Finite Group Databasebeta

← #5955455

Subgroups — #5955455

Order 512.

4680 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2321C211yesmaximal, characteristic, complemented
2C2×#2321C211yesmaximal, characteristic, complemented
3C2×#2312C211yesmaximal, characteristic, complemented
4C22×#390C211yesmaximal, characteristic, complemented
5#15007C212yesmaximal, complemented
6#14999C212yesmaximal, complemented
7#14986C212yesmaximal, complemented
8#14976C212yesmaximal, complemented
9#14815C212yesmaximal, complemented
10#14799C212yesmaximal, complemented
11#14754C212yesmaximal, complemented
12#14751C212yesmaximal, complemented
13#14729C211yesmaximal, characteristic, complemented
14#14728C211yesmaximal, characteristic, complemented
15#14727C211yesmaximal, characteristic, complemented
16#14726C211yesmaximal, characteristic, complemented
17#14725C211yesmaximal, characteristic, complemented
18#14724C211yesmaximal, characteristic, complemented
19#14718C211yesmaximal, characteristic, complemented
20#14715C211yesmaximal, characteristic
21#13775C211yesmaximal, characteristic, complemented
22C4×#385C211yesmaximal, characteristic, complemented
23C4×#386C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#120C2211yescharacteristic
26C22×#120C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#398C2212yescomplemented
35C2×#397C2212yescomplemented
36C2×#396C2212yescomplemented
37C2×#396C2212yescomplemented
38C2×#394C2212yes—
39C2×#394C2212yes—
40C2×#394C2212yescomplemented
41C2×#394C2212yescomplemented
42C2×#392C2212yes—
43C2×#392C2212yes—
44#2321—28no—
45#2321—28no—
46#2312—28no—
47C2×#390—28no—
48C2×#390C2212yes—
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2212yes—
52C2×#390C2211yescharacteristic, complemented
53C2×#390C2212yescomplemented
54C2×#390C2211yescharacteristic, complemented
55C2×#388C2211yescharacteristic, complemented
56C2×#388C2212yescomplemented
57C2×#388C2211yescharacteristic, complemented
58C2×#388C2212yescomplemented
59C2×#388C2211yescharacteristic, complemented
60C2×#388C2211yescharacteristic, complemented
61C2×#388C2212yescomplemented
62C2×#388C2212yescomplemented
63C2×#388C2212yescomplemented
64C2×#388C2212yescomplemented
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic, complemented
70C2×#386C2212yescomplemented
71C2×#386C2211yescharacteristic, complemented
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×C4×C4⋊C4C2212yescomplemented
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic
87C2×C4×C22⋊C4C2211yescharacteristic
88C2×C4×C22⋊C4C2212yescomplemented
89#1444C2212yescomplemented
90#1442C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C4×#95C2212yescomplemented
126C4×#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×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C2×#120—24no—
147C2×#120—24no—
148C2×#120—24no—
149C2×#120—24no—
150C2×#120—24no—
151C2×#120—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C22×C4⋊C4—24no—
156C22×C4⋊C4—44no—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C22⋊C4—24no—
168C22×C22⋊C4—24no—
169C22×C22⋊C4—24no—
170C22×C22⋊C4—24no—
171C22×C22⋊C4—24no—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—44no—
175C22×C22⋊C4—44no—
176C22×C22⋊C4D418yescomplemented
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C42—24no—
218C22×C42—44no—
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2312yes—
226#398—44no—
227#397—44no—
228#396—44no—
229#396—44no—
230#394—44no—
231#394—44no—
232#394—44no—
233#394—44no—
234#392—44no—
235#392—44no—
236#390—24no—
237#390—24no—
238#390—28no—
239#390—28no—
240#390—28no—
241#390—28no—
242#390—28no—
243#388—24no—
244#388—24no—
245#388—24no—
246#388—24no—
247#388—28no—
248#388—28no—
249#388—28no—
250#388—28no—
251#388—28no—
252#388—28no—
253#386—24no—
254#386—24no—
255#386—24no—
256#386—24no—
257#386—24no—
258#386—24no—
259#386—28no—
260#385—24no—
261#385—24no—
262#385—24no—
263#385—24no—
264#380—24no—
265#380—24no—
266#379—24no—
267#379—24no—
268#379—24no—
269#379—24no—
270#379—24no—
271#379—24no—
272C4×C4⋊C4—44no—
273C4×C22⋊C4—24no—
274C4×C22⋊C4—24no—
275C4×C22⋊C4—44no—
276C4×C22⋊C4D418yescomplemented
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25C2×D414yes—
326C25#4114yes—
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2412yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C22×D4—232no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—416no—
363C22×D4—416no—
364C22×D4—432no—
365C22×D4—432no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4#4114yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4C2×D414yes—
401C23×C4C2×D414yes—
402C23×C4C2×D414yes—
403C23×C4#4114yes—
404C23×C4#4114yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423#120—232no—
424#120—232no—
425C4×D4—416no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—416no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—232no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
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—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—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
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—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
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—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—416no—
536C2×C22⋊C4—416no—
537C2×C22⋊C4—416no—
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—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4#4114yes—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—22no—
578C2×C42—24no—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—416no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42—42no—
591C2×C42—42no—
592C2×C42C2×D418yescomplemented
593#95—22no—
594#95—22no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—22no—
599#95—22no—
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—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
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—21no—
628C24—21no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—28no—
674C24—28no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—48no—
679C24—44no—
680C24—48no—
681C24—44no—
682C24—48no—
683C24—48no—
684C24—44no—
685C24—44no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—44no—
690C24—48no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C22×D412yes—
719C24C2×#4114yes—
720C24C2×#4112yes—
721C24C2×#4112yes—
722C24C2×#4112yes—
723C24C2×#4112yes—
724C24C2×#4112yes—
725C24C2×#4112yes—
726C24C2511yescharacteristic
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—216no—
733C2×D4—28no—
734C2×D4—28no—
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—4128no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—82no—
757C2×D4—82no—
758C2×D4—82no—
759C2×D4—82no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—216no—
769C22×C4—28no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—216no—
779C22×C4—28no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
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—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—82no—
878C22×C4—82no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4#121116yes—
885C22×C4C22×D414yes—
886C22×C4C22×D414yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C2×#4112yes—
894C22×C4C2×#4112yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4114yes—
899C22×C4H(5,𝔽2)14yes—
900C22×C4H(5,𝔽2)14yes—
901C22×C4H(5,𝔽2)14yes—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—82no—
908C4⋊C4—82no—
909C4⋊C4—84no—
910C4⋊C4—84no—
911C4⋊C4—84no—
912C22⋊C4—216no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—82no—
936C22⋊C4—82no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—82no—
947C22⋊C4—82no—
948C22⋊C4—82no—
949C22⋊C4—82no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C42—48no—
953C42—48no—
954C42—48no—
955C42—44no—
956C42—82no—
957C42—82no—
958C42—84no—
959C23—24no—
960C23—24no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—416no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
1007C23—42no—
1008C23—41no—
1009C23—41no—
1010C23—42no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—42no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
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—41no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—42no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
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—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—88no—
1086C23—88no—
1087C23—816no—
1088C23—816no—
1089C23—88no—
1090C23—88no—
1091C23—88no—
1092C23—88no—
1093C23—816no—
1094C23—816no—
1095C23—88no—
1096C23—816no—
1097C23—816no—
1098C23—88no—
1099C23—816no—
1100C23—816no—
1101C23C2×#12114yes—
1102C23#52514yes—
1103C23#52514yes—
1104C23#52514yes—
1105C23#52914yes—
1106C23#52914yes—
1107C23#53214yes—
1108C23C23×D411yescharacteristic
1109C23C23×D411yescharacteristic
1110C23C22×#4111yescharacteristic
1111C23C22×#4111yescharacteristic
1112C23C22×#4111yescharacteristic
1113C23C22×#4111yescharacteristic
1114C23C22×#4111yescharacteristic
1115C23C2×H(5,𝔽2)12yes—
1116C23C2×H(5,𝔽2)12yes—
1117C23C2×H(5,𝔽2)12yes—
1118C23#58512yes—
1119D4—432no—
1120D4—432no—
1121D4—416no—
1122D4—88no—
1123D4—816no—
1124D4—88no—
1125C2×C4—232no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—416no—
1163C2×C4—416no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
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—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—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—88no—
1232C2×C4—88no—
1233C2×C4—88no—
1234C2×C4C2×#12114yes—
1235C2×C4C2×#12114yes—
1236C2×C4#53818yes—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—28no—
1241C22—28no—
1242C22—24no—
1243C22—24no—
1244C22—28no—
1245C22—24no—
1246C22—28no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—44no—
1273C22—832no—
1274C22—832no—
1275C22—81no—
1276C22—82no—
1277C22—81no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—81no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—81no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22#239218yes—
1298C22C22×#12111yescharacteristic
1299C22C2×#52511yescharacteristic
1300C22C2×#52511yescharacteristic
1301C22C2×#52511yescharacteristic
1302C22C2×#52911yescharacteristic
1303C22C2×#52911yescharacteristic
1304C22C2×#53211yescharacteristic
1305C22C2×#53812yes—
1306C22#346012yes—
1307C22#348411yescharacteristic
1308C22#348411yescharacteristic
1309C22#348411yescharacteristic
1310C22#348511yescharacteristic
1311C22#349012yes—
1312C22#349612yes—
1313C22#349812yes—
1314C22#350512yes—
1315C22#350512yes—
1316C22#350812yes—
1317C22#351412yes—
1318C22#351412yes—
1319C22#351912yes—
1320C22#351912yes—
1321C4—24no—
1322C4—24no—
1323C4—28no—
1324C4—44no—
1325C4—42no—
1326C4—44no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—81no—
1333C4—81no—
1334C4—82no—
1335C4—81no—
1336C4—82no—
1337C4—81no—
1338C4—82no—
1339C2—28no—
1340C2—82no—
1341C2—82no—
1342C2—82no—
1343C2—84no—
1344C2C2×#239211yescharacteristic
1345C2#3498811yescharacteristic
1346C2#3500712yes—
1347C2#3502512yes—
1348C2#3509111yescharacteristic
1349C2#3535511yescharacteristic
1350C2#3535811yescharacteristic
1351C2#3536112yes—
1352C2#3537812yes—
1353C2#3545111yescharacteristic
1354C2#3552811yescharacteristic
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×#2321C2semidirect
2. C2×#2321C2semidirect
3. C2×#2312C2semidirect
4. C22×#390C2semidirect
5. #15007C2semidirect
6. #14999C2semidirect
7. #14986C2semidirect
8. #14976C2semidirect
9. #14815C2semidirect
10. #14799C2semidirect
11. #14754C2semidirect
12. #14751C2semidirect
13. #14729C2semidirect
14. #14728C2semidirect
15. #14727C2semidirect
16. #14726C2semidirect
17. #14725C2semidirect
18. #14724C2semidirect
19. #14718C2semidirect
21. #13775C2semidirect
22. C4×#385C2semidirect
23. C4×#386C2semidirect
34. C2×#398C22semidirect
35. C2×#397C22semidirect
36. C2×#396C22semidirect
37. C2×#396C22semidirect
40. C2×#394C22semidirect
41. C2×#394C22semidirect
52. C2×#390C22semidirect
53. C2×#390C22semidirect
54. C2×#390C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
59. C2×#388C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
64. C2×#388C22semidirect
69. C2×#386C22semidirect
70. C2×#386C22semidirect
71. C2×#386C22semidirect
84. C2×C4×C4⋊C4C22semidirect
88. C2×C4×C22⋊C4C22semidirect
89. #1444C22semidirect
90. #1442C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
176. C22×C22⋊C4D4semidirect
276. C4×C22⋊C4D4semidirect
592. C2×C42C2×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×#23212
C2×#23122
C22×#3902
#150072
#149992
#149862
#149762
#148152
#147992
#147542
#147512
#147292
#147282
#147272
#147262
#147252
#147242
#147182
#147152
#137752
C4×#3852
C4×#3862