Finite Group Databasebeta

← #4433788

Subgroups — #4433788

Order 512.

3847 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2813C211yesmaximal, characteristic, complemented
2C2×#2539C211yesmaximal, characteristic, complemented
3C2×#2411C211yesmaximal, characteristic, complemented
4C2×#2620C211yesmaximal, characteristic, complemented
5C2×#2663C211yesmaximal, characteristic, complemented
6C2×#2626C211yesmaximal, characteristic, complemented
7#17071C212yesmaximal, complemented
8#17064C211yesmaximal, characteristic, complemented
9#16814C211yesmaximal, characteristic, complemented
10#16809C211yesmaximal, characteristic, complemented
11#16801C212yesmaximal, complemented
12#16509C211yesmaximal, characteristic, complemented
13#15384C212yesmaximal, complemented
14#15370C212yesmaximal, complemented
15#15283C212yesmaximal, complemented
16#15267C212yesmaximal, complemented
17#15172C211yesmaximal, characteristic, complemented
18#15155C211yesmaximal, characteristic, complemented
19#15134C212yesmaximal, complemented
20#15065C211yesmaximal, characteristic, complemented
21#14928C211yesmaximal, characteristic, complemented
22#14815C212yesmaximal, complemented
23#13801C211yesmaximal, characteristic, complemented
24C22×#124C2211yescharacteristic, complemented
25C22×#123C2211yescharacteristic
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2212yes—
30C22×#120C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33#2813—28no—
34#2663—28no—
35#2626—28no—
36#2620—28no—
37#2539—28no—
38#2411—28no—
39C2×#400C2211yescharacteristic, complemented
40C2×#400C2211yescharacteristic, complemented
41C2×#399C2211yescharacteristic
42C2×#399C2211yescharacteristic
43C2×#399C2211yescharacteristic
44C2×#399C2211yescharacteristic
45C2×#399C2212yes—
46C2×#399C2211yescharacteristic, complemented
47C2×#399C2211yescharacteristic, complemented
48C2×#399C2212yescomplemented
49C2×#399C2212yescomplemented
50C2×#397C2212yes—
51C2×#396C2211yescharacteristic
52C2×#396C2212yes—
53C2×#396C2211yescharacteristic
54C2×#396C2212yes—
55C2×#396C2212yescomplemented
56C2×#396C2212yescomplemented
57C2×#396C2212yescomplemented
58C2×#395C2211yescharacteristic, complemented
59C2×#394C2212yes—
60C2×#394C2212yes—
61C2×#394C2212yes—
62C2×#394C2212yes—
63C2×#394C2211yescharacteristic
64C2×#394C2211yescharacteristic
65C2×#394C2211yescharacteristic, complemented
66C2×#394C2212yescomplemented
67C2×#393C2211yescharacteristic
68C2×#393C2211yescharacteristic
69C2×#393C2211yescharacteristic, complemented
70C2×#392C2211yescharacteristic
71C2×#392C2211yescharacteristic
72C2×#392C2212yes—
73C2×#392C2212yes—
74C2×#392C2212yes—
75C2×#392C2211yescharacteristic, complemented
76C2×#391C2211yescharacteristic, complemented
77C2×#390C2212yes—
78C2×#390C2212yes—
79C2×#390C2211yescharacteristic
80C2×#390C2211yescharacteristic
81C2×#390C2212yes—
82C2×#390C2212yes—
83C2×#390C2212yes—
84C2×#390C2211yescharacteristic, complemented
85C2×#390C2212yescomplemented
86C2×#389C2212yescomplemented
87C2×#388C2211yescharacteristic
88C2×#388C2211yescharacteristic
89C2×#388C2212yescomplemented
90C2×#386C2211yescharacteristic
91C2×#385C2212yes—
92C2×#385C2211yescharacteristic
93C2×#384C2211yescharacteristic, complemented
94C2×#384C2212yescomplemented
95C2×#380C2211yescharacteristic
96C2×#379C2212yes—
97C2×#379C2211yescharacteristic
98C2×C4×C4⋊C4C2212yescomplemented
99C2×C4×C22⋊C4C2211yescharacteristic
100#1445C2212yescomplemented
101#1444C2212yescomplemented
102#1444C2212yescomplemented
103#1444C2212yescomplemented
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yes—
118#1438C2212yescomplemented
119#1437C2212yes—
120#1437C2212yes—
121#1437C2212yes—
122#1437C2212yescomplemented
123C4⋊#95C2212yescomplemented
124C4⋊#95C2212yescomplemented
125#1434C2211yescharacteristic, complemented
126#1434C2211yescharacteristic, complemented
127C4×#95C2211yescharacteristic, complemented
128C4×#95C2211yescharacteristic, complemented
129C26C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C2×#124—24no—
142C2×#124—44no—
143C2×#123—24no—
144C2×#123—24no—
145C2×#123—24no—
146C2×#123—28no—
147C2×#123—44no—
148C2×#123—44no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—24no—
152C2×#121—24no—
153C2×#121—24no—
154C2×#121—24no—
155C2×#120—24no—
156C2×#120—28no—
157C2×#120—44no—
158C2×#120—44no—
159C2×#120—44no—
160C2×#117—44no—
161C2×#117D418yescomplemented
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2312yes—
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228#400—24no—
229#400—24no—
230#399—24no—
231#399—24no—
232#399—24no—
233#399—24no—
234#399—24no—
235#399—24no—
236#399—44no—
237#399—44no—
238#399—44no—
239#397—28no—
240#396—28no—
241#396—28no—
242#396—28no—
243#396—28no—
244#396—24no—
245#396—24no—
246#396—28no—
247#395—24no—
248#394—24no—
249#394—24no—
250#394—28no—
251#394—28no—
252#394—28no—
253#394—28no—
254#394—28no—
255#394—24no—
256#393—24no—
257#393—24no—
258#393—24no—
259#392—28no—
260#392—24no—
261#392—24no—
262#392—24no—
263#392—44no—
264#392—44no—
265#391—24no—
266#390—24no—
267#390—24no—
268#390—24no—
269#390—28no—
270#390—28no—
271#390—44no—
272#390—44no—
273#390—44no—
274#390—44no—
275#389—28no—
276#388—28no—
277#388—24no—
278#388—24no—
279#386—24no—
280#385—28no—
281#385—24no—
282#384—24no—
283#384—44no—
284#380D418yescomplemented
285#379—28no—
286#379—24no—
287C4×C4⋊C4—44no—
288C4×C22⋊C4D418yescomplemented
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—41no—
319C25—41no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25C2411yescharacteristic
325C25C2412yes—
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—41no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—41no—
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—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4C2×D414yes—
390C23×C4C2×D414yes—
391C23×C4C2×D414yes—
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2412yes—
410#124—416no—
411#123—432no—
412#123—416no—
413C22⋊Q8—416no—
414#121—416no—
415#120—416no—
416#120—432no—
417#117—416no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
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—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×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⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4C2×D414yes—
469C2×C4⋊C4C2×D414yes—
470C2×C4⋊C4C2×D418yes—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
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—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—41no—
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—416no—
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⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4C2×D414yes—
578C2×C22⋊C4C2×D418yes—
579C2×C22⋊C4C2×D414yes—
580C2×C22⋊C4C2×D418yes—
581C2×C42—24no—
582C2×C42—24no—
583C2×C42—24no—
584C2×C42—24no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42—42no—
591C2×C42C2×D414yes—
592C2×C42C2×D414yes—
593C2×C42C2×D418yes—
594#95—22no—
595#95—22no—
596#95—24no—
597#95—24no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95C2×D414yes—
615#95C2×D414yes—
616#95C2×D414yes—
617#95C2×D414yes—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—22no—
626C24—28no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—21no—
650C24—21no—
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—21no—
664C24—21no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—21no—
672C24—21no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—44no—
679C24—48no—
680C24—44no—
681C24—44no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—82no—
686C24—82no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24C22×D412yes—
696C24C22×D412yes—
697C24C22×D412yes—
698C242−1+412yes—
699C242−1+412yes—
700C24C2511yescharacteristic
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—84no—
705C2×Q8—84no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—44no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—82no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4—82no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
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—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
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—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—44no—
849C22×C4—82no—
850C22×C4—82no—
851C22×C4—84no—
852C22×C4#127116yes—
853C22×C4C22×D414yes—
854C22×C4C22×D414yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C22×D414yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×D414yes—
867C22×C4H(5,𝔽2)14yes—
868C22×C4H(5,𝔽2)14yes—
869C22×C4H(5,𝔽2)14yes—
870C4⋊C4—28no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—84no—
882C4⋊C4—82no—
883C4⋊C4—84no—
884C4⋊C4—84no—
885C4⋊C4—84no—
886C4⋊C4—84no—
887C4⋊C4—82no—
888C4⋊C4—84no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—84no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—82no—
919C22⋊C4—84no—
920C22⋊C4—82no—
921C22⋊C4—82no—
922C22⋊C4—84no—
923C22⋊C4—82no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C42—28no—
929C42—48no—
930C42—44no—
931C42—48no—
932C42—84no—
933C23—22no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—24no—
943C23—24no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—416no—
958C23—42no—
959C23—42no—
960C23—42no—
961C23—42no—
962C23—42no—
963C23—42no—
964C23—42no—
965C23—42no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—42no—
971C23—42no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—41no—
985C23—41no—
986C23—42no—
987C23—42no—
988C23—41no—
989C23—41no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—41no—
1003C23—42no—
1004C23—42no—
1005C23—41no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—41no—
1011C23—42no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—41no—
1019C23—42no—
1020C23—41no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—41no—
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—88no—
1061C23—88no—
1062C23—816no—
1063C23—88no—
1064C23—816no—
1065C23—816no—
1066C23—88no—
1067C23—88no—
1068C23—88no—
1069C23—816no—
1070C23C2×#12714yes—
1071C23C23×D411yescharacteristic
1072C23C23×D411yescharacteristic
1073C23C23×D411yescharacteristic
1074C23C2×H(5,𝔽2)12yes—
1075C23C2×H(5,𝔽2)12yes—
1076C23C2×H(5,𝔽2)12yes—
1077C23C2×2−1+411yescharacteristic
1078C23C2×2−1+411yescharacteristic
1079C23#58512yes—
1080C23#58511yescharacteristic
1081C23#58511yescharacteristic
1082Q8—88no—
1083D4—816no—
1084D4—88no—
1085D4—88no—
1086D4—816no—
1087D4—88no—
1088D4—816no—
1089D4—88no—
1090D4—816no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—416no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—88no—
1195C2×C4C2×#12714yes—
1196C2×C4C2×#12714yes—
1197C2×C4#53414yes—
1198C2×C4#53518yes—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—42no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—44no—
1214C22—44no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—44no—
1219C22—44no—
1220C22—832no—
1221C22—81no—
1222C22—82no—
1223C22—82no—
1224C22—82no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—82no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—82no—
1235C22—81no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—81no—
1245C22—82no—
1246C22—81no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—81no—
1251C22—82no—
1252C22—81no—
1253C22—82no—
1254C22—81no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22C22×#12711yescharacteristic
1260C22C2×#53411yescharacteristic
1261C22C2×#53512yes—
1262C22#344911yescharacteristic
1263C22#348511yescharacteristic
1264C22#348611yescharacteristic
1265C22#348911yescharacteristic
1266C22#348911yescharacteristic
1267C22#348911yescharacteristic
1268C22#348911yescharacteristic
1269C22#349612yes—
1270C22#349612yes—
1271C22#349811yescharacteristic
1272C22#349812yes—
1273C22#349811yescharacteristic
1274C22#353412yes—
1275C22#353512yes—
1276C22#353612yes—
1277C22#353612yes—
1278C22#354012yes—
1279C22#354612yes—
1280C22#356012yes—
1281C22#356112yes—
1282C4—28no—
1283C4—24no—
1284C4—24no—
1285C4—24no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—81no—
1293C4—81no—
1294C4—82no—
1295C4—81no—
1296C4—82no—
1297C4—81no—
1298C4—81no—
1299C4—82no—
1300C2—44no—
1301C2—82no—
1302C2—82no—
1303C2—162no—
1304C2—161no—
1305C2#3500111yescharacteristic
1306C2#3527411yescharacteristic
1307C2#3563411yescharacteristic
1308C2#4051712yes—
1309C2#4195211yescharacteristic
1310C2#4196011yescharacteristic
1311C2#4230811yescharacteristic
1312C2#4244312yes—
1313C2#4298811yescharacteristic
1314C2#4785612yes—
1315C2#4956912yes—
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×#2813C2semidirect
2. C2×#2539C2semidirect
3. C2×#2411C2semidirect
4. C2×#2620C2semidirect
5. C2×#2663C2semidirect
6. C2×#2626C2semidirect
7. #17071C2semidirect
8. #17064C2semidirect
9. #16814C2semidirect
10. #16809C2semidirect
11. #16801C2semidirect
12. #16509C2semidirect
13. #15384C2semidirect
14. #15370C2semidirect
15. #15283C2semidirect
16. #15267C2semidirect
17. #15172C2semidirect
18. #15155C2semidirect
19. #15134C2semidirect
20. #15065C2semidirect
21. #14928C2semidirect
22. #14815C2semidirect
23. #13801C2semidirect
24. C22×#124C22semidirect
39. C2×#400C22semidirect
40. C2×#400C22semidirect
46. C2×#399C22semidirect
47. C2×#399C22semidirect
48. C2×#399C22semidirect
49. C2×#399C22semidirect
55. C2×#396C22semidirect
56. C2×#396C22semidirect
57. C2×#396C22semidirect
58. C2×#395C22semidirect
65. C2×#394C22semidirect
66. C2×#394C22semidirect
69. C2×#393C22semidirect
75. C2×#392C22semidirect
76. C2×#391C22semidirect
84. C2×#390C22semidirect
85. C2×#390C22semidirect
86. C2×#389C22semidirect
89. C2×#388C22semidirect
93. C2×#384C22semidirect
94. C2×#384C22semidirect
98. C2×C4×C4⋊C4C22semidirect
100. #1445C22semidirect
101. #1444C22semidirect
102. #1444C22semidirect
103. #1444C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
118. #1438C22semidirect
122. #1437C22semidirect
123. C4⋊#95C22semidirect
124. C4⋊#95C22semidirect
125. #1434C22semidirect
126. #1434C22semidirect
127. C4×#95C22semidirect
128. C4×#95C22semidirect
161. C2×#117D4semidirect
284. #380D4semidirect
288. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28132
C2×#25392
C2×#24112
C2×#26202
C2×#26632
C2×#26262
#170712
#170642
#168142
#168092
#168012
#165092
#153842
#153702
#152832
#152672
#151722
#151552
#151342
#150652
#149282
#148152
#138012