Finite Group Databasebeta

← #636069

Subgroups — #636069

Order 512.

5200 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2418C211yesmaximal, characteristic, complemented
2C2×#2622C211yesmaximal, characteristic, complemented
3C2×C4×#120C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5#16338C212yesmaximal, complemented
6#16333C212yesmaximal, complemented
7#16282C212yesmaximal, complemented
8#16269C212yesmaximal, complemented
9#14806C212yesmaximal, complemented
10#14755C212yesmaximal, complemented
11#14743C212yesmaximal, complemented
12#14734C211yesmaximal, characteristic, complemented
13#14725C211yesmaximal, characteristic, complemented
14#14724C211yesmaximal, characteristic, complemented
15#14721C212yesmaximal, complemented
16#14715C211yesmaximal, characteristic
17#14693C211yesmaximal, characteristic, complemented
18#14275C211yesmaximal, characteristic, complemented
19#14262C211yesmaximal, characteristic, complemented
20#14259C211yesmaximal, characteristic, complemented
21#14044C211yesmaximal, characteristic, complemented
22#14016C211yesmaximal, characteristic, complemented
23#13873C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic, complemented
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yescomplemented
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2622—28no—
35#2418—28no—
36C2×#399C2211yescharacteristic, complemented
37C2×#399C2212yescomplemented
38C2×#397C2211yescharacteristic, complemented
39C2×#397C2212yescomplemented
40C2×#397C2212yescomplemented
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2211yescharacteristic, complemented
44C2×#394C2211yescharacteristic, complemented
45C2×#394C2212yescomplemented
46C2×#394C2212yescomplemented
47C2×#394C2212yescomplemented
48C2×#392C2212yes—
49C2×#392C2212yes—
50C4×#120—28no—
51C2×#388C2211yescharacteristic, complemented
52C2×#388C2211yescharacteristic, complemented
53C2×#388C2212yescomplemented
54C2×#386—28no—
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2212yes—
58C2×#386C2211yescharacteristic
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic, complemented
64C2×#386C2212yescomplemented
65C2×#385C2211yescharacteristic
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2212yescomplemented
72C2×#385C2212yescomplemented
73C2×#385C2212yescomplemented
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2212yescomplemented
84C22×#95C2211yescharacteristic
85C22×#95C2211yescharacteristic
86#1444C2212yescomplemented
87#1443C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
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#1438C2212yes—
112#1438C2212yes—
113#1438C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117C4⋊#95C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C24×C4—24no—
141C24×C4—24no—
142C24×C4—44no—
143C24×C4—42no—
144C24×C4—44no—
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C2×#123—24no—
154C2×#123—44no—
155C2×#120—24no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—42no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—28no—
164C2×C4×D4—44no—
165C2×C4×D4—42no—
166C2×C4×D4—44no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4D418yescomplemented
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225#399—24no—
226#399—44no—
227#397—24no—
228#397—28no—
229#397—28no—
230#394—24no—
231#394—24no—
232#394—28no—
233#394—28no—
234#394—44no—
235#394—44no—
236#394—44no—
237#392—44no—
238#392—44no—
239#388—24no—
240#388—24no—
241#388—44no—
242#386—24no—
243#386—24no—
244#386—24no—
245#386—24no—
246#386—28no—
247#386—28no—
248#386—28no—
249#386—28no—
250#386—28no—
251#386D418yescomplemented
252#385—24no—
253#385—24no—
254#385—24no—
255#385—24no—
256#385—24no—
257#385—28no—
258#385—44no—
259#385—42no—
260#385—44no—
261#380—24no—
262#380—24no—
263#379—24no—
264#379—24no—
265#379—24no—
266#379—24no—
267#379—24no—
268#379—42no—
269C4×C22⋊C4—24no—
270C4×C22⋊C4—28no—
271C2×#95—24no—
272C2×#95—24no—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
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—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C25—22no—
306C25—22no—
307C25—24no—
308C25—24no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25C2×D414yes—
326C25#4114yes—
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2412yes—
331C25C2411yescharacteristic
332C22×D4—232no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—432no—
371C22×D4—416no—
372C22×D4—416no—
373C22×D4—432no—
374C22×D4C2×D414yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—416no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—41no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—432no—
417C23×C4—416no—
418C23×C4—416no—
419C23×C4—432no—
420C23×C4C2×D414yes—
421C23×C4C2×D414yes—
422C23×C4C2×D414yes—
423C23×C4#4114yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442#123—416no—
443#120—232no—
444#120—416no—
445C4×D4—416no—
446C4×D4—432no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
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—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
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—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—416no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—416no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
577C2×C22⋊C4C2×D414yes—
578C2×C22⋊C4C2×D414yes—
579C2×C22⋊C4C2×D414yes—
580C2×C22⋊C4C2×D414yes—
581C2×C22⋊C4C2×D418yescomplemented
582C2×C22⋊C4#4114yes—
583C2×C42—24no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—24no—
587C2×C42—42no—
588C2×C42—41no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—24no—
600#95—24no—
601#95—22no—
602#95—22no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
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#95—42no—
618#95—42no—
619#95—42no—
620#95C2×D418yescomplemented
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—28no—
626C24—28no—
627C24—216no—
628C24—28no—
629C24—216no—
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—28no—
643C24—28no—
644C24—28no—
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—22no—
658C24—22no—
659C24—22no—
660C24—21no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—22no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—28no—
676C24—28no—
677C24—48no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—44no—
691C24—44no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24C22×D412yes—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C2×#4114yes—
719C24C2×#4112yes—
720C24C2×#4112yes—
721C24C2×#4112yes—
722C24H(5,𝔽2)14yes—
723C24H(5,𝔽2)14yes—
724C24H(5,𝔽2)12yes—
725C242−1+412yes—
726C24C2511yescharacteristic
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—216no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—4128no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—84no—
761C2×D4—82no—
762C2×D4—82no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—216no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—28no—
816C22×C4—28no—
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—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
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—44no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—4128no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—82no—
902C22×C4—84no—
903C22×C4—84no—
904C22×C4—84no—
905C22×C4—84no—
906C22×C4—84no—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D414yes—
912C22×C4C22×D414yes—
913C22×C4C22×D412yes—
914C22×C4C2×#4114yes—
915C22×C4C2×#4114yes—
916C22×C4H(5,𝔽2)14yes—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—82no—
922C4⋊C4—84no—
923C4⋊C4—82no—
924C4⋊C4—84no—
925C4⋊C4—84no—
926C4⋊C4—84no—
927C4⋊C4—84no—
928C22⋊C4—216no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—84no—
956C22⋊C4—82no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C22⋊C4—82no—
962C22⋊C4—82no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C42—44no—
967C42—48no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—232no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—24no—
1022C23—432no—
1023C23—432no—
1024C23—416no—
1025C23—416no—
1026C23—416no—
1027C23—416no—
1028C23—416no—
1029C23—432no—
1030C23—432no—
1031C23—416no—
1032C23—416no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—416no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—416no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—42no—
1076C23—41no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
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—88no—
1102C23—88no—
1103C23—88no—
1104C23—88no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23—816no—
1109C23#52514yes—
1110C23#52514yes—
1111C23#53818yes—
1112C23#53914yes—
1113C23D4214yes—
1114C23#54714yes—
1115C23#54714yes—
1116C23#55914yes—
1117C23C23×D411yescharacteristic
1118C23C23×D411yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C22×#4111yescharacteristic
1121C23C22×#4111yescharacteristic
1122C23C2×H(5,𝔽2)12yes—
1123C23C2×H(5,𝔽2)12yes—
1124C23C2×H(5,𝔽2)12yes—
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×2−1+411yescharacteristic
1127C23#58512yes—
1128D4—432no—
1129D4—432no—
1130D4—432no—
1131D4—416no—
1132D4—88no—
1133D4—88no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—416no—
1163C2×C4—432no—
1164C2×C4—416no—
1165C2×C4—416no—
1166C2×C4—432no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—41no—
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—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—88no—
1245C2×C4—88no—
1246C2×C4—88no—
1247C2×C4#53414yes—
1248C22—24no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—28no—
1254C22—28no—
1255C22—28no—
1256C22—24no—
1257C22—28no—
1258C22—28no—
1259C22—28no—
1260C22—28no—
1261C22—464no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—44no—
1290C22—42no—
1291C22—42no—
1292C22—44no—
1293C22—832no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22—81no—
1306C22—82no—
1307C22—82no—
1308C22#245518yes—
1309C22C2×#52511yescharacteristic
1310C22C2×#52511yescharacteristic
1311C22C2×#53411yescharacteristic
1312C22#344911yescharacteristic
1313C22C2×#53812yes—
1314C22C2×#53911yescharacteristic
1315C22#345912yes—
1316C22#346012yes—
1317C22C2×D4211yescharacteristic
1318C22C2×#54711yescharacteristic
1319C22C2×#54711yescharacteristic
1320C22C2×#55911yescharacteristic
1321C22#348411yescharacteristic
1322C22#348411yescharacteristic
1323C22#348412yes—
1324C22#348812yes—
1325C22#349012yes—
1326C22#351312yes—
1327C22#351912yes—
1328C22#353212yes—
1329C22#353412yes—
1330C22#353512yes—
1331C22#353612yes—
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—44no—
1339C4—44no—
1340C4—44no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—82no—
1346C4—81no—
1347C4—82no—
1348C4—81no—
1349C4—82no—
1350C2—28no—
1351C2—48no—
1352C2—82no—
1353C2—82no—
1354C2—82no—
1355C2#3456211yescharacteristic
1356C2C2×#245511yescharacteristic
1357C2#3498811yescharacteristic
1358C2#3499012yes—
1359C2#3748212yes—
1360C2#3764411yescharacteristic
1361C2#3765211yescharacteristic
1362C2#3776112yes—
1363C2#3891211yescharacteristic
1364C2#3891611yescharacteristic
1365C2#3926412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2418C2semidirect
2. C2×#2622C2semidirect
3. C2×C4×#120C2semidirect
4. C22×#386C2semidirect
5. #16338C2semidirect
6. #16333C2semidirect
7. #16282C2semidirect
8. #16269C2semidirect
9. #14806C2semidirect
10. #14755C2semidirect
11. #14743C2semidirect
12. #14734C2semidirect
13. #14725C2semidirect
14. #14724C2semidirect
15. #14721C2semidirect
17. #14693C2semidirect
18. #14275C2semidirect
19. #14262C2semidirect
20. #14259C2semidirect
21. #14044C2semidirect
22. #14016C2semidirect
23. #13873C2semidirect
26. C22×#123C22semidirect
30. C22×C4×D4C22semidirect
36. C2×#399C22semidirect
37. C2×#399C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
40. C2×#397C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
45. C2×#394C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
51. C2×#388C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
71. C2×#385C22semidirect
72. C2×#385C22semidirect
73. C2×#385C22semidirect
83. C2×C4×C22⋊C4C22semidirect
86. #1444C22semidirect
87. #1443C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
113. #1438C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. C4⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
184. C22×C22⋊C4D4semidirect
251. #386D4semidirect
581. C2×C22⋊C4C2×D4semidirect
620. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24182
C2×#26222
C2×C4×#1202
C22×#3862
#163382
#163332
#162822
#162692
#148062
#147552
#147432
#147342
#147252
#147242
#147212
#147152
#146932
#142752
#142622
#142592
#140442
#140162
#138732