Finite Group Databasebeta

← #617787

Subgroups — #617787

Order 512.

4558 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2437C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C2×#2315C211yesmaximal, characteristic, complemented
4C22×#390C211yesmaximal, characteristic
5#15505C212yesmaximal, complemented
6#15476C212yesmaximal, complemented
7#15358C212yesmaximal, complemented
8#15355C212yesmaximal, complemented
9#15335C212yesmaximal, complemented
10#15330C212yesmaximal, complemented
11#15325C212yesmaximal, complemented
12#15309C212yesmaximal, complemented
13#14734C211yesmaximal, characteristic, complemented
14#14728C211yesmaximal, characteristic, complemented
15#14726C211yesmaximal, characteristic, complemented
16#14720C211yesmaximal, characteristic, complemented
17#14697C211yesmaximal, characteristic, complemented
18#14695C211yesmaximal, characteristic, complemented
19#14262C211yesmaximal, characteristic, complemented
20#14262C211yesmaximal, characteristic, complemented
21#13877C211yesmaximal, characteristic, complemented
22#13867C211yesmaximal, characteristic
23#13867C211yesmaximal, characteristic
24C24×D4C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2626—28no—
36#2437—28no—
37C2×#399C2211yescharacteristic, complemented
38C2×#399C2212yescomplemented
39C2×#399C2212yescomplemented
40C2×#398C2212yescomplemented
41C2×#396C2211yescharacteristic, complemented
42C2×#396C2211yescharacteristic, complemented
43C2×#396C2212yescomplemented
44C2×#396C2212yescomplemented
45C2×#396C2212yescomplemented
46C2×#395C2212yescomplemented
47C2×#393C2211yescharacteristic, complemented
48C2×#393C2212yescomplemented
49#2315—28no—
50C2×#390—28no—
51C2×#390C2212yes—
52C2×#390C2212yes—
53C2×#390C2212yes—
54C2×#390C2212yes—
55C2×#389C2212yescomplemented
56C2×#387C2212yescomplemented
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#385C2211yescharacteristic
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#385C2212yescomplemented
70C2×#385C2212yescomplemented
71C2×#385C2211yescharacteristic, complemented
72C2×#385C2211yescharacteristic, complemented
73C2×#385C2212yescomplemented
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×#380C2212yescomplemented
78C2×#380C2212yescomplemented
79C2×#380C2211yescharacteristic, complemented
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×#379C2211yescharacteristic
85C2×#379C2211yescharacteristic
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1444C2212yescomplemented
89#1442C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
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#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116C4⋊#95C2212yescomplemented
117#1434C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4Q818yescomplemented
135C23×D4C2312yes—
136C23×D4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—42no—
149C2×C22⋊Q8—44no—
150C22×C4⋊C4—24no—
151C22×C4⋊C4—44no—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C22⋊C4—24no—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
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—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4D418yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C42—24no—
223C22×C42—44no—
224C22×C42C2312yes—
225C22×C42C2312yes—
226#399—28no—
227#399—24no—
228#399—44no—
229#398—44no—
230#396—28no—
231#396—24no—
232#396—24no—
233#396—28no—
234#396—44no—
235#395—44no—
236#393—24no—
237#393—28no—
238#390—28no—
239#390—28no—
240#390—28no—
241#390—28no—
242#389—44no—
243#387—44no—
244#386—44no—
245#386—44no—
246#386—44no—
247#386—44no—
248#385—24no—
249#385—24no—
250#385—24no—
251#385—24no—
252#385—28no—
253#385—24no—
254#385—24no—
255#385—24no—
256#385—24no—
257#385—28no—
258#385—44no—
259#385—42no—
260#385D418yescomplemented
261#380—24no—
262#380—28no—
263#380—24no—
264#380—24no—
265#380—24no—
266#380—28no—
267#379—24no—
268#379—24no—
269#379—24no—
270#379—24no—
271#379—24no—
272#379—42no—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
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—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25C2×D414yes—
322C25C2×Q814yes—
323C25C2×Q814yes—
324C25#4114yes—
325C25C2412yes—
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—41no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×D4—232no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—432no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—416no—
349C22×D4—416no—
350C22×D4—432no—
351C22×D4C2×Q818yes—
352C22×D4C2×Q818yes—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—24no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—41no—
379C23×C4—41no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4C2×D414yes—
392C23×C4C2×D414yes—
393C23×C4C2×D414yes—
394C23×C4C2×Q814yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C22⋊Q8—416no—
415C22⋊Q8—416no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—416no—
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⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4C2×D418yescomplemented
468C2×C22⋊C4—232no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
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—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
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—416no—
524C2×C22⋊C4—416no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
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—416no—
538C2×C22⋊C4—416no—
539C2×C22⋊C4—416no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4C2×D414yes—
565C2×C22⋊C4C2×D414yes—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4#4114yes—
571C2×C42—24no—
572C2×C42—24no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—416no—
578#95—22no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—22no—
583#95—22no—
584#95—24no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95C2×D418yescomplemented
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—21no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—28no—
629C24—28no—
630C24—28no—
631C24—28no—
632C24—28no—
633C24—28no—
634C24—28no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—28no—
650C24—28no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—44no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—48no—
665C24—44no—
666C24—48no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24C22⋊Q8116yes—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C22×D412yes—
692C24C22×Q814yes—
693C24C22×Q812yes—
694C24C22×Q812yes—
695C24C22×Q812yes—
696C24C2×#4112yes—
697C24C2×#4112yes—
698C24C2×#4112yes—
699C24C2×#4112yes—
700C24H(5,𝔽2)12yes—
701C242−1+412yes—
702C24C2511yescharacteristic
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—82no—
706C2×Q8—84no—
707C2×Q8—84no—
708C2×D4—216no—
709C2×D4—216no—
710C2×D4—216no—
711C2×D4—216no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—4128no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—216no—
726C22×C4—28no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—216no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—216no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—48no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—82no—
852C22×C4—82no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4C22×D412yes—
862C22×C4C22×D414yes—
863C22×C4C22×D414yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×Q814yes—
870C22×C4C2×#4114yes—
871C22×C4H(5,𝔽2)14yes—
872C22×C4H(5,𝔽2)14yes—
873C22×C4H(5,𝔽2)14yes—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—82no—
885C4⋊C4—82no—
886C4⋊C4—82no—
887C4⋊C4—84no—
888C4⋊C4—84no—
889C4⋊C4—84no—
890C4⋊C4—84no—
891C4⋊C4—84no—
892C4⋊C4—84no—
893C22⋊C4—216no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—82no—
923C22⋊C4—82no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C42—48no—
929C42—48no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—22no—
934C23—22no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—232no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—416no—
983C23—416no—
984C23—416no—
985C23—416no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—416no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—816no—
1032C23—816no—
1033C23—816no—
1034C23—88no—
1035C23—88no—
1036C23—88no—
1037C23—88no—
1038C23—816no—
1039C23—816no—
1040C23—816no—
1041C23—816no—
1042C23—88no—
1043C23—88no—
1044C23—88no—
1045C23—88no—
1046C23—816no—
1047C23C2×C22⋊Q814yes—
1048C23C2×C22⋊Q814yes—
1049C23C2×C22⋊Q814yes—
1050C23#52514yes—
1051C23#53914yes—
1052C23D4214yes—
1053C23#54714yes—
1054C23D4×Q814yes—
1055C23#55414yes—
1056C23C23×D411yescharacteristic
1057C23C23×D411yescharacteristic
1058C23C23×Q811yescharacteristic
1059C23C22×#4111yescharacteristic
1060C23C22×#4111yescharacteristic
1061C23C2×H(5,𝔽2)12yes—
1062C23C2×H(5,𝔽2)11yescharacteristic
1063C23C2×H(5,𝔽2)12yes—
1064C23C2×H(5,𝔽2)12yes—
1065C23C2×2−1+411yescharacteristic
1066C23#58512yes—
1067Q8—88no—
1068D4—432no—
1069D4—432no—
1070C2×C4—232no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—416no—
1104C2×C4—416no—
1105C2×C4—41no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—88no—
1181C2×C4—816no—
1182C2×C4—88no—
1183C2×C4—88no—
1184C2×C4—88no—
1185C2×C4#53414yes—
1186C2×C4#54318yes—
1187C22—28no—
1188C22—28no—
1189C22—24no—
1190C22—24no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—24no—
1195C22—28no—
1196C22—28no—
1197C22—24no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—832no—
1227C22—832no—
1228C22—82no—
1229C22—82no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—82no—
1234C22—82no—
1235C22—82no—
1236C22#244918yes—
1237C22C22×C22⋊Q811yescharacteristic
1238C22C2×#52511yescharacteristic
1239C22C2×#53411yescharacteristic
1240C22#344911yescharacteristic
1241C22C2×#53911yescharacteristic
1242C22C2×#54312yes—
1243C22C2×D4211yescharacteristic
1244C22C2×#54711yescharacteristic
1245C22C2×D4×Q811yescharacteristic
1246C22C2×#55411yescharacteristic
1247C22#348411yescharacteristic
1248C22#348411yescharacteristic
1249C22#349012yes—
1250C22#349612yes—
1251C22#349812yes—
1252C22#350112yes—
1253C22#350512yes—
1254C22#351412yes—
1255C22#351912yes—
1256C22#353612yes—
1257C22#354212yes—
1258C22#354312yes—
1259C22#356112yes—
1260C4—24no—
1261C4—28no—
1262C4—44no—
1263C4—44no—
1264C4—42no—
1265C4—44no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—82no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—82no—
1276C4—81no—
1277C4—81no—
1278C4—82no—
1279C2—28no—
1280C2—44no—
1281C2—44no—
1282C2—84no—
1283C2C2×#244911yescharacteristic
1284C2#3498211yescharacteristic
1285C2#3501011yescharacteristic
1286C2#3536112yes—
1287C2#3680712yes—
1288C2#3803611yescharacteristic
1289C2#3804411yescharacteristic
1290C2#3896212yes—
1291C2#3933211yescharacteristic
1292C2#3933611yescharacteristic
1293C2#3936712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2437C2semidirect
2. C2×#2626C2semidirect
3. C2×#2315C2semidirect
5. #15505C2semidirect
6. #15476C2semidirect
7. #15358C2semidirect
8. #15355C2semidirect
9. #15335C2semidirect
10. #15330C2semidirect
11. #15325C2semidirect
12. #15309C2semidirect
13. #14734C2semidirect
14. #14728C2semidirect
15. #14726C2semidirect
16. #14720C2semidirect
17. #14697C2semidirect
18. #14695C2semidirect
19. #14262C2semidirect
20. #14262C2semidirect
21. #13877C2semidirect
26. C22×C22⋊Q8C22semidirect
37. C2×#399C22semidirect
38. C2×#399C22semidirect
39. C2×#399C22semidirect
40. C2×#398C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
43. C2×#396C22semidirect
44. C2×#396C22semidirect
45. C2×#396C22semidirect
46. C2×#395C22semidirect
47. C2×#393C22semidirect
48. C2×#393C22semidirect
55. C2×#389C22semidirect
56. C2×#387C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
71. C2×#385C22semidirect
72. C2×#385C22semidirect
73. C2×#385C22semidirect
77. C2×#380C22semidirect
78. C2×#380C22semidirect
79. C2×#380C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1444C22semidirect
89. #1442C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. C4⋊#95C22semidirect
117. #1434C22semidirect
126. C22⋊#95C22semidirect
134. C23×D4Q8semidirect
260. #385D4semidirect
467. C2×C4⋊C4C2×D4semidirect
607. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24372
C2×#26262
C2×#23152
C22×#3902
#155052
#154762
#153582
#153552
#153352
#153302
#153252
#153092
#147342
#147282
#147262
#147202
#146972
#146952
#142622
#138772
#138672