Finite Group Databasebeta

← #719397

Subgroups — #719397

Order 512.

4126 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic
2C2×#2413C211yesmaximal, characteristic, complemented
3C2×#2412C211yesmaximal, characteristic, complemented
4C2×#2618C211yesmaximal, characteristic, complemented
5C22×#396C211yesmaximal, characteristic, complemented
6C2×#2342C211yesmaximal, characteristic, complemented
7#16469C212yesmaximal, complemented
8#16290C212yesmaximal, complemented
9#15666C212yesmaximal, complemented
10#15615C212yesmaximal, complemented
11#15507C212yesmaximal, complemented
12#15309C212yesmaximal, complemented
13#15069C211yesmaximal, characteristic, complemented
14#14912C211yesmaximal, characteristic, complemented
15#14911C211yesmaximal, characteristic, complemented
16#14771C212yesmaximal, complemented
17#14754C212yesmaximal, complemented
18#14718C211yesmaximal, characteristic, complemented
19#14137C211yesmaximal, characteristic, complemented
20#14135C211yesmaximal, characteristic, complemented
21#14134C211yesmaximal, characteristic, complemented
22#14130C211yesmaximal, characteristic, complemented
23#13776C211yesmaximal, characteristic, complemented
24C22×#123C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39#2618—28no—
40#2539—28no—
41#2413—28no—
42#2412—28no—
43C2×#399C2211yescharacteristic
44C2×#399C2211yescharacteristic
45C2×#398C2212yescomplemented
46C2×#398C2212yescomplemented
47C2×#397C2212yes—
48C2×#396—28no—
49C2×#396C2212yes—
50C2×#396C2212yes—
51C2×#396C2212yes—
52C2×#396C2212yes—
53C2×#396C2212yescomplemented
54C2×#396C2212yescomplemented
55C2×#396C2212yescomplemented
56C2×#394C2212yes—
57C2×#394C2212yes—
58C2×#394C2212yescomplemented
59C2×#392C2211yescharacteristic
60C2×#392C2211yescharacteristic
61#2342—28no—
62C2×#390C2211yescharacteristic
63C2×#390C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C2×#390C2211yescharacteristic
66C2×#390C2212yescomplemented
67C2×#389C2212yescomplemented
68C2×#389C2212yescomplemented
69C2×#388C2212yes—
70C2×#388C2212yes—
71C2×#388C2212yescomplemented
72C2×#386C2211yescharacteristic
73C2×#386C2211yescharacteristic
74C2×#386C2211yescharacteristic
75C2×#386C2211yescharacteristic
76C2×#386C2212yes—
77C2×#386C2212yes—
78C2×#386C2211yescharacteristic
79C2×#386C2211yescharacteristic
80C2×#385C2211yescharacteristic
81C2×#385C2211yescharacteristic
82C2×#385C2212yes—
83C2×#381C2211yescharacteristic
84C2×#381C2211yescharacteristic
85C2×#381C2211yescharacteristic
86C2×#380C2212yes—
87C2×#380C2211yescharacteristic
88C2×#379C2211yescharacteristic
89C2×C4×C22⋊C4C2211yescharacteristic
90C2×C4×C22⋊C4C2211yescharacteristic
91C2×C4×C22⋊C4C2212yes—
92C22×#95C2211yescharacteristic
93#1444C2212yescomplemented
94#1444C2212yescomplemented
95#1444C2212yescomplemented
96#1442C2212yescomplemented
97#1442C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1440C2212yes—
101#1440C2212yes—
102#1440C2212yescomplemented
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1437C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122C4⋊#95C2212yescomplemented
123C4⋊#95C2212yescomplemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2212yes—
128C22⋊#95C2211yescharacteristic
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C2×#123—24no—
145C2×#123—24no—
146C2×#123—24no—
147C2×#123—24no—
148C2×#123—24no—
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—42no—
153C2×#123—42no—
154C2×#123—42no—
155C2×#123—42no—
156C2×#121—24no—
157C2×#121—24no—
158C2×#121—24no—
159C2×#120—24no—
160C2×#120—24no—
161C2×#120—24no—
162C2×#120—24no—
163C2×#120—42no—
164C2×#120—42no—
165C2×#117—24no—
166C2×#117—24no—
167C2×#117—42no—
168C22×C4⋊C4—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⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C22⋊C4—24no—
194C22×C22⋊C4—24no—
195C22×C22⋊C4—24no—
196C22×C22⋊C4—24no—
197C22×C22⋊C4—24no—
198C22×C22⋊C4—24no—
199C22×C22⋊C4—24no—
200C22×C22⋊C4—44no—
201C22×C22⋊C4—42no—
202C22×C22⋊C4—42no—
203C22×C22⋊C4D418yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243#399—24no—
244#399—24no—
245#398—28no—
246#398—28no—
247#397—28no—
248#396—28no—
249#396—28no—
250#396—28no—
251#396—28no—
252#396—28no—
253#396—28no—
254#396—28no—
255#394—28no—
256#394—28no—
257#394—44no—
258#392—24no—
259#392—24no—
260#390—24no—
261#390—24no—
262#390—24no—
263#390—24no—
264#390—44no—
265#389—28no—
266#389—44no—
267#388—28no—
268#388—28no—
269#388—28no—
270#386—24no—
271#386—24no—
272#386—24no—
273#386—24no—
274#386—28no—
275#386—44no—
276#386—42no—
277#386—42no—
278#385—28no—
279#385—24no—
280#385—24no—
281#381—24no—
282#381—24no—
283#381D418yescomplemented
284#380—28no—
285#380D418yescomplemented
286#379—24no—
287C4×C22⋊C4—24no—
288C4×C22⋊C4—24no—
289C4×C22⋊C4—28no—
290C2×#95—24no—
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×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C25—24no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25C2×D414yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C25C2411yescharacteristic
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—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
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—22no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
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—42no—
410C23×C4C2×D414yes—
411C23×C4C2×D414yes—
412C23×C4C2×D414yes—
413C23×C4C2×D414yes—
414C23×C4#4114yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433#123—416no—
434#123—416no—
435#123—416no—
436#123—416no—
437#121—416no—
438#120—416no—
439#120—416no—
440#117—416no—
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—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—41no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—416no—
490C2×C4⋊C4—416no—
491C2×C4⋊C4—416no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4C2×D418yes—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
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—232no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—416no—
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—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—416no—
581C2×C22⋊C4—416no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4C2×D414yes—
597C2×C22⋊C4C2×D414yes—
598C2×C22⋊C4C2×D414yes—
599C2×C22⋊C4C2×D414yes—
600C2×C22⋊C4C2×D414yes—
601C2×C22⋊C4C2×D414yes—
602C2×C22⋊C4C2×D414yes—
603C2×C22⋊C4#4114yes—
604C2×C42—24no—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—42no—
610C2×C42—42no—
611C2×C42—42no—
612C2×C42—42no—
613C2×C42—42no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—22no—
619#95—22no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—42no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95C2×D418yes—
640#95C2×D418yes—
641#95C2×D418yes—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—28no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—22no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—28no—
667C24—28no—
668C24—28no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—22no—
680C24—22no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24C22×D412yes—
711C24C22×D412yes—
712C24C22×D412yes—
713C24C22×D412yes—
714C24C22×D412yes—
715C24C2×#4112yes—
716C24C2×#4112yes—
717C24H(5,𝔽2)12yes—
718C24H(5,𝔽2)12yes—
719C242−1+414yes—
720C24C2511yescharacteristic
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—82no—
748C2×D4—82no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C2×D4—82no—
753C2×D4—82no—
754C2×D4—82no—
755C2×D4—82no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
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—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
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—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4—84no—
897C22×C4#121116yes—
898C22×C4C22×D412yes—
899C22×C4C22×D414yes—
900C22×C4C22×D414yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D414yes—
904C22×C4C22×D414yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C2×#4112yes—
911C22×C4C2×#4112yes—
912C22×C4C2×#4112yes—
913C22×C4C2×#4112yes—
914C22×C4H(5,𝔽2)14yes—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—48no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—84no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C42—48no—
968C42—82no—
969C42—82no—
970C42—84no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—416no—
1007C23—416no—
1008C23—416no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—41no—
1020C23—416no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
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—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
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—88no—
1083C23—88no—
1084C23—88no—
1085C23—816no—
1086C23—816no—
1087C23—816no—
1088C23—816no—
1089C23C2×#12114yes—
1090C23#53214yes—
1091C23#53614yes—
1092C23#54014yes—
1093C23D4214yes—
1094C23D4214yes—
1095C23#54614yes—
1096C23#55014yes—
1097C23C23×D411yescharacteristic
1098C23C23×D411yescharacteristic
1099C23C23×D411yescharacteristic
1100C23C22×#4111yescharacteristic
1101C23C22×#4111yescharacteristic
1102C23C2×H(5,𝔽2)11yescharacteristic
1103C23C2×H(5,𝔽2)11yescharacteristic
1104C23C2×H(5,𝔽2)12yes—
1105C23C2×2−1+412yes—
1106C23#58512yes—
1107C23#58512yes—
1108D4—88no—
1109D4—88no—
1110D4—88no—
1111D4—88no—
1112D4—88no—
1113D4—88no—
1114D4—88no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—416no—
1153C2×C4—416no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—416no—
1163C2×C4—416no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
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—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
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—816no—
1232C2×C4—88no—
1233C2×C4—88no—
1234C2×C4C2×#12114yes—
1235C2×C4C2×#12114yes—
1236C22—24no—
1237C22—24no—
1238C22—28no—
1239C22—24no—
1240C22—28no—
1241C22—28no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—28no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—42no—
1250C22—44no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—44no—
1255C22—42no—
1256C22—44no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—832no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—82no—
1274C22—82no—
1275C22—81no—
1276C22—81no—
1277C22—82no—
1278C22—82no—
1279C22—81no—
1280C22—81no—
1281C22—82no—
1282C22—82no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—82no—
1290C22—82no—
1291C22#242818yes—
1292C22C22×#12111yescharacteristic
1293C22C2×#53211yescharacteristic
1294C22C2×#53611yescharacteristic
1295C22#344911yescharacteristic
1296C22C2×#54011yescharacteristic
1297C22C2×D4211yescharacteristic
1298C22C2×D4211yescharacteristic
1299C22C2×#54611yescharacteristic
1300C22C2×#55011yescharacteristic
1301C22#348411yescharacteristic
1302C22#348511yescharacteristic
1303C22#348812yes—
1304C22#348912yes—
1305C22#348912yes—
1306C22#349512yes—
1307C22#349612yes—
1308C22#350512yes—
1309C22#352012yes—
1310C22#352112yes—
1311C22#353412yes—
1312C22#353512yes—
1313C22#353612yes—
1314C22#356012yes—
1315C4—24no—
1316C4—24no—
1317C4—42no—
1318C4—44no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—44no—
1324C4—44no—
1325C4—44no—
1326C4—42no—
1327C4—42no—
1328C4—82no—
1329C4—82no—
1330C4—82no—
1331C4—81no—
1332C4—81no—
1333C2—28no—
1334C2—44no—
1335C2—82no—
1336C2—161no—
1337C2—161no—
1338C2C2×#242811yescharacteristic
1339C2#3530611yescharacteristic
1340C2#3535811yescharacteristic
1341C2#3582512yes—
1342C2#3764711yescharacteristic
1343C2#3765211yescharacteristic
1344C2#3802111yescharacteristic
1345C2#3803011yescharacteristic
1346C2#4056512yes—
1347C2#4302912yes—
1348C2#4390712yes—
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×#2412C2semidirect
4. C2×#2618C2semidirect
5. C22×#396C2semidirect
6. C2×#2342C2semidirect
7. #16469C2semidirect
8. #16290C2semidirect
9. #15666C2semidirect
10. #15615C2semidirect
11. #15507C2semidirect
12. #15309C2semidirect
13. #15069C2semidirect
14. #14912C2semidirect
15. #14911C2semidirect
16. #14771C2semidirect
17. #14754C2semidirect
18. #14718C2semidirect
19. #14137C2semidirect
20. #14135C2semidirect
21. #14134C2semidirect
22. #14130C2semidirect
23. #13776C2semidirect
45. C2×#398C22semidirect
46. C2×#398C22semidirect
53. C2×#396C22semidirect
54. C2×#396C22semidirect
55. C2×#396C22semidirect
58. C2×#394C22semidirect
66. C2×#390C22semidirect
67. C2×#389C22semidirect
68. C2×#389C22semidirect
71. C2×#388C22semidirect
93. #1444C22semidirect
94. #1444C22semidirect
95. #1444C22semidirect
96. #1442C22semidirect
97. #1442C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
102. #1440C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
116. #1437C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. C4⋊#95C22semidirect
123. C4⋊#95C22semidirect
283. #381D4semidirect
285. #380D4semidirect

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×#24122
C2×#26182
C22×#3962
C2×#23422
#164692
#162902
#156662
#156152
#155072
#153092
#150692
#149122
#149112
#147712
#147542
#147182
#141372
#141352
#141342
#141302
#137762