Finite Group Databasebeta

← #29601412

Subgroups — #29601412

Order 15616.

4254 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758198C211yesmaximal, characteristic
2C22×C22⋊C4×D61C211yesmaximal, characteristic
3C2×#16839617C211yesmaximal, characteristic
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
6C2×#16839609C212yesmaximal, complemented
7#21444055C212yesmaximal, complemented
8#21444055C212yesmaximal, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×#11758198—28no—
18C22×#11758198C418yescomplemented
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×#11758198C2211yescharacteristic
26C2×C22⋊C4×D61—24no—
27C2×C22⋊C4×D61—24no—
28C2×C22⋊C4×D61C418yescomplemented
29C22×C4×Dic61C2212yescomplemented
30C22×C4×Dic61C2212yescomplemented
31#16839617C418yescomplemented
32C22⋊C4×Dic61—24no—
33C4×C22⋊Dic61—24no—
34#16839609—28no—
35C2×#14519684C2212yescomplemented
36C2×#14519684C2212yescomplemented
37C2×#14519684C2212yescomplemented
38C2×#14519684C2212yescomplemented
39C24×C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C2×#95×C61C2212yescomplemented
43C2×#95×C61C2212yescomplemented
44C24×D61—22no—
45C24×D61—22no—
46C24×D61—22no—
47C24×D61—22no—
48C24×D61—24no—
49C24×D61—24no—
50C24×D61—42no—
51C24×D61—42no—
52C24×D61C2×C414yes—
53C24×D61C2×C414yes—
54C24×D61C2×C414yes—
55C24×D61C2311yescharacteristic
56C24×D61C2311yescharacteristic
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—24no—
60C23×Dic61—42no—
61C23×Dic61C2×C414yescomplemented
62C23×Dic61C2312yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2312yes—
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—42no—
71C22×C4×D61—42no—
72C22×C4×D61C2×C418yescomplemented
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61C2×C414yes—
76C2×C22⋊Dic61C2×C414yescomplemented
77C2×C22⋊Dic61D414yes—
78C2×C22⋊Dic61D414yes—
79C2×#11758198—24no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—232no—
87C2×#11758198—42no—
88C2×#11758198—42no—
89C2×#11758198C2×C414yes—
90C2×#11758198C2×C414yes—
91C2×#11758198C2×C418yescomplemented
92C2×#11758198C2×C414yescomplemented
93C2×#11758198C2×C414yescomplemented
94C2×#11758198C2×C418yescomplemented
95C2×#11758198C2×C418yescomplemented
96C2×#11758198D418yes—
97C22⋊C4×D61—232no—
98C2×C4×Dic61—24no—
99C2×C4×Dic61—24no—
100C2×C4×Dic61—24no—
101C2×C4×Dic61—24no—
102C2×C4×Dic61—42no—
103C2×C4×Dic61—42no—
104#14519684—24no—
105#14519684—24no—
106#14519684—24no—
107#14519684—42no—
108C25×C61C2311yescharacteristic
109C23×C4×C61—22no—
110C23×C4×C61—22no—
111C23×C4×C61—24no—
112C23×C4×C61—42no—
113C23×C4×C61C2×C414yescomplemented
114C23×C4×C61C2312yes—
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2312yes—
117C23×C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61C2×C414yes—
123C2×C22⋊C4×C61C2×C414yescomplemented
124#95×C61—24no—
125#95×C61—42no—
126C24×C61—22no—
127C24×C61—22no—
128C24×C61—22no—
129C24×C61—22no—
130C24×C61C22×C412yes—
131C24×C61C22×C412yes—
132C24×C61C22×C412yes—
133C24×C61C2×D412yes—
134C24×C61C2×D412yes—
135C24×C61#4112yes—
136C24×C61#4112yes—
137C24×C61C2411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—21no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—28no—
145C23×D61—28no—
146C23×D61—28no—
147C23×D61—28no—
148C23×D61—28no—
149C23×D61—28no—
150C23×D61—22no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—22no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—28no—
159C23×D61—28no—
160C23×D61—216no—
161C23×D61—216no—
162C23×D61—48no—
163C23×D61—48no—
164C23×D61—44no—
165C23×D61—44no—
166C23×D61—48no—
167C23×D61—48no—
168C23×D61—48no—
169C23×D61—48no—
170C23×D61—48no—
171C23×D61—48no—
172C23×D61—48no—
173C23×D61—48no—
174C23×D61C42116yescomplemented
175C23×D61C22×C412yes—
176C23×D61C22×C412yes—
177C23×D61C22×C412yes—
178C23×D61C22×C412yes—
179C23×D61C22×C412yes—
180C23×D61C22×C412yes—
181C23×D61C2×D414yes—
182C23×D61#4114yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—22no—
186C22×C4×C61—28no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—21no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—21no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—28no—
204C22×C4×C61—44no—
205C22×C4×C61—48no—
206C22×C4×C61—48no—
207C22×C4×C61C22×C414yes—
208C22×C4×C61C22×C414yes—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61C2×D414yes—
212C22×Dic61—22no—
213C22×Dic61—21no—
214C22×Dic61—22no—
215C22×Dic61—21no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—28no—
220C22×Dic61—21no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—21no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—28no—
231C22×Dic61—44no—
232C22×Dic61—48no—
233C22×Dic61—48no—
234C22×Dic61C22×C412yes—
235C22×Dic61C22×C414yes—
236C22×Dic61C22×C414yes—
237C22×Dic61C22×C412yes—
238C22×Dic61C2×D414yes—
239C22×Dic61C2×D414yes—
240C22×Dic61C2×D414yes—
241C2×C4×D61—216no—
242C2×C4×D61—216no—
243C2×C4×D61—48no—
244C2×C4×D61—48no—
245C2×C4×D61—48no—
246C2×C4×D61—48no—
247C2×C4×D61—48no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61—28no—
250C22⋊Dic61—28no—
251C22⋊Dic61C22⋊C4116yescomplemented
252#11758198—28no—
253#11758198—216no—
254#11758198—28no—
255#11758198—216no—
256#11758198—28no—
257#11758198—48no—
258#11758198C22⋊C4116yescomplemented
259C4×Dic61—48no—
260C4×Dic61—48no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—24no—
264C23×C61—24no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—24no—
268C23×C61—24no—
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—24no—
273C23×C61—24no—
274C23×C61—24no—
275C23×C61—24no—
276C23×C61—24no—
277C23×C61C2×C4214yes—
278C23×C61C2×C22⋊C414yes—
279C23×C61#11714yes—
280C23×C61C4×D414yes—
281C23×C61C4×D414yes—
282C23×C61C4×D414yes—
283C23×C61C4×D414yes—
284C23×C61C23×C411yescharacteristic
285C23×C61C23×C411yescharacteristic
286C23×C61C23×C411yescharacteristic
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C23×C61C22×D411yescharacteristic
290C23×C61C2×#4112yes—
291C23×C61C2×#4111yescharacteristic
292C23×C61C2×#4111yescharacteristic
293C23×C61H(5,𝔽2)12yes—
294C23×C61H(5,𝔽2)12yes—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—24no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—24no—
305C22×D61—24no—
306C22×D61—24no—
307C22×D61—24no—
308C22×D61—24no—
309C22×D61—24no—
310C22×D61—24no—
311C22×D61—24no—
312C22×D61—24no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—24no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—24no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—24no—
324C22×D61—24no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—232no—
328C22×D61—232no—
329C22×D61—416no—
330C22×D61—432no—
331C22×D61—416no—
332C22×D61—416no—
333C22×D61—416no—
334C22×D61—416no—
335C22×D61—432no—
336C22×D61—432no—
337C22×D61—432no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—42no—
346C22×D61C2×C4214yes—
347C22×D61C2×C4214yes—
348C22×D61C2×C22⋊C414yes—
349C22×D61#11714yes—
350C22×D61C4×D418yes—
351C22×D61C4×D418yes—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—24no—
355C2×C4×C61—24no—
356C2×C4×C61—22no—
357C2×C4×C61—24no—
358C2×C4×C61—24no—
359C2×C4×C61—24no—
360C2×C4×C61—24no—
361C2×C4×C61—22no—
362C2×C4×C61—24no—
363C2×C4×C61—24no—
364C2×C4×C61—22no—
365C2×C4×C61—416no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61—42no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61C2×C22⋊C414yescomplemented
377C2×Dic61—24no—
378C2×Dic61—22no—
379C2×Dic61—24no—
380C2×Dic61—22no—
381C2×Dic61—24no—
382C2×Dic61—24no—
383C2×Dic61—24no—
384C2×Dic61—24no—
385C2×Dic61—24no—
386C2×Dic61—24no—
387C2×Dic61—22no—
388C2×Dic61—24no—
389C2×Dic61—24no—
390C2×Dic61—22no—
391C2×Dic61—24no—
392C2×Dic61—22no—
393C2×Dic61—416no—
394C2×Dic61—42no—
395C2×Dic61—42no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61C2×C22⋊C414yescomplemented
401C2×Dic61C2×C22⋊C418yescomplemented
402C4×D61—432no—
403C22⋊C42—611nomaximal, Sylow
404C22×C61—24no—
405C22×C61—24no—
406C22×C61—28no—
407C22×C61—28no—
408C22×C61—24no—
409C22×C61—24no—
410C22×C61—28no—
411C22×C61—28no—
412C22×C61—24no—
413C22×C61—24no—
414C22×C61C4×C22⋊C418yescomplemented
415C22×C61C22×C4211yescharacteristic
416C22×C61C22×C22⋊C411yescharacteristic
417C22×C61C22×C22⋊C411yescharacteristic
418C22×C61C2×#11711yescharacteristic
419C22×C61C2×#11711yescharacteristic
420C22×C61C2×C4×D412yes—
421C22×C61C2×C4×D412yes—
422C22×C61C2×C4×D411yescharacteristic
423C22×C61C2×C4×D411yescharacteristic
424C22×C61C2×C4×D411yescharacteristic
425C22×C61C2×C4×D411yescharacteristic
426C22×C61#51812yes—
427C22×C61#51812yes—
428C22×C61#51811yescharacteristic
429C22×C61#51811yescharacteristic
430C22×C61D4212yes—
431C22×C61D4212yes—
432C22×C61#54612yes—
433C22×C61#54612yes—
434C22×C61#54612yes—
435C22×C61#54612yes—
436C22×C61#55112yes—
437C22×C61#55112yes—
438C2×D61—28no—
439C2×D61—24no—
440C2×D61—24no—
441C2×D61—24no—
442C2×D61—24no—
443C2×D61—28no—
444C2×D61—28no—
445C2×D61—28no—
446C2×D61—24no—
447C2×D61—24no—
448C2×D61—24no—
449C2×D61—24no—
450C2×D61—24no—
451C2×D61—464no—
452C2×D61—42no—
453C2×D61—44no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—42no—
457C2×D61—44no—
458C2×D61—44no—
459C2×D61—44no—
460C2×D61C4×C22⋊C418yescomplemented
461C4×C61—24no—
462C4×C61—44no—
463C4×C61—42no—
464C4×C61—44no—
465Dic61—28no—
466Dic61—24no—
467Dic61—42no—
468Dic61—44no—
469C23×C22⋊C4—611no—
470C23×C22⋊C4—611no—
471C2×#379—611no—
472C2×C4×C22⋊C4—612no—
473C2×C4×C22⋊C4—611no—
474C2×C4×C22⋊C4—611no—
475#1437—612no—
476#1437—612no—
477C22⋊#95—612no—
478C22⋊#95—611no—
479C22⋊#95D6111yescharacteristic, complemented
480C2×C61—28no—
481C2×C61C2×C4×C22⋊C411yescharacteristic
482C2×C61C2×C4×C22⋊C411yescharacteristic
483C2×C61#227311yescharacteristic
484C2×C61D4×C22⋊C411yescharacteristic
485C2×C61D4×C22⋊C412yes—
486C2×C61D4×C22⋊C411yescharacteristic
487C2×C61#234211yescharacteristic
488C2×C61#234211yescharacteristic
489C2×C61#234212yes—
490C2×C61#235812yes—
491C2×C61#235812yes—
492D61—28no—
493D61—44no—
494C26—611no—
495C24×C4—611no—
496C24×C4—612no—
497C24×C4C2×D6111yescharacteristic
498C22×C22⋊C4—611no—
499C22×C22⋊C4—611no—
500C22×C22⋊C4—611no—
501C22×C22⋊C4—618no—
502C22×C22⋊C4—611no—
503C22×C22⋊C4—611no—
504C22×C22⋊C4—612no—
505C22×C22⋊C4—611no—
506C22×C22⋊C4—612no—
507C22×C22⋊C4—612no—
508C22×C22⋊C4—618no—
509C22×C22⋊C4—1224no—
510C22×C22⋊C4—1224no—
511C22×C22⋊C4—1228no—
512C22×C22⋊C4C2×D6111yescharacteristic
513C22×C22⋊C4C2×D6111yescharacteristic
514C22×C42—612no—
515C22×C42—612no—
516#379—618no—
517C4×C22⋊C4—1228no—
518C4×C22⋊C4—1224no—
519C4×C22⋊C4—1224no—
520C2×#95—612no—
521C2×#95—612no—
522C2×#95—612no—
523C2×#95—612no—
524C2×#95C2×D6112yescomplemented
525C2×#95C2×D6112yescomplemented
526C61C22⋊C4211yescharacteristic, complemented, Sylow
527C25—611no—
528C25—611no—
529C25—614no—
530C25—614no—
531C25—614no—
532C25—1224no—
533C25—1224no—
534C25—1222no—
535C25—1222no—
536C25—1222no—
537C25—1222no—
538C25—2442no—
539C25—2442no—
540C25C22×D6111yescharacteristic
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—24no—
544C23×C4—42no—
545C23×C4—612no—
546C23×C4—611no—
547C23×C4—612no—
548C23×C4—611no—
549C23×C4—614no—
550C23×C4—618no—
551C23×C4—1224no—
552C23×C4—1224no—
553C23×C4—1224no—
554C23×C4—1224no—
555C23×C4—1224no—
556C23×C4—1222no—
557C23×C4—1222no—
558C23×C4—2442no—
559C23×C4—2442no—
560C23×C4—2442no—
561C23×C4C4×D6114yescomplemented
562C23×C4C22×D6112yes—
563C23×C4C22×D6111yescharacteristic
564C23×C4C22×D6112yes—
565C23×C4C22×D6111yescharacteristic
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4—614no—
572C2×C22⋊C4—614no—
573C2×C22⋊C4—614no—
574C2×C22⋊C4—618no—
575C2×C22⋊C4—614no—
576C2×C22⋊C4—614no—
577C2×C22⋊C4—614no—
578C2×C22⋊C4—618no—
579C2×C22⋊C4—614no—
580C2×C22⋊C4—618no—
581C2×C22⋊C4—618no—
582C2×C22⋊C4—12232no—
583C2×C22⋊C4—12232no—
584C2×C22⋊C4—1224no—
585C2×C22⋊C4—1224no—
586C2×C22⋊C4—1224no—
587C2×C22⋊C4—1224no—
588C2×C22⋊C4—1224no—
589C2×C22⋊C4—1224no—
590C2×C22⋊C4—1222no—
591C2×C22⋊C4—1222no—
592C2×C22⋊C4—1224no—
593C2×C22⋊C4—2442no—
594C2×C22⋊C4—2442no—
595C2×C22⋊C4C4×D6114yes—
596C2×C22⋊C4C4×D6114yescomplemented
597C2×C42—1224no—
598C2×C42—1224no—
599C2×C42—1224no—
600C2×C42—1224no—
601C2×C42—2442no—
602C2×C42—2442no—
603#95—24no—
604#95—42no—
605#95—1224no—
606#95—1224no—
607#95—1224no—
608#95—2442no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—612no—
614C24—612no—
615C24—612no—
616C24—614no—
617C24—614no—
618C24—612no—
619C24—612no—
620C24—612no—
621C24—6116no—
622C24—1228no—
623C24—1228no—
624C24—12216no—
625C24—12216no—
626C24—1221no—
627C24—1221no—
628C24—1221no—
629C24—1221no—
630C24—1222no—
631C24—1222no—
632C24—1222no—
633C24—1221no—
634C24—1221no—
635C24—1222no—
636C24—1221no—
637C24—1221no—
638C24—1222no—
639C24—1222no—
640C24—1228no—
641C24—1228no—
642C24—1228no—
643C24—1228no—
644C24—1228no—
645C24—1228no—
646C24—2448no—
647C24—2448no—
648C24—2444no—
649C24—2444no—
650C24—2448no—
651C24—2448no—
652C24—2448no—
653C24—2448no—
654C24—2448no—
655C24—2448no—
656C24—2448no—
657C24—2448no—
658C24C2×C4×D6112yes—
659C24C2×C4×D6112yes—
660C24C2×C4×D6112yes—
661C24D4×D6112yes—
662C24D4×D6112yes—
663C24#1175822412yes—
664C24#1175822612yes—
665C24C23×D6111yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—44no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—614no—
691C22×C4—612no—
692C22×C4—614no—
693C22×C4—614no—
694C22×C4—614no—
695C22×C4—614no—
696C22×C4—612no—
697C22×C4—12216no—
698C22×C4—12216no—
699C22×C4—1228no—
700C22×C4—1222no—
701C22×C4—1221no—
702C22×C4—1222no—
703C22×C4—1221no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1221no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—1221no—
714C22×C4—1222no—
715C22×C4—1222no—
716C22×C4—1222no—
717C22×C4—1228no—
718C22×C4—2448no—
719C22×C4—2448no—
720C22×C4—2448no—
721C22×C4—2448no—
722C22×C4—2448no—
723C22×C4—2444no—
724C22×C4—2448no—
725C22×C4—2448no—
726C22×C4C2×C4×D6114yes—
727C22×C4C2×C4×D6112yes—
728C22×C4C2×C4×D6114yes—
729C22×C4C2×C4×D6112yes—
730C22×C4D4×D6114yes—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—6116no—
734C22⋊C4—6116no—
735C22⋊C4—12216no—
736C22⋊C4—1228no—
737C22⋊C4—1228no—
738C22⋊C4—12216no—
739C22⋊C4—1228no—
740C22⋊C4—1228no—
741C22⋊C4—2448no—
742C42—2448no—
743C42—2448no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—22no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—614no—
761C23—614no—
762C23—614no—
763C23—618no—
764C23—618no—
765C23—614no—
766C23—12232no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1224no—
774C23—1224no—
775C23—1222no—
776C23—1222no—
777C23—1224no—
778C23—1224no—
779C23—1224no—
780C23—1224no—
781C23—1224no—
782C23—1224no—
783C23—1224no—
784C23—1224no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—1224no—
790C23—1224no—
791C23—1222no—
792C23—1222no—
793C23—1222no—
794C23—1222no—
795C23—1224no—
796C23—1224no—
797C23—1222no—
798C23—1222no—
799C23—12232no—
800C23—24416no—
801C23—24432no—
802C23—24432no—
803C23—24416no—
804C23—24432no—
805C23—24416no—
806C23—24416no—
807C23—24416no—
808C23—24432no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814C23—2442no—
815C23—2442no—
816C23—2442no—
817C23C42×D6114yes—
818C23C22⋊C4×D6114yes—
819C23#1451973514yes—
820C23#1451973714yes—
821C23#1451973714yes—
822C23#1451973914yes—
823C23#1451973914yes—
824C23C22×C4×D6111yescharacteristic
825C23C22×C4×D6111yescharacteristic
826C23C22×C4×D6111yescharacteristic
827C23C2×D4×D6112yes—
828C23C2×D4×D6111yescharacteristic
829C23C2×D4×D6111yescharacteristic
830C23#41×D6112yes—
831C23C2×#1175822411yescharacteristic
832C23C2×#1175822611yescharacteristic
833C23#1451982212yes—
834C23#1451982312yes—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—416no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—618no—
860C2×C4—614no—
861C2×C4—1224no—
862C2×C4—1222no—
863C2×C4—1224no—
864C2×C4—1222no—
865C2×C4—1224no—
866C2×C4—1224no—
867C2×C4—1224no—
868C2×C4—1224no—
869C2×C4—1224no—
870C2×C4—1224no—
871C2×C4—1222no—
872C2×C4—1224no—
873C2×C4—1224no—
874C2×C4—1222no—
875C2×C4—1224no—
876C2×C4—1222no—
877C2×C4—24432no—
878C2×C4—24416no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4—2442no—
885C2×C4C22⋊C4×D6114yescomplemented
886C22—28no—
887C22—28no—
888C22—24no—
889C22—28no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—28no—
895C22—24no—
896C22—618no—
897C22—1228no—
898C22—1228no—
899C22—1224no—
900C22—1228no—
901C22—1224no—
902C22—1224no—
903C22—1224no—
904C22—1224no—
905C22—1228no—
906C22—1224no—
907C22—1224no—
908C22—1224no—
909C22—1224no—
910C22—24464no—
911C22—2444no—
912C22—2444no—
913C22—2442no—
914C22—2444no—
915C22—2442no—
916C22—2442no—
917C22—2442no—
918C22—2444no—
919C22#1683960918yescomplemented
920C22C2×C42×D6111yescharacteristic
921C22C2×C22⋊C4×D6111yescharacteristic
922C22C2×C22⋊C4×D6111yescharacteristic
923C22#117×D6111yescharacteristic
924C22C2×#1451973511yescharacteristic
925C22C4×D4×D6112yes—
926C22C4×D4×D6112yes—
927C22C2×#1451973711yescharacteristic
928C22C2×#1451973711yescharacteristic
929C22C2×#1451973911yescharacteristic
930C22C2×#1451973911yescharacteristic
931C22#1684023412yes—
932C22#1684023412yes—
933C22#1684023511yescharacteristic
934C22#1684023611yescharacteristic
935C22#1684039412yes—
936C22#1684039612yes—
937C22#1684039912yes—
938C22#1684040112yes—
939C22#1684040312yes—
940C22#1684040412yes—
941C22#1684043512yes—
942C22#1684043912yes—
943C4—24no—
944C4—44no—
945C4—42no—
946C4—44no—
947C4—1228no—
948C4—1224no—
949C4—2444no—
950C4—2442no—
951C2—28no—
952C2—1228no—
953C2—2444no—
954C2C4×C22⋊C4×D6111yescharacteristic
955C2C2×#1683960911yescharacteristic
956C2#2144817111yescharacteristic
957C2#2144863511yescharacteristic
958C2#2144863712yes—
959C2#2144863911yescharacteristic
960C2#2144866111yescharacteristic
961C2#2144866511yescharacteristic
962C2#2144866612yes—
963C2#2144879512yes—
964C2#2144879912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC22⋊#95D61
hypocenterC61C22⋊C42
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic61C2semidirect
5. C2×C4×C22⋊Dic61C2semidirect
6. C2×#16839609C2semidirect
7. #21444055C2semidirect
8. #21444055C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
18. C22×#11758198C4semidirect
28. C2×C22⋊C4×D61C4semidirect
29. C22×C4×Dic61C22semidirect
30. C22×C4×Dic61C22semidirect
31. #16839617C4semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
37. C2×#14519684C22semidirect
38. C2×#14519684C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
61. C23×Dic61C2×C4semidirect
72. C22×C4×D61C2×C4semidirect
76. C2×C22⋊Dic61C2×C4semidirect
91. C2×#11758198C2×C4semidirect
92. C2×#11758198C2×C4semidirect
93. C2×#11758198C2×C4semidirect
94. C2×#11758198C2×C4semidirect
95. C2×#11758198C2×C4semidirect
113. C23×C4×C61C2×C4semidirect
123. C2×C22⋊C4×C61C2×C4semidirect
174. C23×D61C42semidirect
251. C22⋊Dic61C22⋊C4semidirect
258. #11758198C22⋊C4semidirect
376. C2×C4×C61C2×C22⋊C4semidirect
400. C2×Dic61C2×C22⋊C4semidirect
401. C2×Dic61C2×C22⋊C4semidirect
414. C22×C61C4×C22⋊C4semidirect
460. C2×D61C4×C22⋊C4semidirect
479. C22⋊#95D61semidirect
524. C2×#95C2×D61semidirect
525. C2×#95C2×D61semidirect
526. C61C22⋊C42semidirect
561. C23×C4C4×D61semidirect
596. C2×C22⋊C4C4×D61semidirect
885. C2×C4C22⋊C4×D61semidirect
919. C22#16839609semidirect

Maximal subgroups

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

subgroupindex
C23×#117581982
C22×C22⋊C4×D612
C2×#168396172
C2×C22⋊C4×Dic612
C2×C4×C22⋊Dic612
C2×#168396092
#214440552
#214440412
#214440402
C61×C22⋊#952
C22⋊C4261