Finite Group Databasebeta

← #773170

Subgroups — #773170

Order 512.

5428 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#548C211yesmaximal, characteristic
2C2×#2547C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2427C211yesmaximal, characteristic, complemented
5C2×#2434C211yesmaximal, characteristic, complemented
6C2×#2339C211yesmaximal, characteristic, complemented
7#16262C212yesmaximal, complemented
8#15311C212yesmaximal, complemented
9#15311C212yesmaximal, complemented
10#15277C212yesmaximal, complemented
11#15274C212yesmaximal, complemented
12#15179C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic, complemented
14#15177C211yesmaximal, characteristic, complemented
15#14758C212yesmaximal, complemented
16#14731C212yesmaximal, complemented
17#14027C211yesmaximal, characteristic, complemented
18#14024C211yesmaximal, characteristic, complemented
19#14017C211yesmaximal, characteristic, complemented
20#13975C212yesmaximal, complemented
21#13970C211yesmaximal, characteristic, complemented
22#13922C211yesmaximal, characteristic, complemented
23C4×#394C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C24×Q8C2211yescharacteristic
26C2×#548—28no—
27C2×#548—28no—
28C2×#548—28no—
29C22×C4⋊Q8C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×#124C2212yes—
33C22×#124C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2212yes—
36C22×C22⋊Q8C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C22×#121C2212yes—
39C22×#121C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42C22×C4×D4C2212yes—
43C22×C4×D4C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45#2547—28no—
46#2434—28no—
47#2432—28no—
48#2427—28no—
49C2×#397C2212yes—
50C2×#397C2212yes—
51C2×#397C2212yes—
52C2×#395C2212yes—
53C2×#395C2212yes—
54C2×#394C2211yescharacteristic
55C2×#394C2212yes—
56C2×#394C2212yes—
57C2×#394C2212yes—
58#2339—28no—
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#391C2211yescharacteristic
63C2×#391C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#391C2211yescharacteristic
66C2×#391C2211yescharacteristic
67C2×#390C2211yescharacteristic
68C2×#389C2211yescharacteristic
69C2×#386C2212yes—
70C2×#386C2212yes—
71C2×#386C2212yes—
72C2×#386C2212yes—
73C2×#385C2212yes—
74C2×#385C2212yes—
75C2×#385C2212yes—
76C2×#385C2212yes—
77C2×#381C2212yes—
78C2×#380C2211yescharacteristic
79C2×#380C2212yes—
80C2×#380C2212yes—
81C2×#380C2212yes—
82C2×#380C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic
87C2×C4×C22⋊C4C2211yescharacteristic
88C22×#95C2212yes—
89#1446C2212yes—
90#1446C2212yes—
91#1444C2212yes—
92#1444C2212yes—
93#1444C2212yes—
94#1444C2212yes—
95#1442C2211yescharacteristic
96#1442C2212yes—
97#1442C2212yes—
98#1441C2211yescharacteristic
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1440C2211yescharacteristic
103#1440C2211yescharacteristic
104#1440C2212yes—
105#1440C2212yes—
106#1440C2212yes—
107#1440C2212yes—
108#1439C2211yescharacteristic
109#1439C2211yescharacteristic
110#1439C2212yes—
111#1439C2212yes—
112#1439C2212yes—
113#1439C2212yes—
114#1439C2212yes—
115#1438C2211yescharacteristic
116#1438C2212yes—
117#1438C2212yes—
118#1436C2212yes—
119#1436C2212yes—
120#1436C2212yes—
121#1436C2212yes—
122C4⋊#95C2211yescharacteristic
123C4⋊#95C2211yescharacteristic
124C4⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C22⋊#95C2212yes—
129C22⋊#95C2212yes—
130C4×#95C2211yescharacteristic
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—24no—
134C22×#41—24no—
135C22×#41—42no—
136C22×#41—42no—
137C22×#41D418yes—
138C23×Q8—24no—
139C23×Q8—24no—
140C23×Q8—24no—
141C23×Q8—24no—
142C23×Q8—24no—
143C23×Q8—42no—
144C23×Q8—42no—
145C23×Q8C2311yescharacteristic
146C23×Q8C2311yescharacteristic
147C23×Q8C2312yes—
148C23×Q8C2311yescharacteristic
149C23×D4C2311yescharacteristic
150C23×D4C2312yes—
151C23×D4C2312yes—
152C23×D4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2312yes—
156C24×C4C2312yes—
157C24×C4C2312yes—
158C24×C4C2312yes—
159#548—2128no—
160C2×C4⋊Q8—24no—
161C2×C4⋊Q8—24no—
162C2×C4⋊Q8—24no—
163C2×C4⋊Q8—24no—
164C2×C4⋊Q8—24no—
165C2×C4⋊Q8—42no—
166C2×#124—28no—
167C2×#124—24no—
168C2×#124—24no—
169C2×#124—24no—
170C2×#124—24no—
171C2×#124—24no—
172C2×#124—28no—
173C2×#124—28no—
174C2×#124D418yes—
175C2×C22⋊Q8—24no—
176C2×C22⋊Q8—24no—
177C2×C22⋊Q8—28no—
178C2×C22⋊Q8—24no—
179C2×C22⋊Q8—24no—
180C2×C22⋊Q8—24no—
181C2×C22⋊Q8—24no—
182C2×C22⋊Q8—28no—
183C2×C22⋊Q8—28no—
184C2×C22⋊Q8—42no—
185C2×C22⋊Q8—42no—
186C2×C22⋊Q8—42no—
187C2×#121—28no—
188C2×#121—24no—
189C2×#121—24no—
190C2×#121—28no—
191C2×#121—28no—
192C2×#121D418yes—
193C2×C4×Q8—24no—
194C2×C4×Q8—24no—
195C2×C4×Q8—24no—
196C2×C4×D4—28no—
197C2×C4×D4—24no—
198C2×C4×D4—24no—
199C2×C4×D4—28no—
200C2×C4×D4—24no—
201C2×C4×D4—24no—
202C2×C4×D4—24no—
203C2×C4×D4—28no—
204C2×C4×D4—24no—
205C2×C4×D4—24no—
206C2×C4×D4—42no—
207C2×C4×D4—42no—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2311yescharacteristic
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254#397—28no—
255#397—28no—
256#397—28no—
257#395—28no—
258#395—28no—
259#394—28no—
260#394—28no—
261#394—28no—
262#394—24no—
263#391—24no—
264#391—24no—
265#391—24no—
266#391—24no—
267#391—24no—
268#391—24no—
269#391—42no—
270#391D418yescomplemented
271#390—24no—
272#389—24no—
273#386—28no—
274#386—28no—
275#386—28no—
276#386—28no—
277#385—28no—
278#385—28no—
279#385—28no—
280#385—28no—
281#381—28no—
282#380—24no—
283#380—28no—
284#380—28no—
285#380—28no—
286#380—42no—
287C4×C4⋊C4—24no—
288C4×C22⋊C4—24no—
289C4×C22⋊C4—24no—
290C4×C22⋊C4—24no—
291C4×C22⋊C4—24no—
292C2×#95—28no—
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2312yes—
324C2×#95C2312yes—
325C2×#95C2312yes—
326C2×#95C2312yes—
327C2×#95C2312yes—
328C2×#95C2312yes—
329C2×#95C2312yes—
330C2×#95C2312yes—
331C2×#95C2312yes—
332C25C2411yescharacteristic
333C25C2412yes—
334C25C2411yescharacteristic
335C2×#41—232no—
336C2×#41—232no—
337C2×#41—416no—
338C2×#41—416no—
339C2×#41—416no—
340C2×#41—416no—
341C2×#41—416no—
342C22×Q8—232no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—24no—
346C22×Q8—24no—
347C22×Q8—24no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—24no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—24no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—42no—
366C22×Q8—42no—
367C22×Q8—416no—
368C22×Q8—416no—
369C22×Q8—416no—
370C22×Q8—416no—
371C22×Q8—416no—
372C22×Q8—416no—
373C22×Q8C2×D414yes—
374C22×Q8C2×D414yes—
375C22×Q8C2×D414yes—
376C22×Q8#4114yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—24no—
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—24no—
383C22×D4—24no—
384C22×D4—24no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—24no—
390C22×D4—22no—
391C22×D4—24no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—41no—
395C22×D4—42no—
396C22×D4—42no—
397C22×D4—41no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4C2×D418yes—
401C22×D4C2×D418yes—
402C22×D4C2×D414yes—
403C22×D4C2×D414yes—
404C22×D4C2×D414yes—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—24no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—24no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—42no—
443C23×C4—42no—
444C23×C4C2×D414yes—
445C23×C4C2×D414yes—
446C23×C4C2×D418yes—
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2412yes—
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C4⋊Q8—416no—
468C4⋊Q8—416no—
469#124—264no—
470#124—232no—
471#124—416no—
472C22⋊Q8—232no—
473C22⋊Q8—264no—
474C22⋊Q8—416no—
475C22⋊Q8—416no—
476#121—264no—
477#121—232no—
478C4×Q8—232no—
479C4×D4—264no—
480C4×D4—232no—
481C4×D4—416no—
482C4×D4—416no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—42no—
524C2×C4⋊C4—42no—
525C2×C4⋊C4—42no—
526C2×C4⋊C4—42no—
527C2×C4⋊C4—42no—
528C2×C4⋊C4—42no—
529C2×C4⋊C4C2×D414yes—
530C2×C4⋊C4C2×D414yes—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4C2×D418yes—
600C2×C22⋊C4C2×D418yes—
601C2×C22⋊C4C2×D418yes—
602C2×C22⋊C4#4114yescomplemented
603C2×C42—24no—
604C2×C42—24no—
605C2×C42—24no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42C2×D414yes—
620C2×C42C2×D414yes—
621#95—22no—
622#95—24no—
623#95—24no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—24no—
634#95—24no—
635#95—24no—
636#95—24no—
637#95—24no—
638#95—24no—
639#95—24no—
640#95—24no—
641#95—24no—
642#95—24no—
643#95—24no—
644#95—24no—
645#95—24no—
646#95—24no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—41no—
651#95—42no—
652#95—42no—
653#95—42no—
654#95—42no—
655#95—42no—
656#95—42no—
657#95—42no—
658#95C2×D418yes—
659#95C2×D418yes—
660C24—21no—
661C24—22no—
662C24—21no—
663C24—21no—
664C24—22no—
665C24—21no—
666C24—22no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—21no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24C22×D412yes—
699C24C22×D414yes—
700C24C22×D414yes—
701C24C22×D414yes—
702C24C22×D412yes—
703C24C2×#4112yes—
704C242−1+412yes—
705C24C2511yescharacteristic
706#41—4128no—
707C2×Q8—216no—
708C2×Q8—28no—
709C2×Q8—28no—
710C2×Q8—28no—
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—28no—
714C2×Q8—28no—
715C2×Q8—28no—
716C2×Q8—28no—
717C2×Q8—48no—
718C2×Q8—48no—
719C2×Q8—48no—
720C2×Q8—48no—
721C2×Q8—48no—
722C2×Q8—4128no—
723C2×Q8—44no—
724C2×Q8—48no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×Q8—44no—
728C2×Q8—44no—
729C2×Q8—44no—
730C2×Q8—44no—
731C2×Q8—44no—
732C2×Q8—44no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8#121116yes—
736C2×D4—28no—
737C2×D4—216no—
738C2×D4—216no—
739C2×D4—216no—
740C2×D4—28no—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4#120116yes—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—216no—
773C22×C4—216no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—28no—
841C22×C4—28no—
842C22×C4—216no—
843C22×C4—28no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—22no—
848C22×C4—21no—
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—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—22no—
880C22×C4—21no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—22no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—48no—
915C22×C4—84no—
916C22×C4—84no—
917C22×C4—84no—
918C22×C4—84no—
919C22×C4—84no—
920C22×C4—84no—
921C22×C4—84no—
922C22×C4C22×D414yes—
923C22×C4C22×D412yes—
924C22×C4C22×D414yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D414yes—
928C22×C4C22×D412yes—
929C22×C4C22×D412yes—
930C22×C4C22×D414yes—
931C22×C4C22×D414yes—
932C22×C4C22×D412yes—
933C22×C4C22×D412yes—
934C22×C4C22×D412yes—
935C22×C4C22×D412yes—
936C22×C4C22×D412yes—
937C22×C4C2×#4112yes—
938C22×C4C2×#4114yes—
939C22×C4C2×#4112yes—
940C22×C4C2×#4112yes—
941C22×C4H(5,𝔽2)12yes—
942C22×C4H(5,𝔽2)12yes—
943C22×C42−1+412yes—
944C22×C42−1+412yes—
945C22×C42−1+412yes—
946C4⋊C4—216no—
947C4⋊C4—28no—
948C4⋊C4—216no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—48no—
954C4⋊C4—48no—
955C4⋊C4—48no—
956C4⋊C4—48no—
957C4⋊C4—48no—
958C4⋊C4—48no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—84no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—216no—
966C22⋊C4—216no—
967C22⋊C4—216no—
968C22⋊C4—216no—
969C22⋊C4—28no—
970C22⋊C4—44no—
971C22⋊C4—48no—
972C22⋊C4—44no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—84no—
985C22⋊C4—84no—
986C42—216no—
987C42—28no—
988C42—28no—
989C42—44no—
990C42—44no—
991C42—44no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—24no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—22no—
1016C23—22no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—42no—
1049C23—41no—
1050C23—42no—
1051C23—42no—
1052C23—41no—
1053C23—42no—
1054C23—42no—
1055C23—41no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—41no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C2×#12018yes—
1096C23#54714yes—
1097C23C23×D411yescharacteristic
1098C23C23×D411yescharacteristic
1099C23C23×D411yescharacteristic
1100C23C23×D411yescharacteristic
1101C23C22×#4111yescharacteristic
1102C23C22×#4111yescharacteristic
1103C23C2×H(5,𝔽2)11yescharacteristic
1104C23C2×H(5,𝔽2)11yescharacteristic
1105C23C2×2−1+411yescharacteristic
1106C23C2×2−1+411yescharacteristic
1107C23C2×2−1+411yescharacteristic
1108C23C2×2−1+411yescharacteristic
1109C23#58511yescharacteristic
1110C23#58511yescharacteristic
1111C23#58511yescharacteristic
1112Q8—232no—
1113Q8—432no—
1114Q8—416no—
1115Q8—88no—
1116D4—232no—
1117D4—432no—
1118D4—432no—
1119D4—416no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
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—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—432no—
1166C2×C4—432no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
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—42no—
1210C2×C4—41no—
1211C2×C4—416no—
1212C2×C4—416no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—42no—
1229C2×C4—41no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—42no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—41no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—41no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—816no—
1256C2×C4—816no—
1257C2×C4C2×#12014yes—
1258C2×C4C2×#12118yes—
1259C2×C4C2×#12114yes—
1260C2×C4#53414yes—
1261C2×C4D4214yes—
1262C2×C4D4214yes—
1263C2×C4#54614yes—
1264C2×C4#54614yes—
1265C2×C4#54814yescomplemented
1266C22—28no—
1267C22—24no—
1268C22—28no—
1269C22—24no—
1270C22—28no—
1271C22—24no—
1272C22—44no—
1273C22—42no—
1274C22—44no—
1275C22—42no—
1276C22—42no—
1277C22—44no—
1278C22—44no—
1279C22—42no—
1280C22—42no—
1281C22—44no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—42no—
1287C22—44no—
1288C22—44no—
1289C22—42no—
1290C22—42no—
1291C22—44no—
1292C22—44no—
1293C22—42no—
1294C22—44no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22C22×#12011yescharacteristic
1312C22C22×#12111yescharacteristic
1313C22C2×#53411yescharacteristic
1314C22C2×D4211yescharacteristic
1315C22C2×D4211yescharacteristic
1316C22C2×#54611yescharacteristic
1317C22C2×#54611yescharacteristic
1318C22C2×#54711yescharacteristic
1319C22C2×#54811yescharacteristic
1320C22D4×#4111yescharacteristic
1321C22D4×#4111yescharacteristic
1322C22#348211yescharacteristic
1323C22#348511yescharacteristic
1324C22#348611yescharacteristic
1325C22#348911yescharacteristic
1326C22#348911yescharacteristic
1327C22#348911yescharacteristic
1328C22#348911yescharacteristic
1329C22#348911yescharacteristic
1330C22#348911yescharacteristic
1331C22#349911yescharacteristic
1332C22#349911yescharacteristic
1333C22#349911yescharacteristic
1334C22#350011yescharacteristic
1335C22#351111yescharacteristic
1336C22#351411yescharacteristic
1337C22#351611yescharacteristic
1338C22#351611yescharacteristic
1339C22#351811yescharacteristic
1340C22#355211yescharacteristic
1341C22#355211yescharacteristic
1342C22#355411yescharacteristic
1343C22#356111yescharacteristic
1344C22#356111yescharacteristic
1345C22#356211yescharacteristic
1346C4—28no—
1347C4—24no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4—44no—
1356C4—42no—
1357C4—42no—
1358C4—42no—
1359C4—82no—
1360C4—81no—
1361C4—82no—
1362C4—81no—
1363C4—81no—
1364C4—82no—
1365C4#241018yes—
1366C2—48no—
1367C2—44no—
1368C2—82no—
1369C2C2×#241011yescharacteristic
1370C2#3573711yescharacteristic
1371C2#3608511yescharacteristic
1372C2#3621311yescharacteristic
1373C2#3644411yescharacteristic
1374C2#3986411yescharacteristic
1375C2#4291211yescharacteristic
1376C2#4509511yescharacteristic
1377C2#4513411yescharacteristic
1378C2#4530711yescharacteristic
1379C2#4533211yescharacteristic
1380C2#5906111yescharacteristic
1381C2#5912511yescharacteristic
1382C2#5913011yescharacteristic
1383C2#5941511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#548C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2547C2semidirect
3. C2×#2432C2semidirect
4. C2×#2427C2semidirect
5. C2×#2434C2semidirect
6. C2×#2339C2semidirect
7. #16262C2semidirect
8. #15311C2semidirect
9. #15311C2semidirect
10. #15277C2semidirect
11. #15274C2semidirect
12. #15179C2semidirect
13. #15178C2semidirect
14. #15177C2semidirect
15. #14758C2semidirect
16. #14731C2semidirect
17. #14027C2semidirect
18. #14024C2semidirect
19. #14017C2semidirect
20. #13975C2semidirect
21. #13970C2semidirect
22. #13922C2semidirect
23. C4×#394C2semidirect
270. #391D4semidirect
602. C2×C22⋊C4#41semidirect
1265. C2×C4#548semidirect

Maximal subgroups

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

subgroupindex
C22×#5482
C2×#25472
C2×#24322
C2×#24272
C2×#24342
C2×#23392
#162622
#153112
#152772
#152742
#151792
#151782
#151772
#147582
#147312
#140272
#140242
#140172
#139752
#139702
#139222
C4×#3942