Finite Group Databasebeta

← #657046

Subgroups — #657046

Order 512.

5280 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2483C211yesmaximal, characteristic, complemented
2C2×#2405C211yesmaximal, characteristic
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4C22×#386C211yesmaximal, characteristic
5#15502C212yesmaximal, complemented
6#15497C212yesmaximal, complemented
7#15494C212yesmaximal, complemented
8#15390C212yesmaximal, complemented
9#14935C211yesmaximal, characteristic, complemented
10#14920C211yesmaximal, characteristic, complemented
11#14918C211yesmaximal, characteristic, complemented
12#14912C212yesmaximal, complemented
13#14737C212yesmaximal, complemented
14#14727C211yesmaximal, characteristic, complemented
15#14693C211yesmaximal, characteristic, complemented
16#14044C211yesmaximal, characteristic, complemented
17#13972C211yesmaximal, characteristic, complemented
18#13968C212yesmaximal, complemented
19#13899C212yesmaximal, complemented
20#13877C211yesmaximal, characteristic, complemented
21#13869C211yesmaximal, characteristic, complemented
22#13869C211yesmaximal, characteristic, complemented
23C2×C22⋊#95C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×C4×D4C2212yes—
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2483—28no—
36#2405—28no—
37C2×#397C2212yescomplemented
38C2×#397C2212yescomplemented
39C2×#397C2212yescomplemented
40C2×#394C2211yescharacteristic
41C2×#394C2211yescharacteristic
42C2×#394C2211yescharacteristic
43C2×#394C2211yescharacteristic
44D4×C22⋊C4—28no—
45C2×#390C2212yes—
46C2×#386—28no—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2211yescharacteristic
52C2×#386C2212yes—
53C2×#386C2211yescharacteristic
54C2×#386C2212yes—
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2212yescomplemented
62C2×#385C2212yescomplemented
63C2×#385C2212yescomplemented
64C2×#381C2211yescharacteristic
65C2×#381C2211yescharacteristic
66C2×#381C2211yescharacteristic
67C2×#381C2211yescharacteristic
68C2×#381C2212yescomplemented
69C2×#380C2211yescharacteristic
70C2×#380C2212yescomplemented
71C2×#379C2211yescharacteristic
72C2×#379C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C22×#95C2211yescharacteristic
78C22×#95C2211yescharacteristic
79C22×#95C2212yescomplemented
80C22×#95C2212yescomplemented
81#1445C2212yescomplemented
82#1443C2212yescomplemented
83#1443C2212yescomplemented
84#1442C2212yescomplemented
85#1442C2212yescomplemented
86#1442C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1440C2212yescomplemented
99#1440C2212yescomplemented
100#1440C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1436C2212yescomplemented
107#1436C2212yescomplemented
108C4⋊#95C2212yescomplemented
109#1434C2212yescomplemented
110C22⋊#95C2211yescharacteristic
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2212yescomplemented
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—28no—
132C23×D4—44no—
133C23×D4D418yes—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C24×C4—24no—
139C24×C4—24no—
140C24×C4—44no—
141C24×C4—42no—
142C24×C4—44no—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C2×#123—24no—
155C2×#123—24no—
156C2×#123—28no—
157C2×#123—44no—
158C2×C4×D4—28no—
159C2×C4×D4—28no—
160C2×C4×D4—44no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C22⋊C4—24no—
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—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4—42no—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C42C2312yes—
222#397—28no—
223#397—28no—
224#397—44no—
225#394—24no—
226#394—24no—
227#394—24no—
228#394—24no—
229#390—28no—
230#386—24no—
231#386—24no—
232#386—28no—
233#386—28no—
234#386—28no—
235#386—28no—
236#386—28no—
237#386—28no—
238#385—24no—
239#385—24no—
240#385—24no—
241#385—24no—
242#385—24no—
243#385—28no—
244#385—44no—
245#385—42no—
246#385—44no—
247#381—24no—
248#381—24no—
249#381—28no—
250#381—24no—
251#381—42no—
252#380—24no—
253#380—44no—
254#379—24no—
255#379—24no—
256#379—24no—
257#379—24no—
258#379D418yes—
259C4×C22⋊C4—24no—
260C2×#95—24no—
261C2×#95—24no—
262C2×#95—44no—
263C2×#95—44no—
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
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—
302C25—22no—
303C25—22no—
304C25—24no—
305C25—22no—
306C25—24no—
307C25—22no—
308C25—24no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25C2×D414yes—
321C25C2×D414yes—
322C25C2×D414yes—
323C25#4114yes—
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—232no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—232no—
343C22×D4—24no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—416no—
347C22×D4—432no—
348C22×D4—432no—
349C22×D4C2×D414yes—
350C22×D4C2×D414yes—
351C22×D4C2×D414yes—
352C22×D4C2×D414yes—
353C22×D4#4118yes—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—24no—
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—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—416no—
418C23×C4—416no—
419C23×C4—432no—
420C23×C4—416no—
421C23×C4—432no—
422C23×C4C2×D414yes—
423C23×C4#4114yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2412yes—
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442#123—416no—
443#123—416no—
444C4×D4—432no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
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⋊C4—42no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
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—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
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—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—416no—
535C2×C22⋊C4—416no—
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—416no—
548C2×C22⋊C4—416no—
549C2×C22⋊C4—416no—
550C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
560C2×C22⋊C4C2×D418yes—
561C2×C22⋊C4C2×D414yes—
562C2×C22⋊C4C2×D418yes—
563C2×C22⋊C4#4114yes—
564C2×C42—24no—
565C2×C42—24no—
566C2×C42—42no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—21no—
611C24—22no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—28no—
618C24—28no—
619C24—28no—
620C24—28no—
621C24—216no—
622C24—28no—
623C24—28no—
624C24—216no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—28no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—28no—
654C24—28no—
655C24—28no—
656C24—44no—
657C24—44no—
658C24—48no—
659C24—48no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24#121116yes—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C22×D412yes—
692C24C22×D412yes—
693C24C22×D412yes—
694C24C22×D412yes—
695C24C22×D412yes—
696C24C2×#4112yes—
697C24C2×#4114yes—
698C24C2×#4112yes—
699C24C2×#4112yes—
700C24C2×#4114yes—
701C24C2×#4112yes—
702C24C2×#4112yes—
703C24H(5,𝔽2)14yes—
704C24H(5,𝔽2)12yes—
705C242−1+412yes—
706C24C2511yescharacteristic
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—216no—
710C2×D4—216no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—4128no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4#123116yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—22no—
731C22×C4—28no—
732C22×C4—216no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—21no—
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—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—28no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—21no—
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—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—48no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
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—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—4128no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—82no—
887C22×C4—82no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4C22×D412yes—
893C22×C4C22×D414yes—
894C22×C4C22×D414yes—
895C22×C4C22×D412yes—
896C22×C4C2×#4114yes—
897C22×C4C2×#4114yes—
898C22×C4C2×#4114yes—
899C22×C4H(5,𝔽2)14yes—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C4⋊C4—84no—
908C4⋊C4—84no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—216no—
912C22⋊C4—28no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—84no—
937C22⋊C4—82no—
938C22⋊C4—82no—
939C22⋊C4—82no—
940C22⋊C4—82no—
941C22⋊C4—82no—
942C22⋊C4—82no—
943C42—48no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
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—24no—
978C23—22no—
979C23—22no—
980C23—232no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—232no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—22no—
990C23—24no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—432no—
1018C23—416no—
1019C23—432no—
1020C23—432no—
1021C23—432no—
1022C23—416no—
1023C23—416no—
1024C23—416no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—416no—
1045C23—41no—
1046C23—41no—
1047C23—42no—
1048C23—41no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—88no—
1061C23—88no—
1062C23—88no—
1063C23—816no—
1064C23—816no—
1065C23—816no—
1066C23—816no—
1067C23C2×#12114yes—
1068C23C2×#12114yes—
1069C23C2×#12114yes—
1070C23C2×#12314yes—
1071C23C2×#12314yes—
1072C23#52914yes—
1073C23#53414yes—
1074C23#53914yes—
1075C23#54618yes—
1076C23#54614yes—
1077C23#54614yes—
1078C23#54714yes—
1079C23#54714yes—
1080C23#55118yes—
1081C23C23×D411yescharacteristic
1082C23C23×D411yescharacteristic
1083C23C22×#4111yescharacteristic
1084C23C22×#4112yes—
1085C23C22×#4111yescharacteristic
1086C23C22×#4111yescharacteristic
1087C23C2×H(5,𝔽2)12yes—
1088C23C2×H(5,𝔽2)11yescharacteristic
1089C23C2×H(5,𝔽2)12yes—
1090C23C2×2−1+411yescharacteristic
1091C23#58512yes—
1092D4—232no—
1093D4—416no—
1094D4—416no—
1095D4—416no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—416no—
1119C2×C4—416no—
1120C2×C4—416no—
1121C2×C4—432no—
1122C2×C4—432no—
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—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
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—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—816no—
1207C2×C4—816no—
1208C2×C4—88no—
1209C2×C4—88no—
1210C2×C4—88no—
1211C2×C4—88no—
1212C2×C4C2×#12314yes—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—28no—
1222C22—28no—
1223C22—24no—
1224C22—24no—
1225C22—28no—
1226C22—28no—
1227C22—28no—
1228C22—28no—
1229C22—24no—
1230C22—24no—
1231C22—28no—
1232C22—28no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—464no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—42no—
1253C22—42no—
1254C22—44no—
1255C22—44no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—832no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22#241218yes—
1269C22#242518yes—
1270C22C22×#12111yescharacteristic
1271C22C22×#12311yescharacteristic
1272C22C2×#52911yescharacteristic
1273C22C2×#53411yescharacteristic
1274C22C2×#53911yescharacteristic
1275C22C2×#54611yescharacteristic
1276C22C2×#54612yes—
1277C22C2×#54611yescharacteristic
1278C22C2×#54711yescharacteristic
1279C22C2×#54711yescharacteristic
1280C22C2×#55112yes—
1281C22#347512yes—
1282C22#348112yes—
1283C22#348411yescharacteristic
1284C22#348511yescharacteristic
1285C22#349012yes—
1286C22#349612yes—
1287C22#350512yes—
1288C22#351312yes—
1289C22#351312yes—
1290C22#352012yes—
1291C22#353212yes—
1292C22#353512yes—
1293C4—24no—
1294C4—42no—
1295C4—44no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—82no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—82no—
1307C4—81no—
1308C4—81no—
1309C4—82no—
1310C4—81no—
1311C2—28no—
1312C2—28no—
1313C2—44no—
1314C2—44no—
1315C2—82no—
1316C2C2×#241211yescharacteristic
1317C2C2×#242511yescharacteristic
1318C2#3535811yescharacteristic
1319C2#3615511yescharacteristic
1320C2#3623711yescharacteristic
1321C2#3624212yes—
1322C2#3783211yescharacteristic
1323C2#3803811yescharacteristic
1324C2#3810912yes—
1325C2#5931112yes—
1326C2#5980212yes—
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×#2483C2semidirect
5. #15502C2semidirect
6. #15497C2semidirect
7. #15494C2semidirect
8. #15390C2semidirect
9. #14935C2semidirect
10. #14920C2semidirect
11. #14918C2semidirect
12. #14912C2semidirect
13. #14737C2semidirect
14. #14727C2semidirect
15. #14693C2semidirect
16. #14044C2semidirect
17. #13972C2semidirect
18. #13968C2semidirect
19. #13899C2semidirect
20. #13877C2semidirect
21. #13869C2semidirect
22. #13869C2semidirect
23. C2×C22⋊#95C2semidirect
37. C2×#397C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#385C22semidirect
68. C2×#381C22semidirect
70. C2×#380C22semidirect
79. C22×#95C22semidirect
80. C22×#95C22semidirect
81. #1445C22semidirect
82. #1443C22semidirect
83. #1443C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1440C22semidirect
99. #1440C22semidirect
100. #1440C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1436C22semidirect
107. #1436C22semidirect
108. C4⋊#95C22semidirect
109. #1434C22semidirect
118. C22⋊#95C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24832
C2×#24052
C2×D4×C22⋊C42
C22×#3862
#155022
#154972
#154942
#153902
#149352
#149202
#149182
#149122
#147372
#147272
#146932
#140442
#139722
#139682
#138992
#138772
#138692
C2×C22⋊#952