Finite Group Databasebeta

← #533097

Subgroups — #533097

Order 512.

4508 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2431C211yesmaximal, characteristic
2C2×#2366C211yesmaximal, characteristic, complemented
3C2×#2341C211yesmaximal, characteristic, complemented
4C2×#2339C211yesmaximal, characteristic, complemented
5C2×C4×#124C211yesmaximal, characteristic, complemented
6#14520C212yesmaximal, complemented
7#14374C212yesmaximal, complemented
8#14228C212yesmaximal, complemented
9#14207C212yesmaximal, complemented
10#14187C212yesmaximal, complemented
11#14026C211yesmaximal, characteristic, complemented
12#14025C211yesmaximal, characteristic, complemented
13#14017C211yesmaximal, characteristic, complemented
14#13999C212yesmaximal, complemented
15#13998C211yesmaximal, characteristic, complemented
16#13984C212yesmaximal, complemented
17#13979C211yesmaximal, characteristic, complemented
18#13970C211yesmaximal, characteristic, complemented
19#13875C211yesmaximal, characteristic, complemented
20#13817C211yesmaximal, characteristic, complemented
21#13813C212yesmaximal, complemented
22C4×#390C211yesmaximal, 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×D4C2212yes—
33C22×C4×D4C2211yescharacteristic
34#2431C4116yescomplemented
35C2×#392C2212yes—
36C2×#392C2212yes—
37#2366—28no—
38#2341—28no—
39#2339—28no—
40C4×#124—28no—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388C2212yes—
56C2×#388C2211yescharacteristic
57C2×#388C2211yescharacteristic
58C2×#388C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#382C2211yescharacteristic
69C2×#381C2212yes—
70C2×#380C2212yes—
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2212yes—
79C2×C4×C22⋊C4C2212yes—
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2211yescharacteristic
84C22×#95C2212yes—
85C2×C43C2211yescharacteristic
86#1444C2212yes—
87#1443C2212yes—
88#1442C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1438C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1437C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2211yescharacteristic
104#1437C2212yes—
105#1437C2212yes—
106#1437C2211yescharacteristic
107#1437C2212yes—
108#1436C2211yescharacteristic
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118#1434C2212yes—
119#1434C2211yescharacteristic
120#1434C2212yes—
121#1434C2211yescharacteristic
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#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×D4C2311yescharacteristic
140C23×D4C2312yes—
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—42no—
171C2×C4×D4—42no—
172C2×C4×D4—42no—
173C2×C4×D4—44no—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224#392C2×C4116yescomplemented
225#392C2×C4116yescomplemented
226#391—24no—
227#391C2×C418yescomplemented
228#391D418yescomplemented
229#390—24no—
230#390—24no—
231#390—28no—
232#390—28no—
233#390—28no—
234#390—24no—
235#390—44no—
236#390—42no—
237#390C2×C418yescomplemented
238#390D418yescomplemented
239#389—42no—
240#388—24no—
241#388—28no—
242#388—28no—
243#388—24no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—28no—
248#386—28no—
249#386—44no—
250#386—44no—
251#386C2×C4116yescomplemented
252#386C2×C4116yescomplemented
253#382—24no—
254#381—28no—
255#380—24no—
256#380—24no—
257#380—28no—
258C4×C4⋊C4—24no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—42no—
261C4×C22⋊C4—28no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—28no—
265C4×C22⋊C4—28no—
266C4×C22⋊C4—44no—
267C4×C22⋊C4—44no—
268C4×C22⋊C4C2×C418yescomplemented
269C2×#95—28no—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2311yescharacteristic
307C43—24no—
308C25C2412yes—
309C25C2411yescharacteristic
310C25C2412yes—
311C2×#41—232no—
312C2×#41—232no—
313C2×#41—416no—
314C2×#41—416no—
315C2×#41—416no—
316C2×#41—416no—
317C2×#41—416no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8C22×C414yes—
323C22×Q8C2×D414yes—
324C22×Q8#4114yes—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
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×D4C22×C414yes—
360C22×D4C22×C418yes—
361C22×D4C22×C418yes—
362C22×D4C22×C414yes—
363C22×D4C22×C418yes—
364C22×D4C22×C418yes—
365C22×D4C2×D414yes—
366C22×D4#4114yes—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
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—42no—
389C23×C4—42no—
390C23×C4—42no—
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×C4C22×C414yes—
401C23×C4C22×C418yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422#127—232no—
423#124—232no—
424#121—416no—
425C4×Q8—416no—
426C4×Q8—416no—
427C4×D4—416no—
428C4×D4—416no—
429C4×D4—432no—
430C4×D4—416no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4C22×C414yes—
458C2×C4⋊C4C2×D414yes—
459C2×C4⋊C4C2×D414yes—
460C2×C4⋊C4#4114yescomplemented
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
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—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
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⋊C4C22×C418yes—
531C2×C22⋊C4C22×C418yes—
532C2×C22⋊C4C22×C414yes—
533C2×C22⋊C4C22×C418yes—
534C2×C22⋊C4C22×C414yes—
535C2×C22⋊C4C22×C418yes—
536C2×C22⋊C4C22×C418yes—
537C2×C22⋊C4C2×D418yes—
538C2×C22⋊C4C2×D418yes—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—24no—
549C2×C42—22no—
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—24no—
559C2×C42—24no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—24no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—41no—
572C2×C42—41no—
573C2×C42—41no—
574C2×C42—41no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42C22×C414yes—
578C2×C42C22×C414yes—
579C2×C42C2×D414yes—
580C2×C42C2×D414yes—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—22no—
585#95—24no—
586#95—22no—
587#95—22no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—24no—
599#95—22no—
600#95—41no—
601#95—42no—
602#95—41no—
603#95—41no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95C22×C414yes—
612#95C22×C414yes—
613#95C22×C418yes—
614#95C22×C418yes—
615#95C2×D418yes—
616#95C2×D418yes—
617#95#4114yescomplemented
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—21no—
655C24—21no—
656C24—22no—
657C24—22no—
658C24C23×C414yes—
659C24C23×C412yes—
660C24C23×C414yes—
661C24C22×D414yes—
662C24C2×#4114yes—
663C24C2511yescharacteristic
664#41—4128no—
665C2×Q8—28no—
666C2×Q8—28no—
667C2×Q8—28no—
668C2×Q8—28no—
669C2×Q8—28no—
670C2×Q8—28no—
671C2×Q8C4×D4116yescomplemented
672C2×D4—216no—
673C2×D4—216no—
674C2×D4—216no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—216no—
679C2×D4—216no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—84no—
706C2×D4—84no—
707C2×D4—84no—
708C2×D4—84no—
709C2×D4—84no—
710C2×D4—84no—
711C2×D4—84no—
712C2×D4—84no—
713C2×D4C4×D4116yes—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—216no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
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—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—216no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
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—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4C23×C412yes—
860C22×C4C23×C414yes—
861C22×C4C23×C412yes—
862C22×C4C23×C412yes—
863C22×C4C23×C412yes—
864C22×C4C23×C414yes—
865C22×C4C23×C412yes—
866C22×C4C23×C412yes—
867C22×C4C22×D414yes—
868C22×C4C22×D414yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D414yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C2×#4112yes—
877C22×C4C2×#4112yes—
878C22×C4C2×#4114yes—
879C22×C4C2×#4112yes—
880C22×C4C2×#4112yes—
881C22×C4C2×#4112yes—
882C22×C4C2×#4112yes—
883C22×C4C2×#4112yes—
884C22×C4C2×#4112yes—
885C22×C4H(5,𝔽2)12yes—
886C22×C4H(5,𝔽2)12yes—
887C22×C4H(5,𝔽2)12yes—
888C22×C4H(5,𝔽2)12yes—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—84no—
899C22⋊C4—216no—
900C22⋊C4—216no—
901C22⋊C4—28no—
902C22⋊C4—216no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C42—28no—
926C42—28no—
927C42—28no—
928C42—28no—
929C42—44no—
930C42—44no—
931C42—48no—
932C42—48no—
933C42—48no—
934C42—44no—
935C42—44no—
936C42—44no—
937C42—44no—
938C42—84no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—24no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—22no—
969C23—24no—
970C23—22no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—41no—
989C23—42no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—42no—
1000C23—42no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—41no—
1005C23—41no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—41no—
1010C23—42no—
1011C23—42no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—41no—
1019C23—42no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—42no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—41no—
1033C23—42no—
1034C23—41no—
1035C23—42no—
1036C23—41no—
1037C23—41no—
1038C23—42no—
1039C23—42no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23C2×C4×D418yes—
1044C23C24×C411yescharacteristic
1045C23C23×D411yescharacteristic
1046C23C23×D411yescharacteristic
1047C23C22×#4111yescharacteristic
1048C23C22×#4111yescharacteristic
1049C23C22×#4111yescharacteristic
1050C23C22×#4111yescharacteristic
1051C23C2×H(5,𝔽2)11yescharacteristic
1052C23C2×H(5,𝔽2)11yescharacteristic
1053C23C2×H(5,𝔽2)11yescharacteristic
1054C23C2×H(5,𝔽2)11yescharacteristic
1055C23#58511yescharacteristic
1056C23#58511yescharacteristic
1057C23#58511yescharacteristic
1058C23#58511yescharacteristic
1059Q8—232no—
1060D4—232no—
1061D4—432no—
1062D4—432no—
1063D4—416no—
1064D4—816no—
1065D4—816no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—432no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—416no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—816no—
1198C2×C4—816no—
1199C2×C4—816no—
1200C2×C4C2×C4×D418yes—
1201C2×C4C2×C4×D414yes—
1202C2×C4C2×C4×D414yes—
1203C2×C4C4×#4114yes—
1204C2×C4#51814yes—
1205C2×C4D4214yes—
1206C2×C4#54614yes—
1207C2×C4#54614yes—
1208C2×C4#54614yes—
1209C2×C4#55014yes—
1210C2×C4#55114yes—
1211C22—28no—
1212C22—28no—
1213C22—28no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22—44no—
1230C22—44no—
1231C22—42no—
1232C22—44no—
1233C22—42no—
1234C22—42no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—81no—
1241C22—82no—
1242C22—82no—
1243C22—81no—
1244C22—81no—
1245C22—82no—
1246C22—81no—
1247C22—82no—
1248C22—81no—
1249C22—82no—
1250C22—82no—
1251C22—81no—
1252C22—81no—
1253C22—82no—
1254C22—82no—
1255C22—81no—
1256C22C22×C4×D411yescharacteristic
1257C22C22×C4×D411yescharacteristic
1258C22C2×C4×#4111yescharacteristic
1259C22C2×#51811yescharacteristic
1260C22#342811yescharacteristic
1261C22C4×H(5,𝔽2)11yescharacteristic
1262C22C4×H(5,𝔽2)11yescharacteristic
1263C22C2×D4211yescharacteristic
1264C22C2×#54611yescharacteristic
1265C22C2×#54611yescharacteristic
1266C22C2×#54611yescharacteristic
1267C22C2×#55011yescharacteristic
1268C22D4×#4111yescharacteristic
1269C22D4×#4111yescharacteristic
1270C22C2×#55111yescharacteristic
1271C22#347511yescharacteristic
1272C22#348011yescharacteristic
1273C22#348111yescharacteristic
1274C22#348311yescharacteristic
1275C22#348711yescharacteristic
1276C22#348811yescharacteristic
1277C22#349611yescharacteristic
1278C22#350011yescharacteristic
1279C22#351311yescharacteristic
1280C22#351411yescharacteristic
1281C22#351411yescharacteristic
1282C22#351711yescharacteristic
1283C22#351711yescharacteristic
1284C22#351711yescharacteristic
1285C22#352111yescharacteristic
1286C22#352411yescharacteristic
1287C22#354311yescharacteristic
1288C22#354611yescharacteristic
1289C22#355811yescharacteristic
1290C22#356211yescharacteristic
1291C4—28no—
1292C4—24no—
1293C4—24no—
1294C4—24no—
1295C4—42no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—44no—
1305C4—42no—
1306C4—81no—
1307C4—82no—
1308C4—81no—
1309C4—82no—
1310C4#235818yes—
1311C2—48no—
1312C2—84no—
1313C2—82no—
1314C2C2×#235811yescharacteristic
1315C2C4×#54611yescharacteristic
1316C2C4×#55011yescharacteristic
1317C2#3423211yescharacteristic
1318C2#3429511yescharacteristic
1319C2#3430911yescharacteristic
1320C2#3443811yescharacteristic
1321C2#5904611yescharacteristic
1322C2#5905111yescharacteristic
1323C2#5910211yescharacteristic
1324C2#5913111yescharacteristic
1325C2#5941711yescharacteristic
1326C2#5941911yescharacteristic
1327C2#5948311yescharacteristic
1328C2#5948711yescharacteristic
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×#2366C2semidirect
3. C2×#2341C2semidirect
4. C2×#2339C2semidirect
5. C2×C4×#124C2semidirect
6. #14520C2semidirect
7. #14374C2semidirect
8. #14228C2semidirect
9. #14207C2semidirect
10. #14187C2semidirect
11. #14026C2semidirect
12. #14025C2semidirect
13. #14017C2semidirect
14. #13999C2semidirect
15. #13998C2semidirect
16. #13984C2semidirect
17. #13979C2semidirect
18. #13970C2semidirect
19. #13875C2semidirect
20. #13817C2semidirect
21. #13813C2semidirect
22. C4×#390C2semidirect
23. C4×#388C2semidirect
34. #2431C4semidirect
134. C22×#41C2×C4semidirect
152. C2×#124C2×C4semidirect
155. C2×#121C2×C4semidirect
224. #392C2×C4semidirect
225. #392C2×C4semidirect
227. #391C2×C4semidirect
228. #391D4semidirect
237. #390C2×C4semidirect
238. #390D4semidirect
251. #386C2×C4semidirect
252. #386C2×C4semidirect
268. C4×C22⋊C4C2×C4semidirect
460. C2×C4⋊C4#41semidirect
617. #95#41semidirect
671. 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×#23662
C2×#23412
C2×#23392
C2×C4×#1242
#145202
#143742
#142282
#142072
#141872
#140262
#140252
#140172
#139992
#139982
#139842
#139792
#139702
#138752
#138172
#138132
C4×#3902
C4×#3882