Finite Group Databasebeta

← #647705

Subgroups — #647705

Order 512.

5528 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic, complemented
2C2×#2534C211yesmaximal, characteristic, complemented
3C2×#2411C211yesmaximal, characteristic, complemented
4C2×#2359C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6C2×#2280C211yesmaximal, characteristic, complemented
7#15452C212yesmaximal, complemented
8#15376C212yesmaximal, complemented
9#15309C212yesmaximal, complemented
10#15307C212yesmaximal, complemented
11#14927C211yesmaximal, characteristic, complemented
12#14918C211yesmaximal, characteristic, complemented
13#14756C212yesmaximal, complemented
14#14754C212yesmaximal, complemented
15#14726C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14207C212yesmaximal, complemented
18#14036C212yesmaximal, complemented
19#13992C211yesmaximal, characteristic, complemented
20#13967C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic, complemented
22#13878C211yesmaximal, characteristic, complemented
23#13868C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2849—28no—
37#2534—28no—
38#2411—28no—
39C2×#396C2212yescomplemented
40C2×#396C2212yescomplemented
41C2×#396C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#394C2212yescomplemented
44C2×#392C2212yes—
45C2×#392C2212yes—
46#2359—28no—
47C2×#390C2212yes—
48C2×#390C2212yes—
49C2×#390C2212yescomplemented
50C2×#389C2211yescharacteristic, complemented
51C2×#388C2212yescomplemented
52C2×#388C2211yescharacteristic, complemented
53C2×#388C2211yescharacteristic, complemented
54C2×#388C2212yescomplemented
55C2×#387C2211yescharacteristic, complemented
56C2×#387C2211yescharacteristic, complemented
57C2×#386—28no—
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yescomplemented
65C2×#386C2212yescomplemented
66C2×#386C2212yescomplemented
67C2×#386C2212yescomplemented
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#385C2212yescomplemented
71C2×#385C2212yescomplemented
72C2×#385C2211yescharacteristic, complemented
73#2280—28no—
74C2×#381C2211yescharacteristic
75C2×#381C2211yescharacteristic
76C2×#381C2211yescharacteristic
77C2×#381C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2212yescomplemented
81C2×#380C2212yescomplemented
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×#379C2211yescharacteristic
85C2×#379C2211yescharacteristic
86C2×#379C2211yescharacteristic
87C2×#379C2211yescharacteristic
88C2×C4×C4⋊C4C2211yescharacteristic, complemented
89C2×C4×C22⋊C4C2211yescharacteristic
90C2×C4×C22⋊C4C2211yescharacteristic, complemented
91C2×C4×C22⋊C4C2212yescomplemented
92C2×C4×C22⋊C4C2212yescomplemented
93C22×#95C2211yescharacteristic
94C22×#95C2211yescharacteristic
95#1444C2212yescomplemented
96#1443C2212yescomplemented
97#1442C2212yescomplemented
98#1442C2212yescomplemented
99#1442C2212yescomplemented
100#1441C2212yescomplemented
101#1440C2212yescomplemented
102#1440C2212yescomplemented
103#1440C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121#1436C2212yescomplemented
122#1436C2212yescomplemented
123#1436C2212yescomplemented
124#1434C2212yescomplemented
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2211yescharacteristic
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×D4—28no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—42no—
135C23×D4—44no—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C24×C4—24no—
142C24×C4—24no—
143C24×C4—24no—
144C24×C4—24no—
145C24×C4—24no—
146C24×C4—42no—
147C24×C4—42no—
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150C24×C4C2312yes—
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C2×#123—24no—
157C2×#123—24no—
158C2×#123—24no—
159C2×#123—24no—
160C2×#123—42no—
161C2×#123D418yescomplemented
162C2×#120—24no—
163C2×#120—24no—
164C2×#120—24no—
165C2×#120—24no—
166C2×#120—42no—
167C2×#120—42no—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4—42no—
171C2×#117—24no—
172C2×#117—24no—
173C2×#117—24no—
174C2×#117—24no—
175C2×#117—42no—
176C2×#117—42no—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C22⋊C4—24no—
190C22×C22⋊C4—24no—
191C22×C22⋊C4—24no—
192C22×C22⋊C4—24no—
193C22×C22⋊C4—24no—
194C22×C22⋊C4—24no—
195C22×C22⋊C4—44no—
196C22×C22⋊C4—42no—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237#396—28no—
238#396—28no—
239#396—44no—
240#394—28no—
241#394—28no—
242#392—28no—
243#392—44no—
244#390—28no—
245#390—28no—
246#390—44no—
247#389—24no—
248#388—28no—
249#388—24no—
250#388—24no—
251#388—28no—
252#387—24no—
253#387—24no—
254#386—24no—
255#386—24no—
256#386—28no—
257#386—28no—
258#386—28no—
259#386—28no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—44no—
264#385—24no—
265#385—28no—
266#385—28no—
267#385—24no—
268#385—24no—
269#381—24no—
270#381—24no—
271#381—24no—
272#381D418yescomplemented
273#380—24no—
274#380—28no—
275#380—28no—
276#380—42no—
277#379—24no—
278#379—24no—
279#379—24no—
280#379—24no—
281#379—24no—
282#379—42no—
283C4×C4⋊C4—24no—
284C4×C22⋊C4—24no—
285C4×C22⋊C4—24no—
286C4×C22⋊C4—28no—
287C4×C22⋊C4—28no—
288C2×#95—24no—
289C2×#95D418yescomplemented
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
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×#95C2312yes—
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2312yes—
321C2×#95C2312yes—
322C25—22no—
323C25—24no—
324C25—24no—
325C25—22no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—24no—
331C25—22no—
332C25—22no—
333C25—22no—
334C25—22no—
335C25—22no—
336C25—22no—
337C25—22no—
338C25—42no—
339C25—42no—
340C25—42no—
341C25—42no—
342C25—42no—
343C25#4114yes—
344C25C2411yescharacteristic
345C25C2412yes—
346C25C2412yes—
347C25C2411yescharacteristic
348C22×D4—232no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—416no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—432no—
384C22×D4—416no—
385C22×D4—432no—
386C22×D4C2×D414yes—
387C22×D4#4118yes—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—232no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—24no—
414C23×C4—24no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—416no—
425C23×C4—416no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—41no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—416no—
434C23×C4—416no—
435C23×C4—416no—
436C23×C4—416no—
437C23×C4C2×D414yes—
438C23×C4C2×D414yes—
439C23×C4C2×D414yes—
440C23×C4C2×D414yes—
441C23×C4C2×D414yes—
442C23×C4#4114yes—
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2412yes—
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462#123—232no—
463#123—416no—
464#120—416no—
465#120—416no—
466C4×D4—416no—
467#117—416no—
468#117—416no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4C2×D414yescomplemented
502C2×C4⋊C4C2×D414yescomplemented
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
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—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
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—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
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—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—22no—
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⋊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—41no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—416no—
587C2×C22⋊C4—416no—
588C2×C22⋊C4—416no—
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⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4C2×D414yes—
602C2×C22⋊C4C2×D414yes—
603C2×C22⋊C4C2×D414yes—
604C2×C22⋊C4C2×D414yescomplemented
605C2×C22⋊C4C2×D414yescomplemented
606C2×C42—24no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—24no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—24no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—42no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42—42no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—24no—
631#95—24no—
632#95—24no—
633#95—24no—
634#95—24no—
635#95—22no—
636#95—24no—
637#95—22no—
638#95—24no—
639#95—24no—
640#95—42no—
641#95—42no—
642#95—42no—
643#95—42no—
644#95—42no—
645#95—42no—
646#95—42no—
647#95—42no—
648#95C2×D414yes—
649#95C2×D414yes—
650#95C2×D414yes—
651#95C2×D414yes—
652#95C2×D418yescomplemented
653#95C2×D418yescomplemented
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—28no—
659C24—28no—
660C24—216no—
661C24—28no—
662C24—216no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—28no—
676C24—28no—
677C24—28no—
678C24—21no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—22no—
685C24—22no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—21no—
692C24—22no—
693C24—21no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—48no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—44no—
718C24—44no—
719C24—48no—
720C24—44no—
721C24—44no—
722C24—44no—
723C24—44no—
724C24—44no—
725C24—44no—
726C24—44no—
727C24—44no—
728C24—44no—
729C24—44no—
730C24—44no—
731C24—44no—
732C24—44no—
733C24—44no—
734C24—84no—
735C24—84no—
736C24—84no—
737C24—84no—
738C24—84no—
739C24—84no—
740C24C22×D412yes—
741C24C22×D412yes—
742C24C22×D412yes—
743C24C22×D412yes—
744C24C2×#4114yes—
745C24C2×#4114yes—
746C24C2×#4114yes—
747C24C2×#4112yes—
748C24C2×#4112yes—
749C24H(5,𝔽2)14yes—
750C24H(5,𝔽2)12yes—
751C24H(5,𝔽2)12yes—
752C24C2511yescharacteristic
753C2×D4—216no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—216no—
758C2×D4—216no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—4128no—
771C2×D4—48no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—84no—
783C2×D4—84no—
784C2×D4—84no—
785C2×D4—84no—
786C2×D4—84no—
787C2×D4—84no—
788C2×D4—84no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—216no—
807C22×C4—216no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
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—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
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—28no—
859C22×C4—28no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—4128no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—82no—
926C22×C4—84no—
927C22×C4—84no—
928C22×C4—84no—
929C22×C4—84no—
930C22×C4—84no—
931C22×C4—84no—
932C22×C4#121116yes—
933C22×C4C22×D412yes—
934C22×C4C22×D412yes—
935C22×C4C22×D414yes—
936C22×C4C22×D412yes—
937C22×C4C22×D412yes—
938C22×C4C22×D412yes—
939C22×C4C22×D412yes—
940C22×C4C22×D414yes—
941C22×C4C22×D412yes—
942C22×C4C22×D412yes—
943C22×C4C22×D412yes—
944C22×C4C22×D412yes—
945C22×C4C22×D412yes—
946C22×C4C22×D412yes—
947C22×C4C22×D412yes—
948C22×C4C2×#4112yes—
949C22×C4C2×#4112yes—
950C22×C4C2×#4114yes—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—44no—
954C4⋊C4—48no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—48no—
958C4⋊C4—44no—
959C4⋊C4—84no—
960C4⋊C4—82no—
961C4⋊C4—84no—
962C4⋊C4—84no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—44no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—44no—
991C22⋊C4—82no—
992C22⋊C4—84no—
993C22⋊C4—84no—
994C22⋊C4—84no—
995C22⋊C4—84no—
996C22⋊C4—84no—
997C42—44no—
998C42—48no—
999C42—44no—
1000C42—44no—
1001C42—44no—
1002C42—82no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—232no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—22no—
1039C23—24no—
1040C23—22no—
1041C23—22no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—432no—
1051C23—432no—
1052C23—416no—
1053C23—416no—
1054C23—432no—
1055C23—416no—
1056C23—416no—
1057C23—416no—
1058C23—432no—
1059C23—416no—
1060C23—416no—
1061C23—416no—
1062C23—42no—
1063C23—416no—
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—41no—
1081C23—41no—
1082C23—42no—
1083C23—41no—
1084C23—42no—
1085C23—41no—
1086C23—42no—
1087C23—42no—
1088C23—41no—
1089C23—42no—
1090C23—42no—
1091C23—41no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—41no—
1101C23—42no—
1102C23—41no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—42no—
1125C23—816no—
1126C23—816no—
1127C23—816no—
1128C23—816no—
1129C23—88no—
1130C23—88no—
1131C23—88no—
1132C23—88no—
1133C23C2×#12114yes—
1134C23#52514yes—
1135C23#53814yes—
1136C23D4214yes—
1137C23D4214yes—
1138C23#54614yes—
1139C23#54614yes—
1140C23#55118yes—
1141C23C23×D411yescharacteristic
1142C23C23×D411yescharacteristic
1143C23C23×D411yescharacteristic
1144C23C22×#4111yescharacteristic
1145C23C22×#4111yescharacteristic
1146C23C22×#4112yes—
1147C23C2×H(5,𝔽2)11yescharacteristic
1148C23C2×H(5,𝔽2)11yescharacteristic
1149C23C2×H(5,𝔽2)12yes—
1150C23#58512yes—
1151C23#58512yes—
1152D4—432no—
1153D4—432no—
1154D4—416no—
1155D4—816no—
1156D4—816no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—232no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—416no—
1201C2×C4—432no—
1202C2×C4—432no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—416no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
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—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—88no—
1273C2×C4—88no—
1274C2×C4—88no—
1275C2×C4C2×#12114yes—
1276C2×C4C2×#12114yes—
1277C2×C4#52514yes—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—28no—
1282C22—24no—
1283C22—28no—
1284C22—28no—
1285C22—24no—
1286C22—24no—
1287C22—28no—
1288C22—28no—
1289C22—28no—
1290C22—28no—
1291C22—464no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—42no—
1307C22—44no—
1308C22—44no—
1309C22—42no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—42no—
1315C22—44no—
1316C22—832no—
1317C22—81no—
1318C22—81no—
1319C22—82no—
1320C22—81no—
1321C22—82no—
1322C22—82no—
1323C22—82no—
1324C22—82no—
1325C22—82no—
1326C22—81no—
1327C22—82no—
1328C22—82no—
1329C22—82no—
1330C22—82no—
1331C22#242418yes—
1332C22C22×#12111yescharacteristic
1333C22C2×#52511yescharacteristic
1334C22C2×#52511yescharacteristic
1335C22#344911yescharacteristic
1336C22C2×#53811yescharacteristic
1337C22C2×D4211yescharacteristic
1338C22C2×D4211yescharacteristic
1339C22C2×#54611yescharacteristic
1340C22C2×#54611yescharacteristic
1341C22D4×#4112yes—
1342C22D4×#4112yes—
1343C22C2×#55112yes—
1344C22#347512yes—
1345C22#348411yescharacteristic
1346C22#348711yescharacteristic
1347C22#348812yes—
1348C22#348812yes—
1349C22#349012yes—
1350C22#349112yes—
1351C22#349412yes—
1352C22#351312yes—
1353C22#353312yes—
1354C22#353412yes—
1355C4—24no—
1356C4—24no—
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—81no—
1369C4—81no—
1370C4—82no—
1371C4—82no—
1372C4—82no—
1373C4—82no—
1374C2—28no—
1375C2—48no—
1376C2—82no—
1377C2—84no—
1378C2C2×#242411yescharacteristic
1379C2#3493511yescharacteristic
1380C2#3556311yescharacteristic
1381C2#3610211yescharacteristic
1382C2#3615811yescharacteristic
1383C2#3622212yes—
1384C2#3765211yescharacteristic
1385C2#3784311yescharacteristic
1386C2#3839812yes—
1387C2#5899212yes—
1388C2#5901112yes—
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×#2849C2semidirect
2. C2×#2534C2semidirect
3. C2×#2411C2semidirect
4. C2×#2359C2semidirect
5. C22×#386C2semidirect
6. C2×#2280C2semidirect
7. #15452C2semidirect
8. #15376C2semidirect
9. #15309C2semidirect
10. #15307C2semidirect
11. #14927C2semidirect
12. #14918C2semidirect
13. #14756C2semidirect
14. #14754C2semidirect
15. #14726C2semidirect
17. #14207C2semidirect
18. #14036C2semidirect
19. #13992C2semidirect
20. #13967C2semidirect
21. #13902C2semidirect
22. #13878C2semidirect
23. #13868C2semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
41. C2×#396C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
49. C2×#390C22semidirect
50. C2×#389C22semidirect
51. C2×#388C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#387C22semidirect
56. C2×#387C22semidirect
64. C2×#386C22semidirect
65. C2×#386C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
70. C2×#385C22semidirect
71. C2×#385C22semidirect
72. C2×#385C22semidirect
80. C2×#380C22semidirect
81. C2×#380C22semidirect
88. C2×C4×C4⋊C4C22semidirect
90. C2×C4×C22⋊C4C22semidirect
91. C2×C4×C22⋊C4C22semidirect
92. C2×C4×C22⋊C4C22semidirect
95. #1444C22semidirect
96. #1443C22semidirect
97. #1442C22semidirect
98. #1442C22semidirect
99. #1442C22semidirect
100. #1441C22semidirect
101. #1440C22semidirect
102. #1440C22semidirect
103. #1440C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
117. #1438C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
123. #1436C22semidirect
124. #1434C22semidirect
161. C2×#123D4semidirect
272. #381D4semidirect
289. C2×#95D4semidirect
501. C2×C4⋊C4C2×D4semidirect
502. C2×C4⋊C4C2×D4semidirect
604. C2×C22⋊C4C2×D4semidirect
605. C2×C22⋊C4C2×D4semidirect
652. #95C2×D4semidirect
653. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#25342
C2×#24112
C2×#23592
C22×#3862
C2×#22802
#154522
#153762
#153092
#153072
#149272
#149182
#147562
#147542
#147262
#147152
#142072
#140362
#139922
#139672
#139022
#138782
#138682