Finite Group Databasebeta

← #687010

Subgroups — #687010

Order 512.

3934 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2592C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic
3C2×#2396C211yesmaximal, characteristic, complemented
4C2×#2309C211yesmaximal, characteristic
5#16374C212yesmaximal, complemented
6#16371C212yesmaximal, complemented
7#15467C212yesmaximal, complemented
8#15297C212yesmaximal, complemented
9#15297C212yesmaximal, complemented
10#15284C212yesmaximal, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15217C211yesmaximal, characteristic, complemented
13#15157C211yesmaximal, characteristic, complemented
14#15147C211yesmaximal, characteristic, complemented
15#14999C212yesmaximal, complemented
16#14947C212yesmaximal, complemented
17#14258C211yesmaximal, characteristic, complemented
18#14153C211yesmaximal, characteristic, complemented
19#14138C211yesmaximal, characteristic, complemented
20#14022C211yesmaximal, characteristic, complemented
21#14022C211yesmaximal, characteristic, complemented
22#13902C211yesmaximal, characteristic
23#13801C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic, complemented
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2592—28no—
32#2435—28no—
33#2396—28no—
34C2×#400C2211yescharacteristic, complemented
35C2×#399C2211yescharacteristic
36C2×#398C2211yescharacteristic, complemented
37C2×#398C2211yescharacteristic, complemented
38C2×#397C2212yescomplemented
39C2×#397C2212yescomplemented
40C2×#396C2211yescharacteristic
41C2×#396C2211yescharacteristic
42C2×#395C2211yescharacteristic, complemented
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#393C2211yescharacteristic
46C2×#393C2212yescomplemented
47C2×#393C2212yescomplemented
48#2309—28no—
49C2×#391C2211yescharacteristic, complemented
50C2×#391C2211yescharacteristic, complemented
51C2×#391C2211yescharacteristic, complemented
52C2×#391C2211yescharacteristic, complemented
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2212yes—
61C2×#390C2212yes—
62C2×#390C2211yescharacteristic
63C2×#390C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C2×#388C2212yescomplemented
66C2×#388C2212yescomplemented
67C2×#388C2212yescomplemented
68C2×#388C2212yescomplemented
69C2×#380C2211yescharacteristic
70C2×#379C2212yes—
71C2×#379C2212yes—
72C2×#379C2212yes—
73C2×#379C2212yes—
74C2×#379C2212yes—
75C2×#379C2212yes—
76C2×C4×C4⋊C4C2211yescharacteristic, complemented
77C2×C4×C4⋊C4C2211yescharacteristic, complemented
78C2×C4×C4⋊C4C2211yescharacteristic, complemented
79C2×C4×C4⋊C4C2211yescharacteristic, complemented
80C2×C4×C4⋊C4C2211yescharacteristic, complemented
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83#1441C2212yescomplemented
84#1441C2212yescomplemented
85#1440C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1438C2212yes—
110#1438C2212yes—
111#1437C2212yes—
112#1437C2212yes—
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119C4⋊#95C2211yescharacteristic, complemented
120C4⋊#95C2211yescharacteristic, complemented
121C4⋊#95C2211yescharacteristic, complemented
122C4⋊#95C2211yescharacteristic, complemented
123C4⋊#95C2211yescharacteristic, complemented
124C4⋊#95C2211yescharacteristic, complemented
125#1434C2212yescomplemented
126C4×#95C2212yescomplemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—24no—
135C23×D4—42no—
136C23×D4—42no—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C24×C4C2311yescharacteristic
141C2×#124—24no—
142C2×#124—24no—
143C2×#124—24no—
144C2×#124—24no—
145C2×#124—42no—
146C2×#124—42no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C4×Q8—24no—
151C2×C4×Q8—24no—
152C2×C4×Q8—42no—
153C2×#117—24no—
154C2×#117—24no—
155C2×#117—24no—
156C2×#117—24no—
157C2×#117—42no—
158C2×#117—42no—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218#400—24no—
219#399—24no—
220#398—24no—
221#398—24no—
222#397—28no—
223#397—44no—
224#396—24no—
225#396—24no—
226#395—24no—
227#394—28no—
228#394—28no—
229#393—28no—
230#393—24no—
231#393—44no—
232#391—24no—
233#391—24no—
234#391—42no—
235#391—42no—
236#390—24no—
237#390—24no—
238#390—24no—
239#390—24no—
240#390—28no—
241#390—28no—
242#390—24no—
243#390—24no—
244#390—24no—
245#390—42no—
246#390—42no—
247#390D418yes—
248#388—28no—
249#388—28no—
250#388—44no—
251#388—44no—
252#380—24no—
253#379—28no—
254#379—28no—
255#379—28no—
256#379—28no—
257#379—44no—
258#379—44no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—24no—
262C4×C4⋊C4—24no—
263C4×C4⋊C4—42no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4D418yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C25—24no—
300C25—24no—
301C25—24no—
302C25—24no—
303C25—24no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25C2412yes—
315C25C2412yes—
316C25C2411yescharacteristic
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—41no—
328C22×Q8—41no—
329C22×Q8—41no—
330C22×Q8—41no—
331C22×D4—232no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—416no—
350C22×D4—416no—
351C22×D4—416no—
352C22×D4—416no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—416no—
356C22×D4—416no—
357C22×D4C2×D414yes—
358C22×D4#4114yes—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4C2×D414yes—
364C23×C4#4114yes—
365C23×C4#4114yes—
366C23×C4C2411yescharacteristic
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2411yescharacteristic
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386#124—416no—
387#124—416no—
388C22⋊Q8—416no—
389C4×Q8—416no—
390#117—416no—
391#117—416no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
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—41no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4C2×D414yes—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
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—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—41no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
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⋊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⋊C4C2×D414yes—
539C2×C22⋊C4C2×D414yes—
540C2×C22⋊C4C2×D418yes—
541C2×C22⋊C4C2×D418yes—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—24no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—24no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—24no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42C2×D414yes—
567C2×C42C2×D414yes—
568C2×C42C2×D414yes—
569#95—22no—
570#95—22no—
571#95—24no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95C2×D414yes—
601#95C2×D414yes—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—216no—
615C24—22no—
616C24—22no—
617C24—22no—
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—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—84no—
654C24—84no—
655C24—84no—
656C24—84no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24C22×D414yes—
678C24C22×D412yes—
679C24C2×#4114yes—
680C24C2×#4112yes—
681C24C2×#4112yes—
682C24C2511yescharacteristic
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×D4—216no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—4128no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—21no—
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—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4#124116yes—
847C22×C4C22×D412yes—
848C22×C4C22×D414yes—
849C22×C4C22×D412yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C2×#4112yes—
858C22×C4C2×#4112yes—
859C22×C4C2×#4112yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4112yes—
862C22×C4H(5,𝔽2)12yes—
863C22×C4H(5,𝔽2)12yes—
864C22×C4H(5,𝔽2)12yes—
865C22×C4H(5,𝔽2)12yes—
866C4⋊C4—28no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C22⋊C4—84no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C42—28no—
917C42—28no—
918C42—28no—
919C42—48no—
920C42—44no—
921C42—44no—
922C42—44no—
923C42—84no—
924C42—84no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
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—432no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
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—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—816no—
1031C23—816no—
1032C23—816no—
1033C23—816no—
1034C23—816no—
1035C23—816no—
1036C23—816no—
1037C23—816no—
1038C23—816no—
1039C23—816no—
1040C23—816no—
1041C23—816no—
1042C23—816no—
1043C23—816no—
1044C23C2×#12414yes—
1045C23C23×D411yescharacteristic
1046C23C23×D411yescharacteristic
1047C23C22×#4111yescharacteristic
1048C23C22×#4111yescharacteristic
1049C23C22×#4111yescharacteristic
1050C23C2×H(5,𝔽2)11yescharacteristic
1051C23C2×H(5,𝔽2)11yescharacteristic
1052C23C2×H(5,𝔽2)11yescharacteristic
1053C23C2×H(5,𝔽2)11yescharacteristic
1054C23#58511yescharacteristic
1055C23#58511yescharacteristic
1056C23#58511yescharacteristic
1057C23#58511yescharacteristic
1058C23#58511yescharacteristic
1059C23#58511yescharacteristic
1060Q8—416no—
1061Q8—88no—
1062D4—432no—
1063D4—416no—
1064D4—416no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—232no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
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—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4#52514yes—
1199C2×C4C2×#12414yes—
1200C2×C4C2×#12414yes—
1201C2×C4#53814yes—
1202C2×C4D4214yes—
1203C2×C4#54614yes—
1204C2×C4#54614yes—
1205C2×C4#55114yes—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—864no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22C2×#52511yescharacteristic
1253C22C22×#12411yescharacteristic
1254C22#344911yescharacteristic
1255C22#344911yescharacteristic
1256C22C2×#53811yescharacteristic
1257C22C2×D4211yescharacteristic
1258C22C2×#54611yescharacteristic
1259C22C2×#54611yescharacteristic
1260C22C2×#55111yescharacteristic
1261C22#348511yescharacteristic
1262C22#348811yescharacteristic
1263C22#348811yescharacteristic
1264C22#348811yescharacteristic
1265C22#349611yescharacteristic
1266C22#350011yescharacteristic
1267C22#350611yescharacteristic
1268C22#350611yescharacteristic
1269C22#350811yescharacteristic
1270C22#351011yescharacteristic
1271C22#351011yescharacteristic
1272C22#351011yescharacteristic
1273C22#351011yescharacteristic
1274C22#351011yescharacteristic
1275C22#351311yescharacteristic
1276C22#351411yescharacteristic
1277C22#352111yescharacteristic
1278C22#352111yescharacteristic
1279C22#354011yescharacteristic
1280C22#354211yescharacteristic
1281C22#354611yescharacteristic
1282C22#354611yescharacteristic
1283C22#355111yescharacteristic
1284C22#355811yescharacteristic
1285C22#356211yescharacteristic
1286C22#356211yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—44no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—81no—
1298C4—82no—
1299C4—81no—
1300C4—82no—
1301C4—81no—
1302C4—81no—
1303C4—82no—
1304C4—82no—
1305C4—82no—
1306C4#247218yes—
1307C2—44no—
1308C2—84no—
1309C2—84no—
1310C2C2×#247211yescharacteristic
1311C2#3533811yescharacteristic
1312C2#3555611yescharacteristic
1313C2#3580811yescharacteristic
1314C2#3603311yescharacteristic
1315C2#3765811yescharacteristic
1316C2#3803411yescharacteristic
1317C2#3890211yescharacteristic
1318C2#3933411yescharacteristic
1319C2#4297611yescharacteristic
1320C2#4298311yescharacteristic
1321C2#4495511yescharacteristic
1322C2#4496111yescharacteristic
1323C2#4509711yescharacteristic
1324C2#4536511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2592C2semidirect
3. C2×#2396C2semidirect
5. #16374C2semidirect
6. #16371C2semidirect
7. #15467C2semidirect
8. #15297C2semidirect
9. #15297C2semidirect
10. #15284C2semidirect
11. #15217C2semidirect
12. #15217C2semidirect
13. #15157C2semidirect
14. #15147C2semidirect
15. #14999C2semidirect
16. #14947C2semidirect
17. #14258C2semidirect
18. #14153C2semidirect
19. #14138C2semidirect
20. #14022C2semidirect
21. #14022C2semidirect
23. #13801C2semidirect
28. C22×C4×Q8C22semidirect
34. C2×#400C22semidirect
36. C2×#398C22semidirect
37. C2×#398C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
42. C2×#395C22semidirect
46. C2×#393C22semidirect
47. C2×#393C22semidirect
49. C2×#391C22semidirect
50. C2×#391C22semidirect
51. C2×#391C22semidirect
52. C2×#391C22semidirect
65. C2×#388C22semidirect
66. C2×#388C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
76. C2×C4×C4⋊C4C22semidirect
77. C2×C4×C4⋊C4C22semidirect
78. C2×C4×C4⋊C4C22semidirect
79. C2×C4×C4⋊C4C22semidirect
80. C2×C4×C4⋊C4C22semidirect
83. #1441C22semidirect
84. #1441C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. C4⋊#95C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
122. C4⋊#95C22semidirect
123. C4⋊#95C22semidirect
124. C4⋊#95C22semidirect
125. #1434C22semidirect
126. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25922
C2×#24352
C2×#23962
C2×#23092
#163742
#163712
#154672
#152972
#152842
#152172
#151572
#151472
#149992
#149472
#142582
#141532
#141382
#140222
#139022
#138012