Finite Group Databasebeta

← #988818

Subgroups — #988818

Order 512.

3680 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic, complemented
2C2×#2414C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic, complemented
4C2×#2407C211yesmaximal, characteristic, complemented
5#17086C212yesmaximal, complemented
6#16819C212yesmaximal, complemented
7#16334C212yesmaximal, complemented
8#16308C212yesmaximal, complemented
9#15962C212yesmaximal, complemented
10#15634C212yesmaximal, complemented
11#15501C212yesmaximal, complemented
12#15189C211yesmaximal, characteristic, complemented
13#15181C211yesmaximal, characteristic, complemented
14#15177C211yesmaximal, characteristic, complemented
15#15138C211yesmaximal, characteristic, complemented
16#15126C211yesmaximal, characteristic, complemented
17#14541C212yesmaximal, complemented
18#14138C211yesmaximal, characteristic, complemented
19#13998C211yesmaximal, characteristic, complemented
20#13997C211yesmaximal, characteristic, complemented
21#13994C211yesmaximal, characteristic, complemented
22#13937C211yesmaximal, characteristic, complemented
23C4×#392C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2485—28no—
34#2414—28no—
35#2407—28no—
36#2407—28no—
37C2×#397C2212yes—
38C2×#397C2212yes—
39C2×#394C2212yes—
40C2×#394C2212yes—
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#392C2212yes—
45C2×#392C2211yescharacteristic
46C2×#392C2212yes—
47C2×#392C2212yes—
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#390C2212yes—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2212yes—
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#388C2212yes—
63C2×#388C2212yes—
64C2×#388C2212yes—
65C2×#387C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#385C2212yes—
69C2×#385C2212yes—
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80#1445C2212yes—
81#1444C2211yescharacteristic
82#1444C2212yes—
83#1443C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1441C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2211yescharacteristic
98#1439C2211yescharacteristic
99#1439C2211yescharacteristic
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1438C2211yescharacteristic
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2211yescharacteristic
111#1438C2211yescharacteristic
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1437C2212yes—
116#1437C2212yes—
117#1436C2212yes—
118#1436C2212yes—
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2212yes—
123#1434C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C4×#95C2211yescharacteristic
127C22×#41—24no—
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—42no—
131C22×#41—42no—
132C22×#41—42no—
133C22×#41—42no—
134C23×Q8C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—42no—
151C2×C22⋊Q8—42no—
152C2×#121—24no—
153C2×#121—24no—
154C2×#121—42no—
155C2×#121—42no—
156C2×#121—42no—
157C2×#121D418yescomplemented
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—42no—
163C2×C4×D4—42no—
164C2×C4×D4—42no—
165C2×C4×D4—42no—
166C2×C4×D4—42no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117—42no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2312yes—
222#397—28no—
223#397—28no—
224#394—28no—
225#394—28no—
226#394—28no—
227#394—28no—
228#394—44no—
229#392—28no—
230#392—28no—
231#392—28no—
232#392—24no—
233#391—24no—
234#391—24no—
235#391—42no—
236#391—42no—
237#390—24no—
238#390—24no—
239#390—24no—
240#390—28no—
241#390—44no—
242#390—42no—
243#389—24no—
244#389—24no—
245#389—24no—
246#389—42no—
247#388—28no—
248#388—28no—
249#388—44no—
250#387—28no—
251#386—28no—
252#386—28no—
253#385—28no—
254#385—28no—
255#380—24no—
256#380—24no—
257#380—24no—
258#380—24no—
259#380—42no—
260#380D418yescomplemented
261C4×C4⋊C4—42no—
262C4×C22⋊C4—42no—
263C4×C22⋊C4—42no—
264C4×C22⋊C4—42no—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C25C2411yescharacteristic
301C25C2412yes—
302C25C2411yescharacteristic
303C25C2411yescharacteristic
304C2×#41—416no—
305C2×#41—416no—
306C2×#41—416no—
307C2×#41—416no—
308C2×#41—416no—
309C2×#41—416no—
310C2×#41—416no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8#4114yes—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4—41no—
350C22×D4—41no—
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×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4C2×D414yes—
366C22×D4C2×D418yes—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4C2×D414yes—
394C23×C4C2×D414yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2412yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C22⋊Q8—416no—
415C22⋊Q8—416no—
416#121—416no—
417#121—416no—
418C4×D4—416no—
419C4×D4—416no—
420C4×D4—416no—
421#117—416no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
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⋊C4—42no—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4C2×D414yes—
466C2×C4⋊C4C2×D414yes—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
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—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4C2×D418yes—
559C2×C22⋊C4C2×D418yes—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—24no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—42no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—42no—
596#95—42no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95C2×D418yes—
612#95#4114yescomplemented
613C24—21no—
614C24—21no—
615C24—22no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—22no—
626C24—21no—
627C24—22no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—21no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—22no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24C22×D412yes—
670C24C22×D414yes—
671C24C22×D412yes—
672C242−1+412yes—
673C24C2511yescharacteristic
674#41—4128no—
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—84no—
724C2×D4—84no—
725C2×D4—84no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—84no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
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—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—22no—
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—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4C22×D414yes—
876C22×C4C22×D414yes—
877C22×C4C22×D412yes—
878C22×C4C22×D414yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C2×#4112yes—
883C22×C4C2×#4112yes—
884C22×C4C2×#4112yes—
885C22×C4C2×#4114yes—
886C22×C4C2×#4112yes—
887C22×C4H(5,𝔽2)12yes—
888C22×C4H(5,𝔽2)12yes—
889C22×C4H(5,𝔽2)12yes—
890C22×C4H(5,𝔽2)12yes—
891C22×C4H(5,𝔽2)12yes—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—84no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C42—48no—
939C42—44no—
940C42—44no—
941C42—44no—
942C42—44no—
943C42—84no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—42no—
976C23—41no—
977C23—42no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—42no—
985C23—41no—
986C23—41no—
987C23—42no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—42no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—42no—
1000C23—41no—
1001C23—42no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—42no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—42no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—41no—
1031C23—41no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—42no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—42no—
1048C23—41no—
1049C23—42no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—42no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—42no—
1058C23—42no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—42no—
1064C23—41no—
1065C23—42no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—42no—
1070C23—41no—
1071C23—41no—
1072C23—42no—
1073C23—41no—
1074C23—41no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23C23×D411yescharacteristic
1085C23C23×D411yescharacteristic
1086C23C22×#4111yescharacteristic
1087C23C22×#4111yescharacteristic
1088C23C2×H(5,𝔽2)11yescharacteristic
1089C23C2×H(5,𝔽2)11yescharacteristic
1090C23C2×H(5,𝔽2)11yescharacteristic
1091C23C2×H(5,𝔽2)11yescharacteristic
1092C23C2×H(5,𝔽2)11yescharacteristic
1093C23C2×2−1+411yescharacteristic
1094C23#58511yescharacteristic
1095C23#58511yescharacteristic
1096C23#58511yescharacteristic
1097C23#58511yescharacteristic
1098C23#58511yescharacteristic
1099Q8—416no—
1100D4—416no—
1101D4—416no—
1102D4—416no—
1103D4—432no—
1104D4—416no—
1105D4—816no—
1106D4—816no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—432no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
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—42no—
1177C2×C4—42no—
1178C2×C4—416no—
1179C2×C4—416no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—41no—
1227C2×C4—42no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—88no—
1237C2×C4#53414yes—
1238C2×C4#53514yes—
1239C2×C4#53814yes—
1240C2×C4D4214yes—
1241C2×C4#54614yes—
1242C2×C4#54614yes—
1243C2×C4#56014yes—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—44no—
1255C22—44no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—44no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—82no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—82no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—82no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—82no—
1289C22—81no—
1290C22—82no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—82no—
1296C22—81no—
1297C22—81no—
1298C22—82no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—82no—
1304C22C2×#53411yescharacteristic
1305C22C2×#53511yescharacteristic
1306C22C2×#53811yescharacteristic
1307C22C2×D4211yescharacteristic
1308C22C2×#54611yescharacteristic
1309C22C2×#54611yescharacteristic
1310C22D4×#4111yescharacteristic
1311C22D4×#4111yescharacteristic
1312C22#348311yescharacteristic
1313C22#348511yescharacteristic
1314C22#348711yescharacteristic
1315C22#348911yescharacteristic
1316C22#348911yescharacteristic
1317C22#349611yescharacteristic
1318C22#349611yescharacteristic
1319C22#350611yescharacteristic
1320C22#350611yescharacteristic
1321C22#350611yescharacteristic
1322C22#351611yescharacteristic
1323C22#352011yescharacteristic
1324C22#352411yescharacteristic
1325C22#352411yescharacteristic
1326C22C2×#56011yescharacteristic
1327C22#353611yescharacteristic
1328C22#353911yescharacteristic
1329C22#353911yescharacteristic
1330C22#354011yescharacteristic
1331C22#354111yescharacteristic
1332C22#354111yescharacteristic
1333C22#354211yescharacteristic
1334C22#354211yescharacteristic
1335C22#354611yescharacteristic
1336C22#355111yescharacteristic
1337C22#355111yescharacteristic
1338C22#355111yescharacteristic
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4—81no—
1350C4—82no—
1351C4—81no—
1352C4—82no—
1353C4—81no—
1354C4—81no—
1355C4—82no—
1356C4—81no—
1357C4#267818yes—
1358C2—82no—
1359C2—84no—
1360C2—82no—
1361C2—82no—
1362C2#3986311yescharacteristic
1363C2#3988411yescharacteristic
1364C2#4011811yescharacteristic
1365C2#4243211yescharacteristic
1366C2#4243311yescharacteristic
1367C2#4290611yescharacteristic
1368C2#4510311yescharacteristic
1369C2#4513611yescharacteristic
1370C2#4526511yescharacteristic
1371C2#4633311yescharacteristic
1372C2C2×#267811yescharacteristic
1373C2#5309811yescharacteristic
1374C2#5899911yescharacteristic
1375C2#5981011yescharacteristic
1376C2#5981011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2485C2semidirect
2. C2×#2414C2semidirect
3. C2×#2407C2semidirect
4. C2×#2407C2semidirect
5. #17086C2semidirect
6. #16819C2semidirect
7. #16334C2semidirect
8. #16308C2semidirect
9. #15962C2semidirect
10. #15634C2semidirect
11. #15501C2semidirect
12. #15189C2semidirect
13. #15181C2semidirect
14. #15177C2semidirect
15. #15138C2semidirect
16. #15126C2semidirect
17. #14541C2semidirect
18. #14138C2semidirect
19. #13998C2semidirect
20. #13997C2semidirect
21. #13994C2semidirect
22. #13937C2semidirect
23. C4×#392C2semidirect
157. C2×#121D4semidirect
260. #380D4semidirect
612. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24142
C2×#24072
#170862
#168192
#163342
#163082
#159622
#156342
#155012
#151892
#151812
#151772
#151382
#151262
#145412
#141382
#139982
#139972
#139942
#139372
C4×#3922