Finite Group Databasebeta

← #917314

Subgroups — #917314

Order 512.

4293 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C211yesmaximal, characteristic, complemented
2C2×#2411C211yesmaximal, characteristic, complemented
3C2×#2622C211yesmaximal, characteristic, complemented
4C22×#394C211yesmaximal, characteristic, complemented
5#17109C212yesmaximal, complemented
6#17101C212yesmaximal, complemented
7#16549C212yesmaximal, complemented
8#16526C212yesmaximal, complemented
9#16347C212yesmaximal, complemented
10#16290C212yesmaximal, complemented
11#15660C212yesmaximal, complemented
12#15617C212yesmaximal, complemented
13#14912C211yesmaximal, characteristic, complemented
14#14911C211yesmaximal, characteristic, complemented
15#14729C211yesmaximal, characteristic, complemented
16#14726C211yesmaximal, characteristic, complemented
17#14724C211yesmaximal, characteristic, complemented
18#14715C211yesmaximal, characteristic
19#14262C211yesmaximal, characteristic, complemented
20#14128C211yesmaximal, characteristic, complemented
21#14043C211yesmaximal, characteristic, complemented
22#13995C211yesmaximal, characteristic, complemented
23#13903C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#120C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2622—28no—
35#2482—28no—
36#2411—28no—
37C2×#399C2212yescomplemented
38C2×#397C2212yescomplemented
39C2×#397C2212yescomplemented
40C2×#397C2212yescomplemented
41C2×#396C2211yescharacteristic, complemented
42C2×#396C2211yescharacteristic, complemented
43C2×#396C2212yescomplemented
44C2×#396C2212yescomplemented
45C2×#394—28no—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#394C2212yes—
52C2×#394C2212yescomplemented
53C2×#394C2211yescharacteristic, complemented
54C2×#394C2212yescomplemented
55C2×#394C2211yescharacteristic, complemented
56C2×#392C2212yes—
57C2×#392C2212yes—
58C2×#390C2211yescharacteristic, complemented
59C2×#390C2211yescharacteristic, complemented
60C2×#390C2212yescomplemented
61C2×#389C2212yescomplemented
62C2×#388C2212yescomplemented
63C2×#388C2211yescharacteristic, complemented
64C2×#388C2212yescomplemented
65C2×#388C2211yescharacteristic, complemented
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2211yescharacteristic
76C2×#381C2211yescharacteristic
77C2×#381C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×#379C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C22×#95C2211yescharacteristic
87#1444C2212yescomplemented
88#1444C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1440C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1438C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122#1436C2212yescomplemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—44no—
131C23×D4—42no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C2×#123—24no—
146C2×#123—42no—
147C2×#123—42no—
148C2×#120—24no—
149C2×#120—24no—
150C2×#120—24no—
151C2×#120—42no—
152C2×#120—42no—
153C2×#120—42no—
154C2×#117—24no—
155C2×#117—24no—
156C2×#117—42no—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—44no—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—44no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4—42no—
181C22×C22⋊C4—42no—
182C22×C22⋊C4—42no—
183C22×C22⋊C4D418yescomplemented
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⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228#399—28no—
229#397—28no—
230#397—28no—
231#397—28no—
232#396—24no—
233#396—24no—
234#396—44no—
235#396—44no—
236#394—28no—
237#394—28no—
238#394—28no—
239#394—28no—
240#394—28no—
241#394—24no—
242#394—24no—
243#394—28no—
244#394—44no—
245#394—44no—
246#392—44no—
247#392—44no—
248#390—24no—
249#390—24no—
250#390—44no—
251#389—44no—
252#388—28no—
253#388—24no—
254#388—24no—
255#388—28no—
256#386—24no—
257#386—24no—
258#386—24no—
259#386—42no—
260#385—24no—
261#385—24no—
262#385—24no—
263#385—42no—
264#385—42no—
265#385D418yescomplemented
266#381—24no—
267#381—24no—
268#380—42no—
269#379—24no—
270#379—24no—
271#379—24no—
272#379—24no—
273#379—24no—
274#379—42no—
275C4×C22⋊C4—42no—
276C2×#95—24no—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C25—22no—
306C25—24no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25C2×D414yes—
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2412yes—
331C25C2411yescharacteristic
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—22no—
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—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—416no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—416no—
372C22×D4—416no—
373C22×D4—432no—
374C22×D4—432no—
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—22no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4C2×D414yes—
400C23×C4C2×D414yes—
401C23×C4C2×D414yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2412yes—
420#123—416no—
421#120—416no—
422#120—416no—
423#117—416no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—416no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4C2×D418yescomplemented
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
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—24no—
493C2×C22⋊C4—24no—
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—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
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—416no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—416no—
550C2×C22⋊C4—416no—
551C2×C22⋊C4—416no—
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⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4C2×D414yes—
580C2×C22⋊C4C2×D414yes—
581C2×C22⋊C4C2×D414yes—
582C2×C22⋊C4C2×D414yes—
583C2×C22⋊C4C2×D414yes—
584C2×C22⋊C4C2×D414yes—
585C2×C22⋊C4#4114yes—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—41no—
591C2×C42—41no—
592C2×C42—42no—
593C2×C42—42no—
594C2×C42—42no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—22no—
600#95—22no—
601#95—24no—
602#95—24no—
603#95—22no—
604#95—22no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95C2×D418yescomplemented
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—28no—
628C24—28no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—28no—
664C24—28no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—22no—
669C24—21no—
670C24—22no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—22no—
675C24—22no—
676C24—44no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—44no—
687C24—48no—
688C24—48no—
689C24—44no—
690C24—44no—
691C24—48no—
692C24—48no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24C22×D412yes—
719C24C22×D412yes—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C2×#4112yes—
723C24H(5,𝔽2)14yes—
724C24H(5,𝔽2)12yes—
725C24H(5,𝔽2)12yes—
726C24H(5,𝔽2)12yes—
727C242−1+412yes—
728C24C2511yescharacteristic
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—4128no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—82no—
761C2×D4—82no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
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—28no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4C22×D414yes—
896C22×C4C22×D414yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C2×#4114yes—
904C22×C4H(5,𝔽2)14yes—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—82no—
913C4⋊C4—82no—
914C4⋊C4—84no—
915C4⋊C4—84no—
916C4⋊C4—84no—
917C4⋊C4—84no—
918C4⋊C4—84no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—82no—
946C22⋊C4—82no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—82no—
957C22⋊C4—82no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C42—44no—
961C42—44no—
962C42—84no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—416no—
1001C23—416no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—42no—
1006C23—42no—
1007C23—41no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—416no—
1012C23—42no—
1013C23—41no—
1014C23—41no—
1015C23—42no—
1016C23—42no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
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—42no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—42no—
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—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—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—41no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—88no—
1090C23—88no—
1091C23—88no—
1092C23—88no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23—88no—
1100C23—816no—
1101C23—816no—
1102C23—88no—
1103C23—88no—
1104C23—88no—
1105C23#53414yes—
1106C23#53714yes—
1107C23#53814yes—
1108C23D4214yes—
1109C23#54714yes—
1110C23#55014yes—
1111C23#56214yes—
1112C23C23×D411yescharacteristic
1113C23C23×D411yescharacteristic
1114C23C22×#4111yescharacteristic
1115C23C2×H(5,𝔽2)11yescharacteristic
1116C23C2×H(5,𝔽2)11yescharacteristic
1117C23C2×H(5,𝔽2)11yescharacteristic
1118C23C2×H(5,𝔽2)12yes—
1119C23C2×H(5,𝔽2)12yes—
1120C23C2×2−1+411yescharacteristic
1121C23#58512yes—
1122C23#58512yes—
1123D4—432no—
1124D4—432no—
1125D4—88no—
1126D4—816no—
1127D4—88no—
1128D4—88no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—416no—
1158C2×C4—416no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—416no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
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—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
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—41no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—88no—
1243C2×C4—88no—
1244C22—24no—
1245C22—24no—
1246C22—28no—
1247C22—28no—
1248C22—24no—
1249C22—24no—
1250C22—28no—
1251C22—28no—
1252C22—24no—
1253C22—24no—
1254C22—44no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—42no—
1268C22—42no—
1269C22—44no—
1270C22—44no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—832no—
1276C22—832no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—81no—
1294C22—81no—
1295C22—82no—
1296C22—82no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—82no—
1301C22—82no—
1302C22—81no—
1303C22—81no—
1304C22#268218yes—
1305C22C2×#53411yescharacteristic
1306C22C2×#53711yescharacteristic
1307C22#344911yescharacteristic
1308C22#344911yescharacteristic
1309C22C2×#53811yescharacteristic
1310C22C2×D4211yescharacteristic
1311C22C2×#54711yescharacteristic
1312C22C2×#55011yescharacteristic
1313C22#348411yescharacteristic
1314C22#348411yescharacteristic
1315C22#348812yes—
1316C22#349612yes—
1317C22#351312yes—
1318C22#351412yes—
1319C22C2×#56211yescharacteristic
1320C22#353212yes—
1321C22#353212yes—
1322C22#353312yes—
1323C22#353312yes—
1324C22#353412yes—
1325C22#353512yes—
1326C22#354212yes—
1327C22#356112yes—
1328C4—42no—
1329C4—44no—
1330C4—44no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—81no—
1339C4—82no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—82no—
1344C4—82no—
1345C4—81no—
1346C2—28no—
1347C2—84no—
1348C2—82no—
1349C2—82no—
1350C2—161no—
1351C2#3670211yescharacteristic
1352C2#3744311yescharacteristic
1353C2#3765211yescharacteristic
1354C2#3804411yescharacteristic
1355C2#3891211yescharacteristic
1356C2#3933211yescharacteristic
1357C2#4051412yes—
1358C2#4075912yes—
1359C2#4391312yes—
1360C2C2×#268211yescharacteristic
1361C2#5237312yes—
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×#2482C2semidirect
2. C2×#2411C2semidirect
3. C2×#2622C2semidirect
4. C22×#394C2semidirect
5. #17109C2semidirect
6. #17101C2semidirect
7. #16549C2semidirect
8. #16526C2semidirect
9. #16347C2semidirect
10. #16290C2semidirect
11. #15660C2semidirect
12. #15617C2semidirect
13. #14912C2semidirect
14. #14911C2semidirect
15. #14729C2semidirect
16. #14726C2semidirect
17. #14724C2semidirect
19. #14262C2semidirect
20. #14128C2semidirect
21. #14043C2semidirect
22. #13995C2semidirect
23. #13903C2semidirect
37. C2×#399C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
40. C2×#397C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
43. C2×#396C22semidirect
44. C2×#396C22semidirect
52. C2×#394C22semidirect
53. C2×#394C22semidirect
54. C2×#394C22semidirect
55. C2×#394C22semidirect
58. C2×#390C22semidirect
59. C2×#390C22semidirect
60. C2×#390C22semidirect
61. C2×#389C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
64. C2×#388C22semidirect
65. C2×#388C22semidirect
87. #1444C22semidirect
88. #1444C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
95. #1440C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
183. C22×C22⋊C4D4semidirect
265. #385D4semidirect
464. C2×C4⋊C4C2×D4semidirect
622. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
C2×#24112
C2×#26222
C22×#3942
#171092
#171012
#165492
#165262
#163472
#162902
#156602
#156172
#149122
#149112
#147292
#147262
#147242
#147152
#142622
#141282
#140432
#139952
#139032