Finite Group Databasebeta

← #687085

Subgroups — #687085

Order 512.

4099 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic
2C2×#2413C211yesmaximal, characteristic, complemented
3C2×#2411C211yesmaximal, characteristic, complemented
4C2×#2425C211yesmaximal, characteristic, complemented
5C22×#396C211yesmaximal, characteristic, complemented
6C2×#2322C211yesmaximal, characteristic, complemented
7#16550C212yesmaximal, complemented
8#16290C212yesmaximal, complemented
9#15661C212yesmaximal, complemented
10#15419C212yesmaximal, complemented
11#15365C212yesmaximal, complemented
12#15309C212yesmaximal, complemented
13#15141C212yesmaximal, complemented
14#15069C211yesmaximal, characteristic, complemented
15#14976C212yesmaximal, complemented
16#14918C211yesmaximal, characteristic, complemented
17#14911C211yesmaximal, characteristic, complemented
18#14719C211yesmaximal, characteristic, complemented
19#14256C211yesmaximal, characteristic, complemented
20#14043C211yesmaximal, characteristic, complemented
21#13995C211yesmaximal, characteristic, complemented
22#13967C211yesmaximal, characteristic, complemented
23#13799C211yesmaximal, characteristic, complemented
24C22×#123C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39#2539—28no—
40#2425—28no—
41#2413—28no—
42#2411—28no—
43C2×#399C2212yes—
44C2×#398C2212yescomplemented
45C2×#398C2211yescharacteristic, complemented
46C2×#397C2211yescharacteristic, complemented
47C2×#396—28no—
48C2×#396C2212yes—
49C2×#396C2212yes—
50C2×#396C2212yes—
51C2×#396C2212yes—
52C2×#396C2212yes—
53C2×#396C2211yescharacteristic, complemented
54C2×#396C2212yescomplemented
55C2×#394C2212yes—
56C2×#394C2211yescharacteristic, complemented
57C2×#394C2212yescomplemented
58C2×#392C2212yes—
59#2322—28no—
60C2×#390C2212yes—
61C2×#390C2212yes—
62C2×#390C2212yes—
63C2×#390C2212yes—
64C2×#389C2211yescharacteristic, complemented
65C2×#389C2212yescomplemented
66C2×#389C2212yescomplemented
67C2×#389C2212yescomplemented
68C2×#388C2212yes—
69C2×#388C2212yescomplemented
70C2×#388C2211yescharacteristic, complemented
71C2×#388C2212yescomplemented
72C2×#387C2212yescomplemented
73C2×#386C2211yescharacteristic
74C2×#386C2211yescharacteristic
75C2×#386C2211yescharacteristic
76C2×#386C2211yescharacteristic
77C2×#386C2212yes—
78C2×#386C2211yescharacteristic
79C2×#386C2211yescharacteristic, complemented
80C2×#385C2211yescharacteristic
81C2×#385C2211yescharacteristic
82C2×#385C2211yescharacteristic
83C2×#385C2212yescomplemented
84C2×#381C2211yescharacteristic
85C2×#381C2211yescharacteristic
86C2×#381C2211yescharacteristic
87C2×#380C2211yescharacteristic, complemented
88C2×#379C2211yescharacteristic
89C2×#379C2211yescharacteristic
90C2×C4×C22⋊C4C2211yescharacteristic
91C2×C4×C22⋊C4C2211yescharacteristic
92C22×#95C2211yescharacteristic
93#1444C2212yescomplemented
94#1444C2212yescomplemented
95#1444C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1440C2212yes—
101#1440C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yes—
118#1437C2212yes—
119#1437C2212yes—
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122#1436C2212yescomplemented
123#1434C2212yescomplemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C4×#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C2×#123—24no—
143C2×#123—24no—
144C2×#123—24no—
145C2×#123—24no—
146C2×#123—24no—
147C2×#123—24no—
148C2×#123—24no—
149C2×#123—24no—
150C2×#123—42no—
151C2×#123—42no—
152C2×#123—42no—
153C2×#123D418yes—
154C2×#121—24no—
155C2×#121—24no—
156C2×#121—42no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—24no—
161C2×#120—24no—
162C2×#120—42no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—42no—
166C2×#117—24no—
167C2×#117—24no—
168C2×#117—24no—
169C22×C4⋊C4—24no—
170C22×C4⋊C4—24no—
171C22×C4⋊C4—24no—
172C22×C4⋊C4—24no—
173C22×C4⋊C4—24no—
174C22×C4⋊C4—44no—
175C22×C4⋊C4—42no—
176C22×C4⋊C4—42no—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C22⋊C4—24no—
197C22×C22⋊C4—24no—
198C22×C22⋊C4—24no—
199C22×C22⋊C4—24no—
200C22×C22⋊C4—24no—
201C22×C22⋊C4—44no—
202C22×C22⋊C4—42no—
203C22×C22⋊C4—42no—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2312yes—
241#399—28no—
242#398—28no—
243#398—24no—
244#397—24no—
245#396—28no—
246#396—28no—
247#396—28no—
248#396—28no—
249#396—28no—
250#396—28no—
251#396—24no—
252#394—28no—
253#394—24no—
254#394—44no—
255#392—28no—
256#390—28no—
257#390—28no—
258#390—28no—
259#390—44no—
260#389—28no—
261#389—28no—
262#389—24no—
263#389—44no—
264#388—28no—
265#388—28no—
266#388—28no—
267#388—24no—
268#387—28no—
269#386—24no—
270#386—24no—
271#386—24no—
272#386—24no—
273#386—24no—
274#386—44no—
275#386—42no—
276#385—24no—
277#385—28no—
278#385—24no—
279#385D418yescomplemented
280#381—24no—
281#381—24no—
282#381—24no—
283#380—24no—
284#379—24no—
285#379—42no—
286C4×C22⋊C4—24no—
287C4×C22⋊C4—24no—
288C2×#95D418yescomplemented
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C25—22no—
320C25—24no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—22no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2412yes—
333C25C2411yescharacteristic
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4C2×D414yes—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
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—41no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4C2×D414yes—
402C23×C4C2×D414yes—
403C23×C4C2×D414yes—
404C23×C4C2×D414yes—
405C23×C4C2×D414yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425#123—232no—
426#123—416no—
427#123—416no—
428#123—416no—
429#121—416no—
430#120—416no—
431#120—416no—
432C4×D4—416no—
433#117—416no—
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—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
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—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
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×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—416no—
487C2×C4⋊C4—416no—
488C2×C4⋊C4—416no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4C2×D418yes—
491C2×C4⋊C4C2×D418yes—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
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—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
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—41no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—416no—
570C2×C22⋊C4—416no—
571C2×C22⋊C4—416no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D418yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4C2×D414yes—
590C2×C22⋊C4#4114yes—
591C2×C22⋊C4#4114yes—
592C2×C42—24no—
593C2×C42—24no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—24no—
597C2×C42—24no—
598C2×C42—24no—
599C2×C42—41no—
600C2×C42—42no—
601C2×C42—42no—
602C2×C42—42no—
603C2×C42—42no—
604#95—24no—
605#95—24no—
606#95—22no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—22no—
612#95—22no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—22no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95C2×D414yes—
630#95C2×D414yes—
631#95C2×D414yes—
632#95C2×D414yes—
633#95C2×D418yes—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—28no—
639C24—22no—
640C24—21no—
641C24—22no—
642C24—21no—
643C24—22no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—22no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—22no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24C22×D412yes—
697C24C22×D412yes—
698C24C22×D412yes—
699C24C22×D412yes—
700C24C2×#4112yes—
701C24C2×#4112yes—
702C24H(5,𝔽2)12yes—
703C24H(5,𝔽2)12yes—
704C242−1+414yes—
705C24C2511yescharacteristic
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—48no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—48no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—82no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
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—28no—
818C22×C4—28no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
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—48no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—82no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4C22×D412yes—
880C22×C4C22×D414yes—
881C22×C4C22×D414yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D414yes—
891C22×C4C22×D414yes—
892C22×C4C2×#4114yes—
893C22×C4C2×#4114yes—
894C22×C4H(5,𝔽2)14yes—
895C4⋊C4—216no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—82no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—216no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—82no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4#121116yes—
947C42—44no—
948C42—48no—
949C42—84no—
950C42—84no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—416no—
980C23—416no—
981C23—416no—
982C23—42no—
983C23—41no—
984C23—42no—
985C23—41no—
986C23—41no—
987C23—42no—
988C23—42no—
989C23—41no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—41no—
994C23—42no—
995C23—41no—
996C23—42no—
997C23—42no—
998C23—41no—
999C23—41no—
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—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—816no—
1052C23—816no—
1053C23—816no—
1054C23—816no—
1055C23—88no—
1056C23—88no—
1057C23—88no—
1058C23—88no—
1059C23C2×#12114yes—
1060C23#53214yes—
1061C23#54014yes—
1062C23D4214yes—
1063C23D4214yes—
1064C23#54614yes—
1065C23#55014yes—
1066C23C23×D411yescharacteristic
1067C23C23×D411yescharacteristic
1068C23C23×D411yescharacteristic
1069C23C22×#4111yescharacteristic
1070C23C22×#4111yescharacteristic
1071C23C2×H(5,𝔽2)11yescharacteristic
1072C23C2×H(5,𝔽2)11yescharacteristic
1073C23C2×H(5,𝔽2)12yes—
1074C23C2×2−1+412yes—
1075C23#58512yes—
1076C23#58512yes—
1077D4—416no—
1078D4—816no—
1079D4—816no—
1080D4—88no—
1081D4—88no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—416no—
1126C2×C4—416no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—416no—
1136C2×C4—416no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—88no—
1203C2×C4—88no—
1204C2×C4—88no—
1205C2×C4C2×#12118yes—
1206C22—28no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—28no—
1211C22—24no—
1212C22—24no—
1213C22—28no—
1214C22—24no—
1215C22—28no—
1216C22—44no—
1217C22—44no—
1218C22—42no—
1219C22—42no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—832no—
1229C22—82no—
1230C22—82no—
1231C22—81no—
1232C22—82no—
1233C22—82no—
1234C22—81no—
1235C22—81no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—81no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—82no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—82no—
1252C22—81no—
1253C22—82no—
1254C22#242818yes—
1255C22C22×#12111yescharacteristic
1256C22C2×#53211yescharacteristic
1257C22#344911yescharacteristic
1258C22#344911yescharacteristic
1259C22C2×#54011yescharacteristic
1260C22C2×D4211yescharacteristic
1261C22C2×D4211yescharacteristic
1262C22C2×#54611yescharacteristic
1263C22C2×#55011yescharacteristic
1264C22#348411yescharacteristic
1265C22#348611yescharacteristic
1266C22#348812yes—
1267C22#348912yes—
1268C22#348912yes—
1269C22#349612yes—
1270C22#352012yes—
1271C22#352012yes—
1272C22#352112yes—
1273C22#352112yes—
1274C22#353412yes—
1275C22#353512yes—
1276C22#353512yes—
1277C22#354212yes—
1278C4—28no—
1279C4—44no—
1280C4—44no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—81no—
1293C4—81no—
1294C4—82no—
1295C4—81no—
1296C4—82no—
1297C2—28no—
1298C2—82no—
1299C2—84no—
1300C2—161no—
1301C2C2×#242811yescharacteristic
1302C2#3514511yescharacteristic
1303C2#3539711yescharacteristic
1304C2#3582112yes—
1305C2#3765211yescharacteristic
1306C2#3765311yescharacteristic
1307C2#3765311yescharacteristic
1308C2#3933211yescharacteristic
1309C2#4083912yes—
1310C2#4302912yes—
1311C2#4404412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2539C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2413C2semidirect
3. C2×#2411C2semidirect
4. C2×#2425C2semidirect
5. C22×#396C2semidirect
6. C2×#2322C2semidirect
7. #16550C2semidirect
8. #16290C2semidirect
9. #15661C2semidirect
10. #15419C2semidirect
11. #15365C2semidirect
12. #15309C2semidirect
13. #15141C2semidirect
14. #15069C2semidirect
15. #14976C2semidirect
16. #14918C2semidirect
17. #14911C2semidirect
18. #14719C2semidirect
19. #14256C2semidirect
20. #14043C2semidirect
21. #13995C2semidirect
22. #13967C2semidirect
23. #13799C2semidirect
44. C2×#398C22semidirect
45. C2×#398C22semidirect
46. C2×#397C22semidirect
53. C2×#396C22semidirect
54. C2×#396C22semidirect
56. C2×#394C22semidirect
57. C2×#394C22semidirect
64. C2×#389C22semidirect
65. C2×#389C22semidirect
66. C2×#389C22semidirect
67. C2×#389C22semidirect
69. C2×#388C22semidirect
70. C2×#388C22semidirect
71. C2×#388C22semidirect
72. C2×#387C22semidirect
79. C2×#386C22semidirect
83. C2×#385C22semidirect
87. C2×#380C22semidirect
93. #1444C22semidirect
94. #1444C22semidirect
95. #1444C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
123. #1434C22semidirect
128. C4×#95C22semidirect
279. #385D4semidirect
288. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25392
C2×#24132
C2×#24112
C2×#24252
C22×#3962
C2×#23222
#165502
#162902
#156612
#154192
#153652
#153092
#151412
#150692
#149762
#149182
#149112
#147192
#142562
#140432
#139952
#139672
#137992