Finite Group Databasebeta

← #773256

Subgroups — #773256

Order 512.

4518 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2454C211yesmaximal, characteristic, complemented
2C2×#2454C211yesmaximal, characteristic, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4C2×D4×C22⋊C4C211yesmaximal, characteristic
5#16298C212yesmaximal, complemented
6#15958C212yesmaximal, complemented
7#15439C212yesmaximal, complemented
8#15327C212yesmaximal, complemented
9#15324C212yesmaximal, complemented
10#15220C211yesmaximal, characteristic, complemented
11#15216C211yesmaximal, characteristic, complemented
12#15131C211yesmaximal, characteristic, complemented
13#14734C212yesmaximal, complemented
14#14726C212yesmaximal, complemented
15#14018C211yesmaximal, characteristic, complemented
16#14018C211yesmaximal, characteristic, complemented
17#13979C211yesmaximal, characteristic, complemented
18#13977C211yesmaximal, characteristic, complemented
19#13941C211yesmaximal, characteristic, complemented
20#13906C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic
22#13877C212yesmaximal, complemented
23C4×#399C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#125C2211yescharacteristic, complemented
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C22⋊C4C2212yes—
31C23×C22⋊C4C2212yes—
32#2454—28no—
33#2454—28no—
34C2×#399C2211yescharacteristic
35C2×#399C2212yescomplemented
36C2×#399C2212yescomplemented
37C2×#396C2212yes—
38C2×#396C2212yescomplemented
39C2×#396C2212yescomplemented
40D4×C22⋊C4—28no—
41D4×C22⋊C4—28no—
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic, complemented
51C2×#389C2211yescharacteristic, complemented
52C2×#389C2211yescharacteristic, complemented
53C2×#389C2211yescharacteristic, complemented
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#385C2212yescomplemented
59C2×#385C2212yescomplemented
60C2×#385C2212yescomplemented
61C2×#385C2212yescomplemented
62C2×#385C2212yescomplemented
63C2×#385C2212yescomplemented
64C2×#384C2211yescharacteristic, complemented
65C2×#382C2211yescharacteristic, complemented
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2212yescomplemented
70C2×#380C2212yescomplemented
71C2×#380C2212yescomplemented
72C2×#380C2212yescomplemented
73C2×#379C2212yes—
74C2×#379C2212yes—
75C2×#379C2212yes—
76C2×#379C2212yes—
77C2×C4×C4⋊C4C2211yescharacteristic, complemented
78C2×C4×C4⋊C4C2211yescharacteristic, complemented
79C2×C4×C4⋊C4C2211yescharacteristic, complemented
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83#1445C2211yescharacteristic, complemented
84#1445C2211yescharacteristic, complemented
85#1445C2211yescharacteristic, complemented
86#1444C2211yescharacteristic, complemented
87#1443C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1439C2212yes—
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2212yes—
114#1438C2212yes—
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118C4⋊#95C2211yescharacteristic, complemented
119C4⋊#95C2211yescharacteristic, complemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—42no—
134C23×D4Q818yes—
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2312yes—
141C24×C4C2312yes—
142C24×C4C2312yes—
143C2×#125—24no—
144C2×#125—24no—
145C2×#125—42no—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—42no—
155C2×C4×D4—42no—
156C2×C4×D4—42no—
157C2×C4×D4—42no—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—28no—
180C22×C22⋊C4—28no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219#399—28no—
220#399—28no—
221#399—24no—
222#396—28no—
223#396—28no—
224#396—44no—
225#390—24no—
226#390—24no—
227#390—24no—
228#390—24no—
229#390—24no—
230#390—24no—
231#390D418yes—
232#390D418yes—
233#389—24no—
234#389—24no—
235#389—24no—
236#389—24no—
237#386—28no—
238#386—28no—
239#386—28no—
240#386—28no—
241#385—28no—
242#385—28no—
243#385—44no—
244#385—44no—
245#385—44no—
246#385—44no—
247#384—42no—
248#382—42no—
249#380—24no—
250#380—24no—
251#380—28no—
252#380—28no—
253#380—44no—
254#380—42no—
255#380—44no—
256#379—28no—
257#379—28no—
258#379—44no—
259#379—44no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—24no—
262C4×C4⋊C4—42no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4—42no—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C25—24no—
302C25—24no—
303C25—24no—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25C2×Q818yes—
316C25C2412yes—
317C25C2412yes—
318C25C2411yescharacteristic
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—232no—
324C22×D4—232no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—416no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—416no—
337C22×D4—416no—
338C22×D4—416no—
339C22×D4—416no—
340C22×D4C2×D414yes—
341C22×D4C2×D414yes—
342C22×D4C2×Q818yes—
343C22×D4C2×Q814yes—
344C22×D4C2×Q814yes—
345C22×D4#4114yes—
346C22×D4#4114yes—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4C2×Q814yes—
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402#125—416no—
403C4×D4—416no—
404C4×D4—416no—
405C4×D4—416no—
406C4×D4—416no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
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—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
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—42no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—41no—
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⋊C4C2×D414yes—
466C2×C4⋊C4C2×D414yes—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
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—432no—
511C2×C22⋊C4—432no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
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—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
552C2×C22⋊C4C2×D418yes—
553C2×C22⋊C4C2×D418yes—
554C2×C22⋊C4C2×D418yes—
555C2×C22⋊C4#4114yes—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42C2×D414yes—
573C2×C42C2×D414yes—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—22no—
589#95—24no—
590#95—22no—
591#95—24no—
592#95—22no—
593#95—41no—
594#95—42no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
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#95—42no—
608#95—42no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—216no—
646C24—216no—
647C24—216no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24C22×D414yes—
681C24C22×D414yes—
682C24C22×Q814yes—
683C24C22×Q814yes—
684C24C22×Q812yes—
685C24C2×#4114yes—
686C24C2×#4114yes—
687C24C2×#4112yes—
688C24H(5,𝔽2)12yes—
689C24C2511yescharacteristic
690C2×D4—216no—
691C2×D4—216no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—48no—
705C2×D4—4128no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4C22⋊Q8116yes—
711C2×D4C22⋊Q8116yes—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
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—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4—84no—
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×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D414yes—
872C22×C4C22×D414yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×Q812yes—
877C22×C4C22×Q812yes—
878C22×C4C2×#4112yes—
879C22×C4C2×#4112yes—
880C22×C4C2×#4112yes—
881C22×C4C2×#4112yes—
882C22×C4H(5,𝔽2)12yes—
883C22×C4H(5,𝔽2)12yes—
884C22×C4H(5,𝔽2)12yes—
885C22×C4H(5,𝔽2)12yes—
886C22×C4H(5,𝔽2)12yes—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—84no—
902C4⋊C4—84no—
903C4⋊C4—84no—
904C4⋊C4—84no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—216no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C42—28no—
937C42—28no—
938C42—44no—
939C42—44no—
940C42—44no—
941C42—44no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—24no—
990C23—22no—
991C23—24no—
992C23—22no—
993C23—24no—
994C23—22no—
995C23—22no—
996C23—432no—
997C23—432no—
998C23—432no—
999C23—41no—
1000C23—42no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—41no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—42no—
1011C23—42no—
1012C23—41no—
1013C23—42no—
1014C23—41no—
1015C23—42no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—41no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—41no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—816no—
1048C23—816no—
1049C23—816no—
1050C23—816no—
1051C23—816no—
1052C23—816no—
1053C23—816no—
1054C23—816no—
1055C23—816no—
1056C23—816no—
1057C23—816no—
1058C23—816no—
1059C23C2×C22⋊Q818yes—
1060C23C2×C22⋊Q818yes—
1061C23#55414yes—
1062C23C23×D411yescharacteristic
1063C23C23×D411yescharacteristic
1064C23C23×Q811yescharacteristic
1065C23C22×#4111yescharacteristic
1066C23C22×#4111yescharacteristic
1067C23C22×#4111yescharacteristic
1068C23C2×H(5,𝔽2)11yescharacteristic
1069C23C2×H(5,𝔽2)11yescharacteristic
1070C23C2×H(5,𝔽2)11yescharacteristic
1071C23C2×H(5,𝔽2)11yescharacteristic
1072C23C2×H(5,𝔽2)11yescharacteristic
1073C23C2×H(5,𝔽2)11yescharacteristic
1074C23#58511yescharacteristic
1075C23#58511yescharacteristic
1076C23#58511yescharacteristic
1077D4—232no—
1078D4—232no—
1079D4—432no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—42no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—416no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—816no—
1214C2×C4—816no—
1215C2×C4—816no—
1216C2×C4—816no—
1217C2×C4C2×C22⋊Q814yes—
1218C2×C4C2×C22⋊Q814yes—
1219C2×C4#54314yes—
1220C2×C4D4214yes—
1221C2×C4#54614yes—
1222C2×C4#54614yes—
1223C2×C4#54614yes—
1224C2×C4#55114yes—
1225C22—24no—
1226C22—24no—
1227C22—28no—
1228C22—28no—
1229C22—28no—
1230C22—24no—
1231C22—28no—
1232C22—28no—
1233C22—28no—
1234C22—44no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—44no—
1253C22—42no—
1254C22—44no—
1255C22—42no—
1256C22—44no—
1257C22—44no—
1258C22—42no—
1259C22—44no—
1260C22—44no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—44no—
1266C22—44no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—864no—
1271C22C22×C22⋊Q811yescharacteristic
1272C22C22×C22⋊Q811yescharacteristic
1273C22C2×#54311yescharacteristic
1274C22C2×D4211yescharacteristic
1275C22C2×#54611yescharacteristic
1276C22C2×#54611yescharacteristic
1277C22C2×#54611yescharacteristic
1278C22D4×#4111yescharacteristic
1279C22C2×#55111yescharacteristic
1280C22C2×#55411yescharacteristic
1281C22#347511yescharacteristic
1282C22#348111yescharacteristic
1283C22#348411yescharacteristic
1284C22#348511yescharacteristic
1285C22#348811yescharacteristic
1286C22#348811yescharacteristic
1287C22#349611yescharacteristic
1288C22#349811yescharacteristic
1289C22#350111yescharacteristic
1290C22#350111yescharacteristic
1291C22#350111yescharacteristic
1292C22#351311yescharacteristic
1293C22#351311yescharacteristic
1294C22#351311yescharacteristic
1295C22#351411yescharacteristic
1296C22#351911yescharacteristic
1297C22#351911yescharacteristic
1298C22#351911yescharacteristic
1299C22#352111yescharacteristic
1300C22#354211yescharacteristic
1301C22#354211yescharacteristic
1302C22#354311yescharacteristic
1303C22#354311yescharacteristic
1304C22#354611yescharacteristic
1305C22#356211yescharacteristic
1306C4—24no—
1307C4—44no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—82no—
1320C4—82no—
1321C4—81no—
1322C4—81no—
1323C4—82no—
1324C4—82no—
1325C4#243718yes—
1326C2—48no—
1327C2—48no—
1328C2—44no—
1329C2C2×#243711yescharacteristic
1330C2#3577611yescharacteristic
1331C2#3583611yescharacteristic
1332C2#3615411yescharacteristic
1333C2#3621511yescharacteristic
1334C2#3896211yescharacteristic
1335C2#4248611yescharacteristic
1336C2#4487211yescharacteristic
1337C2#4493211yescharacteristic
1338C2#4500211yescharacteristic
1339C2#4506111yescharacteristic
1340C2#5903011yescharacteristic
1341C2#5910311yescharacteristic
1342C2#5938211yescharacteristic
1343C2#5941211yescharacteristic
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×#2454C2semidirect
2. C2×#2454C2semidirect
5. #16298C2semidirect
6. #15958C2semidirect
7. #15439C2semidirect
8. #15327C2semidirect
9. #15324C2semidirect
10. #15220C2semidirect
11. #15216C2semidirect
12. #15131C2semidirect
13. #14734C2semidirect
14. #14726C2semidirect
15. #14018C2semidirect
16. #14018C2semidirect
17. #13979C2semidirect
18. #13977C2semidirect
19. #13941C2semidirect
20. #13906C2semidirect
22. #13877C2semidirect
23. C4×#399C2semidirect
25. C22×#125C22semidirect
35. C2×#399C22semidirect
36. C2×#399C22semidirect
38. C2×#396C22semidirect
39. C2×#396C22semidirect
50. C2×#389C22semidirect
51. C2×#389C22semidirect
52. C2×#389C22semidirect
53. C2×#389C22semidirect
58. C2×#385C22semidirect
59. C2×#385C22semidirect
60. C2×#385C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#385C22semidirect
64. C2×#384C22semidirect
65. C2×#382C22semidirect
69. C2×#380C22semidirect
70. C2×#380C22semidirect
71. C2×#380C22semidirect
72. C2×#380C22semidirect
77. C2×C4×C4⋊C4C22semidirect
78. C2×C4×C4⋊C4C22semidirect
79. C2×C4×C4⋊C4C22semidirect
83. #1445C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1443C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
119. C4⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24542
C2×D4×C22⋊C42
#162982
#159582
#154392
#153272
#153242
#152202
#152162
#151312
#147342
#147262
#140182
#139792
#139772
#139412
#139062
#139022
#138772
C4×#3992