Finite Group Databasebeta

← #726200

Subgroups — #726200

Order 512.

4736 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C211yesmaximal, characteristic, complemented
2C2×#2534C211yesmaximal, characteristic, complemented
3C2×#2417C211yesmaximal, characteristic, complemented
4C2×#2626C211yesmaximal, characteristic, complemented
5C22×#394C211yesmaximal, characteristic, complemented
6C2×#2321C211yesmaximal, characteristic, complemented
7#17015C212yesmaximal, complemented
8#16801C212yesmaximal, complemented
9#15833C212yesmaximal, complemented
10#15696C212yesmaximal, complemented
11#15493C212yesmaximal, complemented
12#15453C212yesmaximal, complemented
13#15163C212yesmaximal, complemented
14#14936C211yesmaximal, characteristic, complemented
15#14911C211yesmaximal, characteristic, complemented
16#14815C212yesmaximal, complemented
17#14734C211yesmaximal, characteristic, complemented
18#14715C211yesmaximal, characteristic
19#13996C211yesmaximal, characteristic, complemented
20#13995C211yesmaximal, characteristic, complemented
21#13903C211yesmaximal, characteristic, complemented
22#13902C211yesmaximal, characteristic, complemented
23C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2626—28no—
37#2561—28no—
38#2534—28no—
39#2417—28no—
40C2×#399C2212yescomplemented
41C2×#399C2212yescomplemented
42C2×#398C2211yescharacteristic, complemented
43C2×#398C2211yescharacteristic, complemented
44C2×#397C2212yescomplemented
45C2×#396C2212yescomplemented
46C2×#396C2212yescomplemented
47C2×#396C2212yescomplemented
48C2×#396C2211yescharacteristic, complemented
49C2×#396C2211yescharacteristic, complemented
50C2×#394—28no—
51C2×#394C2212yes—
52C2×#394C2212yes—
53C2×#394C2212yes—
54C2×#394C2212yes—
55C2×#394C2212yescomplemented
56C2×#393C2212yescomplemented
57C2×#393C2212yescomplemented
58C2×#392C2212yes—
59C2×#392C2212yes—
60#2321—28no—
61C2×#391C2211yescharacteristic, complemented
62C2×#390C2212yes—
63C2×#390C2212yes—
64C2×#390C2212yescomplemented
65C2×#390C2212yescomplemented
66C2×#389C2211yescharacteristic, complemented
67C2×#388C2212yescomplemented
68C2×#388C2212yescomplemented
69C2×#388C2212yescomplemented
70C2×#388C2212yescomplemented
71C2×#388C2212yescomplemented
72C2×#386C2211yescharacteristic
73C2×#386C2211yescharacteristic
74C2×#386C2211yescharacteristic
75C2×#386C2212yescomplemented
76C2×#386C2212yescomplemented
77C2×#385C2211yescharacteristic
78C2×#385C2211yescharacteristic
79C2×#385C2211yescharacteristic
80C2×#381C2211yescharacteristic
81C2×#381C2211yescharacteristic
82C2×#381C2211yescharacteristic
83C2×#380C2211yescharacteristic
84C2×#380C2211yescharacteristic
85C2×#380C2211yescharacteristic
86C2×#380C2211yescharacteristic, complemented
87C2×#379C2211yescharacteristic
88C2×#379C2211yescharacteristic
89C2×#379C2211yescharacteristic
90C2×#379C2211yescharacteristic
91C2×#379C2211yescharacteristic
92C2×#379C2211yescharacteristic
93C2×C4×C4⋊C4C2212yescomplemented
94C2×C4×C22⋊C4C2211yescharacteristic
95C2×C4×C22⋊C4C2211yescharacteristic
96C2×C4×C22⋊C4C2211yescharacteristic
97C22×#95C2211yescharacteristic
98#1445C2212yescomplemented
99#1445C2212yescomplemented
100#1445C2212yescomplemented
101#1445C2212yescomplemented
102#1444C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yescomplemented
117#1438C2212yescomplemented
118#1438C2212yescomplemented
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121#1437C2212yescomplemented
122#1437C2212yescomplemented
123#1436C2212yescomplemented
124#1436C2212yescomplemented
125C4⋊#95C2212yescomplemented
126C4⋊#95C2212yescomplemented
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2211yescharacteristic
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×Q8C2311yescharacteristic
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—44no—
135C23×D4—42no—
136C23×D4—44no—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C2×#123—24no—
149C2×#123—24no—
150C2×#123—42no—
151C2×C22⋊Q8—24no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—44no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—24no—
161C2×#120—42no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C22×C4⋊C4—44no—
166C22×C4⋊C4D418yescomplemented
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—24no—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—24no—
188C22×C22⋊C4—24no—
189C22×C22⋊C4—24no—
190C22×C22⋊C4—24no—
191C22×C22⋊C4—24no—
192C22×C22⋊C4—24no—
193C22×C22⋊C4—44no—
194C22×C22⋊C4—42no—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2312yes—
235#399—28no—
236#399—44no—
237#398—24no—
238#398—24no—
239#397—28no—
240#396—24no—
241#396—24no—
242#396—28no—
243#396—28no—
244#396—28no—
245#394—28no—
246#394—28no—
247#394—28no—
248#394—28no—
249#394—28no—
250#393—28no—
251#393—28no—
252#392—44no—
253#392—44no—
254#391—24no—
255#390—28no—
256#390—44no—
257#390—44no—
258#390—44no—
259#389—24no—
260#388—28no—
261#388—28no—
262#388—28no—
263#388—28no—
264#388—28no—
265#386—24no—
266#386—24no—
267#386—24no—
268#386—28no—
269#386—28no—
270#385—24no—
271#385—24no—
272#385—24no—
273#381—24no—
274#381—24no—
275#381—24no—
276#380—24no—
277#380—24no—
278#380—24no—
279#380D418yescomplemented
280#379—24no—
281#379—24no—
282#379—24no—
283#379—24no—
284#379—24no—
285#379—24no—
286C4×C4⋊C4—44no—
287C4×C22⋊C4—42no—
288C4×C22⋊C4—42no—
289C4×C22⋊C4D418yescomplemented
290C2×#95—24no—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C25—22no—
320C25—22no—
321C25—24no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—22no—
331C25—22no—
332C25—22no—
333C25—42no—
334C25—42no—
335C25—42no—
336C25—42no—
337C25—42no—
338C25—42no—
339C25—42no—
340C25#4114yes—
341C25C2412yes—
342C25C2411yescharacteristic
343C25C2412yes—
344C25C2411yescharacteristic
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—42no—
349C22×Q8—42no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—416no—
377C22×D4—416no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—432no—
387C22×D4—416no—
388C22×D4—432no—
389C22×D4#4114yes—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
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×C4C2×D414yes—
418C23×C4C2×D414yes—
419C23×C4C2×D414yes—
420C23×C4C2×D414yes—
421C23×C4C2×D414yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441#123—416no—
442C22⋊Q8—416no—
443C22⋊Q8—416no—
444#120—232no—
445#120—416no—
446C4×D4—416no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—416no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D414yes—
488C2×C4⋊C4C2×D414yes—
489C2×C4⋊C4C2×D414yes—
490C2×C4⋊C4C2×D418yescomplemented
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
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—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
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—416no—
570C2×C22⋊C4—416no—
571C2×C22⋊C4—416no—
572C2×C22⋊C4—416no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4C2×D414yes—
597C2×C22⋊C4C2×D414yes—
598C2×C22⋊C4C2×D414yes—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—24no—
603C2×C42—42no—
604C2×C42—42no—
605C2×C42—42no—
606C2×C42—42no—
607C2×C42—42no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42C2×D418yescomplemented
611#95—24no—
612#95—24no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—24no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—24no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95C2×D418yescomplemented
638#95C2×D418yescomplemented
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—28no—
644C24—28no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—21no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—21no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—28no—
684C24—28no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—48no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—44no—
712C24—44no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24—84no—
721C24—84no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24C22×D412yes—
728C24C22×D412yes—
729C24C22×D412yes—
730C24C2×#4114yes—
731C24C2×#4112yes—
732C24C2×#4112yes—
733C24C2×#4112yes—
734C24H(5,𝔽2)14yes—
735C24H(5,𝔽2)12yes—
736C242−1+412yes—
737C24C2511yescharacteristic
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—44no—
741C2×Q8—84no—
742C2×Q8—84no—
743C2×D4—216no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—216no—
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—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—4128no—
762C2×D4—48no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—48no—
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—84no—
778C2×D4—84no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—28no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
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—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
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—28no—
830C22×C4—28no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4#127116yes—
904C22×C4C22×D412yes—
905C22×C4C22×D414yes—
906C22×C4C22×D414yes—
907C22×C4C22×D414yes—
908C22×C4C22×D412yes—
909C22×C4C22×D414yes—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913C22×C4C22×D412yes—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C2×#4112yes—
919C22×C4H(5,𝔽2)14yes—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—82no—
933C4⋊C4—82no—
934C4⋊C4—84no—
935C4⋊C4—84no—
936C4⋊C4—84no—
937C22⋊C4—216no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—82no—
962C22⋊C4—82no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C22⋊C4—84no—
968C22⋊C4—84no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C22⋊C4—84no—
973C42—48no—
974C42—44no—
975C42—84no—
976C42—84no—
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—22no—
995C23—22no—
996C23—24no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—42no—
1026C23—42no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—41no—
1033C23—42no—
1034C23—41no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
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—42no—
1090C23—42no—
1091C23—416no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23—816no—
1100C23—88no—
1101C23—88no—
1102C23—88no—
1103C23—88no—
1104C23—88no—
1105C23—88no—
1106C23—88no—
1107C23—88no—
1108C23#52514yes—
1109C23C2×#12714yes—
1110C23#53714yes—
1111C23#54614yes—
1112C23#54614yes—
1113C23#54814yes—
1114C23#54814yes—
1115C23C23×D411yescharacteristic
1116C23C23×D411yescharacteristic
1117C23C23×D411yescharacteristic
1118C23C22×#4111yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C2×H(5,𝔽2)12yes—
1121C23C2×H(5,𝔽2)11yescharacteristic
1122C23C2×H(5,𝔽2)12yes—
1123C23C2×2−1+411yescharacteristic
1124C23#58512yes—
1125C23#58512yes—
1126Q8—88no—
1127D4—432no—
1128D4—432no—
1129D4—416no—
1130D4—816no—
1131D4—816no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—416no—
1169C2×C4—416no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
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—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
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×#12714yes—
1245C2×C4C2×#12714yes—
1246C2×C4#53414yes—
1247C22—28no—
1248C22—28no—
1249C22—28no—
1250C22—28no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—42no—
1272C22—44no—
1273C22—44no—
1274C22—42no—
1275C22—44no—
1276C22—832no—
1277C22—832no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—81no—
1290C22—82no—
1291C22—82no—
1292C22—81no—
1293C22—82no—
1294C22—81no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—81no—
1299C22—82no—
1300C22#254018yes—
1301C22C2×#52511yescharacteristic
1302C22C22×#12711yescharacteristic
1303C22C2×#53411yescharacteristic
1304C22C2×#53711yescharacteristic
1305C22#344911yescharacteristic
1306C22C2×#54611yescharacteristic
1307C22C2×#54611yescharacteristic
1308C22C2×#54811yescharacteristic
1309C22C2×#54811yescharacteristic
1310C22#348411yescharacteristic
1311C22#348711yescharacteristic
1312C22#348812yes—
1313C22#348812yes—
1314C22#349012yes—
1315C22#349112yes—
1316C22#349612yes—
1317C22#349612yes—
1318C22#351312yes—
1319C22#351412yes—
1320C22#353212yes—
1321C22#353312yes—
1322C22#353512yes—
1323C22#356112yes—
1324C4—24no—
1325C4—24no—
1326C4—24no—
1327C4—44no—
1328C4—42no—
1329C4—44no—
1330C4—44no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—82no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—82no—
1343C2—28no—
1344C2—82no—
1345C2—84no—
1346C2—84no—
1347C2C2×#254011yescharacteristic
1348C2#3500111yescharacteristic
1349C2#3556511yescharacteristic
1350C2#3576212yes—
1351C2#3783211yescharacteristic
1352C2#3784311yescharacteristic
1353C2#3911611yescharacteristic
1354C2#3912311yescharacteristic
1355C2#4051412yes—
1356C2#4302412yes—
1357C2#4391012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2561C2semidirect
2. C2×#2534C2semidirect
3. C2×#2417C2semidirect
4. C2×#2626C2semidirect
5. C22×#394C2semidirect
6. C2×#2321C2semidirect
7. #17015C2semidirect
8. #16801C2semidirect
9. #15833C2semidirect
10. #15696C2semidirect
11. #15493C2semidirect
12. #15453C2semidirect
13. #15163C2semidirect
14. #14936C2semidirect
15. #14911C2semidirect
16. #14815C2semidirect
17. #14734C2semidirect
19. #13996C2semidirect
20. #13995C2semidirect
21. #13903C2semidirect
22. #13902C2semidirect
23. C22⋊C4×C4⋊C4C2semidirect
27. C22×C22⋊Q8C22semidirect
40. C2×#399C22semidirect
41. C2×#399C22semidirect
42. C2×#398C22semidirect
43. C2×#398C22semidirect
44. C2×#397C22semidirect
45. C2×#396C22semidirect
46. C2×#396C22semidirect
47. C2×#396C22semidirect
48. C2×#396C22semidirect
49. C2×#396C22semidirect
55. C2×#394C22semidirect
56. C2×#393C22semidirect
57. C2×#393C22semidirect
61. C2×#391C22semidirect
64. C2×#390C22semidirect
65. C2×#390C22semidirect
66. C2×#389C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
69. C2×#388C22semidirect
70. C2×#388C22semidirect
71. C2×#388C22semidirect
75. C2×#386C22semidirect
76. C2×#386C22semidirect
86. C2×#380C22semidirect
93. C2×C4×C4⋊C4C22semidirect
98. #1445C22semidirect
99. #1445C22semidirect
100. #1445C22semidirect
101. #1445C22semidirect
102. #1444C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
116. #1438C22semidirect
117. #1438C22semidirect
118. #1438C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
121. #1437C22semidirect
122. #1437C22semidirect
123. #1436C22semidirect
124. #1436C22semidirect
125. C4⋊#95C22semidirect
126. C4⋊#95C22semidirect
166. C22×C4⋊C4D4semidirect
279. #380D4semidirect
289. C4×C22⋊C4D4semidirect
490. C2×C4⋊C4C2×D4semidirect
610. C2×C42C2×D4semidirect
637. #95C2×D4semidirect
638. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#25342
C2×#24172
C2×#26262
C22×#3942
C2×#23212
#170152
#168012
#158332
#156962
#154932
#154532
#151632
#149362
#149112
#148152
#147342
#147152
#139962
#139952
#139032
#139022
C22⋊C4×C4⋊C42