Finite Group Databasebeta

← #704574

Subgroups — #704574

Order 512.

4584 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×#2405C211yesmaximal, characteristic
2C22×#394C211yesmaximal, characteristic
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4C2×#2315C211yesmaximal, characteristic, complemented
5#16816C212yesmaximal, complemented
6#16401C212yesmaximal, complemented
7#15383C212yesmaximal, complemented
8#15300C212yesmaximal, complemented
9#15271C212yesmaximal, complemented
10#15269C212yesmaximal, complemented
11#15129C212yesmaximal, complemented
12#14920C211yesmaximal, characteristic, complemented
13#14824C212yesmaximal, complemented
14#14728C211yesmaximal, characteristic, complemented
15#14727C211yesmaximal, characteristic, complemented
16#14727C211yesmaximal, characteristic, complemented
17#14341C211yesmaximal, characteristic, complemented
18#14044C211yesmaximal, characteristic, complemented
19#14043C211yesmaximal, characteristic, complemented
20#13877C211yesmaximal, characteristic, complemented
21#13877C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13869C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×C4×D4C2212yes—
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2405—28no—
37C2×#398C2212yescomplemented
38C2×#397C2212yescomplemented
39C2×#397C2212yescomplemented
40C2×#394—28no—
41C2×#394C2211yescharacteristic
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2211yescharacteristic
45C2×#394C2212yes—
46C2×#394C2211yescharacteristic
47C2×#394C2211yescharacteristic
48C2×#394C2212yes—
49D4×C22⋊C4—28no—
50#2315—28no—
51C2×#390C2212yes—
52C2×#389C2212yescomplemented
53C2×#386C2212yes—
54C2×#386C2211yescharacteristic
55C2×#386C2212yes—
56C2×#386C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#385C2212yescomplemented
66C2×#385C2212yescomplemented
67C2×#381C2212yescomplemented
68C2×#380C2211yescharacteristic
69C2×#380C2212yescomplemented
70C2×#380C2212yescomplemented
71C2×#380C2212yescomplemented
72C2×#380C2212yescomplemented
73C2×#380C2212yescomplemented
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C22×#95C2211yescharacteristic
81#1445C2212yescomplemented
82#1444C2212yescomplemented
83#1444C2212yescomplemented
84#1442C2212yescomplemented
85#1442C2212yescomplemented
86#1442C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1440C2212yescomplemented
99#1440C2212yescomplemented
100#1440C2212yescomplemented
101#1440C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1436C2212yescomplemented
111#1436C2212yescomplemented
112C4⋊#95C2212yescomplemented
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—44no—
132C23×D4—44no—
133C23×D4D418yes—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C2×#123—24no—
148C2×#123—24no—
149C2×#123—44no—
150C2×#123—44no—
151C2×C4×D4—28no—
152C2×C4×D4—44no—
153C2×C4×D4—44no—
154C22×C4⋊C4—24no—
155C22×C4⋊C4—44no—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C22⋊C4—24no—
170C22×C22⋊C4—24no—
171C22×C22⋊C4—24no—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4D418yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C42C2312yes—
224#398—44no—
225#397—44no—
226#397—44no—
227#394—28no—
228#394—28no—
229#394—28no—
230#394—28no—
231#394—24no—
232#394—24no—
233#394—24no—
234#394—24no—
235#390—28no—
236#389—44no—
237#386—24no—
238#386—24no—
239#386—28no—
240#386—28no—
241#385—24no—
242#385—24no—
243#385—24no—
244#385—24no—
245#385—24no—
246#385—24no—
247#385—28no—
248#385—28no—
249#385—24no—
250#385—24no—
251#381—44no—
252#380—28no—
253#380—28no—
254#380—24no—
255#380—44no—
256#380—44no—
257#380—44no—
258#379—24no—
259#379—24no—
260#379—24no—
261#379—24no—
262#379—24no—
263C4×C22⋊C4—24no—
264C2×#95—24no—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
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×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C25—22no—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—24no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25C2×D414yes—
318C25C2×D414yes—
319C25C2×D414yes—
320C25#4114yes—
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—24no—
329C22×D4—232no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—416no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—416no—
345C22×D4—432no—
346C22×D4—432no—
347C22×D4C2×D414yes—
348C22×D4C2×D414yes—
349C22×D4C2×D414yes—
350C22×D4C2×D414yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4—22no—
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—22no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
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×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4C2×D414yes—
399C23×C4C2×D418yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418#123—416no—
419#123—416no—
420C4×D4—432no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
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—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
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—416no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—232no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
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—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
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—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
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—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—416no—
540C2×C22⋊C4—416no—
541C2×C22⋊C4—416no—
542C2×C22⋊C4—416no—
543C2×C22⋊C4—416no—
544C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
556C2×C22⋊C4C2×D418yes—
557C2×C22⋊C4C2×D414yes—
558C2×C22⋊C4#4114yes—
559C2×C22⋊C4#4114yes—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—42no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
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—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—28no—
627C24—28no—
628C24—28no—
629C24—28no—
630C24—28no—
631C24—28no—
632C24—28no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—28no—
644C24—28no—
645C24—28no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—48no—
652C24—48no—
653C24—44no—
654C24—44no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24#121116yes—
682C24C22×D412yes—
683C24C22×D412yes—
684C24C22×D412yes—
685C24C22×D412yes—
686C24C22×D412yes—
687C24C22×D412yes—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C2×#4112yes—
691C24C2×#4112yes—
692C24C2×#4112yes—
693C24C2×#4112yes—
694C24C2×#4112yes—
695C24H(5,𝔽2)14yes—
696C242−1+412yes—
697C242−1+412yes—
698C24C2511yescharacteristic
699C2×D4—216no—
700C2×D4—216no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—4128no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—21no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—28no—
746C22×C4—216no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
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—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—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—44no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—48no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—82no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4—82no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4C22×D412yes—
868C22×C4C22×D414yes—
869C22×C4C22×D414yes—
870C22×C4C22×D412yes—
871C22×C4C2×#4114yes—
872C22×C4C2×#4114yes—
873C22×C4H(5,𝔽2)14yes—
874C22×C4H(5,𝔽2)14yes—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—84no—
884C4⋊C4—84no—
885C4⋊C4—84no—
886C4⋊C4—84no—
887C4⋊C4—84no—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—84no—
916C22⋊C4—82no—
917C22⋊C4—82no—
918C22⋊C4—82no—
919C22⋊C4—82no—
920C22⋊C4—82no—
921C22⋊C4—82no—
922C22⋊C4—84no—
923C22⋊C4#123116yescomplemented
924C42—48no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—22no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—232no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—416no—
990C23—416no—
991C23—416no—
992C23—416no—
993C23—416no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
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—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—416no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—88no—
1038C23—88no—
1039C23—88no—
1040C23—88no—
1041C23—88no—
1042C23—816no—
1043C23—816no—
1044C23—816no—
1045C23—816no—
1046C23—88no—
1047C23—88no—
1048C23—816no—
1049C23—816no—
1050C23—816no—
1051C23—816no—
1052C23C2×#12114yes—
1053C23C2×#12114yes—
1054C23C2×#12114yes—
1055C23C2×#12314yes—
1056C23#53414yes—
1057C23#53614yes—
1058C23#54714yes—
1059C23#54714yes—
1060C23#55214yes—
1061C23#55214yes—
1062C23C23×D411yescharacteristic
1063C23C23×D411yescharacteristic
1064C23C22×#4111yescharacteristic
1065C23C22×#4111yescharacteristic
1066C23C22×#4111yescharacteristic
1067C23C2×H(5,𝔽2)12yes—
1068C23C2×H(5,𝔽2)12yes—
1069C23C2×H(5,𝔽2)12yes—
1070C23C2×2−1+411yescharacteristic
1071C23C2×2−1+411yescharacteristic
1072C23#58512yes—
1073D4—232no—
1074D4—416no—
1075D4—416no—
1076D4—416no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—416no—
1097C2×C4—416no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
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—42no—
1182C2×C4—42no—
1183C2×C4—816no—
1184C2×C4—816no—
1185C2×C4—88no—
1186C2×C4—88no—
1187C2×C4—88no—
1188C2×C4—88no—
1189C2×C4—88no—
1190C2×C4C2×#12318yes—
1191C2×C4#53414yes—
1192C22—24no—
1193C22—24no—
1194C22—24no—
1195C22—28no—
1196C22—28no—
1197C22—28no—
1198C22—28no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—832no—
1243C22—832no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22#248618yes—
1249C22C22×#12111yescharacteristic
1250C22C22×#12311yescharacteristic
1251C22C2×#53411yescharacteristic
1252C22C2×#53411yescharacteristic
1253C22C2×#53611yescharacteristic
1254C22C2×#54711yescharacteristic
1255C22C2×#54711yescharacteristic
1256C22C2×#55211yescharacteristic
1257C22C2×#55211yescharacteristic
1258C22#348411yescharacteristic
1259C22#348412yes—
1260C22#348511yescharacteristic
1261C22#349012yes—
1262C22#349612yes—
1263C22#350512yes—
1264C22#351312yes—
1265C22#351412yes—
1266C22#351912yes—
1267C22#351912yes—
1268C22#353512yes—
1269C22#353612yes—
1270C22#353612yes—
1271C22#356112yes—
1272C4—28no—
1273C4—24no—
1274C4—44no—
1275C4—44no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—82no—
1280C4—81no—
1281C4—81no—
1282C4—82no—
1283C4—82no—
1284C4—81no—
1285C4—82no—
1286C4—81no—
1287C4—82no—
1288C4—81no—
1289C4—81no—
1290C2—28no—
1291C2—44no—
1292C2—44no—
1293C2—44no—
1294C2—82no—
1295C2C2×#248611yescharacteristic
1296C2#3498111yescharacteristic
1297C2#3535811yescharacteristic
1298C2#3571312yes—
1299C2#3803611yescharacteristic
1300C2#3803811yescharacteristic
1301C2#3891611yescharacteristic
1302C2#3891811yescharacteristic
1303C2#4048712yes—
1304C2#4304912yes—
1305C2#4307612yes—
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
4. C2×#2315C2semidirect
5. #16816C2semidirect
6. #16401C2semidirect
7. #15383C2semidirect
8. #15300C2semidirect
9. #15271C2semidirect
10. #15269C2semidirect
11. #15129C2semidirect
12. #14920C2semidirect
13. #14824C2semidirect
14. #14728C2semidirect
15. #14727C2semidirect
16. #14727C2semidirect
17. #14341C2semidirect
18. #14044C2semidirect
19. #14043C2semidirect
20. #13877C2semidirect
21. #13877C2semidirect
22. #13877C2semidirect
23. #13869C2semidirect
37. C2×#398C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
52. C2×#389C22semidirect
65. C2×#385C22semidirect
66. C2×#385C22semidirect
67. C2×#381C22semidirect
69. C2×#380C22semidirect
70. C2×#380C22semidirect
71. C2×#380C22semidirect
72. C2×#380C22semidirect
73. C2×#380C22semidirect
81. #1445C22semidirect
82. #1444C22semidirect
83. #1444C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1440C22semidirect
99. #1440C22semidirect
100. #1440C22semidirect
101. #1440C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. C4⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
923. C22⋊C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C22×#3942
C2×D4×C22⋊C42
C2×#23152
#168162
#164012
#153832
#153002
#152712
#152692
#151292
#149202
#148242
#147282
#147272
#143412
#140442
#140432
#138772
#138692