Finite Group Databasebeta

← #535282

Subgroups — #535282

Order 512.

6992 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#534C211yesmaximal, characteristic
2C2×#2358C212yesmaximal, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#2308C211yesmaximal, characteristic, complemented
5#14417C212yesmaximal, complemented
6#14361C212yesmaximal, complemented
7#14359C212yesmaximal, complemented
8#14357C212yesmaximal, complemented
9#14134C212yesmaximal, complemented
10#14100C212yesmaximal, complemented
11#14096C212yesmaximal, complemented
12#13996C212yesmaximal, complemented
13#13970C212yesmaximal, complemented
14#13968C212yesmaximal, 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×#120C2212yes—
30C22×#120C2211yescharacteristic
31C22×#120C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×C4×D4C2212yescomplemented
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2212yescomplemented
38C23×C22⋊C4C2212yescomplemented
39C23×C22⋊C4C2211yescharacteristic, complemented
40#2358—216no—
41D4×C22⋊C4—28no—
42#2308—28no—
43C2×#390C2212yescomplemented
44C2×#390C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#388C2212yescomplemented
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yescomplemented
53C2×#386C2212yescomplemented
54C2×#386C2212yescomplemented
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#385C2212yescomplemented
60C2×#385C2212yescomplemented
61C2×#381C2212yescomplemented
62C2×#380C2211yescharacteristic, complemented
63C2×#380C2212yescomplemented
64C2×#379C2211yescharacteristic
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic, complemented
67C2×#379C2212yescomplemented
68C2×C4×C22⋊C4C2211yescharacteristic, complemented
69C2×C4×C22⋊C4C2212yescomplemented
70C2×C4×C22⋊C4C2212yescomplemented
71C2×C4×C22⋊C4C2212yescomplemented
72C22×#95C2212yescomplemented
73#1445C2212yescomplemented
74#1445C2212yescomplemented
75#1441C2212yescomplemented
76#1441C2212yescomplemented
77#1440C2212yescomplemented
78#1440C2212yescomplemented
79#1440C2212yescomplemented
80#1440C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yescomplemented
88#1438C2212yescomplemented
89#1438C2211yescharacteristic, complemented
90#1438C2212yescomplemented
91#1438C2212yescomplemented
92#1438C2211yescharacteristic, complemented
93#1438C2211yescharacteristic, complemented
94#1438C2211yescharacteristic, complemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101C4⋊#95C2212yescomplemented
102C4⋊#95C2212yescomplemented
103C22⋊#95C2212yescomplemented
104C22⋊#95C2212yescomplemented
105C22⋊#95C2212yescomplemented
106C22⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C22⋊#95C2212yescomplemented
111C22⋊#95C2212yescomplemented
112C26C2311yescharacteristic
113C26C2311yescharacteristic
114C26C2311yescharacteristic
115C23×D4—24no—
116C23×D4—24no—
117C23×D4—28no—
118C23×D4—24no—
119C23×D4—24no—
120C23×D4—28no—
121C23×D4—44no—
122C23×D4—44no—
123C23×D4C2×C418yescomplemented
124C23×D4C2×C418yescomplemented
125C23×D4C2311yescharacteristic
126C23×D4C2312yes—
127C23×D4C2312yes—
128C23×D4C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C24×C4C2312yes—
140C24×C4C2312yes—
141#534—2128no—
142C2×#123—28no—
143C2×#123—28no—
144C2×#123—28no—
145C2×#123—28no—
146C2×#123C2×C418yescomplemented
147C2×#123C2×C4116yescomplemented
148C2×#123C2×C418yescomplemented
149C2×#121—28no—
150C2×#121—28no—
151C2×#121—28no—
152C2×#121—28no—
153C2×#121C2×C4116yescomplemented
154C2×#121C2×C4116yescomplemented
155C2×#120—28no—
156C2×#120—28no—
157C2×#120—28no—
158C2×#120C2×C418yes—
159C2×#120C2×C418yescomplemented
160C2×#120C2×C4116yescomplemented
161C2×#120D4116yes—
162C2×C4×D4—28no—
163C2×C4×D4—28no—
164C2×C4×D4—28no—
165C2×C4×D4—44no—
166C2×C4×D4—44no—
167C2×C4×D4—44no—
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—28no—
176C22×C22⋊C4—28no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4C2×C418yescomplemented
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224#390—28no—
225#390—28no—
226#388—28no—
227#388—28no—
228#386—28no—
229#386—28no—
230#386—28no—
231#386—28no—
232#386—28no—
233#386—28no—
234#386—28no—
235#386—28no—
236#386—28no—
237#386—44no—
238#386—44no—
239#386—44no—
240#385—28no—
241#385—28no—
242#381—28no—
243#380—24no—
244#380—44no—
245#379—24no—
246#379—24no—
247#379—44no—
248#379D418yescomplemented
249C4×C22⋊C4—24no—
250C4×C22⋊C4—28no—
251C4×C22⋊C4—28no—
252C4×C22⋊C4—44no—
253C2×#95—44no—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
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—22no—
281C25—24no—
282C25—22no—
283C25—24no—
284C25—24no—
285C25—22no—
286C25—22no—
287C25—24no—
288C25—42no—
289C25—42no—
290C25—42no—
291C25—42no—
292C25—42no—
293C25—42no—
294C25—42no—
295C25—42no—
296C25—42no—
297C25—42no—
298C25—42no—
299C25—42no—
300C25—42no—
301C25C22×C414yes—
302C25C22×C414yes—
303C25C22×C414yes—
304C25C2×D418yes—
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—232no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—232no—
339C22×D4—24no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—416no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—416no—
356C22×D4—432no—
357C22×D4—432no—
358C22×D4—432no—
359C22×D4—432no—
360C22×D4C22×C414yes—
361C22×D4C22×C418yes—
362C22×D4C22×C418yes—
363C22×D4C22×C414yes—
364C22×D4C22×C414yes—
365C22×D4C22×C414yes—
366C22×D4C22×C418yes—
367C22×D4C22×C418yes—
368C22×D4C2×D418yes—
369C22×D4C2×D418yes—
370C22×D4C2×D418yes—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—22no—
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—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—24no—
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×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4C22×C414yes—
421C23×C4C22×C414yes—
422C23×C4C22×C418yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436#123—232no—
437#123—264no—
438#123—232no—
439#121—264no—
440#121—264no—
441#120—232no—
442#120—264no—
443#120C22⋊C4164yescomplemented
444C4×D4—432no—
445C4×D4—432no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4C22×C418yes—
460C2×C4⋊C4C22×C418yes—
461C2×C22⋊C4—22no—
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—24no—
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—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—232no—
480C2×C22⋊C4—22no—
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—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
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—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—432no—
511C2×C22⋊C4—416no—
512C2×C22⋊C4—416no—
513C2×C22⋊C4—416no—
514C2×C22⋊C4—432no—
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⋊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⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4C22×C414yes—
546C2×C22⋊C4C22×C418yes—
547C2×C22⋊C4C22×C418yes—
548C2×C22⋊C4C22×C418yes—
549C2×C22⋊C4C22×C418yes—
550C2×C22⋊C4C22×C414yes—
551C2×C22⋊C4C22×C418yes—
552C2×C22⋊C4C2×D418yes—
553C2×C22⋊C4C2×D414yes—
554C2×C22⋊C4C2×D414yes—
555C2×C22⋊C4C2×D418yes—
556C2×C22⋊C4C2×D418yes—
557C2×C22⋊C4C2×D418yes—
558C2×C22⋊C4C2×D418yes—
559C2×C42—24no—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—24no—
563C2×C42—24no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42—42no—
568#95—24no—
569#95—24no—
570#95—24no—
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—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—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—21no—
600C24—22no—
601C24—22no—
602C24—21no—
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—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—28no—
630C24—28no—
631C24—28no—
632C24—28no—
633C24—216no—
634C24—216no—
635C24—216no—
636C24—216no—
637C24—21no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—28no—
646C24—28no—
647C24—44no—
648C24—48no—
649C24—44no—
650C24—44no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—44no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—44no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—44no—
667C24—44no—
668C24—48no—
669C24—82no—
670C24—84no—
671C24—82no—
672C24—84no—
673C24—82no—
674C24—82no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—82no—
690C24—82no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24C2×C22⋊C4116yescomplemented
699C24C4×D4116yescomplemented
700C24C23×C412yes—
701C24C23×C412yes—
702C24C23×C414yes—
703C24C23×C412yes—
704C24C23×C412yes—
705C24C23×C412yes—
706C24C22×D414yes—
707C24C22×D414yes—
708C24C22×D414yes—
709C24C22×D412yes—
710C24C22×D412yes—
711C24C22×D414yes—
712C24C22×D412yes—
713C24C2×#4112yes—
714C24C2×#4112yes—
715C24C2×#4112yes—
716C24H(5,𝔽2)14yes—
717C24C2511yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—216no—
726C2×D4—28no—
727C2×D4—216no—
728C2×D4—28no—
729C2×D4—216no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—216no—
733C2×D4—28no—
734C2×D4—48no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—44no—
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—4128no—
749C2×D4—4128no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4C2×C22⋊C4116yes—
767C2×D4C2×C22⋊C4132yescomplemented
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—21no—
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—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—22no—
818C22×C4—22no—
819C22×C4—28no—
820C22×C4—216no—
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—22no—
848C22×C4—22no—
849C22×C4—44no—
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—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
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—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4C23×C414yes—
896C22×C4C23×C414yes—
897C22×C4C23×C412yes—
898C22×C4C23×C414yes—
899C22×C4C23×C412yes—
900C22×C4C22×D414yes—
901C22×C4C22×D414yes—
902C22×C4C22×D414yes—
903C22×C4C22×D414yes—
904C22×C4C22×D414yes—
905C22×C4H(5,𝔽2)14yes—
906C22×C4H(5,𝔽2)14yes—
907C4⋊C4—216no—
908C4⋊C4—216no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—84no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—216no—
917C22⋊C4—216no—
918C22⋊C4—216no—
919C22⋊C4—216no—
920C22⋊C4—216no—
921C22⋊C4—44no—
922C22⋊C4—44no—
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—44no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—82no—
940C22⋊C4—82no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4C2×C22⋊C4116yescomplemented
945C22⋊C4C2×C22⋊C4132yescomplemented
946C42—48no—
947C42—48no—
948C42—84no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—22no—
999C23—22no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—232no—
1018C23—232no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—24no—
1023C23—24no—
1024C23—432no—
1025C23—416no—
1026C23—416no—
1027C23—416no—
1028C23—416no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—41no—
1038C23—42no—
1039C23—41no—
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—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—41no—
1074C23—42no—
1075C23—42no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—816no—
1088C23—816no—
1089C23—816no—
1090C23—816no—
1091C23—816no—
1092C23—816no—
1093C23—816no—
1094C23—88no—
1095C23—88no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23—88no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23C22×C22⋊C414yes—
1108C23C22×C22⋊C418yes—
1109C23C22×C22⋊C414yes—
1110C23C2×C4×D414yes—
1111C23C2×C4×D414yes—
1112C23C2×C4×D414yes—
1113C23#51814yes—
1114C23D4218yes—
1115C23#54618yes—
1116C23C24×C411yescharacteristic
1117C23C23×D412yes—
1118C23C23×D411yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C2×H(5,𝔽2)12yes—
1121C23C2×H(5,𝔽2)12yes—
1122C23C2×H(5,𝔽2)12yes—
1123C23#58512yes—
1124C23#58512yes—
1125D4—232no—
1126D4—432no—
1127D4—416no—
1128D4—432no—
1129D4—416no—
1130D4—432no—
1131D4—416no—
1132D4—816no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
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—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—416no—
1165C2×C4—416no—
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—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—816no—
1221C2×C4—816no—
1222C2×C4—816no—
1223C2×C4—816no—
1224C2×C4—816no—
1225C2×C4—816no—
1226C2×C4C22×C22⋊C418yes—
1227C2×C4C22×C22⋊C414yes—
1228C22—28no—
1229C22—28no—
1230C22—28no—
1231C22—28no—
1232C22—24no—
1233C22—24no—
1234C22—28no—
1235C22—28no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—28no—
1240C22—28no—
1241C22—28no—
1242C22—28no—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—44no—
1266C22—42no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—42no—
1279C22—44no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—832no—
1284C22—832no—
1285C22—832no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22D4×C22⋊C418yes—
1291C22C23×C22⋊C411yescharacteristic
1292C22C22×C4×D411yescharacteristic
1293C22C2×#51811yescharacteristic
1294C22C4×H(5,𝔽2)12yes—
1295C22C4×H(5,𝔽2)12yes—
1296C22C2×D4212yes—
1297C22C2×#54612yes—
1298C22#348412yes—
1299C22#348411yescharacteristic
1300C22#348512yes—
1301C22#348511yescharacteristic
1302C22#349011yescharacteristic
1303C22#349111yescharacteristic
1304C22#349612yes—
1305C22#349612yes—
1306C22#349612yes—
1307C22#350512yes—
1308C22#353412yes—
1309C22#353412yes—
1310C22#354312yes—
1311C22#354512yes—
1312C4—24no—
1313C4—28no—
1314C4—44no—
1315C4—44no—
1316C4—42no—
1317C4—44no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—82no—
1322C4—82no—
1323C4—82no—
1324C4—82no—
1325C2—28no—
1326C2—44no—
1327C2—44no—
1328C2—48no—
1329C2—44no—
1330C2—82no—
1331C2C2×D4×C22⋊C411yescharacteristic
1332C2#3425612yes—
1333C2#3426411yescharacteristic
1334C2#3427311yescharacteristic
1335C2#3440812yes—
1336C2#4299612yes—
1337C2#4299712yes—
1338C2#4301612yes—
1339C2#4301712yes—
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×#2358C2semidirect
3. C2×D4×C22⋊C4C2semidirect
4. C2×#2308C2semidirect
5. #14417C2semidirect
6. #14361C2semidirect
7. #14359C2semidirect
8. #14357C2semidirect
9. #14134C2semidirect
10. #14100C2semidirect
11. #14096C2semidirect
12. #13996C2semidirect
13. #13970C2semidirect
14. #13968C2semidirect
15. #13967C2semidirect
16. #13877C2semidirect
17. #13867C2semidirect
18. C2×#1438C2semidirect
19. C22⋊C42C2semidirect
23. C2×#534C4semidirect
33. C22×C4×D4C22semidirect
37. C23×C22⋊C4C22semidirect
38. C23×C22⋊C4C22semidirect
39. C23×C22⋊C4C22semidirect
43. C2×#390C22semidirect
44. C2×#390C22semidirect
45. C2×#388C22semidirect
46. C2×#388C22semidirect
52. C2×#386C22semidirect
53. C2×#386C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#385C22semidirect
60. C2×#385C22semidirect
61. C2×#381C22semidirect
62. C2×#380C22semidirect
63. C2×#380C22semidirect
66. C2×#379C22semidirect
67. C2×#379C22semidirect
68. C2×C4×C22⋊C4C22semidirect
69. C2×C4×C22⋊C4C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C22×#95C22semidirect
73. #1445C22semidirect
74. #1445C22semidirect
75. #1441C22semidirect
76. #1441C22semidirect
77. #1440C22semidirect
78. #1440C22semidirect
79. #1440C22semidirect
80. #1440C22semidirect
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. #1437C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. C4⋊#95C22semidirect
102. C4⋊#95C22semidirect
103. C22⋊#95C22semidirect
104. C22⋊#95C22semidirect
105. C22⋊#95C22semidirect
106. C22⋊#95C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
110. C22⋊#95C22semidirect
111. C22⋊#95C22semidirect
123. C23×D4C2×C4semidirect
124. C23×D4C2×C4semidirect
146. C2×#123C2×C4semidirect
147. C2×#123C2×C4semidirect
148. C2×#123C2×C4semidirect
153. C2×#121C2×C4semidirect
154. C2×#121C2×C4semidirect
159. C2×#120C2×C4semidirect
160. C2×#120C2×C4semidirect
186. C22×C22⋊C4C2×C4semidirect
248. #379D4semidirect
443. #120C22⋊C4semidirect
698. C24C2×C22⋊C4semidirect
699. C24C4×D4semidirect
767. C2×D4C2×C22⋊C4semidirect
944. C22⋊C4C2×C22⋊C4semidirect
945. 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×#23582
C2×D4×C22⋊C42
C2×#23082
#144172
#143612
#143592
#143572
#141342
#141002
#140962
#139962
#139702
#139682
#139672
#138772
#138672
C2×#14382
C22⋊C422