Finite Group Databasebeta

← #674191

Subgroups — #674191

Order 512.

3460 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic, complemented
2C2×#2486C211yesmaximal, characteristic, complemented
3C2×#2352C211yesmaximal, characteristic, complemented
4C2×C4×#127C211yesmaximal, characteristic
5#15416C212yesmaximal, complemented
6#15388C212yesmaximal, complemented
7#15287C212yesmaximal, complemented
8#15261C212yesmaximal
9#15181C211yesmaximal, characteristic, complemented
10#15181C211yesmaximal, characteristic, complemented
11#15181C211yesmaximal, characteristic, complemented
12#15129C211yesmaximal, characteristic, complemented
13#14949C212yesmaximal, complemented
14#14780C212yesmaximal, complemented
15#14707C211yesmaximal, characteristic, complemented
16#14095C212yesmaximal, complemented
17#14007C212yesmaximal, complemented
18#13905C211yesmaximal, characteristic, complemented
19#13905C211yesmaximal, characteristic, complemented
20#13905C211yesmaximal, characteristic, complemented
21#13872C211yesmaximal, characteristic, complemented
22#13871C211yesmaximal, characteristic, complemented
23C4×#389C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#123C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34#2486—28no—
35#2485—28no—
36C2×#398C2212yes—
37C2×#397C2212yes—
38C2×#397C2212yes—
39C2×#394C2212yes—
40C2×#394C2212yes—
41#2352—28no—
42C4×#127—28no—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388C2212yes—
54C2×#388C2212yes—
55C2×#387C2212yes—
56C2×#387C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#384C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#382C2211yescharacteristic
62C2×#381C2212yes—
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2212yes—
80C2×C4×C22⋊C4C2212yes—
81C2×C43C2211yescharacteristic
82#1445C2212yes—
83#1445C2212yes—
84#1445C2212yes—
85#1442C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1437C2212yes—
108#1437C2212yes—
109#1437C2212yes—
110#1437C2212yes—
111#1437C2212yes—
112#1437C2212yes—
113#1437C2212yes—
114#1436C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117#1436C2212yes—
118#1436C2212yes—
119#1436C2212yes—
120#1436C2212yes—
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2211yescharacteristic
123C4⋊#95C2211yescharacteristic
124C4⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C4×#95C2212yes—
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C2×#127—24no—
139C2×#127—24no—
140C2×#127—24no—
141C2×#123—28no—
142C2×#123—28no—
143C2×#123—44no—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—42no—
158C2×C4×D4—42no—
159C2×C4×D4—42no—
160C2×C4×D4—42no—
161C2×C4×D4D418yes—
162C2×#117—24no—
163C2×#117—24no—
164C2×#117—42no—
165C22×C4⋊C4—24no—
166C22×C4⋊C4—24no—
167C22×C4⋊C4—42no—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
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×C42C2311yescharacteristic
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224#398—28no—
225#397—28no—
226#397—28no—
227#394—28no—
228#394—44no—
229#390—24no—
230#390—24no—
231#390—24no—
232#390—24no—
233#390—24no—
234#390—24no—
235#389—24no—
236#389—24no—
237#389—24no—
238#389D418yescomplemented
239#388—28no—
240#388—28no—
241#387—28no—
242#387—28no—
243#386—28no—
244#386—28no—
245#384—24no—
246#382—24no—
247#382—24no—
248#381—28no—
249#380—24no—
250#380—24no—
251#380—24no—
252#380—24no—
253#380—24no—
254#380—24no—
255#380—24no—
256#380—24no—
257#380—42no—
258#380—42no—
259#380—42no—
260#380—42no—
261#380—42no—
262#380—42no—
263C4×C4⋊C4—24no—
264C4×C4⋊C4—24no—
265C4×C4⋊C4—44no—
266C4×C22⋊C4—28no—
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×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C43—24no—
300C25C2411yescharacteristic
301C25C2411yescharacteristic
302C25C2411yescharacteristic
303C25C2411yescharacteristic
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4C2×D414yes—
344C22×D4#4114yes—
345C22×D4#4114yes—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
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—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4C2×D414yes—
380C23×C4C2×D414yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400#127—232no—
401#123—432no—
402C4×D4—232no—
403C4×D4—416no—
404C4×D4—416no—
405C4×D4—416no—
406C4×D4—416no—
407C4×D4—416no—
408#117—416no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
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—24no—
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—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—416no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4C2×D414yes—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4C2×D418yes—
466C2×C4⋊C4C2×D414yes—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
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⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4C2×D414yes—
547C2×C22⋊C4C2×D414yes—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—24no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—24no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42—41no—
567C2×C42—41no—
568C2×C42—42no—
569C2×C42—41no—
570C2×C42—41no—
571C2×C42—42no—
572C2×C42—42no—
573C2×C42C2×D414yes—
574C2×C42C2×D414yes—
575C2×C42#4114yes—
576C2×C42#4114yes—
577C2×C42#4114yes—
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—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95C2×D418yes—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24C22×D412yes—
665C24C22×D412yes—
666C24C2×#4112yes—
667C24C2×#4112yes—
668C24C2×#4112yes—
669C24C2×#4112yes—
670C24C2511yescharacteristic
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
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—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4C22×D414yes—
857C22×C4C22×D412yes—
858C22×C4C22×D414yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C2×#4112yes—
867C22×C4C2×#4112yes—
868C22×C4C2×#4112yes—
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4C2×#4112yes—
874C22×C4C2×#4112yes—
875C22×C4C2×#4112yes—
876C22×C4C2×#4112yes—
877C22×C4H(5,𝔽2)12yes—
878C22×C4H(5,𝔽2)12yes—
879C22×C4H(5,𝔽2)12yes—
880C22×C42−1+412yes—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—216no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—84no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C42—28no—
928C42—28no—
929C42—28no—
930C42—44no—
931C42—44no—
932C42—48no—
933C42—44no—
934C42—48no—
935C42—84no—
936C42#123116yescomplemented
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23#52514yes—
1077C23C23×D411yescharacteristic
1078C23C23×D411yescharacteristic
1079C23C22×#4111yescharacteristic
1080C23C22×#4111yescharacteristic
1081C23C22×#4111yescharacteristic
1082C23C22×#4111yescharacteristic
1083C23C22×#4111yescharacteristic
1084C23C2×H(5,𝔽2)11yescharacteristic
1085C23C2×H(5,𝔽2)11yescharacteristic
1086C23C2×H(5,𝔽2)11yescharacteristic
1087C23C2×2−1+411yescharacteristic
1088C23#58511yescharacteristic
1089C23#58511yescharacteristic
1090C23#58511yescharacteristic
1091C23#58511yescharacteristic
1092D4—416no—
1093D4—416no—
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097D4—416no—
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—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—416no—
1165C2×C4—416no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—816no—
1223C2×C4—88no—
1224C2×C4—88no—
1225C2×C4C2×#12314yes—
1226C2×C4C2×#12314yes—
1227C2×C4C2×#12314yes—
1228C2×C4#53214yes—
1229C2×C4#54014yes—
1230C2×C4D4214yes—
1231C2×C4#54614yes—
1232C2×C4#54614yes—
1233C2×C4#55014yes—
1234C2×C4#55214yes—
1235C2×C4#55914yes—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22C22×#12311yescharacteristic
1297C22C2×#52511yescharacteristic
1298C22C2×#53211yescharacteristic
1299C22#344911yescharacteristic
1300C22C2×#54011yescharacteristic
1301C22C2×D4211yescharacteristic
1302C22C2×#54611yescharacteristic
1303C22C2×#54611yescharacteristic
1304C22C2×#55011yescharacteristic
1305C22D4×#4111yescharacteristic
1306C22C2×#55211yescharacteristic
1307C22#347511yescharacteristic
1308C22#347511yescharacteristic
1309C22#347511yescharacteristic
1310C22#347511yescharacteristic
1311C22#347511yescharacteristic
1312C22C2×#55911yescharacteristic
1313C22#348811yescharacteristic
1314C22#348911yescharacteristic
1315C22#349711yescharacteristic
1316C22#350011yescharacteristic
1317C22#350511yescharacteristic
1318C22#350511yescharacteristic
1319C22#350611yescharacteristic
1320C22#350611yescharacteristic
1321C22#350711yescharacteristic
1322C22#351111yescharacteristic
1323C22#351211yescharacteristic
1324C22#351211yescharacteristic
1325C22#351911yescharacteristic
1326C22#352011yescharacteristic
1327C22#354611yescharacteristic
1328C22#354711yescharacteristic
1329C22#355111yescharacteristic
1330C22#355111yescharacteristic
1331C4—24no—
1332C4—24no—
1333C4—24no—
1334C4—24no—
1335C4—44no—
1336C4—42no—
1337C4—44no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—82no—
1342C4—82no—
1343C4—82no—
1344C4—82no—
1345C4—81no—
1346C4—81no—
1347C4—82no—
1348C4—82no—
1349C4#244518yes—
1350C2—44no—
1351C2—82no—
1352C2—82no—
1353C2—82no—
1354C2C2×#244511yescharacteristic
1355C2#3480911yescharacteristic
1356C2#3551711yescharacteristic
1357C2#3609611yescharacteristic
1358C2#3615611yescharacteristic
1359C2#3627011yescharacteristic
1360C2#3641511yescharacteristic
1361C2#3933511yescharacteristic
1362C2#3946211yescharacteristic
1363C2#3999611yescharacteristic
1364C2#3999811yescharacteristic
1365C2#5941011yescharacteristic
1366C2#5944211yescharacteristic
1367C2#5982411yescharacteristic
1368C2#5986511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#127C22
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×#2486C2semidirect
3. C2×#2352C2semidirect
5. #15416C2semidirect
6. #15388C2semidirect
7. #15287C2semidirect
9. #15181C2semidirect
10. #15181C2semidirect
11. #15181C2semidirect
12. #15129C2semidirect
13. #14949C2semidirect
14. #14780C2semidirect
15. #14707C2semidirect
16. #14095C2semidirect
17. #14007C2semidirect
18. #13905C2semidirect
19. #13905C2semidirect
20. #13905C2semidirect
21. #13872C2semidirect
22. #13871C2semidirect
23. C4×#389C2semidirect
238. #389D4semidirect
936. C42#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24862
C2×#23522
C2×C4×#1272
#154162
#153882
#152872
#152612
#151812
#151292
#149492
#147802
#147072
#140952
#140072
#139052
#138722
#138712
C4×#3892