Finite Group Databasebeta

← #533092

Subgroups — #533092

Order 512.

4644 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2431C211yesmaximal, characteristic
2C2×#2367C211yesmaximal, characteristic, complemented
3C2×#2341C211yesmaximal, characteristic, complemented
4C2×#2339C211yesmaximal, characteristic, complemented
5C2×C4×#127C211yesmaximal, characteristic, complemented
6#14521C212yesmaximal, complemented
7#14374C212yesmaximal, complemented
8#14228C212yesmaximal, complemented
9#14189C212yesmaximal, complemented
10#14187C212yesmaximal, complemented
11#14026C211yesmaximal, characteristic, complemented
12#14025C211yesmaximal, characteristic, complemented
13#14018C211yesmaximal, characteristic, complemented
14#14007C212yesmaximal, complemented
15#13998C211yesmaximal, characteristic, complemented
16#13976C211yesmaximal, characteristic, complemented
17#13975C212yesmaximal, complemented
18#13970C211yesmaximal, characteristic, complemented
19#13876C211yesmaximal, characteristic, complemented
20#13820C211yesmaximal, characteristic, complemented
21#13813C212yesmaximal, complemented
22C4×#391C211yesmaximal, characteristic, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2212yes—
34C22×C4×D4C2212yes—
35#2431C4116yescomplemented
36C2×#392C2212yes—
37C2×#392C2212yes—
38#2367—28no—
39#2341—28no—
40#2339—28no—
41C4×#127—28no—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2212yes—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388C2212yes—
58C2×#388C2212yes—
59C2×#388C2211yescharacteristic
60C2×#388C2211yescharacteristic
61C2×#388C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#385C2212yes—
70C2×#385C2212yes—
71C2×#384C2211yescharacteristic
72C2×#381C2212yes—
73C2×#380C2212yes—
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2212yes—
84C2×C4×C22⋊C4C2211yescharacteristic
85C22×#95C2212yes—
86C2×C43C2211yescharacteristic
87#1444C2212yes—
88#1444C2212yes—
89#1442C2212yes—
90#1440C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1437C2212yes—
102#1437C2211yescharacteristic
103#1437C2212yes—
104#1437C2212yes—
105#1437C2211yescharacteristic
106#1437C2212yes—
107#1437C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2211yescharacteristic
113#1436C2212yes—
114#1436C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119#1434C2211yescharacteristic
120#1434C2211yescharacteristic
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2212yes—
125C4×#95C2212yes—
126C4×#95C2211yescharacteristic
127C4×#95C2211yescharacteristic
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—42no—
133C22×#41—42no—
134C22×#41C2×C418yescomplemented
135C23×Q8C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2312yes—
146C24×C4C2312yes—
147C2×#127—24no—
148C2×#127—24no—
149C2×#127C2×C418yes—
150C2×#124—24no—
151C2×#124—24no—
152C2×#124C2×C418yescomplemented
153C2×#121—42no—
154C2×#121—42no—
155C2×#121C2×C418yescomplemented
156C2×C4×Q8—24no—
157C2×C4×Q8—24no—
158C2×C4×Q8—24no—
159C2×C4×Q8—24no—
160C2×C4×Q8—42no—
161C2×C4×Q8—42no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×C4×D4—28no—
167C2×C4×D4—28no—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4—28no—
171C2×C4×D4—44no—
172C2×C4×D4—42no—
173C2×C4×D4—44no—
174C2×C4×D4—42no—
175C2×C4×D4—42no—
176C2×C4×D4—44no—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228C22×C42C2312yes—
229#392C2×C4116yescomplemented
230#392C2×C4116yescomplemented
231#391—24no—
232#391C2×C418yescomplemented
233#391D418yescomplemented
234#390—24no—
235#390—24no—
236#390—28no—
237#390—28no—
238#390—28no—
239#390—28no—
240#390—24no—
241#390—44no—
242#390—42no—
243#390C2×C418yescomplemented
244#390D418yescomplemented
245#389—42no—
246#388—24no—
247#388—28no—
248#388—28no—
249#388—24no—
250#388—44no—
251#386—28no—
252#386—28no—
253#386—28no—
254#386—44no—
255#386—44no—
256#386C2×C4116yescomplemented
257#386C2×C4116yescomplemented
258#385—28no—
259#385—44no—
260#384—24no—
261#381—28no—
262#380—24no—
263#380—24no—
264#380—28no—
265C4×C4⋊C4—24no—
266C4×C4⋊C4—24no—
267C4×C4⋊C4—42no—
268C4×C22⋊C4—28no—
269C4×C22⋊C4—24no—
270C4×C22⋊C4—24no—
271C4×C22⋊C4—28no—
272C4×C22⋊C4—44no—
273C4×C22⋊C4C2×C418yescomplemented
274C2×#95—28no—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2311yescharacteristic
310C43—24no—
311C25C2412yes—
312C25C2411yescharacteristic
313C25C2412yes—
314C2×#41—232no—
315C2×#41—232no—
316C2×#41—416no—
317C2×#41—416no—
318C2×#41—416no—
319C2×#41—416no—
320C2×#41—416no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8C22×C414yes—
326C22×Q8C2×D414yes—
327C22×Q8#4114yes—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4C22×C414yes—
363C22×D4C22×C418yes—
364C22×D4C22×C418yes—
365C22×D4C22×C418yes—
366C22×D4C22×C414yes—
367C22×D4C22×C418yes—
368C22×D4C2×D414yes—
369C22×D4#4114yes—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4C22×C414yes—
404C23×C4C22×C418yes—
405C23×C4C2411yescharacteristic
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425#127—232no—
426#124—232no—
427#121—416no—
428C4×Q8—416no—
429C4×Q8—416no—
430C4×D4—432no—
431C4×D4—416no—
432C4×D4—416no—
433C4×D4—432no—
434C4×D4—416no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
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—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—41no—
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⋊C4C22×C414yes—
469C2×C4⋊C4C2×D414yes—
470C2×C4⋊C4C2×D414yes—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
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—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
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⋊C4C22×C418yes—
541C2×C22⋊C4C22×C418yes—
542C2×C22⋊C4C22×C414yes—
543C2×C22⋊C4C22×C414yes—
544C2×C22⋊C4C22×C418yes—
545C2×C22⋊C4C22×C418yes—
546C2×C22⋊C4C22×C418yes—
547C2×C22⋊C4C2×D418yes—
548C2×C22⋊C4C2×D418yes—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—24no—
564C2×C42—24no—
565C2×C42—24no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—24no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—24no—
577C2×C42—24no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—41no—
581C2×C42—41no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42C22×C414yes—
587C2×C42C22×C414yes—
588C2×C42C2×D414yes—
589C2×C42C2×D414yes—
590C2×C42#4114yescomplemented
591#95—22no—
592#95—24no—
593#95—24no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—24no—
598#95—22no—
599#95—24no—
600#95—22no—
601#95—24no—
602#95—24no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—24no—
608#95—22no—
609#95—24no—
610#95—22no—
611#95—42no—
612#95—41no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95C22×C414yes—
620#95C22×C414yes—
621#95C22×C418yes—
622#95C22×C418yes—
623#95C2×D418yes—
624#95C2×D418yes—
625#95#4114yescomplemented
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—21no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—22no—
666C24C23×C414yes—
667C24C23×C412yes—
668C24C23×C414yes—
669C24C22×D414yes—
670C24C2×#4114yes—
671C24C2511yescharacteristic
672#41—4128no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—28no—
679C2×Q8C4×D4116yescomplemented
680C2×D4—216no—
681C2×D4—216no—
682C2×D4—216no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—216no—
687C2×D4—216no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—216no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—84no—
718C2×D4—84no—
719C2×D4—84no—
720C2×D4—84no—
721C2×D4C4×D4116yes—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—216no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—216no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4C23×C414yes—
866C22×C4C23×C412yes—
867C22×C4C23×C412yes—
868C22×C4C23×C412yes—
869C22×C4C23×C414yes—
870C22×C4C23×C412yes—
871C22×C4C23×C412yes—
872C22×C4C23×C412yes—
873C22×C4C22×D414yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D414yes—
877C22×C4C22×D414yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C2×#4112yes—
883C22×C4C2×#4112yes—
884C22×C4C2×#4114yes—
885C22×C4C2×#4112yes—
886C22×C4C2×#4112yes—
887C22×C4C2×#4112yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4112yes—
890C22×C4C2×#4112yes—
891C22×C4H(5,𝔽2)12yes—
892C22×C4H(5,𝔽2)12yes—
893C22×C4H(5,𝔽2)12yes—
894C22×C4H(5,𝔽2)12yes—
895C22×C4H(5,𝔽2)12yes—
896C22×C42−1+412yes—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—84no—
909C22⋊C4—216no—
910C22⋊C4—216no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—216no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C42—28no—
936C42—28no—
937C42—28no—
938C42—28no—
939C42—28no—
940C42—28no—
941C42—44no—
942C42—44no—
943C42—48no—
944C42—48no—
945C42—44no—
946C42—44no—
947C42—84no—
948C42—84no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—22no—
976C23—24no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—41no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—42no—
1005C23—41no—
1006C23—42no—
1007C23—41no—
1008C23—42no—
1009C23—41no—
1010C23—42no—
1011C23—41no—
1012C23—42no—
1013C23—42no—
1014C23—41no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—41no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—41no—
1023C23—42no—
1024C23—41no—
1025C23—42no—
1026C23—41no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
1041C23—42no—
1042C23—41no—
1043C23—42no—
1044C23—41no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—41no—
1052C23—42no—
1053C23C2×C4×D418yes—
1054C23C24×C411yescharacteristic
1055C23C23×D411yescharacteristic
1056C23C23×D411yescharacteristic
1057C23C22×#4111yescharacteristic
1058C23C22×#4111yescharacteristic
1059C23C22×#4111yescharacteristic
1060C23C22×#4111yescharacteristic
1061C23C2×H(5,𝔽2)11yescharacteristic
1062C23C2×H(5,𝔽2)11yescharacteristic
1063C23C2×H(5,𝔽2)11yescharacteristic
1064C23C2×H(5,𝔽2)11yescharacteristic
1065C23C2×H(5,𝔽2)11yescharacteristic
1066C23C2×2−1+411yescharacteristic
1067C23#58511yescharacteristic
1068C23#58511yescharacteristic
1069Q8—232no—
1070D4—232no—
1071D4—432no—
1072D4—432no—
1073D4—432no—
1074D4—416no—
1075D4—816no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—432no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—416no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—42no—
1206C2×C4—816no—
1207C2×C4—816no—
1208C2×C4—816no—
1209C2×C4C2×C4×D418yes—
1210C2×C4C2×C4×D414yes—
1211C2×C4C2×C4×D414yes—
1212C2×C4C4×#4114yes—
1213C2×C4#51814yes—
1214C2×C4#52014yes—
1215C2×C4D4214yes—
1216C2×C4#54614yes—
1217C2×C4#54614yes—
1218C2×C4#54614yes—
1219C2×C4#55014yes—
1220C2×C4#55114yes—
1221C22—28no—
1222C22—28no—
1223C22—28no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22—44no—
1241C22—42no—
1242C22—44no—
1243C22—42no—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—81no—
1251C22—82no—
1252C22—81no—
1253C22—82no—
1254C22—81no—
1255C22—82no—
1256C22—81no—
1257C22—82no—
1258C22—82no—
1259C22—81no—
1260C22—81no—
1261C22—82no—
1262C22—82no—
1263C22—81no—
1264C22—82no—
1265C22—81no—
1266C22C22×C4×D411yescharacteristic
1267C22C22×C4×D411yescharacteristic
1268C22C2×C4×#4111yescharacteristic
1269C22C2×#51811yescharacteristic
1270C22C2×#52011yescharacteristic
1271C22C4×H(5,𝔽2)11yescharacteristic
1272C22C4×H(5,𝔽2)11yescharacteristic
1273C22C2×D4211yescharacteristic
1274C22C2×#54611yescharacteristic
1275C22C2×#54611yescharacteristic
1276C22C2×#54611yescharacteristic
1277C22C2×#55011yescharacteristic
1278C22D4×#4111yescharacteristic
1279C22D4×#4111yescharacteristic
1280C22C2×#55111yescharacteristic
1281C22#347511yescharacteristic
1282C22#348011yescharacteristic
1283C22#348111yescharacteristic
1284C22#348311yescharacteristic
1285C22#348411yescharacteristic
1286C22#348911yescharacteristic
1287C22#349711yescharacteristic
1288C22#349811yescharacteristic
1289C22#350811yescharacteristic
1290C22#350811yescharacteristic
1291C22#351111yescharacteristic
1292C22#351111yescharacteristic
1293C22#351311yescharacteristic
1294C22#351711yescharacteristic
1295C22#352011yescharacteristic
1296C22#352211yescharacteristic
1297C22#354311yescharacteristic
1298C22#354611yescharacteristic
1299C22#355811yescharacteristic
1300C22#356211yescharacteristic
1301C4—28no—
1302C4—24no—
1303C4—24no—
1304C4—24no—
1305C4—24no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—81no—
1317C4—82no—
1318C4—81no—
1319C4—82no—
1320C4#235818yes—
1321C2—48no—
1322C2—82no—
1323C2—84no—
1324C2C2×#235811yescharacteristic
1325C2C4×#54611yescharacteristic
1326C2C4×#55011yescharacteristic
1327C2#3422611yescharacteristic
1328C2#3428811yescharacteristic
1329C2#3431311yescharacteristic
1330C2#3443811yescharacteristic
1331C2#5909311yescharacteristic
1332C2#5909711yescharacteristic
1333C2#5912411yescharacteristic
1334C2#5912811yescharacteristic
1335C2#5941011yescharacteristic
1336C2#5941411yescharacteristic
1337C2#5947411yescharacteristic
1338C2#5947811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2431C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2367C2semidirect
3. C2×#2341C2semidirect
4. C2×#2339C2semidirect
5. C2×C4×#127C2semidirect
6. #14521C2semidirect
7. #14374C2semidirect
8. #14228C2semidirect
9. #14189C2semidirect
10. #14187C2semidirect
11. #14026C2semidirect
12. #14025C2semidirect
13. #14018C2semidirect
14. #14007C2semidirect
15. #13998C2semidirect
16. #13976C2semidirect
17. #13975C2semidirect
18. #13970C2semidirect
19. #13876C2semidirect
20. #13820C2semidirect
21. #13813C2semidirect
22. C4×#391C2semidirect
23. C4×#388C2semidirect
35. #2431C4semidirect
134. C22×#41C2×C4semidirect
152. C2×#124C2×C4semidirect
155. C2×#121C2×C4semidirect
229. #392C2×C4semidirect
230. #392C2×C4semidirect
232. #391C2×C4semidirect
233. #391D4semidirect
243. #390C2×C4semidirect
244. #390D4semidirect
256. #386C2×C4semidirect
257. #386C2×C4semidirect
273. C4×C22⋊C4C2×C4semidirect
590. C2×C42#41semidirect
625. #95#41semidirect
679. C2×Q8C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24312
C2×#23672
C2×#23412
C2×#23392
C2×C4×#1272
#145212
#143742
#142282
#141892
#141872
#140262
#140252
#140182
#140072
#139982
#139762
#139752
#139702
#138762
#138202
#138132
C4×#3912
C4×#3882