C4C2212yes—
68C2×C4×C22⋊C4C2212yes—
69C2×C4×C22⋊C4C2212yes—
70C2×C4×C22⋊C4C2212yes—
71C2×C4×C22⋊C4C2212yescomplemented
72C2×#376C2211yescharacteristic, complemented
73C22×#95C2211yescharacteristic
74C22×#95C2212yes—
75#1446C2212yescomplemented
76#1445C2212yescomplemented
77#1441C2212yescomplemented
78#1441C2212yescomplemented
79#1441C2212yescomplemented
80#1441C2211yescharacteristic, complemented
81#1441C2211yescharacteristic, complemented
82#1441C2211yescharacteristic, complemented
83#1441C2211yescharacteristic, complemented
84#1439C2212yes—
85#1439C2212yes—
86#1439C2211yescharacteristic
87#1439C2211yescharacteristic
88#1439C2211yescharacteristic
89#1439C2211yescharacteristic
90#1439C2212yes—
91#1439C2212yes—
92#1439C2211yescharacteristic
93#1439C2211yescharacteristic
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2212yescomplemented
97#1439C2211yescharacteristic, complemented
98#1439C2211yescharacteristic, complemented
99#1439C2211yescharacteristic, complemented
100#1439C2211yescharacteristic, complemented
101#1438C2212yes—
102#1438C2212yes—
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1437C2212yes—
109#1437C2212yes—
110#1437C2212yes—
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119C4⋊#95C2212yescomplemented
120#1434C2212yescomplemented
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yescomplemented
127C4×#95C2212yescomplemented
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C24×C4C2312yes—
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140#551—2128no—
141C2×#126—24no—
142C2×#126—24no—
143C2×#126—24no—
144C2×#126—24no—
145C2×#126C2×C418yescomplemented
146C2×#126C2×C418yescomplemented
147C2×#124—24no—
148C2×#124—24no—
149C2×#124C2×C418yescomplemented
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—24no—
153C2×#123—24no—
154C2×#123—24no—
155C2×#123—24no—
156C2×#123C2×C418yes—
157C2×#123C2×C418yescomplemented
158C2×#123C2×C418yescomplemented
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—24no—
163C2×C22⋊Q8C2×C418yes—
164C2×C22⋊Q8C2×C418yescomplemented
165C2×#120—24no—
166C2×#120—24no—
167C2×#120C2×C418yes—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4—24no—
171C2×C4×D4—24no—
172C2×C4×D4C2×C418yes—
173C2×C4×D4C2×C418yescomplemented
174C2×#117—24no—
175C2×#117—28no—
176C2×#117—24no—
177C2×#117—24no—
178C2×#117C2×C418yes—
179C2×#117C2×C418yescomplemented
180C2×#117D418yes—
181C2×#117D418yes—
182C22×C4⋊C4—24no—
183C22×C4⋊C4—28no—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C22⋊C4—24no—
200C22×C22⋊C4—24no—
201C22×C22⋊C4—24no—
202C22×C22⋊C4—24no—
203C22×C22⋊C4—28no—
204C22×C22⋊C4—44no—
205C22×C22⋊C4—44no—
206C22×C22⋊C4C2×C418yes—
207C22×C22⋊C4C2×C418yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2312yes—
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2312yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2312yes—
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246#391—44no—
247#390—44no—
248#390—44no—
249#387—28no—
250#387—28no—
251#386—28no—
252#386—28no—
253#385—28no—
254#383—24no—
255#382—24no—
256#381—24no—
257#379—28no—
258C4×C4⋊C4—28no—
259C4×C4⋊C4—28no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—24no—
262C4×C4⋊C4—24no—
263C4×C4⋊C4—24no—
264C4×C4⋊C4—24no—
265C4×C22⋊C4—28no—
266C4×C22⋊C4—28no—
267C4×C22⋊C4—28no—
268C4×C22⋊C4—44no—
269C4×C22⋊C4—44no—
270C4×C22⋊C4—44no—
271#376—24no—
272C2×#95—24no—
273C2×#95—44no—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—24no—
313C25—24no—
314C25—42no—
315C25—42no—
316C25—41no—
317C25—41no—
318C25C22×C414yes—
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—42no—
326C22×Q8—42no—
327C22×Q8C22×C414yes—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4C22×C414yes—
343C22×D4C22×C414yes—
344C22×D4C22×C414yes—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4C22×C414yes—
379C23×C4C22×C414yes—
380C23×C4C22×C414yes—
381C23×C4C22×C414yes—
382C23×C4C22×C414yes—
383C23×C4C2×D414yes—
384C23×C4C2×D414yes—
385C23×C4#4118yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405#126—232no—
406#126—232no—
407#124—232no—
408#123—232no—
409#123—232no—
410#123—232no—
411C22⋊Q8—232no—
412C22⋊Q8—232no—
413#120—232no—
414C4×D4—232no—
415C4×D4—232no—
416#117—232no—
417#117—232no—
418#117C22⋊C4164yescomplemented
419C2×C4⋊C4—232no—
420C2×C4⋊C4—24no—
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—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4C22×C414yes—
450C2×C4⋊C4C22×C414yes—
451C2×C4⋊C4C22×C414yes—
452C2×C4⋊C4C22×C414yes—
453C2×C4⋊C4C22×C414yes—
454C2×C4⋊C4C22×C414yes—
455C2×C4⋊C4C22×C414yes—
456C2×C4⋊C4C22×C414yes—
457C2×C4⋊C4C2×D414yes—
458C2×C4⋊C4C2×D414yes—
459C2×C4⋊C4C2×D414yes—
460C2×C4⋊C4C2×D414yes—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—232no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
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—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—232no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—432no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4C22×C414yes—
530C2×C22⋊C4C22×C414yes—
531C2×C22⋊C4C22×C414yes—
532C2×C22⋊C4C22×C414yes—
533C2×C22⋊C4C22×C414yes—
534C2×C22⋊C4C22×C414yes—
535C2×C22⋊C4C22×C414yes—
536C2×C22⋊C4C22×C414yes—
537C2×C22⋊C4C22×C414yes—
538C2×C22⋊C4C22×C414yes—
539C2×C22⋊C4C22×C414yes—
540C2×C22⋊C4C22×C414yes—
541C2×C22⋊C4C22×C414yes—
542C2×C22⋊C4C22×C414yes—
543C2×C22⋊C4C2×D414yes—
544C2×C22⋊C4C2×D414yes—
545C2×C22⋊C4C2×D414yes—
546C2×C22⋊C4C2×D414yes—
547C2×C22⋊C4#4118yes—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—24no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—24no—
558C2×C42—24no—
559C2×C42—24no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42C22×C414yes—
572C2×C42C22×C414yes—
573C2×C42C22×C414yes—
574C2×C42C2×D414yes—
575C2×C42C2×D414yes—
576C2×C42C2×D414yes—
577C2×C42C2×D414yes—
578#95—22no—
579#95—22no—
580#95—24no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—42no—
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—
612C24—22no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—21no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—28no—
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—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—28no—
648C24—216no—
649C24—44no—
650C24—48no—
651C24—48no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—44no—
660C24—44no—
661C24—48no—
662C24—84no—
663C24—82no—
664C24—82no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24C23×C412yes—
670C24C23×C412yes—
671C24C23×C412yes—
672C24C23×C412yes—
673C24C22×D412yes—
674C24C22×D412yes—
675C24C2×#4114yes—
676C24C2×#4114yes—
677C24H(5,𝔽2)12yes—
678C242−1+412yes—
679C24C2511yescharacteristic
680C2×Q8—28no—
681C2×Q8—48no—
682C2×Q8—84no—
683C2×Q8—82no—
684C2×Q8—82no—
685C2×D4—28no—
686C2×D4—216no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—48no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—84no—
700C2×D4—82no—
701C2×D4—82no—
702C22×C4—216no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—216no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—22no—
722C22×C4—28no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
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—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—28no—
776C22×C4—216no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—44no—
802C22×C4—48no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—84no—
816C22×C4—84no—
817C22×C4—82no—
818C22×C4—82no—
819C22×C4—82no—
820C22×C4—82no—
821C22×C4—84no—
822C22×C4—84no—
823C22×C4—84no—
824C22×C4—84no—
825C22×C4—84no—
826C22×C4—82no—
827C22×C4—82no—
828C22×C4—84no—
829C22×C4—84no—
830C22×C4—84no—
831C22×C4C2×C22⋊C4116yes—
832C22×C4C23×C412yes—
833C22×C4C23×C412yes—
834C22×C4C23×C412yes—
835C22×C4C23×C412yes—
836C22×C4C23×C412yes—
837C22×C4C23×C412yes—
838C22×C4C23×C412yes—
839C22×C4C23×C412yes—
840C22×C4C23×C412yes—
841C22×C4C23×C412yes—
842C22×C4C23×C412yes—
843C22×C4C22×D412yes—
844C22×C4C22×D412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×D412yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C2×#4114yes—
856C22×C4C2×#4114yes—
857C22×C4C2×#4114yes—
858C22×C4C2×#4114yes—
859C22×C4H(5,𝔽2)14yes—
860C4⋊C4—216no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—48no—
872C4⋊C4—84no—
873C4⋊C4C2×C22⋊C4116yescomplemented
874C4⋊C4C2×C22⋊C4116yescomplemented
875C22⋊C4—216no—
876C22⋊C4—28no—
877C22⋊C4—216no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—84no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4C2×C22⋊C4116yes—
902C22⋊C4C2×C22⋊C4116yes—
903C42—216no—
904C42—28no—
905C42—48no—
906C42—84no—
907C42—84no—
908C42—84no—
909C42—84no—
910C42—84no—
911C42C2×C22⋊C4116yescomplemented
912C42C2×C22⋊C4116yescomplemented
913C23—22no—
914C23—22no—
915C23—24no—
916C23—24no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—22no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—22no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—416no—
954C23—432no—
955C23—41no—
956C23—41no—
957C23—42no—
958C23—42no—
959C23—41no—
960C23—41no—
961C23—42no—
962C23—42no—
963C23—42no—
964C23—42no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—41no—
973C23—41no—
974C23—42no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
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—416no—
1002C23—816no—
1003C23—88no—
1004C23—88no—
1005C23—88no—
1006C23—816no—
1007C23—88no—
1008C23—88no—
1009C23—816no—
1010C23C22×C22⋊C414yes—
1011C23C4×#4118yes—
1012C23#52014yes—
1013C23#52514yes—
1014C23#52514yes—
1015C23#53218yes—
1016C23C24×C411yescharacteristic
1017C23C23×D411yescharacteristic
1018C23C23×D411yescharacteristic
1019C23C22×#4112yes—
1020C23C22×#4112yes—
1021C23C2×H(5,𝔽2)11yescharacteristic
1022C23C2×H(5,𝔽2)12yes—
1023C23C2×2−1+411yescharacteristic
1024C23#58511yescharacteristic
1025C23#58511yescharacteristic
1026C23#58512yes—
1027Q8—88no—
1028D4—416no—
1029D4—416no—
1030D4—88no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—232no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—416no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—42no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
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—42no—
1124C2×C4—42no—
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—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—88no—
1145C2×C4—88no—
1146C2×C4—816no—
1147C2×C4—88no—
1148C2×C4—816no—
1149C2×C4C22×C22⋊C414yes—
1150C2×C4C22×C22⋊C414yes—
1151C2×C4C22×C22⋊C414yes—
1152C2×C4C22×C22⋊C414yes—
1153C2×C4C22×C22⋊C414yes—
1154C2×C4C22×C22⋊C414yes—
1155C22—28no—
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—28no—
1160C22—24no—
1161C22—24no—
1162C22—24no—
1163C22—28no—
1164C22—28no—
1165C22—24no—
1166C22—28no—
1167C22—44no—
1168C22—42no—
1169C22—42no—
1170C22—44no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—44no—
1176C22—44no—
1177C22—44no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—44no—
1185C22—44no—
1186C22—832no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—82no—
1192C22—82no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—82no—
1198C22—82no—
1199C22#229718yes—
1200C22C23×C22⋊C411yescharacteristic
1201C22C2×C4×#4112yes—
1202C22C2×#52011yescharacteristic
1203C22#342811yescharacteristic
1204C22C4×H(5,𝔽2)12yes—
1205C22C2×#52511yescharacteristic
1206C22C2×#52511yescharacteristic
1207C22C2×#53212yes—
1208C22#348811yescharacteristic
1209C22#348811yescharacteristic
1210C22#348812yes—
1211C22#348911yescharacteristic
1212C22#348911yescharacteristic
1213C22#349012yes—
1214C22#349512yes—
1215C22#349811yescharacteristic
1216C22#350011yescharacteristic
1217C22#350512yes—
1218C22#351012yes—
1219C22#351312yes—
1220C22#351312yes—
1221C22#352012yes—
1222C22#352112yes—
1223C4—24no—
1224C4—24no—
1225C4—24no—
1226C4—24no—
1227C4—24no—
1228C4—24no—
1229C4—44no—
1230C4—44no—
1231C4—42no—
1232C4—44no—
1233C4—44no—
1234C4—44no—
1235C4—42no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—82no—
1240C4—82no—
1241C4—82no—
1242C2—28no—
1243C2—44no—
1244C2—82no—
1245C2—82no—
1246C2C2×#229711yescharacteristic
1247C2#3417511yescharacteristic
1248C2#3425811yescharacteristic
1249C2#3429612yes—
1250C2#3431512yes—
1251C2#3568311yescharacteristic
1252C2#3573212yes—
1253C2#3582512yes—
1254C2#3597911yescharacteristic
1255C2#3599011yescharacteristic
1256C2#3607911yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#120C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2343C2semidirect
3. C2×#2274C2semidirect
4. #14291C2semidirect
5. #14288C2semidirect
6. #14256C2semidirect
7. #14166C2semidirect
8. #14153C2semidirect
9. #14135C2semidirect
10. #14101C2semidirect
11. #14099C2semidirect
12. #14095C2semidirect
13. #14095C2semidirect
14. #14052C2semidirect
16. #13941C2semidirect
17. #13938C2semidirect
18. #13868C2semidirect
19. #13852C2semidirect
20. #13847C2semidirect
21. C2×#1439C2semidirect
22. #13813C2semidirect
23. C22⋊C42C2semidirect
26. C2×#551C4semidirect
46. C2×#391C22semidirect
49. C2×#387C22semidirect
50. C2×#387C22semidirect
54. C2×#383C22semidirect
55. C2×#382C22semidirect
59. C2×C4×C4⋊C4C22semidirect
60. C2×C4×C4⋊C4C22semidirect
61. C2×C4×C4⋊C4C22semidirect
62. C2×C4×C4⋊C4C22semidirect
63. C2×C4×C4⋊C4C22semidirect
64. C2×C4×C4⋊C4C22semidirect
65. C2×C4×C4⋊C4C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×#376C22semidirect
75. #1446C22semidirect
76. #1445C22semidirect
77. #1441C22semidirect
78. #1441C22semidirect
79. #1441C22semidirect
80. #1441C22semidirect
81. #1441C22semidirect
82. #1441C22semidirect
83. #1441C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. C4⋊#95C22semidirect
120. #1434C22semidirect
126. C22⋊#95C22semidirect
127. C4×#95C22semidirect
145. C2×#126C2×C4semidirect
146. C2×#126C2×C4semidirect
149. C2×#124C2×C4semidirect
157. C2×#123C2×C4semidirect
158. C2×#123C2×C4semidirect
164. C2×C22⋊Q8C2×C4semidirect
173. C2×C4×D4C2×C4semidirect
179. C2×#117C2×C4semidirect
418. #117C22⋊C4semidirect
873. C4⋊C4C2×C22⋊C4semidirect
874. C4⋊C4C2×C22⋊C4semidirect
911. C42C2×C22⋊C4semidirect
912. C42C2×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5512
C2×#23432
C2×#22742
#142912
#142882
#142562
#141662
#141532
#141352
#141012
#140992
#140952
#140522
#139952
#139412
#139382
#138682
#138522
#138472
C2×#14392
#138132
C22⋊C422