Finite Group Databasebeta

← #523383

Subgroups — #523383

Order 512.

5268 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2410C211yesmaximal, characteristic
2C2×#2358C211yesmaximal, characteristic, complemented
3C2×#2321C211yesmaximal, characteristic, complemented
4C2×#2315C211yesmaximal, characteristic, complemented
5C22×#390C211yesmaximal, characteristic, complemented
6#14696C211yesmaximal, characteristic, complemented
7#14534C212yesmaximal, complemented
8#14518C212yesmaximal, complemented
9#14397C212yesmaximal, complemented
10#14361C212yesmaximal, complemented
11#14262C211yesmaximal, characteristic, complemented
12#14255C211yesmaximal, characteristic, complemented
13#14195C212yesmaximal, complemented
14#14189C212yesmaximal, complemented
15#14043C211yesmaximal, characteristic, complemented
16#14015C211yesmaximal, characteristic, complemented
17#14012C212yesmaximal, complemented
18#13998C212yesmaximal, complemented
19#13995C211yesmaximal, characteristic, complemented
20#13991C211yesmaximal, characteristic, complemented
21#13867C211yesmaximal, characteristic, complemented
22C22⋊C42C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#121C2212yes—
26C22×#120C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic, complemented
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C42C2211yescharacteristic
38#2410C4116yescomplemented
39C2×#394C2212yes—
40C2×#392C2212yes—
41#2358—28no—
42#2321—28no—
43#2315—28no—
44C2×#390—28no—
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2212yes—
48C2×#390C2212yes—
49C2×#390C2212yescomplemented
50C2×#390C2211yescharacteristic, complemented
51C2×#390C2212yescomplemented
52C2×#389C2212yescomplemented
53C2×#388C2212yescomplemented
54C2×#388C2212yescomplemented
55C2×#388C2211yescharacteristic, complemented
56C2×#388C2211yescharacteristic, complemented
57C2×#388C2212yescomplemented
58C2×#388C2212yescomplemented
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2211yescharacteristic
66C2×#386C2212yescomplemented
67C2×#386C2211yescharacteristic, complemented
68C2×#386C2211yescharacteristic, complemented
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2212yescomplemented
76C2×#385C2212yescomplemented
77C2×#385C2211yescharacteristic, complemented
78C2×#385C2212yescomplemented
79C2×#380C2212yescomplemented
80C2×#380C2212yescomplemented
81C2×#379C2211yescharacteristic
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×#379C2211yescharacteristic
85C2×C4×C4⋊C4C2212yescomplemented
86C2×C4×C22⋊C4C2211yescharacteristic
87C2×C4×C22⋊C4C2211yescharacteristic
88C2×C4×C22⋊C4C2211yescharacteristic
89C2×C4×C22⋊C4C2211yescharacteristic, complemented
90C2×C4×C22⋊C4C2212yescomplemented
91#1444C2212yescomplemented
92#1444C2212yescomplemented
93#1441C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1434C2212yescomplemented
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yescomplemented
127C4×#95C2212yescomplemented
128C26C2311yescharacteristic
129C26C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4C2×C418yescomplemented
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×#121—44no—
151C2×#121—44no—
152C2×#121C2×C4116yescomplemented
153C2×#120—24no—
154C2×#120—24no—
155C2×#120—24no—
156C2×#120—24no—
157C2×#120C2×C418yes—
158C2×#120C2×C418yescomplemented
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—44no—
163C2×C4×D4—42no—
164C22×C4⋊C4—24no—
165C22×C4⋊C4—44no—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4—42no—
189C22×C22⋊C4—42no—
190C22×C22⋊C4C2×C418yescomplemented
191C22×C22⋊C4D418yescomplemented
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C42—24no—
230C22×C42—44no—
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238#394C2×C4116yescomplemented
239#392C2×C4116yescomplemented
240#390—28no—
241#390—24no—
242#390—28no—
243#390—28no—
244#390—28no—
245#390—28no—
246#390—44no—
247#389—44no—
248#388—28no—
249#388—24no—
250#388—24no—
251#388—28no—
252#388—44no—
253#388—44no—
254#386—24no—
255#386—24no—
256#386—24no—
257#386—24no—
258#386—28no—
259#386—44no—
260#386—44no—
261#386—42no—
262#386C2×C4116yescomplemented
263#386C2×C418yescomplemented
264#385—24no—
265#385—24no—
266#385—28no—
267#385—24no—
268#385—24no—
269#385—24no—
270#385—28no—
271#385—44no—
272#385C2×C418yescomplemented
273#385D418yescomplemented
274#380—28no—
275#380—28no—
276#379—24no—
277#379—24no—
278#379—42no—
279#379C2×C418yescomplemented
280C4×C4⋊C4—44no—
281C4×C22⋊C4—24no—
282C4×C22⋊C4—24no—
283C4×C22⋊C4—24no—
284C4×C22⋊C4—24no—
285C4×C22⋊C4—44no—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25—42no—
331C25—42no—
332C25C22×C414yes—
333C25C22×C414yes—
334C25C2×D414yes—
335C25#4114yes—
336C25C2412yes—
337C25C2411yescharacteristic
338C25C2411yescharacteristic
339C25C2411yescharacteristic
340C25C2411yescharacteristic
341C22×D4—232no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—432no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—416no—
370C22×D4—416no—
371C22×D4—432no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4C22×C414yes—
379C22×D4C22×C418yes—
380C22×D4C22×C418yes—
381C22×D4C22×C414yes—
382C22×D4C22×C414yes—
383C22×D4C22×C418yes—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—41no—
411C23×C4—41no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—41no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4C22×C414yes—
427C23×C4C22×C418yes—
428C23×C4C2×D414yes—
429C23×C4C2×D414yes—
430C23×C4C2×D414yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449#121—432no—
450#120—232no—
451#120—232no—
452C4×D4—416no—
453C4×D4—416no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—416no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4C22×C418yes—
482C2×C4⋊C4C2×D418yescomplemented
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—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—232no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—416no—
538C2×C22⋊C4—416no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
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—41no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—416no—
558C2×C22⋊C4—416no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4C22×C414yes—
578C2×C22⋊C4C22×C418yes—
579C2×C22⋊C4C22×C414yes—
580C2×C22⋊C4C22×C414yes—
581C2×C22⋊C4C22×C414yes—
582C2×C22⋊C4C22×C418yes—
583C2×C22⋊C4C22×C418yes—
584C2×C22⋊C4C22×C418yes—
585C2×C22⋊C4C22×C418yes—
586C2×C22⋊C4C22×C414yes—
587C2×C22⋊C4C2×D414yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4C2×D414yes—
590C2×C22⋊C4C2×D414yes—
591C2×C22⋊C4C2×D414yes—
592C2×C22⋊C4C2×D414yes—
593C2×C22⋊C4#4114yes—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—24no—
598C2×C42—24no—
599C2×C42—24no—
600C2×C42—24no—
601C2×C42—24no—
602C2×C42—24no—
603C2×C42—24no—
604C2×C42—22no—
605C2×C42—24no—
606C2×C42—41no—
607C2×C42—42no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42—416no—
611C2×C42—42no—
612C2×C42—42no—
613C2×C42—42no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—22no—
623#95—22no—
624#95—24no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95C22×C418yes—
640#95C22×C418yes—
641#95C2×D418yescomplemented
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—21no—
660C24—22no—
661C24—22no—
662C24—28no—
663C24—28no—
664C24—28no—
665C24—28no—
666C24—28no—
667C24—28no—
668C24—28no—
669C24—22no—
670C24—22no—
671C24—21no—
672C24—21no—
673C24—22no—
674C24—21no—
675C24—21no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—21no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—28no—
694C24—28no—
695C24—44no—
696C24—48no—
697C24—48no—
698C24—44no—
699C24—44no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24—44no—
704C24—48no—
705C24—44no—
706C24—44no—
707C24—44no—
708C24—48no—
709C24—44no—
710C24—48no—
711C24—44no—
712C24—44no—
713C24—44no—
714C24—44no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24—84no—
721C24—84no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24—84no—
728C24—84no—
729C24—84no—
730C24—84no—
731C24C4×D4116yes—
732C24C23×C414yes—
733C24C23×C412yes—
734C24C23×C412yes—
735C24C23×C412yes—
736C24C23×C412yes—
737C24C22×D412yes—
738C24C22×D412yes—
739C24C22×D412yes—
740C24C22×D412yes—
741C24C2×#4112yes—
742C24C2×#4112yes—
743C24C2×#4112yes—
744C24C2×#4112yes—
745C24H(5,𝔽2)12yes—
746C242−1+412yes—
747C24C2511yescharacteristic
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—216no—
752C2×D4—216no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—216no—
756C2×D4—216no—
757C2×D4—216no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—4128no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—84no—
781C2×D4—84no—
782C2×D4—84no—
783C2×D4—84no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—84no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—216no—
790C22×C4—28no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—216no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
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—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—216no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—44no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—84no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4—84no—
909C22×C4—82no—
910C22×C4—84no—
911C22×C4—84no—
912C22×C4—84no—
913C22×C4—82no—
914C22×C4—82no—
915C22×C4—84no—
916C22×C4—84no—
917C22×C4—84no—
918C22×C4—84no—
919C22×C4—84no—
920C22×C4—84no—
921C22×C4—84no—
922C22×C4C23×C412yes—
923C22×C4C23×C412yes—
924C22×C4C23×C414yes—
925C22×C4C23×C412yes—
926C22×C4C23×C414yes—
927C22×C4C23×C414yes—
928C22×C4C22×D412yes—
929C22×C4C22×D414yes—
930C22×C4C22×D412yes—
931C22×C4C22×D412yes—
932C22×C4C22×D412yes—
933C22×C4C22×D412yes—
934C22×C4C22×D414yes—
935C22×C4C22×D412yes—
936C22×C4C2×#4114yes—
937C22×C4H(5,𝔽2)14yes—
938C22×C4H(5,𝔽2)14yes—
939C22×C4H(5,𝔽2)14yes—
940C4⋊C4—216no—
941C4⋊C4—48no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—84no—
947C4⋊C4—82no—
948C4⋊C4—84no—
949C4⋊C4—84no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—216no—
956C22⋊C4—216no—
957C22⋊C4—216no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C22⋊C4—44no—
978C22⋊C4—82no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C22⋊C4—84no—
982C22⋊C4—84no—
983C22⋊C4—84no—
984C22⋊C4—84no—
985C22⋊C4—84no—
986C22⋊C4C4×D4116yescomplemented
987C42—48no—
988C42—48no—
989C42—48no—
990C42—44no—
991C42—44no—
992C42—82no—
993C42—84no—
994C23—24no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—24no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—24no—
1023C23—24no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—24no—
1037C23—24no—
1038C23—232no—
1039C23—24no—
1040C23—22no—
1041C23—22no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—22no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—416no—
1052C23—416no—
1053C23—416no—
1054C23—416no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—416no—
1072C23—42no—
1073C23—41no—
1074C23—41no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—41no—
1081C23—41no—
1082C23—42no—
1083C23—41no—
1084C23—42no—
1085C23—41no—
1086C23—42no—
1087C23—41no—
1088C23—41no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—816no—
1119C23—816no—
1120C23—816no—
1121C23—88no—
1122C23—88no—
1123C23—88no—
1124C23—88no—
1125C23—816no—
1126C23—816no—
1127C23—816no—
1128C23—816no—
1129C23—88no—
1130C23—88no—
1131C23—88no—
1132C23—88no—
1133C23—816no—
1134C23C2×C4×D414yes—
1135C23C2×C4×D414yes—
1136C23C2×C4×D414yes—
1137C23C2×C4×D414yes—
1138C23#52014yes—
1139C23D4214yes—
1140C23#54714yes—
1141C23#54814yes—
1142C23#55314yes—
1143C23C24×C411yescharacteristic
1144C23C23×D411yescharacteristic
1145C23C23×D411yescharacteristic
1146C23C22×#4111yescharacteristic
1147C23C22×#4111yescharacteristic
1148C23C2×H(5,𝔽2)12yes—
1149C23C2×H(5,𝔽2)12yes—
1150C23C2×H(5,𝔽2)11yescharacteristic
1151C23C2×H(5,𝔽2)12yes—
1152C23C2×2−1+411yescharacteristic
1153C23#58512yes—
1154D4—432no—
1155D4—432no—
1156D4—416no—
1157D4—416no—
1158D4—816no—
1159D4—88no—
1160C2×C4—232no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—416no—
1204C2×C4—416no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—41no—
1241C2×C4—42no—
1242C2×C4—41no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—41no—
1246C2×C4—42no—
1247C2×C4—41no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—816no—
1267C2×C4—88no—
1268C2×C4—88no—
1269C2×C4—88no—
1270C2×C4—88no—
1271C2×C4—88no—
1272C2×C4C2×C4×D418yes—
1273C2×C4#51818yes—
1274C2×C4#53414yes—
1275C22—28no—
1276C22—24no—
1277C22—28no—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—24no—
1282C22—24no—
1283C22—28no—
1284C22—28no—
1285C22—24no—
1286C22—24no—
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—44no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—42no—
1311C22—44no—
1312C22—42no—
1313C22—44no—
1314C22—44no—
1315C22—42no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—832no—
1320C22—832no—
1321C22—82no—
1322C22—82no—
1323C22—82no—
1324C22—81no—
1325C22—82no—
1326C22—81no—
1327C22—82no—
1328C22—81no—
1329C22—82no—
1330C22—81no—
1331C22—82no—
1332C22—82no—
1333C22—82no—
1334C22—82no—
1335C22#236118yes—
1336C22C22×C4×D411yescharacteristic
1337C22C22×C4×D411yescharacteristic
1338C22C2×#51812yes—
1339C22C2×#52011yescharacteristic
1340C22C4×H(5,𝔽2)12yes—
1341C22C2×#53411yescharacteristic
1342C22#344911yescharacteristic
1343C22#345912yes—
1344C22C2×D4211yescharacteristic
1345C22C2×#54711yescharacteristic
1346C22C2×#54811yescharacteristic
1347C22C2×#55311yescharacteristic
1348C22#348411yescharacteristic
1349C22#348411yescharacteristic
1350C22#349012yes—
1351C22#349612yes—
1352C22#349812yes—
1353C22#351412yes—
1354C22#351912yes—
1355C22#353612yes—
1356C22#354212yes—
1357C22#354312yes—
1358C22#356112yes—
1359C4—28no—
1360C4—24no—
1361C4—28no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—44no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—82no—
1373C4—81no—
1374C4—82no—
1375C4—81no—
1376C4—82no—
1377C2—28no—
1378C2—44no—
1379C2—44no—
1380C2—82no—
1381C2—84no—
1382C2C4×#53411yescharacteristic
1383C2C2×#236111yescharacteristic
1384C2#3419811yescharacteristic
1385C2#3431012yes—
1386C2#3447612yes—
1387C2#3803611yescharacteristic
1388C2#3804411yescharacteristic
1389C2#3820812yes—
1390C2#3933211yescharacteristic
1391C2#3933611yescharacteristic
1392C2#3942012yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2410C2
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×#2358C2semidirect
3. C2×#2321C2semidirect
4. C2×#2315C2semidirect
5. C22×#390C2semidirect
6. #14696C2semidirect
7. #14534C2semidirect
8. #14518C2semidirect
9. #14397C2semidirect
10. #14361C2semidirect
11. #14262C2semidirect
12. #14255C2semidirect
13. #14195C2semidirect
14. #14189C2semidirect
15. #14043C2semidirect
16. #14015C2semidirect
17. #14012C2semidirect
18. #13998C2semidirect
19. #13995C2semidirect
20. #13991C2semidirect
21. #13867C2semidirect
22. C22⋊C42C2semidirect
23. C4×#385C2semidirect
29. C22×C4×D4C22semidirect
38. #2410C4semidirect
49. C2×#390C22semidirect
50. C2×#390C22semidirect
51. C2×#390C22semidirect
52. C2×#389C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
75. C2×#385C22semidirect
76. C2×#385C22semidirect
77. C2×#385C22semidirect
78. C2×#385C22semidirect
79. C2×#380C22semidirect
80. C2×#380C22semidirect
85. C2×C4×C4⋊C4C22semidirect
89. C2×C4×C22⋊C4C22semidirect
90. C2×C4×C22⋊C4C22semidirect
91. #1444C22semidirect
92. #1444C22semidirect
93. #1441C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1434C22semidirect
126. C22⋊#95C22semidirect
127. C4×#95C22semidirect
134. C23×D4C2×C4semidirect
152. C2×#121C2×C4semidirect
158. C2×#120C2×C4semidirect
190. C22×C22⋊C4C2×C4semidirect
191. C22×C22⋊C4D4semidirect
238. #394C2×C4semidirect
239. #392C2×C4semidirect
262. #386C2×C4semidirect
263. #386C2×C4semidirect
272. #385C2×C4semidirect
273. #385D4semidirect
279. #379C2×C4semidirect
482. C2×C4⋊C4C2×D4semidirect
641. #95C2×D4semidirect
986. C22⋊C4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24102
C2×#23582
C2×#23212
C2×#23152
C22×#3902
#146962
#145342
#145182
#143972
#143612
#142622
#142552
#141952
#141892
#140432
#140152
#140122
#139982
#139952
#139912
#138672
C22⋊C422
C4×#3852