Finite Group Databasebeta

← #537761

Subgroups — #537761

Order 512.

4408 conjugacy classes of subgroups.

The subgroup lattice has 1323 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×#2326C211yesmaximal, characteristic, complemented
6#14534C212yesmaximal, complemented
7#14521C212yesmaximal, complemented
8#14519C212yesmaximal, complemented
9#14373C212yesmaximal, complemented
10#14189C212yesmaximal, complemented
11#14140C212yesmaximal, complemented
12#14026C211yesmaximal, characteristic, complemented
13#14025C211yesmaximal, characteristic, complemented
14#14017C211yesmaximal, characteristic, complemented
15#14007C212yesmaximal, complemented
16#13998C211yesmaximal, characteristic, complemented
17#13977C211yesmaximal, characteristic, complemented
18#13975C212yesmaximal, complemented
19#13970C211yesmaximal, characteristic, complemented
20#13876C211yesmaximal, characteristic, complemented
21#13842C211yesmaximal, characteristic, complemented
22#13817C211yesmaximal, characteristic, complemented
23#13785C211yesmaximal, 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—
34#2431C4116yescomplemented
35C2×#392C2212yes—
36C2×#392C2212yes—
37#2366—28no—
38#2341—28no—
39#2339—28no—
40#2326—28no—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2211yescharacteristic
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388C2212yes—
56C2×#388C2212yes—
57C2×#388C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#385C2212yes—
68C2×#385C2212yes—
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⋊C4C2211yescharacteristic
83C2×#376C2211yescharacteristic
84C22×#95C2212yes—
85#1444C2212yes—
86#1443C2211yescharacteristic
87#1443C2211yescharacteristic
88#1442C2211yescharacteristic
89#1442C2211yescharacteristic
90#1442C2212yes—
91#1442C2212yes—
92#1440C2211yescharacteristic
93#1440C2211yescharacteristic
94#1440C2212yes—
95#1439C2211yescharacteristic
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1437C2212yes—
108#1437C2212yes—
109#1437C2212yes—
110#1437C2212yes—
111#1437C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121#1434C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C4×#95C2212yes—
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—24no—
168C2×C4×D4—24no—
169C2×C4×D4—42no—
170C2×C4×D4—42no—
171C2×C4×D4—44no—
172C2×C4×D4—42no—
173C2×C4×D4—44no—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222#392C2×C4116yescomplemented
223#392C2×C4116yescomplemented
224#391—24no—
225#391C2×C418yescomplemented
226#391D418yescomplemented
227#390—24no—
228#390—24no—
229#390—28no—
230#390—28no—
231#390—28no—
232#390—24no—
233#390—42no—
234#390—44no—
235#390C2×C418yescomplemented
236#390D418yescomplemented
237#389—42no—
238#388—28no—
239#388—28no—
240#388—44no—
241#386—28no—
242#386—28no—
243#386—28no—
244#386—28no—
245#386—44no—
246#386—44no—
247#386—44no—
248#386C2×C4116yescomplemented
249#386C2×C4116yescomplemented
250#385—28no—
251#385—28no—
252#385—44no—
253#385—44no—
254#384—24no—
255#381—28no—
256#380—24no—
257#380—24no—
258#380—28no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—42no—
262C4×C22⋊C4—28no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4C2×C418yescomplemented
266#376—24no—
267C2×#95—28no—
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
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×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2312yes—
306C2×#95C2312yes—
307C25C2412yes—
308C25C2411yescharacteristic
309C25C2412yes—
310C2×#41—232no—
311C2×#41—232no—
312C2×#41—416no—
313C2×#41—416no—
314C2×#41—416no—
315C2×#41—416no—
316C2×#41—416no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8C22×C414yes—
322C22×Q8C2×D414yes—
323C22×Q8#4114yes—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—42no—
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×D4C22×C414yes—
359C22×D4C22×C418yes—
360C22×D4C22×C418yes—
361C22×D4C22×C414yes—
362C22×D4C22×C418yes—
363C22×D4C22×C418yes—
364C22×D4C2×D414yes—
365C22×D4#4114yes—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
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×C4C22×C414yes—
400C23×C4C22×C418yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421#127—232no—
422#124—232no—
423#121—416no—
424C4×Q8—416no—
425C4×Q8—416no—
426C4×D4—416no—
427C4×D4—416no—
428C4×D4—416no—
429C4×D4—432no—
430C2×C4⋊C4—22no—
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—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4C22×C414yes—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4C2×D414yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—41no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
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⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4C22×C418yes—
536C2×C22⋊C4C22×C418yes—
537C2×C22⋊C4C22×C414yes—
538C2×C22⋊C4C22×C418yes—
539C2×C22⋊C4C22×C414yes—
540C2×C22⋊C4C22×C418yes—
541C2×C22⋊C4C22×C418yes—
542C2×C22⋊C4C2×D418yes—
543C2×C22⋊C4C2×D418yes—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—24no—
554C2×C42—22no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—22no—
558C2×C42—24no—
559C2×C42—24no—
560C2×C42—22no—
561C2×C42—24no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42C22×C414yes—
571C2×C42C22×C414yes—
572C2×C42C2×D414yes—
573C2×C42C2×D414yes—
574#95—22no—
575#95—24no—
576#95—24no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—24no—
587#95—22no—
588#95—24no—
589#95—22no—
590#95—22no—
591#95—24no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—22no—
596#95—42no—
597#95—42no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95C22×C414yes—
608#95C22×C414yes—
609#95C22×C418yes—
610#95C22×C418yes—
611#95C2×D418yes—
612#95C2×D418yes—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24C23×C414yes—
654C24C23×C412yes—
655C24C23×C414yes—
656C24C22×D414yes—
657C24C2×#4114yes—
658C24C2511yescharacteristic
659#41—4128no—
660C2×Q8—28no—
661C2×Q8—28no—
662C2×Q8—28no—
663C2×Q8—28no—
664C2×Q8—28no—
665C2×Q8—28no—
666C2×Q8C4×D4116yescomplemented
667C2×D4—216no—
668C2×D4—216no—
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—216no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—216no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
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—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—84no—
701C2×D4—84no—
702C2×D4—84no—
703C2×D4—84no—
704C2×D4—84no—
705C2×D4—84no—
706C2×D4—84no—
707C2×D4—84no—
708C2×D4C4×D4116yes—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—216no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
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—216no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—48no—
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—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
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×C4C23×C412yes—
859C22×C4C23×C414yes—
860C22×C4C23×C412yes—
861C22×C4C23×C412yes—
862C22×C4C23×C412yes—
863C22×C4C23×C414yes—
864C22×C4C23×C412yes—
865C22×C4C23×C412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D414yes—
870C22×C4C22×D412yes—
871C22×C4C22×D414yes—
872C22×C4C22×D414yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C2×#4114yes—
876C22×C4C2×#4112yes—
877C22×C4C2×#4112yes—
878C22×C4H(5,𝔽2)12yes—
879C22×C4H(5,𝔽2)12yes—
880C22×C4H(5,𝔽2)12yes—
881C22×C4H(5,𝔽2)12yes—
882C22×C4H(5,𝔽2)12yes—
883C22×C42−1+412yes—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—84no—
894C4⋊C4—84no—
895C4⋊C4—84no—
896C22⋊C4—216no—
897C22⋊C4—216no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C42—28no—
923C42—28no—
924C42—28no—
925C42—28no—
926C42—48no—
927C42—48no—
928C42—48no—
929C42—44no—
930C42—44no—
931C42—84no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
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—22no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—24no—
964C23—42no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—42no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—42no—
985C23—42no—
986C23—41no—
987C23—42no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—42no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—41no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—42no—
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—41no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—41no—
1018C23—42no—
1019C23—41no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—42no—
1026C23—41no—
1027C23—41no—
1028C23—42no—
1029C23—41no—
1030C23—42no—
1031C23—41no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—42no—
1036C23C2×C4×D418yes—
1037C23C24×C411yescharacteristic
1038C23C23×D411yescharacteristic
1039C23C23×D411yescharacteristic
1040C23C22×#4111yescharacteristic
1041C23C22×#4111yescharacteristic
1042C23C2×H(5,𝔽2)11yescharacteristic
1043C23C2×H(5,𝔽2)11yescharacteristic
1044C23C2×H(5,𝔽2)11yescharacteristic
1045C23C2×H(5,𝔽2)11yescharacteristic
1046C23C2×H(5,𝔽2)11yescharacteristic
1047C23C2×2−1+411yescharacteristic
1048C23#58511yescharacteristic
1049C23#58511yescharacteristic
1050C23#58511yescharacteristic
1051C23#58511yescharacteristic
1052Q8—232no—
1053D4—232no—
1054D4—432no—
1055D4—432no—
1056D4—416no—
1057D4—816no—
1058D4—816no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—432no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
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—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—416no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—816no—
1193C2×C4—816no—
1194C2×C4—816no—
1195C2×C4C2×C4×D418yes—
1196C2×C4C2×C4×D414yes—
1197C2×C4C2×C4×D414yes—
1198C2×C4#51814yes—
1199C2×C4#52014yes—
1200C2×C4D4214yes—
1201C2×C4#54614yes—
1202C2×C4#54614yes—
1203C2×C4#55114yes—
1204C22—28no—
1205C22—28no—
1206C22—28no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—42no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—42no—
1231C22—44no—
1232C22—42no—
1233C22—81no—
1234C22—82no—
1235C22—82no—
1236C22—81no—
1237C22—81no—
1238C22—82no—
1239C22—82no—
1240C22—81no—
1241C22—81no—
1242C22—82no—
1243C22—81no—
1244C22—82no—
1245C22—81no—
1246C22—82no—
1247C22—81no—
1248C22—82no—
1249C22C22×C4×D411yescharacteristic
1250C22C22×C4×D411yescharacteristic
1251C22C2×#51811yescharacteristic
1252C22C2×#52011yescharacteristic
1253C22#342811yescharacteristic
1254C22C4×H(5,𝔽2)11yescharacteristic
1255C22C4×H(5,𝔽2)11yescharacteristic
1256C22C2×D4211yescharacteristic
1257C22C2×#54611yescharacteristic
1258C22C2×#54611yescharacteristic
1259C22C2×#55111yescharacteristic
1260C22#348411yescharacteristic
1261C22#348511yescharacteristic
1262C22#348711yescharacteristic
1263C22#348811yescharacteristic
1264C22#348811yescharacteristic
1265C22#348911yescharacteristic
1266C22#349711yescharacteristic
1267C22#349811yescharacteristic
1268C22#351311yescharacteristic
1269C22#351411yescharacteristic
1270C22#351711yescharacteristic
1271C22#351711yescharacteristic
1272C22#352011yescharacteristic
1273C22#352111yescharacteristic
1274C22#352211yescharacteristic
1275C22#352411yescharacteristic
1276C22#354311yescharacteristic
1277C22#354611yescharacteristic
1278C22#354611yescharacteristic
1279C22#354611yescharacteristic
1280C22#355411yescharacteristic
1281C22#355411yescharacteristic
1282C22#355811yescharacteristic
1283C22#356211yescharacteristic
1284C4—28no—
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—42no—
1292C4—44no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—82no—
1300C4—81no—
1301C4—81no—
1302C4—82no—
1303C4#235818yes—
1304C2—48no—
1305C2—82no—
1306C2—84no—
1307C2C2×#235811yescharacteristic
1308C2#3428811yescharacteristic
1309C2#3429211yescharacteristic
1310C2#3429511yescharacteristic
1311C2#3431311yescharacteristic
1312C2#3439311yescharacteristic
1313C2#3443811yescharacteristic
1314C2#4492711yescharacteristic
1315C2#4493511yescharacteristic
1316C2#4498711yescharacteristic
1317C2#4499811yescharacteristic
1318C2#4501811yescharacteristic
1319C2#4502611yescharacteristic
1320C2#4524111yescharacteristic
1321C2#4531911yescharacteristic
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×#2326C2semidirect
6. #14534C2semidirect
7. #14521C2semidirect
8. #14519C2semidirect
9. #14373C2semidirect
10. #14189C2semidirect
11. #14140C2semidirect
12. #14026C2semidirect
13. #14025C2semidirect
14. #14017C2semidirect
15. #14007C2semidirect
16. #13998C2semidirect
17. #13977C2semidirect
18. #13975C2semidirect
19. #13970C2semidirect
20. #13876C2semidirect
21. #13842C2semidirect
22. #13817C2semidirect
23. #13785C2semidirect
34. #2431C4semidirect
134. C22×#41C2×C4semidirect
152. C2×#124C2×C4semidirect
155. C2×#121C2×C4semidirect
222. #392C2×C4semidirect
223. #392C2×C4semidirect
225. #391C2×C4semidirect
226. #391D4semidirect
235. #390C2×C4semidirect
236. #390D4semidirect
248. #386C2×C4semidirect
249. #386C2×C4semidirect
265. C4×C22⋊C4C2×C4semidirect
666. 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×#23262
#145342
#145212
#145192
#143732
#141892
#141402
#140262
#140252
#140172
#140072
#139982
#139772
#139752
#139702
#138762
#138422
#138172
#137852