Finite Group Databasebeta

← #794479

Subgroups — #794479

Order 512.

4828 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2598C211yesmaximal, characteristic, complemented
2C22×#394C211yesmaximal, characteristic, complemented
3C2×#2352C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#16809C211yesmaximal, characteristic, complemented
6#16664C211yesmaximal, characteristic, complemented
7#15418C212yesmaximal, complemented
8#15391C212yesmaximal, complemented
9#15376C212yesmaximal, complemented
10#15372C212yesmaximal, complemented
11#15159C211yesmaximal, characteristic, complemented
12#15107C211yesmaximal, characteristic, complemented
13#14886C211yesmaximal, characteristic, complemented
14#14860C211yesmaximal, characteristic, complemented
15#14836C211yesmaximal, characteristic, complemented
16#14822C211yesmaximal, characteristic, complemented
17#14715C211yesmaximal, characteristic
18#14176C211yesmaximal, characteristic, complemented
19#14134C212yesmaximal, complemented
20#13967C212yesmaximal, complemented
21#13901C211yesmaximal, characteristic, complemented
22#13877C212yesmaximal, complemented
23#13873C212yesmaximal, complemented
24C24×D4C2211yescharacteristic
25C22×#120C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2211yescharacteristic, complemented
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32C23×C22⋊C4C2212yes—
33C23×C22⋊C4C2212yes—
34#2598—28no—
35C2×#400C2211yescharacteristic, complemented
36C2×#400C2211yescharacteristic, complemented
37C2×#399C2211yescharacteristic, complemented
38C2×#394—28no—
39C2×#394C2211yescharacteristic
40C2×#394C2211yescharacteristic
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2211yescharacteristic
44C2×#394C2211yescharacteristic
45C2×#392C2211yescharacteristic
46C2×#392C2212yes—
47C2×#392C2211yescharacteristic
48#2352—28no—
49D4×C22⋊C4—28no—
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#388C2212yescomplemented
53C2×#388C2211yescharacteristic, complemented
54C2×#388C2211yescharacteristic, complemented
55C2×#388C2212yescomplemented
56C2×#387C2211yescharacteristic, complemented
57C2×#387C2211yescharacteristic, complemented
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2211yescharacteristic
62C2×#386C2212yes—
63C2×#386C2212yescomplemented
64C2×#386C2212yescomplemented
65C2×#386C2212yescomplemented
66C2×#386C2212yescomplemented
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#383C2211yescharacteristic, complemented
70C2×#382C2211yescharacteristic, complemented
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2212yes—
74C2×#380C2211yescharacteristic, complemented
75C2×#379C2212yes—
76C2×#379C2212yes—
77C2×C4×C4⋊C4C2211yescharacteristic, complemented
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C22×#95C2211yescharacteristic
81#1445C2211yescharacteristic, complemented
82#1445C2212yescomplemented
83#1444C2211yescharacteristic, complemented
84#1443C2212yescomplemented
85#1443C2212yescomplemented
86#1442C2212yescomplemented
87#1442C2212yescomplemented
88#1441C2211yescharacteristic, complemented
89#1441C2211yescharacteristic, complemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2211yescharacteristic, complemented
104#1438C2211yescharacteristic
105#1438C2211yescharacteristic
106#1438C2212yes—
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1434C2211yescharacteristic, complemented
116#1434C2211yescharacteristic, complemented
117#1434C2211yescharacteristic, complemented
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2312yes—
128C23×D4—28no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—42no—
132C23×D4—44no—
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2312yes—
146C2×#120—28no—
147C2×#120—28no—
148C2×#120—44no—
149C2×C4×D4—24no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—42no—
156C2×C4×D4—44no—
157C2×#117—24no—
158C2×#117—24no—
159C2×#117—42no—
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—42no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4—28no—
175C22×C22⋊C4—28no—
176C22×C22⋊C4—28no—
177C22×C22⋊C4—28no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—44no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220#400—24no—
221#400—42no—
222#399—24no—
223#394—24no—
224#394—24no—
225#394—28no—
226#394—28no—
227#394—24no—
228#394D418yescomplemented
229#392—24no—
230#392—42no—
231#392—44no—
232#390—24no—
233#390—24no—
234#388—28no—
235#388—24no—
236#388—24no—
237#388—44no—
238#387—24no—
239#387—24no—
240#386—24no—
241#386—28no—
242#386—28no—
243#386—24no—
244#386—28no—
245#386—28no—
246#386—44no—
247#386—44no—
248#386—44no—
249#385—28no—
250#385—44no—
251#383—24no—
252#382—24no—
253#380—24no—
254#380—24no—
255#380—24no—
256#380—44no—
257#379—28no—
258#379—44no—
259C4×C4⋊C4—24no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4D418yescomplemented
262C2×#95—24no—
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C25—24no—
301C25—24no—
302C25—24no—
303C25—24no—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25#4118yes—
315C25C2412yes—
316C25C2411yescharacteristic
317C25C2412yes—
318C25C2411yescharacteristic
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—232no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—416no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—432no—
356C22×D4—416no—
357C22×D4—432no—
358C22×D4C2×D414yes—
359C22×D4#4114yes—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—24no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—41no—
384C23×C4—41no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—41no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4C2×D414yes—
404C23×C4#4114yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424#120—432no—
425C4×D4—232no—
426C4×D4—416no—
427C4×D4—416no—
428#117—416no—
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—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—416no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
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⋊C4C2×D414yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
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—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
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—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
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—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—24no—
516C2×C22⋊C4—432no—
517C2×C22⋊C4—432no—
518C2×C22⋊C4—432no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
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⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4C2×D414yes—
554C2×C22⋊C4C2×D418yes—
555C2×C22⋊C4C2×D418yes—
556C2×C22⋊C4C2×D414yes—
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—41no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42C2×D414yes—
569C2×C42C2×D414yes—
570#95—24no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—24no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—24no—
582#95—24no—
583#95—22no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—22no—
588#95—42no—
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#95C2×D414yes—
605#95C2×D414yes—
606#95C2×D414yes—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—22no—
611C24—21no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—216no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—216no—
651C24—216no—
652C24—216no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24C22×D414yes—
685C24C22×D412yes—
686C24C2×#4114yes—
687C24C2×#4112yes—
688C24C2×#4114yes—
689C24C2×#4112yes—
690C24C2×#4114yes—
691C24C2×#4112yes—
692C24H(5,𝔽2)14yes—
693C24H(5,𝔽2)14yes—
694C24C2511yescharacteristic
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—216no—
698C2×D4—216no—
699C2×D4—28no—
700C2×D4—216no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—44no—
709C2×D4—4128no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—44no—
724C2×D4—84no—
725C2×D4—84no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
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—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
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—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—44no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—48no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—82no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4C22×D412yes—
876C22×C4C22×D414yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C2×#4112yes—
886C22×C4C2×#4112yes—
887C22×C4C2×#4112yes—
888C22×C4H(5,𝔽2)12yes—
889C22×C4H(5,𝔽2)12yes—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—84no—
900C4⋊C4—84no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—216no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—82no—
924C22⋊C4—82no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C42—28no—
934C42—28no—
935C42—44no—
936C42—44no—
937C42—82no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—24no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
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—22no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—432no—
987C23—432no—
988C23—432no—
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—432no—
1006C23—41no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—42no—
1012C23—42no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—816no—
1053C23—816no—
1054C23—816no—
1055C23—816no—
1056C23—816no—
1057C23—816no—
1058C23—816no—
1059C23—816no—
1060C23—816no—
1061C23—816no—
1062C23—816no—
1063C23#52514yes—
1064C23#52514yes—
1065C23#53514yes—
1066C23#54618yes—
1067C23#55118yes—
1068C23#55318yes—
1069C23C23×D411yescharacteristic
1070C23C23×D411yescharacteristic
1071C23C22×#4112yes—
1072C23C22×#4111yescharacteristic
1073C23C22×#4111yescharacteristic
1074C23C2×H(5,𝔽2)12yes—
1075C23C2×H(5,𝔽2)11yescharacteristic
1076C23C2×H(5,𝔽2)12yes—
1077C23C2×H(5,𝔽2)11yescharacteristic
1078C23#58511yescharacteristic
1079C23#58512yes—
1080D4—232no—
1081D4—416no—
1082D4—432no—
1083D4—416no—
1084D4—816no—
1085D4—816no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—416no—
1122C2×C4—416no—
1123C2×C4—416no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
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—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—88no—
1201C2×C4—816no—
1202C2×C4—816no—
1203C2×C4—816no—
1204C2×C4D4214yes—
1205C2×C4#54614yes—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—28no—
1210C22—28no—
1211C22—28no—
1212C22—28no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—28no—
1217C22—28no—
1218C22—28no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—42no—
1232C22—44no—
1233C22—42no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—42no—
1242C22—44no—
1243C22—864no—
1244C22—82no—
1245C22—81no—
1246C22—81no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—81no—
1256C22—82no—
1257C22—81no—
1258C22#259818yescomplemented
1259C22C2×#52511yescharacteristic
1260C22C2×#52511yescharacteristic
1261C22C2×#53511yescharacteristic
1262C22C2×D4211yescharacteristic
1263C22C2×#54611yescharacteristic
1264C22C2×#54612yes—
1265C22D4×#4111yescharacteristic
1266C22C2×#55112yes—
1267C22C2×#55312yes—
1268C22#348411yescharacteristic
1269C22#348811yescharacteristic
1270C22#348812yes—
1271C22#349012yes—
1272C22#349112yes—
1273C22#349412yes—
1274C22#350011yescharacteristic
1275C22#350511yescharacteristic
1276C22#350512yes—
1277C22#351312yes—
1278C22#351911yescharacteristic
1279C22#353412yes—
1280C22#353712yes—
1281C22#355812yes—
1282C4—24no—
1283C4—24no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—82no—
1296C4—82no—
1297C4—82no—
1298C4—82no—
1299C4—81no—
1300C4—82no—
1301C2—28no—
1302C2—48no—
1303C2—82no—
1304C2—84no—
1305C2C2×#259811yescharacteristic
1306C2#3572911yescharacteristic
1307C2#3575311yescharacteristic
1308C2#3609611yescharacteristic
1309C2#3609811yescharacteristic
1310C2#3767711yescharacteristic
1311C2#4059411yescharacteristic
1312C2#4305412yes—
1313C2#4307712yes—
1314C2#5901112yes—
1315C2#5901312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#2598C2semidirect
2. C22×#394C2semidirect
3. C2×#2352C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #16809C2semidirect
6. #16664C2semidirect
7. #15418C2semidirect
8. #15391C2semidirect
9. #15376C2semidirect
10. #15372C2semidirect
11. #15159C2semidirect
12. #15107C2semidirect
13. #14886C2semidirect
14. #14860C2semidirect
15. #14836C2semidirect
16. #14822C2semidirect
18. #14176C2semidirect
19. #14134C2semidirect
20. #13967C2semidirect
21. #13901C2semidirect
22. #13877C2semidirect
23. #13873C2semidirect
29. C22×#117C22semidirect
35. C2×#400C22semidirect
36. C2×#400C22semidirect
37. C2×#399C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#387C22semidirect
57. C2×#387C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
65. C2×#386C22semidirect
66. C2×#386C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#383C22semidirect
70. C2×#382C22semidirect
74. C2×#380C22semidirect
77. C2×C4×C4⋊C4C22semidirect
81. #1445C22semidirect
82. #1445C22semidirect
83. #1444C22semidirect
84. #1443C22semidirect
85. #1443C22semidirect
86. #1442C22semidirect
87. #1442C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1434C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
228. #394D4semidirect
261. C4×C22⋊C4D4semidirect
1258. C22#2598semidirect

Maximal subgroups

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

subgroupindex
C2×#25982
C22×#3942
C2×#23522
C2×D4×C22⋊C42
#168092
#166642
#154182
#153912
#153762
#153722
#151592
#151072
#148862
#148602
#148362
#148222
#147152
#141762
#141342
#139672
#139012
#138772
#138732