Finite Group Databasebeta

← #879795

Subgroups — #879795

Order 512.

5246 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2682C211yesmaximal, characteristic, complemented
2C2×#2424C212yesmaximal, complemented
3C2×#2418C212yesmaximal, complemented
4C22×#390C211yesmaximal, characteristic, complemented
5#17071C211yesmaximal, characteristic, complemented
6#17068C211yesmaximal, characteristic, complemented
7#16526C212yesmaximal, complemented
8#15666C212yesmaximal, complemented
9#15617C212yesmaximal, complemented
10#15370C212yesmaximal, complemented
11#15315C212yesmaximal, complemented
12#14726C212yesmaximal, complemented
13#14725C212yesmaximal, complemented
14#14715C212yesmaximal, complemented
15#14698C211yesmaximal, characteristic, complemented
16#14697C211yesmaximal, characteristic, complemented
17#14534C212yesmaximal, complemented
18#14445C211yesmaximal, characteristic, complemented
19#14015C212yesmaximal, complemented
20C24×D4C2211yescharacteristic
21C22×#123C2212yescomplemented
22C22×#121C2211yescharacteristic
23C22×#121C2212yescomplemented
24C22×#120C2212yes—
25C22×#120C2212yes—
26C22×C4×D4C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29C23×C22⋊C4C2212yes—
30C23×C42C2211yescharacteristic
31#2682—28no—
32#2424—216no—
33#2418—216no—
34C2×#399C2212yescomplemented
35C2×#397C2212yescomplemented
36C2×#396C2212yescomplemented
37C2×#396C2212yescomplemented
38C2×#396C2212yescomplemented
39C2×#394C2212yescomplemented
40C2×#394C2212yescomplemented
41C2×#394C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#394C2212yescomplemented
44C2×#394C2212yescomplemented
45C2×#392C2212yes—
46C2×#392C2212yes—
47C2×#392C2212yes—
48C2×#392C2212yes—
49C2×#392C2212yescomplemented
50C2×#390—28no—
51C2×#390C2212yes—
52C2×#390C2212yes—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2212yescomplemented
58C2×#390C2211yescharacteristic, complemented
59C2×#390C2211yescharacteristic, complemented
60C2×#389C2211yescharacteristic, complemented
61C2×#389C2211yescharacteristic, complemented
62C2×#388C2212yescomplemented
63C2×#388C2212yescomplemented
64C2×#388C2212yescomplemented
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#385C2212yes—
71C2×#385C2212yes—
72C2×#385C2212yescomplemented
73C2×#385C2212yescomplemented
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×#379C2212yes—
78C2×#379C2212yes—
79#1444C2212yescomplemented
80#1444C2212yescomplemented
81#1440C2212yescomplemented
82#1440C2212yescomplemented
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1439C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1438C2212yes—
94#1438C2212yes—
95#1438C2212yes—
96#1438C2212yes—
97#1438C2212yescomplemented
98#1438C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104#1436C2212yescomplemented
105C4⋊#95C2211yescharacteristic, complemented
106C4⋊#95C2211yescharacteristic, complemented
107C4⋊#95C2211yescharacteristic, complemented
108C4⋊#95C2211yescharacteristic, complemented
109C22⋊#95C2212yes—
110C22⋊#95C2212yes—
111C26C2312yes—
112C23×D4—24no—
113C23×D4—24no—
114C23×D4—24no—
115C23×D4—42no—
116C23×D4—42no—
117C23×D4—42no—
118C23×D4—42no—
119C23×D4C2312yes—
120C23×D4C2312yes—
121C23×D4C2312yes—
122C23×D4C2312yes—
123C23×D4C2312yes—
124C23×D4C2312yes—
125C23×D4C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2312yes—
130C24×C4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C24×C4C2312yes—
133C2×#123—28no—
134C2×#123—28no—
135C2×#123—44no—
136C2×#121—28no—
137C2×#121—28no—
138C2×#121—44no—
139C2×#121—42no—
140C2×#121—42no—
141C2×#121D418yescomplemented
142C2×#120—28no—
143C2×#120—28no—
144C2×#120—28no—
145C2×#120—44no—
146C2×#120—44no—
147C2×#120—44no—
148C2×C4×D4—28no—
149C2×C4×D4—28no—
150C2×C4×D4—44no—
151C22×C4⋊C4—24no—
152C22×C4⋊C4—42no—
153C22×C4⋊C4—42no—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4—28no—
170C22×C22⋊C4—28no—
171C22×C22⋊C4—28no—
172C22×C22⋊C4—28no—
173C22×C22⋊C4—44no—
174C22×C22⋊C4—44no—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C42—24no—
207C22×C42—42no—
208C22×C42—42no—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214#399—28no—
215#397—28no—
216#396—28no—
217#396—28no—
218#396—44no—
219#394—28no—
220#394—28no—
221#394—28no—
222#394—28no—
223#394—28no—
224#394—44no—
225#392—28no—
226#392—28no—
227#392—28no—
228#392—44no—
229#392—44no—
230#390—24no—
231#390—24no—
232#390—28no—
233#390—28no—
234#390—28no—
235#390—24no—
236#390—24no—
237#390—42no—
238#390D418yescomplemented
239#389—24no—
240#389—42no—
241#388—28no—
242#388—28no—
243#388—28no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—28no—
248#386—28no—
249#385—28no—
250#385—28no—
251#385—28no—
252#385—44no—
253#380—42no—
254#380—42no—
255#380D418yescomplemented
256#379—28no—
257#379—44no—
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—
279C25—24no—
280C25—24no—
281C25—24no—
282C25—24no—
283C25—24no—
284C25—24no—
285C25—24no—
286C25—24no—
287C25—24no—
288C25—42no—
289C25—42no—
290C25—42no—
291C25—42no—
292C25—42no—
293C25—42no—
294C25C2412yes—
295C25C2412yes—
296C25C2412yes—
297C25C2411yescharacteristic
298C22×D4—232no—
299C22×D4—24no—
300C22×D4—24no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—41no—
327C22×D4—41no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—42no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—42no—
336C22×D4—416no—
337C22×D4—416no—
338C22×D4—416no—
339C22×D4—416no—
340C22×D4—416no—
341C22×D4—416no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—41no—
349C22×D4—41no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—41no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4C2×D418yes—
365C22×D4C2×D414yes—
366C22×D4C2×D414yescomplemented
367C22×D4#4114yes—
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—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—41no—
390C23×C4—41no—
391C23×C4—41no—
392C23×C4—41no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4C2×D414yes—
401C23×C4C2×D414yes—
402C23×C4#4114yes—
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418#123—432no—
419#121—432no—
420#121—416no—
421#120—432no—
422#120—432no—
423C4×D4—432no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
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—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—416no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4C2×D414yes—
467C2×C4⋊C4C2×D414yescomplemented
468C2×C4⋊C4C2×D414yescomplemented
469C2×C4⋊C4C2×D414yescomplemented
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—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—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—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—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—432no—
526C2×C22⋊C4—432no—
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⋊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⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4C2×D418yes—
562C2×C22⋊C4C2×D418yes—
563C2×C22⋊C4C2×D418yes—
564C2×C22⋊C4C2×D418yescomplemented
565C2×C42—24no—
566C2×C42—24no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—42no—
573C2×C42—41no—
574C2×C42—41no—
575C2×C42—41no—
576C2×C42—41no—
577C2×C42—41no—
578C2×C42—41no—
579C2×C42—416no—
580C2×C42C2×D414yes—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95C2×D418yescomplemented
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—216no—
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—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—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24C22×D414yes—
688C24C22×D414yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C2×#4114yes—
692C24C2×#4112yes—
693C24H(5,𝔽2)12yes—
694C24H(5,𝔽2)12yes—
695C24H(5,𝔽2)12yes—
696C242−1+412yes—
697C24C2511yescharacteristic
698C2×D4—216no—
699C2×D4—216no—
700C2×D4—216no—
701C2×D4—216no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—4128no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—82no—
741C2×D4—82no—
742C2×D4—82no—
743C2×D4—82no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—28no—
824C22×C4—28no—
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—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4C22×D412yes—
885C22×C4C22×D414yes—
886C22×C4C22×D414yes—
887C22×C4C22×D412yes—
888C22×C4C22×D414yes—
889C22×C4C22×D414yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4H(5,𝔽2)12yes—
899C22×C4H(5,𝔽2)12yes—
900C22×C4H(5,𝔽2)12yes—
901C22×C4H(5,𝔽2)12yes—
902C4⋊C4—28no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—82no—
912C4⋊C4—82no—
913C4⋊C4—82no—
914C4⋊C4—82no—
915C4⋊C4—84no—
916C4⋊C4—84no—
917C22⋊C4—216no—
918C22⋊C4—216no—
919C22⋊C4—216no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C42—44no—
949C42—44no—
950C42—44no—
951C42—48no—
952C42—44no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—432no—
1003C23—432no—
1004C23—432no—
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—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—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—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—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—816no—
1090C23—816no—
1091C23—816no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23#53414yes—
1102C23#53714yes—
1103C23#53814yes—
1104C23D4214yes—
1105C23#54714yes—
1106C23#55014yes—
1107C23#56214yes—
1108C23C23×D411yescharacteristic
1109C23C23×D411yescharacteristic
1110C23C23×D411yescharacteristic
1111C23C22×#4111yescharacteristic
1112C23C22×#4111yescharacteristic
1113C23C2×H(5,𝔽2)11yescharacteristic
1114C23C2×H(5,𝔽2)11yescharacteristic
1115C23C2×H(5,𝔽2)11yescharacteristic
1116C23C2×H(5,𝔽2)11yescharacteristic
1117C23C2×H(5,𝔽2)11yescharacteristic
1118C23C2×H(5,𝔽2)11yescharacteristic
1119C23C2×H(5,𝔽2)11yescharacteristic
1120C23C2×2−1+411yescharacteristic
1121C23#58511yescharacteristic
1122C23#58511yescharacteristic
1123D4—416no—
1124D4—416no—
1125D4—432no—
1126D4—432no—
1127D4—88no—
1128D4—816no—
1129D4—816no—
1130D4—816no—
1131D4—816no—
1132C2×C4—232no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—416no—
1176C2×C4—416no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—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—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—816no—
1237C2×C4—816no—
1238C2×C4#52514yes—
1239C2×C4#53814yes—
1240C2×C4D4214yes—
1241C2×C4D4214yes—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—864no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22#268218yescomplemented
1303C22C2×#52511yescharacteristic
1304C22C2×#53411yescharacteristic
1305C22C2×#53711yescharacteristic
1306C22C2×#53811yescharacteristic
1307C22C2×#53811yescharacteristic
1308C22C2×D4211yescharacteristic
1309C22C2×D4211yescharacteristic
1310C22C2×D4211yescharacteristic
1311C22C2×#54711yescharacteristic
1312C22C2×#55011yescharacteristic
1313C22D4×#4111yescharacteristic
1314C22D4×#4111yescharacteristic
1315C22#348411yescharacteristic
1316C22#348411yescharacteristic
1317C22#348811yescharacteristic
1318C22#348911yescharacteristic
1319C22#349011yescharacteristic
1320C22#349011yescharacteristic
1321C22#349611yescharacteristic
1322C22#349611yescharacteristic
1323C22#349811yescharacteristic
1324C22#349811yescharacteristic
1325C22#350611yescharacteristic
1326C22#350611yescharacteristic
1327C22#351911yescharacteristic
1328C22#352011yescharacteristic
1329C22C2×#56211yescharacteristic
1330C22#353411yescharacteristic
1331C22#353411yescharacteristic
1332C22#353611yescharacteristic
1333C22#353711yescharacteristic
1334C22#354311yescharacteristic
1335C22#354511yescharacteristic
1336C22#355811yescharacteristic
1337C22#356111yescharacteristic
1338C4—24no—
1339C4—24no—
1340C4—24no—
1341C4—24no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—44no—
1347C4—44no—
1348C4—82no—
1349C4—82no—
1350C4—82no—
1351C4—82no—
1352C4—82no—
1353C2—28no—
1354C2—84no—
1355C2—84no—
1356C2—84no—
1357C2#3498811yescharacteristic
1358C2#3610011yescharacteristic
1359C2#3610111yescharacteristic
1360C2#3719811yescharacteristic
1361C2#3767211yescharacteristic
1362C2#3767311yescharacteristic
1363C2#3842411yescharacteristic
1364C2#3842611yescharacteristic
1365C2#3937511yescharacteristic
1366C2#3938311yescharacteristic
1367C2#4597611yescharacteristic
1368C2#4608811yescharacteristic
1369C2C2×#268211yescharacteristic
1370C2#5912611yescharacteristic
1371C2#5981411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2682C2semidirect
2. C2×#2424C2semidirect
3. C2×#2418C2semidirect
4. C22×#390C2semidirect
5. #17071C2semidirect
6. #17068C2semidirect
7. #16526C2semidirect
8. #15666C2semidirect
9. #15617C2semidirect
10. #15370C2semidirect
11. #15315C2semidirect
12. #14726C2semidirect
13. #14725C2semidirect
14. #14715C2semidirect
15. #14698C2semidirect
16. #14697C2semidirect
17. #14534C2semidirect
18. #14445C2semidirect
19. #14015C2semidirect
21. C22×#123C22semidirect
23. C22×#121C22semidirect
34. C2×#399C22semidirect
35. C2×#397C22semidirect
36. C2×#396C22semidirect
37. C2×#396C22semidirect
38. C2×#396C22semidirect
39. C2×#394C22semidirect
40. C2×#394C22semidirect
41. C2×#394C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
49. C2×#392C22semidirect
57. C2×#390C22semidirect
58. C2×#390C22semidirect
59. C2×#390C22semidirect
60. C2×#389C22semidirect
61. C2×#389C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
64. C2×#388C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
72. C2×#385C22semidirect
73. C2×#385C22semidirect
79. #1444C22semidirect
80. #1444C22semidirect
81. #1440C22semidirect
82. #1440C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
97. #1438C22semidirect
98. #1438C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. C4⋊#95C22semidirect
106. C4⋊#95C22semidirect
107. C4⋊#95C22semidirect
108. C4⋊#95C22semidirect
141. C2×#121D4semidirect
238. #390D4semidirect
255. #380D4semidirect
366. C22×D4C2×D4semidirect
467. C2×C4⋊C4C2×D4semidirect
468. C2×C4⋊C4C2×D4semidirect
469. C2×C4⋊C4C2×D4semidirect
564. C2×C22⋊C4C2×D4semidirect
601. #95C2×D4semidirect
1302. C22#2682semidirect

Maximal subgroups

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

subgroupindex
C2×#26822
C2×#24242
C2×#24182
C22×#3902
#170712
#170682
#165262
#156662
#156172
#153702
#153152
#147262
#147252
#147152
#146982
#146972
#145342
#144452
#140152