Finite Group Databasebeta

← #4341766

Subgroups — #4341766

Order 512.

4524 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2678C212yesmaximal, complemented
2C2×#2408C211yesmaximal, characteristic, complemented
3C2×#2325C211yesmaximal, characteristic, complemented
4#16816C211yesmaximal, characteristic, complemented
5#16815C211yesmaximal, characteristic, complemented
6#16519C211yesmaximal, characteristic, complemented
7#16516C211yesmaximal, characteristic, complemented
8#16284C212yesmaximal, complemented
9#16256C212yesmaximal, complemented
10#15607C212yesmaximal, complemented
11#15498C212yesmaximal, complemented
12#15297C212yesmaximal, complemented
13#15266C212yesmaximal, complemented
14#14926C211yesmaximal, characteristic, complemented
15#14913C211yesmaximal, characteristic, complemented
16#14815C211yesmaximal, characteristic, complemented
17#14813C211yesmaximal, characteristic, complemented
18#14724C211yesmaximal, characteristic, complemented
19#14722C211yesmaximal, characteristic, complemented
20#14722C211yesmaximal, characteristic, complemented
21#14715C211yesmaximal, characteristic, complemented
22#14357C212yesmaximal, complemented
23#13941C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2212yescomplemented
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2212yes—
30C22×#120C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic, complemented
33#2678—216no—
34#2408—28no—
35C2×#397C2212yes—
36C2×#396C2212yescomplemented
37C2×#396C2212yescomplemented
38C2×#394C2212yes—
39C2×#394C2212yes—
40C2×#394C2212yes—
41C2×#394C2211yescharacteristic
42C2×#394C2211yescharacteristic
43C2×#394C2212yescomplemented
44C2×#394C2212yescomplemented
45C2×#392C2212yes—
46C2×#392C2211yescharacteristic
47C2×#392C2211yescharacteristic
48C2×#392C2212yes—
49C2×#392C2212yescomplemented
50C2×#392C2212yescomplemented
51#2325—28no—
52C2×#390C2212yes—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2212yescomplemented
56C2×#388C2211yescharacteristic
57C2×#388C2211yescharacteristic, complemented
58C2×#388C2212yescomplemented
59C2×#387C2211yescharacteristic, complemented
60C2×#387C2211yescharacteristic, complemented
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic, complemented
65C2×#386C2212yescomplemented
66C2×#386C2212yescomplemented
67C2×#386C2212yescomplemented
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic, complemented
72C2×#382C2211yescharacteristic, complemented
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic, complemented
75C2×#379C2212yes—
76C2×#379C2212yes—
77C2×#379C2212yes—
78C2×#379C2212yes—
79C2×C4×C4⋊C4C2211yescharacteristic, complemented
80C22×#95C2211yescharacteristic, complemented
81#1444C2211yescharacteristic, complemented
82#1444C2211yescharacteristic, complemented
83#1443C2212yescomplemented
84#1442C2211yescharacteristic, complemented
85#1442C2211yescharacteristic, complemented
86#1442C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2211yescharacteristic, complemented
89#1441C2211yescharacteristic, complemented
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1439C2212yes—
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2211yescharacteristic, complemented
106#1439C2211yescharacteristic, complemented
107#1439C2212yescomplemented
108#1438C2211yescharacteristic
109#1438C2211yescharacteristic
110#1438C2211yescharacteristic
111#1438C2211yescharacteristic
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1438C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121C4⋊#95C2212yescomplemented
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic, complemented
125C22⋊#95C2211yescharacteristic, complemented
126C26C2312yes—
127C23×D4—24no—
128C23×D4—42no—
129C23×D4—42no—
130C23×D4—44no—
131C23×D4—44no—
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C23×D4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×#123—28no—
148C2×#123—44no—
149C2×#123—44no—
150C2×#121—24no—
151C2×#121—24no—
152C2×#121—24no—
153C2×#121—24no—
154C2×#121—44no—
155C2×#121—44no—
156C2×#121D418yescomplemented
157C2×#120—28no—
158C2×#120—28no—
159C2×#120—28no—
160C2×#120—28no—
161C2×#120—44no—
162C2×#120—44no—
163C2×C4×D4—24no—
164C2×C4×D4—42no—
165C2×C4×D4—42no—
166C2×C4×D4—42no—
167C2×C4×D4—42no—
168C2×C4×D4D418yescomplemented
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220#397—28no—
221#396—28no—
222#396—44no—
223#394—28no—
224#394—28no—
225#394—28no—
226#394—42no—
227#394—42no—
228#394—44no—
229#394—44no—
230#392—28no—
231#392—28no—
232#392—28no—
233#392—42no—
234#392—42no—
235#392—44no—
236#390—28no—
237#390—28no—
238#390—24no—
239#390—24no—
240#388—28no—
241#388—24no—
242#388—24no—
243#387—24no—
244#387—24no—
245#386—24no—
246#386—24no—
247#386—28no—
248#386—24no—
249#386—24no—
250#386—44no—
251#386—44no—
252#386—44no—
253#386—44no—
254#385—24no—
255#385—24no—
256#382—42no—
257#380—24no—
258#380—24no—
259#379—28no—
260#379—28no—
261#379—44no—
262#379—44no—
263C4×C4⋊C4—42no—
264C2×#95—24no—
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C25—24no—
298C25—24no—
299C25—24no—
300C25—24no—
301C25—24no—
302C25—42no—
303C25—42no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25C2411yescharacteristic
313C25C2412yes—
314C25C2412yes—
315C25C2411yescharacteristic
316C25C2411yescharacteristic
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—41no—
356C22×D4—41no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—416no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—416no—
378C22×D4—416no—
379C22×D4—432no—
380C22×D4—432no—
381C22×D4C2×D414yes—
382C22×D4C2×D414yes—
383C22×D4C2×D414yes—
384C22×D4C2×D414yescomplemented
385C22×D4#4114yes—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—41no—
397C23×C4—41no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—41no—
403C23×C4—41no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4C2×D414yes—
409C23×C4C2×D414yes—
410C23×C4C2×D414yescomplemented
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429#123—432no—
430#121—232no—
431#121—416no—
432#121—416no—
433#120—432no—
434#120—432no—
435C4×D4—416no—
436C4×D4—416no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4C2×D414yescomplemented
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
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—22no—
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—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
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—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
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⋊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⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yescomplemented
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—24no—
577C2×C42—41no—
578C2×C42—41no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42C2×D414yes—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—24no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—24no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—22no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24C22×D412yes—
704C24C22×D412yes—
705C24C22×D412yes—
706C24C22×D412yes—
707C24C22×D412yes—
708C24C2×#4112yes—
709C24C2×#4112yes—
710C24H(5,𝔽2)14yes—
711C24H(5,𝔽2)14yes—
712C24C2511yescharacteristic
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—44no—
718C2×D4—44no—
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—44no—
732C2×D4—44no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—4128no—
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—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—84no—
760C2×D4—82no—
761C2×D4—84no—
762C2×D4—82no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4#121116yes—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
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—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
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—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—82no—
887C22×C4—82no—
888C22×C4—82no—
889C22×C4—84no—
890C22×C4—82no—
891C22×C4—82no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C2×#4112yes—
906C22×C4H(5,𝔽2)14yes—
907C22×C4H(5,𝔽2)12yes—
908C22×C4H(5,𝔽2)12yes—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—84no—
918C4⋊C4—82no—
919C4⋊C4—82no—
920C22⋊C4—216no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—84no—
937C22⋊C4—82no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—82no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—82no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—82no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C42—28no—
958C42—44no—
959C42—84no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—22no—
996C23—22no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
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—432no—
1024C23—42no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—41no—
1052C23—41no—
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—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23—816no—
1109C23—816no—
1110C23—816no—
1111C23—816no—
1112C23C2×#12114yes—
1113C23C2×#12114yes—
1114C23C23×D411yescharacteristic
1115C23C23×D411yescharacteristic
1116C23C22×#4111yescharacteristic
1117C23C2×H(5,𝔽2)11yescharacteristic
1118C23C2×H(5,𝔽2)11yescharacteristic
1119C23C2×H(5,𝔽2)12yes—
1120C23C2×H(5,𝔽2)12yes—
1121C23C2×H(5,𝔽2)12yes—
1122C23#58511yescharacteristic
1123C23#58511yescharacteristic
1124C23#58512yes—
1125D4—416no—
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129D4—432no—
1130D4—88no—
1131D4—816no—
1132D4—816no—
1133D4—816no—
1134D4—816no—
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—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—416no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
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—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—41no—
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—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—41no—
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—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—88no—
1241C2×C4—88no—
1242C2×C4—88no—
1243C2×C4—88no—
1244C2×C4C2×#12114yes—
1245C2×C4#53414yes—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—44no—
1253C22—44no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
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—44no—
1282C22—44no—
1283C22—42no—
1284C22—42no—
1285C22—44no—
1286C22—44no—
1287C22—864no—
1288C22—82no—
1289C22—82no—
1290C22—81no—
1291C22—82no—
1292C22—81no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—81no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—81no—
1303C22—82no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22C22×#12111yescharacteristic
1311C22C2×#53411yescharacteristic
1312C22#344911yescharacteristic
1313C22#348412yes—
1314C22#348411yescharacteristic
1315C22#348411yescharacteristic
1316C22#348812yes—
1317C22#349611yescharacteristic
1318C22#349611yescharacteristic
1319C22#349811yescharacteristic
1320C22#350011yescharacteristic
1321C22#350511yescharacteristic
1322C22#350511yescharacteristic
1323C22#351312yes—
1324C22#351912yes—
1325C22#353212yes—
1326C22#353212yes—
1327C22#353312yes—
1328C22#353412yes—
1329C22#354212yes—
1330C22#354612yes—
1331C22#355812yes—
1332C22#356012yes—
1333C4—24no—
1334C4—24no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—82no—
1343C4—82no—
1344C4—81no—
1345C4—81no—
1346C4—82no—
1347C4—81no—
1348C4—82no—
1349C4—82no—
1350C4—81no—
1351C2—44no—
1352C2—44no—
1353C2—82no—
1354C2—84no—
1355C2—84no—
1356C2#3500011yescharacteristic
1357C2#3569111yescharacteristic
1358C2#3572811yescharacteristic
1359C2#3671411yescharacteristic
1360C2#3730011yescharacteristic
1361C2#4050211yescharacteristic
1362C2#4050611yescharacteristic
1363C2#4636712yes—
1364C2#4678712yes—
1365C2#4793412yes—
1366C2#4824112yes—
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×#2678C2semidirect
2. C2×#2408C2semidirect
3. C2×#2325C2semidirect
4. #16816C2semidirect
5. #16815C2semidirect
6. #16519C2semidirect
7. #16516C2semidirect
8. #16284C2semidirect
9. #16256C2semidirect
10. #15607C2semidirect
11. #15498C2semidirect
12. #15297C2semidirect
13. #15266C2semidirect
14. #14926C2semidirect
15. #14913C2semidirect
16. #14815C2semidirect
17. #14813C2semidirect
18. #14724C2semidirect
19. #14722C2semidirect
20. #14722C2semidirect
21. #14715C2semidirect
22. #14357C2semidirect
23. #13941C2semidirect
25. C22×#123C22semidirect
32. C22×C4×D4C22semidirect
36. C2×#396C22semidirect
37. C2×#396C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
49. C2×#392C22semidirect
50. C2×#392C22semidirect
55. C2×#390C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
59. C2×#387C22semidirect
60. C2×#387C22semidirect
64. C2×#386C22semidirect
65. C2×#386C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
71. C2×#385C22semidirect
72. C2×#382C22semidirect
74. C2×#380C22semidirect
79. C2×C4×C4⋊C4C22semidirect
80. C22×#95C22semidirect
81. #1444C22semidirect
82. #1444C22semidirect
83. #1443C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
121. C4⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
156. C2×#121D4semidirect
168. C2×C4×D4D4semidirect
384. C22×D4C2×D4semidirect
410. C23×C4C2×D4semidirect
465. C2×C4⋊C4C2×D4semidirect
572. C2×C22⋊C4C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26782
C2×#24082
C2×#23252
#168162
#168152
#165192
#165162
#162842
#162562
#156072
#154982
#152972
#152662
#149262
#149132
#148152
#148132
#147242
#147222
#147152
#143572
#139412