Finite Group Databasebeta

← #535281

Subgroups — #535281

Order 512.

6804 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#534C211yesmaximal, characteristic
2C2×#2359C212yesmaximal, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#2309C211yesmaximal, characteristic, complemented
5#14418C212yesmaximal, complemented
6#14361C212yesmaximal, complemented
7#14360C212yesmaximal, complemented
8#14358C212yesmaximal, complemented
9#14135C212yesmaximal, complemented
10#14100C212yesmaximal, complemented
11#14095C212yesmaximal, complemented
12#13998C212yesmaximal, complemented
13#13995C212yesmaximal, complemented
14#13995C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16#13877C211yesmaximal, characteristic, complemented
17#13867C211yesmaximal, characteristic, complemented
18C2×#1438C211yesmaximal, characteristic, complemented
19C22⋊C42C211yesmaximal, characteristic, complemented
20C24×D4C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C2×#534—216no—
23C2×#534C4116yescomplemented
24C22×#123C2212yes—
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#121C2212yes—
28C22×#121C2212yes—
29C22×#120C2211yescharacteristic
30C22×#120C2212yes—
31C22×#120C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×#117C2212yescomplemented
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic, complemented
38C23×C22⋊C4C2212yescomplemented
39#2359—216no—
40D4×C22⋊C4—28no—
41#2309—28no—
42C2×#390C2212yes—
43C2×#390C2212yes—
44C2×#390C2212yescomplemented
45C2×#390C2212yescomplemented
46C2×#390C2212yescomplemented
47C2×#390C2212yescomplemented
48C2×#390C2212yescomplemented
49C2×#389C2212yescomplemented
50C2×#388C2212yescomplemented
51C2×#388C2212yescomplemented
52C2×#387C2212yescomplemented
53C2×#387C2212yescomplemented
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#386C2212yescomplemented
60C2×#385C2212yescomplemented
61C2×#385C2212yescomplemented
62C2×#380C2211yescharacteristic, complemented
63C2×#380C2212yescomplemented
64C2×#379C2211yescharacteristic
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic, complemented
67C2×#379C2212yescomplemented
68C2×#379C2212yescomplemented
69C2×C4×C4⋊C4C2212yescomplemented
70C2×C4×C22⋊C4C2211yescharacteristic, complemented
71C2×C4×C22⋊C4C2212yescomplemented
72C2×C4×C22⋊C4C2212yescomplemented
73C2×C4×C22⋊C4C2212yescomplemented
74C22×#95C2212yescomplemented
75#1441C2212yescomplemented
76#1441C2212yescomplemented
77#1439C2212yescomplemented
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yescomplemented
88#1438C2212yescomplemented
89#1438C2211yescharacteristic, complemented
90#1438C2212yescomplemented
91#1438C2212yescomplemented
92#1438C2212yescomplemented
93#1438C2211yescharacteristic, complemented
94#1438C2211yescharacteristic, complemented
95#1438C2211yescharacteristic, complemented
96#1438C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1437C2212yescomplemented
104#1437C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C22⋊#95C2212yescomplemented
111C22⋊#95C2212yescomplemented
112C26C2311yescharacteristic
113C26C2311yescharacteristic
114C26C2311yescharacteristic
115C23×D4—24no—
116C23×D4—24no—
117C23×D4—24no—
118C23×D4—24no—
119C23×D4—28no—
120C23×D4—28no—
121C23×D4—44no—
122C23×D4—44no—
123C23×D4C2×C418yes—
124C23×D4C2×C418yescomplemented
125C23×D4C2311yescharacteristic
126C23×D4C2312yes—
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2312yes—
134C24×C4C2312yes—
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139#534—2128no—
140C2×#123—28no—
141C2×#123—28no—
142C2×#123—28no—
143C2×#123C2×C418yes—
144C2×#123C2×C418yescomplemented
145C2×#123C2×C4116yescomplemented
146C2×#123D4116yes—
147C2×#121—28no—
148C2×#121—28no—
149C2×#121—28no—
150C2×#121—28no—
151C2×#121C2×C4116yescomplemented
152C2×#121C2×C4116yescomplemented
153C2×#120—28no—
154C2×#120—28no—
155C2×#120—28no—
156C2×#120—28no—
157C2×#120C2×C418yes—
158C2×#120C2×C4116yescomplemented
159C2×#120C2×C418yescomplemented
160C2×C4×D4—28no—
161C2×C4×D4—28no—
162C2×C4×D4—44no—
163C2×#117—28no—
164C2×#117—28no—
165C2×#117—44no—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C22⋊C4—28no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—44no—
178C22×C22⋊C4—44no—
179C22×C22⋊C4—44no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4C2×C418yescomplemented
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2312yes—
225#390—28no—
226#390—28no—
227#390—28no—
228#390—28no—
229#390—28no—
230#390—44no—
231#390—44no—
232#389—28no—
233#388—28no—
234#388—28no—
235#387—28no—
236#387—28no—
237#386—28no—
238#386—28no—
239#386—28no—
240#386—44no—
241#386—44no—
242#386—44no—
243#385—28no—
244#385—28no—
245#380—24no—
246#380—44no—
247#379—24no—
248#379—28no—
249#379—24no—
250#379—44no—
251#379D418yescomplemented
252C4×C4⋊C4—28no—
253C4×C22⋊C4—24no—
254C4×C22⋊C4—28no—
255C4×C22⋊C4—28no—
256C4×C22⋊C4—44no—
257C2×#95—28no—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C25—24no—
281C25—24no—
282C25—24no—
283C25—22no—
284C25—22no—
285C25—24no—
286C25—24no—
287C25—22no—
288C25—22no—
289C25—42no—
290C25—42no—
291C25—42no—
292C25—42no—
293C25—42no—
294C25—42no—
295C25—42no—
296C25—42no—
297C25—42no—
298C25—42no—
299C25—42no—
300C25—42no—
301C25—42no—
302C25C22×C414yes—
303C25C22×C414yes—
304C25C22×C414yes—
305C25C2×D414yes—
306C25#4114yes—
307C25C2411yescharacteristic
308C25C2412yes—
309C25C2411yescharacteristic
310C25C2411yescharacteristic
311C25C2411yescharacteristic
312C25C2411yescharacteristic
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—24no—
316C22×D4—232no—
317C22×D4—232no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—22no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—232no—
334C22×D4—232no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—416no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—432no—
350C22×D4—432no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—416no—
360C22×D4—432no—
361C22×D4—432no—
362C22×D4C22×C414yes—
363C22×D4C22×C418yes—
364C22×D4C22×C414yes—
365C22×D4C22×C414yes—
366C22×D4C22×C418yes—
367C22×D4C22×C414yes—
368C22×D4C22×C418yes—
369C22×D4C22×C418yes—
370C22×D4C2×D418yes—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
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×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4C22×C414yes—
406C23×C4C22×C414yes—
407C23×C4C22×C418yes—
408C23×C4C2×D418yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422#123—232no—
423#123—264no—
424#123C22⋊C4164yescomplemented
425#121—264no—
426#121—264no—
427#120—232no—
428#120—264no—
429#120—232no—
430C4×D4—432no—
431#117—432no—
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—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
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⋊C4C22×C418yes—
450C2×C4⋊C4C22×C418yes—
451C2×C4⋊C4C2×D418yes—
452C2×C4⋊C4C2×D418yes—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—232no—
469C2×C22⋊C4—22no—
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—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
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—416no—
499C2×C22⋊C4—416no—
500C2×C22⋊C4—416no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—432no—
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—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4C22×C414yes—
543C2×C22⋊C4C22×C418yes—
544C2×C22⋊C4C22×C418yes—
545C2×C22⋊C4C22×C418yes—
546C2×C22⋊C4C22×C418yes—
547C2×C22⋊C4C22×C414yes—
548C2×C22⋊C4C22×C418yes—
549C2×C22⋊C4C2×D418yes—
550C2×C22⋊C4C2×D414yes—
551C2×C22⋊C4C2×D414yes—
552C2×C22⋊C4C2×D418yes—
553C2×C22⋊C4C2×D418yes—
554C2×C22⋊C4C2×D418yes—
555C2×C22⋊C4C2×D418yes—
556C2×C42—24no—
557C2×C42—24no—
558C2×C42—24no—
559C2×C42—24no—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—24no—
563C2×C42—24no—
564C2×C42—24no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—22no—
599C24—22no—
600C24—21no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—28no—
617C24—28no—
618C24—216no—
619C24—216no—
620C24—28no—
621C24—21no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—28no—
644C24—28no—
645C24—28no—
646C24—28no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—44no—
656C24—48no—
657C24—44no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—44no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—44no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—82no—
672C24—82no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—82no—
678C24—82no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—82no—
692C24—82no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24C4×D4116yes—
701C24C23×C412yes—
702C24C23×C414yes—
703C24C23×C412yes—
704C24C23×C412yes—
705C24C23×C412yes—
706C24C23×C412yes—
707C24C22×D414yes—
708C24C22×D412yes—
709C24C22×D412yes—
710C24C22×D414yes—
711C24C22×D412yes—
712C24C2×#4112yes—
713C24C2×#4112yes—
714C24C2×#4112yes—
715C24H(5,𝔽2)14yes—
716C24C2511yescharacteristic
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—216no—
720C2×D4—216no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—28no—
725C2×D4—216no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—216no—
730C2×D4—216no—
731C2×D4—28no—
732C2×D4—216no—
733C2×D4—216no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—4128no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—4128no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4C2×C22⋊C4116yes—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—216no—
770C22×C4—216no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—28no—
783C22×C4—21no—
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—21no—
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—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—28no—
818C22×C4—216no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4C2×C22⋊C4116yescomplemented
878C22×C4C23×C414yes—
879C22×C4C23×C412yes—
880C22×C4C23×C414yes—
881C22×C4C23×C414yes—
882C22×C4C23×C412yes—
883C22×C4C22×D414yes—
884C22×C4C22×D414yes—
885C22×C4C22×D414yes—
886C22×C4C22×D414yes—
887C22×C4C22×D414yes—
888C22×C4C22×D414yes—
889C22×C4C22×D414yes—
890C22×C4H(5,𝔽2)14yes—
891C22×C4H(5,𝔽2)14yes—
892C4⋊C4—216no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—84no—
898C4⋊C4C2×C22⋊C4132yescomplemented
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—216no—
903C22⋊C4—216no—
904C22⋊C4—216no—
905C22⋊C4—216no—
906C22⋊C4—216no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—82no—
929C22⋊C4—82no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4C2×C22⋊C4116yescomplemented
934C22⋊C4C2×C22⋊C4132yescomplemented
935C42—48no—
936C42—48no—
937C42—48no—
938C42—48no—
939C42—84no—
940C23—24no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—232no—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—432no—
1007C23—416no—
1008C23—41no—
1009C23—41no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—41no—
1015C23—41no—
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—416no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—41no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—41no—
1052C23—42no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—816no—
1080C23—816no—
1081C23—816no—
1082C23—816no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23—88no—
1087C23—88no—
1088C23—816no—
1089C23—88no—
1090C23—816no—
1091C23—816no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23C22×C22⋊C414yes—
1100C23C22×C22⋊C414yes—
1101C23C2×C4×D414yes—
1102C23C2×C4×D414yes—
1103C23C2×C4×D414yes—
1104C23#51814yes—
1105C23D4218yes—
1106C23#54618yes—
1107C23C24×C411yescharacteristic
1108C23C23×D412yes—
1109C23C23×D411yescharacteristic
1110C23C22×#4111yescharacteristic
1111C23C2×H(5,𝔽2)12yes—
1112C23C2×H(5,𝔽2)12yes—
1113C23C2×H(5,𝔽2)12yes—
1114C23#58512yes—
1115C23#58512yes—
1116D4—232no—
1117D4—432no—
1118D4—432no—
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122D4—816no—
1123D4—816no—
1124C2×C4—232no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—416no—
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—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—816no—
1211C2×C4—816no—
1212C2×C4—816no—
1213C2×C4—816no—
1214C2×C4C22×C22⋊C418yes—
1215C2×C4C22×C22⋊C414yes—
1216C2×C4C22×C22⋊C418yes—
1217C22—28no—
1218C22—28no—
1219C22—28no—
1220C22—28no—
1221C22—28no—
1222C22—28no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—28no—
1229C22—24no—
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—44no—
1262C22—44no—
1263C22—42no—
1264C22—832no—
1265C22—832no—
1266C22—832no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22D4×C22⋊C418yes—
1280C22C23×C22⋊C411yescharacteristic
1281C22C22×C4×D411yescharacteristic
1282C22C2×#51811yescharacteristic
1283C22C4×H(5,𝔽2)12yes—
1284C22C4×H(5,𝔽2)12yes—
1285C22C2×D4212yes—
1286C22C2×#54612yes—
1287C22#348411yescharacteristic
1288C22#348511yescharacteristic
1289C22#348812yes—
1290C22#348812yes—
1291C22#349011yescharacteristic
1292C22#349111yescharacteristic
1293C22#349612yes—
1294C22#349812yes—
1295C22#350012yes—
1296C22#350512yes—
1297C22#353212yes—
1298C22#353312yes—
1299C22#354212yes—
1300C22#354212yes—
1301C4—28no—
1302C4—24no—
1303C4—28no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—44no—
1308C4—44no—
1309C4—44no—
1310C4—82no—
1311C4—82no—
1312C4—82no—
1313C4—82no—
1314C2—28no—
1315C2—44no—
1316C2—44no—
1317C2—44no—
1318C2—84no—
1319C2—82no—
1320C2C2×D4×C22⋊C411yescharacteristic
1321C2#3425812yes—
1322C2#3426411yescharacteristic
1323C2#3427311yescharacteristic
1324C2#3440712yes—
1325C2#4388612yes—
1326C2#4390412yes—
1327C2#4393012yes—
1328C2#4393212yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#534C2
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×#2359C2semidirect
3. C2×D4×C22⋊C4C2semidirect
4. C2×#2309C2semidirect
5. #14418C2semidirect
6. #14361C2semidirect
7. #14360C2semidirect
8. #14358C2semidirect
9. #14135C2semidirect
10. #14100C2semidirect
11. #14095C2semidirect
12. #13998C2semidirect
13. #13995C2semidirect
14. #13995C2semidirect
15. #13967C2semidirect
16. #13877C2semidirect
17. #13867C2semidirect
18. C2×#1438C2semidirect
19. C22⋊C42C2semidirect
23. C2×#534C4semidirect
33. C22×#117C22semidirect
37. C23×C22⋊C4C22semidirect
38. C23×C22⋊C4C22semidirect
44. C2×#390C22semidirect
45. C2×#390C22semidirect
46. C2×#390C22semidirect
47. C2×#390C22semidirect
48. C2×#390C22semidirect
49. C2×#389C22semidirect
50. C2×#388C22semidirect
51. C2×#388C22semidirect
52. C2×#387C22semidirect
53. C2×#387C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#386C22semidirect
60. C2×#385C22semidirect
61. C2×#385C22semidirect
62. C2×#380C22semidirect
63. C2×#380C22semidirect
66. C2×#379C22semidirect
67. C2×#379C22semidirect
68. C2×#379C22semidirect
69. C2×C4×C4⋊C4C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C22×#95C22semidirect
75. #1441C22semidirect
76. #1441C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
87. #1438C22semidirect
88. #1438C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1438C22semidirect
92. #1438C22semidirect
93. #1438C22semidirect
94. #1438C22semidirect
95. #1438C22semidirect
96. #1438C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1437C22semidirect
104. #1437C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
110. C22⋊#95C22semidirect
111. C22⋊#95C22semidirect
124. C23×D4C2×C4semidirect
144. C2×#123C2×C4semidirect
145. C2×#123C2×C4semidirect
151. C2×#121C2×C4semidirect
152. C2×#121C2×C4semidirect
158. C2×#120C2×C4semidirect
159. C2×#120C2×C4semidirect
183. C22×C22⋊C4C2×C4semidirect
251. #379D4semidirect
424. #123C22⋊C4semidirect
877. C22×C4C2×C22⋊C4semidirect
898. C4⋊C4C2×C22⋊C4semidirect
933. C22⋊C4C2×C22⋊C4semidirect
934. C22⋊C4C2×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5342
C2×#23592
C2×D4×C22⋊C42
C2×#23092
#144182
#143612
#143602
#143582
#141352
#141002
#140952
#139982
#139952
#139672
#138772
#138672
C2×#14382
C22⋊C422