Finite Group Databasebeta

← #687014

Subgroups — #687014

Order 512.

4642 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2418C211yesmaximal, characteristic, complemented
2C2×#2410C211yesmaximal, characteristic
3C22×#394C211yesmaximal, characteristic, complemented
4C2×#2321C211yesmaximal, characteristic, complemented
5#16526C212yesmaximal, complemented
6#16312C212yesmaximal, complemented
7#15647C212yesmaximal, complemented
8#15498C212yesmaximal, complemented
9#15295C212yesmaximal, complemented
10#15260C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#14945C211yesmaximal, characteristic, complemented
13#14820C211yesmaximal, characteristic, complemented
14#14741C212yesmaximal, complemented
15#14724C211yesmaximal, characteristic, complemented
16#14718C211yesmaximal, characteristic, complemented
17#14262C211yesmaximal, characteristic, complemented
18#14043C211yesmaximal, characteristic, complemented
19#14015C211yesmaximal, characteristic, complemented
20#13995C211yesmaximal, characteristic, complemented
21#13965C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23C22⋊C42C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic, complemented
26C22×#121C2212yes—
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2418—28no—
37#2410—28no—
38C2×#399C2211yescharacteristic, complemented
39C2×#397C2211yescharacteristic, complemented
40C2×#397C2212yescomplemented
41C2×#394—28no—
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2211yescharacteristic, complemented
50C2×#394C2211yescharacteristic, complemented
51C2×#394C2212yescomplemented
52C2×#392C2212yes—
53#2321—28no—
54C2×#390C2212yescomplemented
55C2×#390C2212yescomplemented
56C2×#389C2212yescomplemented
57C2×#388C2212yescomplemented
58C2×#388C2212yescomplemented
59C2×#388C2211yescharacteristic, complemented
60C2×#388C2211yescharacteristic, complemented
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2212yes—
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2212yescomplemented
67C2×#386C2211yescharacteristic, complemented
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2212yescomplemented
75C2×#380C2211yescharacteristic
76C2×#380C2212yescomplemented
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2212yescomplemented
85C22×#95C2211yescharacteristic
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1444C2212yescomplemented
89#1444C2212yescomplemented
90#1443C2212yescomplemented
91#1443C2212yescomplemented
92#1441C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117C4⋊#95C2212yescomplemented
118C4⋊#95C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—44no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×#123—24no—
148C2×#123—44no—
149C2×#121—28no—
150C2×#121—44no—
151C2×#121—44no—
152C2×#120—24no—
153C2×#120—24no—
154C2×#120—24no—
155C2×#120—24no—
156C2×#120—42no—
157C2×#120D418yes—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—42no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—44no—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4D418yescomplemented
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228C22×C42C2312yes—
229#399—24no—
230#397—24no—
231#397—44no—
232#394—28no—
233#394—28no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—24no—
238#394—24no—
239#394—44no—
240#394—44no—
241#394—44no—
242#392—28no—
243#390—28no—
244#390—44no—
245#389—44no—
246#388—28no—
247#388—28no—
248#388—24no—
249#388—24no—
250#386—24no—
251#386—28no—
252#386—24no—
253#386—24no—
254#386—28no—
255#386—24no—
256#386—24no—
257#385—24no—
258#385—24no—
259#385—24no—
260#385—24no—
261#385—42no—
262#385—42no—
263#385—44no—
264#380—24no—
265#380—44no—
266#379—24no—
267#379—24no—
268#379—24no—
269#379—24no—
270#379—24no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—44no—
274C2×#95—24no—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
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—
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—42no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25C2×D414yes—
326C25C2×D414yes—
327C25C2412yes—
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—416no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—432no—
370C22×D4—416no—
371C22×D4—416no—
372C22×D4—432no—
373C22×D4C2×D414yes—
374C22×D4C2×D418yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
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—24no—
395C23×C4—24no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—41no—
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×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430#123—416no—
431#121—432no—
432#120—232no—
433#120—416no—
434C4×D4—416no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—416no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
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—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—416no—
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—42no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—416no—
551C2×C22⋊C4—416no—
552C2×C22⋊C4—416no—
553C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D418yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4C2×D414yes—
577C2×C22⋊C4#4114yes—
578C2×C22⋊C4#4114yes—
579C2×C22⋊C4#4114yes—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—24no—
583C2×C42—24no—
584C2×C42—41no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—42no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—24no—
596#95—24no—
597#95—22no—
598#95—24no—
599#95—24no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—21no—
629C24—22no—
630C24—21no—
631C24—22no—
632C24—28no—
633C24—28no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—28no—
669C24—28no—
670C24—28no—
671C24—28no—
672C24—28no—
673C24—44no—
674C24—44no—
675C24—48no—
676C24—44no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—48no—
688C24—44no—
689C24—48no—
690C24—44no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24C22×D414yes—
713C24C22×D412yes—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C2×#4112yes—
719C24C2×#4112yes—
720C24C2×#4112yes—
721C24H(5,𝔽2)14yes—
722C24H(5,𝔽2)12yes—
723C242−1+412yes—
724C24C2511yescharacteristic
725C2×D4—216no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—216no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—4128no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—48no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—82no—
760C2×D4—82no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
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—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
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—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
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—48no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—82no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D414yes—
902C22×C4C2×#4114yes—
903C22×C4C2×#4114yes—
904C22×C4C2×#4114yes—
905C22×C4H(5,𝔽2)14yes—
906C22×C4H(5,𝔽2)14yes—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—84no—
915C4⋊C4—82no—
916C4⋊C4—82no—
917C4⋊C4—84no—
918C4⋊C4—84no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—216no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—82no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—82no—
953C22⋊C4—82no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4#123116yescomplemented
958C42—44no—
959C42—84no—
960C42—84no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—22no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—416no—
1009C23—416no—
1010C23—416no—
1011C23—416no—
1012C23—416no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—41no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—416no—
1029C23—416no—
1030C23—41no—
1031C23—42no—
1032C23—41no—
1033C23—41no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—41no—
1043C23—41no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—88no—
1088C23—816no—
1089C23—88no—
1090C23—88no—
1091C23—816no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—88no—
1099C23—88no—
1100C23—88no—
1101C23—88no—
1102C23C2×#12314yes—
1103C23#53214yes—
1104C23#53414yes—
1105C23#54214yes—
1106C23D4214yes—
1107C23#54714yes—
1108C23#54714yes—
1109C23#55314yes—
1110C23C23×D411yescharacteristic
1111C23C23×D411yescharacteristic
1112C23C22×#4111yescharacteristic
1113C23C22×#4111yescharacteristic
1114C23C22×#4111yescharacteristic
1115C23C2×H(5,𝔽2)12yes—
1116C23C2×H(5,𝔽2)11yescharacteristic
1117C23C2×H(5,𝔽2)12yes—
1118C23C2×H(5,𝔽2)12yes—
1119C23C2×2−1+411yescharacteristic
1120C23#58512yes—
1121D4—432no—
1122D4—432no—
1123D4—416no—
1124D4—816no—
1125D4—88no—
1126D4—88no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
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—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
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—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
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—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—816no—
1235C2×C4—88no—
1236C2×C4—88no—
1237C2×C4—88no—
1238C2×C4—88no—
1239C2×C4C2×#12318yes—
1240C22—24no—
1241C22—28no—
1242C22—28no—
1243C22—24no—
1244C22—28no—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—28no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—44no—
1254C22—44no—
1255C22—42no—
1256C22—42no—
1257C22—44no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—44no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—42no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—42no—
1280C22—832no—
1281C22—832no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—81no—
1291C22—82no—
1292C22—82no—
1293C22—81no—
1294C22—82no—
1295C22—81no—
1296C22—82no—
1297C22—82no—
1298C22—81no—
1299C22—82no—
1300C22#242218yes—
1301C22C22×#12311yescharacteristic
1302C22C2×#53211yescharacteristic
1303C22C2×#53411yescharacteristic
1304C22#344911yescharacteristic
1305C22C2×#54211yescharacteristic
1306C22C2×D4211yescharacteristic
1307C22C2×#54711yescharacteristic
1308C22C2×#54711yescharacteristic
1309C22C2×#55311yescharacteristic
1310C22#348411yescharacteristic
1311C22#348412yes—
1312C22#348411yescharacteristic
1313C22#349612yes—
1314C22#351312yes—
1315C22#351312yes—
1316C22#351412yes—
1317C22#351912yes—
1318C22#351912yes—
1319C22#351912yes—
1320C22#353212yes—
1321C22#353612yes—
1322C22#354212yes—
1323C22#356112yes—
1324C4—28no—
1325C4—44no—
1326C4—42no—
1327C4—42no—
1328C4—44no—
1329C4—44no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—82no—
1337C4—81no—
1338C4—82no—
1339C4—81no—
1340C4—82no—
1341C4—81no—
1342C2—28no—
1343C2—44no—
1344C2—82no—
1345C2—82no—
1346C2—84no—
1347C2C2×#242211yescharacteristic
1348C2#3506411yescharacteristic
1349C2#3539511yescharacteristic
1350C2#3571312yes—
1351C2#3764411yescharacteristic
1352C2#3803611yescharacteristic
1353C2#3804411yescharacteristic
1354C2#3933211yescharacteristic
1355C2#4072212yes—
1356C2#4299912yes—
1357C2#4406212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2410C2
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×#2418C2semidirect
3. C22×#394C2semidirect
4. C2×#2321C2semidirect
5. #16526C2semidirect
6. #16312C2semidirect
7. #15647C2semidirect
8. #15498C2semidirect
9. #15295C2semidirect
10. #15260C2semidirect
11. #15126C2semidirect
12. #14945C2semidirect
13. #14820C2semidirect
14. #14741C2semidirect
15. #14724C2semidirect
16. #14718C2semidirect
17. #14262C2semidirect
18. #14043C2semidirect
19. #14015C2semidirect
20. #13995C2semidirect
21. #13965C2semidirect
22. #13877C2semidirect
23. C22⋊C42C2semidirect
25. C22×#123C22semidirect
38. C2×#399C22semidirect
39. C2×#397C22semidirect
40. C2×#397C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
51. C2×#394C22semidirect
54. C2×#390C22semidirect
55. C2×#390C22semidirect
56. C2×#389C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
59. C2×#388C22semidirect
60. C2×#388C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
74. C2×#385C22semidirect
76. C2×#380C22semidirect
84. C2×C4×C22⋊C4C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1444C22semidirect
89. #1444C22semidirect
90. #1443C22semidirect
91. #1443C22semidirect
92. #1441C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
186. C22×C22⋊C4D4semidirect
957. C22⋊C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24182
C2×#24102
C22×#3942
C2×#23212
#165262
#163122
#156472
#154982
#152952
#152602
#151262
#149452
#148202
#147412
#147242
#147182
#142622
#140432
#140152
#139952
#139652
#138772
C22⋊C422