Finite Group Databasebeta

← #522629

Subgroups — #522629

Order 512.

4074 conjugacy classes of subgroups.

The subgroup lattice has 1333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2619C211yesmaximal, characteristic
2C2×#2366C211yesmaximal, characteristic, complemented
3C2×#2324C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5C2×#2296C211yesmaximal, characteristic, complemented
6#14698C211yesmaximal, characteristic, complemented
7#14563C212yesmaximal, complemented
8#14534C212yesmaximal, complemented
9#14519C212yesmaximal, complemented
10#14518C212yesmaximal, complemented
11#14257C211yesmaximal, characteristic, complemented
12#14205C212yesmaximal, complemented
13#14189C212yesmaximal, complemented
14#14185C212yesmaximal, complemented
15#14171C212yesmaximal, complemented
16#14154C211yesmaximal, characteristic, complemented
17#14150C211yesmaximal, characteristic, complemented
18#14022C211yesmaximal, characteristic, complemented
19#14022C211yesmaximal, characteristic, complemented
20#14018C211yesmaximal, characteristic, complemented
21#14018C211yesmaximal, characteristic, complemented
22#13804C211yesmaximal, characteristic, complemented
23#13777C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2212yes—
30C22×C4×D4C2212yes—
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2619C4116yescomplemented
35C2×#394C2212yes—
36C2×#394C2212yes—
37C2×#392C2212yes—
38C2×#392C2212yes—
39#2366—28no—
40#2324—28no—
41C4×#121—28no—
42#2296—28no—
43C2×#390C2211yescharacteristic
44C2×#390C2212yes—
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2212yes—
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#388C2212yes—
62C2×#388C2212yes—
63C2×#388C2212yes—
64C2×#388C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#386C2212yes—
71C2×#385C2212yes—
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2211yescharacteristic
76C2×#385C2212yes—
77C2×#385C2212yes—
78C2×#382C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C4⋊C4C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86C2×C4×C4⋊C4C2211yescharacteristic
87C2×C4×C4⋊C4C2211yescharacteristic
88C2×C4×C4⋊C4C2211yescharacteristic
89C2×C4×C22⋊C4C2212yes—
90#1444C2212yes—
91#1442C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1437C2212yes—
109#1437C2212yes—
110#1437C2212yes—
111#1437C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117#1436C2212yes—
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2211yescharacteristic
123C4⋊#95C2211yescharacteristic
124#1434C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C4×#95C2212yes—
128C23×D4C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2312yes—
133C23×D4C2312yes—
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139C2×#127—24no—
140C2×#127—24no—
141C2×#127C2×C418yescomplemented
142C2×#121—24no—
143C2×#121—24no—
144C2×#121—24no—
145C2×#121—24no—
146C2×#121C2×C418yescomplemented
147C2×#121C2×C418yescomplemented
148C2×C4×D4—24no—
149C2×C4×D4—28no—
150C2×C4×D4—24no—
151C2×C4×D4—28no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—42no—
155C2×C4×D4—42no—
156C2×C4×D4—44no—
157C2×C4×D4—44no—
158C2×C4×D4—44no—
159C2×C4×D4—44no—
160C2×#117—24no—
161C2×#117—24no—
162C2×#117—24no—
163C2×#117—24no—
164C2×#117—42no—
165C2×#117C2×C418yescomplemented
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C42—24no—
213C22×C42—24no—
214C22×C42—42no—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2312yes—
226C22×C42C2311yescharacteristic
227#394C2×C4116yescomplemented
228#394C2×C4116yescomplemented
229#392C2×C4116yescomplemented
230#392C2×C4116yescomplemented
231#390—24no—
232#390—28no—
233#390—24no—
234#390—28no—
235#390—24no—
236#390—24no—
237#390—42no—
238#390—42no—
239#390—44no—
240#390—44no—
241#390C2×C418yescomplemented
242#390C2×C418yescomplemented
243#389—24no—
244#389—24no—
245#389—24no—
246#389—24no—
247#389—24no—
248#389—24no—
249#388—28no—
250#388—28no—
251#388—44no—
252#388—44no—
253#386—28no—
254#386—28no—
255#386—28no—
256#386—28no—
257#386—44no—
258#386—44no—
259#385—24no—
260#385—24no—
261#385—28no—
262#385—24no—
263#385—24no—
264#385—44no—
265#385—44no—
266#382C2×C418yescomplemented
267#380—24no—
268#380D418yescomplemented
269C4×C4⋊C4—24no—
270C4×C4⋊C4—24no—
271C4×C4⋊C4—24no—
272C4×C4⋊C4—24no—
273C4×C4⋊C4—24no—
274C4×C4⋊C4—24no—
275C4×C4⋊C4—24no—
276C4×C4⋊C4D418yescomplemented
277C4×C22⋊C4—28no—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C25C2412yes—
309C25C2412yes—
310C25C2411yescharacteristic
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—24no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—24no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4C22×C414yes—
348C22×D4C22×C414yes—
349C22×D4C22×C418yes—
350C22×D4C22×C418yes—
351C22×D4C22×C418yes—
352C22×D4C22×C418yes—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—41no—
372C23×C4—41no—
373C23×C4—41no—
374C23×C4—41no—
375C23×C4—41no—
376C23×C4—41no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4C22×C414yes—
386C23×C4C2×D414yes—
387C23×C4#4114yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408#127—232no—
409#121—232no—
410#121—232no—
411C4×D4—416no—
412C4×D4—416no—
413C4×D4—432no—
414C4×D4—432no—
415#117—232no—
416#117—416no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
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—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—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
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—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4C22×C414yes—
470C2×C4⋊C4C22×C414yes—
471C2×C4⋊C4C22×C414yes—
472C2×C4⋊C4C22×C414yes—
473C2×C4⋊C4C2×D414yes—
474C2×C4⋊C4C2×D414yes—
475C2×C4⋊C4C2×D414yes—
476C2×C4⋊C4C2×D414yes—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
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—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—42no—
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—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⋊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⋊C4C22×C414yes—
547C2×C22⋊C4C22×C414yes—
548C2×C22⋊C4C22×C418yes—
549C2×C22⋊C4C22×C418yes—
550C2×C22⋊C4C22×C418yes—
551C2×C22⋊C4C22×C418yes—
552C2×C22⋊C4C22×C418yes—
553C2×C22⋊C4C22×C418yes—
554C2×C22⋊C4C2×D418yes—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—24no—
564C2×C42—24no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—24no—
573C2×C42—22no—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—416no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—41no—
581C2×C42—41no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42C22×C414yes—
587C2×C42C22×C414yes—
588C2×C42C2×D414yes—
589C2×C42C2×D414yes—
590C2×C42C2×D414yes—
591C2×C42#4114yes—
592#95—24no—
593#95—24no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95C22×C418yes—
618#95C22×C418yes—
619#95C2×D418yes—
620#95C2×D414yes—
621#95C2×D414yes—
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—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24C23×C414yes—
663C24C23×C414yes—
664C24C23×C412yes—
665C24C22×D412yes—
666C24C2×#4112yes—
667C24C2511yescharacteristic
668C2×D4—216no—
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—216no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—216no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—84no—
703C2×D4—84no—
704C2×D4—84no—
705C2×D4—84no—
706C2×D4—84no—
707C2×D4—84no—
708C2×D4—84no—
709C2×D4—84no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
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—28no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
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—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4C4×D4116yescomplemented
855C22×C4C23×C414yes—
856C22×C4C23×C414yes—
857C22×C4C23×C412yes—
858C22×C4C23×C412yes—
859C22×C4C23×C412yes—
860C22×C4C23×C412yes—
861C22×C4C23×C412yes—
862C22×C4C23×C412yes—
863C22×C4C22×D414yes—
864C22×C4C22×D414yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C2×#4112yes—
875C22×C4C2×#4112yes—
876C22×C4C2×#4112yes—
877C22×C4C2×#4112yes—
878C22×C4C2×#4112yes—
879C22×C4H(5,𝔽2)12yes—
880C22×C4H(5,𝔽2)12yes—
881C22×C4H(5,𝔽2)12yes—
882C22×C4H(5,𝔽2)12yes—
883C22×C4H(5,𝔽2)12yes—
884C22×C42−1+412yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—84no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—216no—
908C22⋊C4—216no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C42—28no—
932C42—28no—
933C42—28no—
934C42—44no—
935C42—44no—
936C42—48no—
937C42—48no—
938C42—44no—
939C42—44no—
940C42—84no—
941C42—84no—
942C42C4×D4116yescomplemented
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—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—41no—
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—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—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23C2×C4×D414yes—
1048C23C24×C411yescharacteristic
1049C23C23×D411yescharacteristic
1050C23C23×D411yescharacteristic
1051C23C22×#4111yescharacteristic
1052C23C22×#4111yescharacteristic
1053C23C2×H(5,𝔽2)11yescharacteristic
1054C23C2×H(5,𝔽2)11yescharacteristic
1055C23C2×H(5,𝔽2)11yescharacteristic
1056C23C2×H(5,𝔽2)11yescharacteristic
1057C23C2×H(5,𝔽2)11yescharacteristic
1058C23C2×2−1+411yescharacteristic
1059C23#58511yescharacteristic
1060C23#58511yescharacteristic
1061C23#58511yescharacteristic
1062C23#58511yescharacteristic
1063D4—432no—
1064D4—432no—
1065D4—416no—
1066D4—416no—
1067D4—816no—
1068D4—816no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
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—232no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
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—416no—
1128C2×C4—416no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
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—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—816no—
1202C2×C4—816no—
1203C2×C4C2×C4×D414yes—
1204C2×C4C2×C4×D414yes—
1205C2×C4C2×C4×D414yes—
1206C2×C4C2×C4×D414yes—
1207C2×C4C2×C4×D414yes—
1208C2×C4#52014yes—
1209C2×C4#53514yes—
1210C2×C4D4214yes—
1211C2×C4#54714yes—
1212C2×C4#54814yes—
1213C2×C4#55314yes—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22C22×C4×D411yescharacteristic
1260C22C22×C4×D411yescharacteristic
1261C22C2×#52011yescharacteristic
1262C22C4×H(5,𝔽2)11yescharacteristic
1263C22C4×H(5,𝔽2)11yescharacteristic
1264C22C4×H(5,𝔽2)11yescharacteristic
1265C22C4×H(5,𝔽2)11yescharacteristic
1266C22C2×#53511yescharacteristic
1267C22#344911yescharacteristic
1268C22#346011yescharacteristic
1269C22#346011yescharacteristic
1270C22C2×D4211yescharacteristic
1271C22C2×#54711yescharacteristic
1272C22C2×#54811yescharacteristic
1273C22C2×#55311yescharacteristic
1274C22#348411yescharacteristic
1275C22#348711yescharacteristic
1276C22#348811yescharacteristic
1277C22#348811yescharacteristic
1278C22#348811yescharacteristic
1279C22#348811yescharacteristic
1280C22#350611yescharacteristic
1281C22#350611yescharacteristic
1282C22#350811yescharacteristic
1283C22#350811yescharacteristic
1284C22#351011yescharacteristic
1285C22#351011yescharacteristic
1286C22#353711yescharacteristic
1287C22#353911yescharacteristic
1288C22#354211yescharacteristic
1289C22#354211yescharacteristic
1290C22#354811yescharacteristic
1291C22#355411yescharacteristic
1292C22#355411yescharacteristic
1293C22#355711yescharacteristic
1294C4—24no—
1295C4—24no—
1296C4—24no—
1297C4—24no—
1298C4—42no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—42no—
1308C4—44no—
1309C4—81no—
1310C4—81no—
1311C4—82no—
1312C4—82no—
1313C4#236118yes—
1314C2—44no—
1315C2—84no—
1316C2—84no—
1317C2C4×#53511yescharacteristic
1318C2C2×#236111yescharacteristic
1319C2#3426511yescharacteristic
1320C2#3426911yescharacteristic
1321C2#3426911yescharacteristic
1322C2#3441811yescharacteristic
1323C2#3442311yescharacteristic
1324C2#3765011yescharacteristic
1325C2#3765711yescharacteristic
1326C2#3779211yescharacteristic
1327C2#3779711yescharacteristic
1328C2#3971811yescharacteristic
1329C2#3972511yescharacteristic
1330C2#3981811yescharacteristic
1331C2#3982311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2619C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2366C2semidirect
3. C2×#2324C2semidirect
4. C2×C4×#121C2semidirect
5. C2×#2296C2semidirect
6. #14698C2semidirect
7. #14563C2semidirect
8. #14534C2semidirect
9. #14519C2semidirect
10. #14518C2semidirect
11. #14257C2semidirect
12. #14205C2semidirect
13. #14189C2semidirect
14. #14185C2semidirect
15. #14171C2semidirect
16. #14154C2semidirect
17. #14150C2semidirect
18. #14022C2semidirect
19. #14022C2semidirect
20. #14018C2semidirect
21. #14018C2semidirect
22. #13804C2semidirect
23. #13777C2semidirect
34. #2619C4semidirect
141. C2×#127C2×C4semidirect
146. C2×#121C2×C4semidirect
147. C2×#121C2×C4semidirect
165. C2×#117C2×C4semidirect
227. #394C2×C4semidirect
228. #394C2×C4semidirect
229. #392C2×C4semidirect
230. #392C2×C4semidirect
241. #390C2×C4semidirect
242. #390C2×C4semidirect
266. #382C2×C4semidirect
268. #380D4semidirect
276. C4×C4⋊C4D4semidirect
854. C22×C4C4×D4semidirect
942. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26192
C2×#23662
C2×#23242
C2×C4×#1212
C2×#22962
#146982
#145632
#145342
#145192
#145182
#142572
#142052
#141892
#141852
#141712
#141542
#141502
#140222
#140182
#138042
#137772