Finite Group Databasebeta

← C4×#16839638 #29601158

Subgroups — C4×#16839638 #29601158

Order 15616.

3366 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C22×C42×D61C211yesmaximal, characteristic, complemented
3C2×#16839638C212yesmaximal
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
6#21444056C212yesmaximal, complemented
7#21444050C212yesmaximal, complemented
8#21444040C212yesmaximal, complemented
9C4×#14519684C211yesmaximal, characteristic, complemented
10C4×#14519684C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×C4×C22⋊D61—24no—
16C2×C4×C22⋊D61—24no—
17C2×C4×C22⋊D61C418yescomplemented
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×C4×Dic61C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C2×C42×D61—24no—
28C2×C42×D61—24no—
29C2×C42×D61—24no—
30#16839638C4116yesdirect product factor
31C4×#11758198—24no—
32C4×C22⋊Dic61—24no—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C2×#14519684C2212yes—
39C24×C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2212yes—
41C22×C42×C61C2211yescharacteristic
42C22×C42×C61C2211yescharacteristic
43C4×C22⋊C4×C61—24no—
44C2×#95×C61C2212yes—
45C24×D61C2311yescharacteristic
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—24no—
49C22×C22⋊D61C2×C414yes—
50C22×C22⋊D61C2×C418yes—
51C23×Dic61C2312yes—
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—22no—
59C22×C4×D61—24no—
60C22×C4×D61—22no—
61C22×C4×D61—24no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61C2×C414yes—
67C22×C4×D61C2×C418yescomplemented
68C22×C4×D61D414yes—
69C22×C4×D61D414yes—
70C4×C22⋊D61—232no—
71C2×#11758196—22no—
72C2×#11758196—22no—
73C2×#11758196C2×C414yescomplemented
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—24no—
77C2×C22⋊Dic61—24no—
78C2×C22⋊Dic61C2×C414yescomplemented
79C2×C22⋊Dic61C2×C418yescomplemented
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198C2×C414yes—
85C2×#11758198C2×C418yescomplemented
86C2×C4×Dic61—22no—
87C2×C4×Dic61—24no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61—24no—
92C2×C4×Dic61—24no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61C2×C414yescomplemented
97C2×C4×Dic61D414yescomplemented
98C42×D61—232no—
99#14519684—24no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103#14519684C2×C418yescomplemented
104#14519684C2×C418yescomplemented
105C25×C61C2311yescharacteristic
106C23×C4×C61—22no—
107C23×C4×C61—22no—
108C23×C4×C61—22no—
109C23×C4×C61—22no—
110C23×C4×C61—22no—
111C23×C4×C61—22no—
112C23×C4×C61C2×C414yescomplemented
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2312yes—
115C23×C4×C61C2312yes—
116C23×C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—24no—
118C2×C22⋊C4×C61—24no—
119C2×C22⋊C4×C61C2×C418yescomplemented
120C2×C42×C61—22no—
121C2×C42×C61—22no—
122C2×C42×C61—22no—
123C2×C42×C61—22no—
124C2×C42×C61—22no—
125C2×C42×C61D414yescomplemented
126#95×C61—24no—
127C24×C61—21no—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—22no—
132C24×C61—22no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—22no—
136C24×C61C22×C414yes—
137C24×C61C22×C412yes—
138C24×C61C2411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—22no—
144C23×D61—22no—
145C23×D61C22×C412yes—
146C23×D61C22×C414yes—
147C23×D61C2×D412yes—
148C23×D61C2×D412yes—
149C23×D61#4114yes—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—28no—
167C22×C4×C61—28no—
168C22×C4×C61—28no—
169C22×C4×C61—44no—
170C22×C4×C61—44no—
171C22×C4×C61—44no—
172C22×C4×C61—44no—
173C22×C4×C61C22×C414yes—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C22×C414yes—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C2×D414yes—
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2×D412yes—
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2×D412yes—
182C22×C4×C61#4114yes—
183C22×C4×C61#4112yes—
184C22×C4×C61#4112yes—
185C2×C22⋊D61—28no—
186C2×C22⋊D61—28no—
187C2×C22⋊D61—216no—
188C2×C22⋊D61—216no—
189C2×C22⋊D61C42116yescomplemented
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61C22×C414yes—
212C22×Dic61C22×C412yes—
213C22×Dic61C22×C414yes—
214C22×Dic61C22×C412yes—
215C22×Dic61C22×C412yes—
216C22×Dic61C22×C414yes—
217C22×Dic61C2×D412yes—
218C22×Dic61C2×D412yes—
219C22×Dic61C2×D414yes—
220C22×Dic61#4114yes—
221C2×C4×D61—216no—
222C2×C4×D61—216no—
223C2×C4×D61—216no—
224C2×C4×D61—216no—
225C2×C4×D61—216no—
226C2×C4×D61—28no—
227C2×C4×D61—28no—
228C2×C4×D61—216no—
229C2×C4×D61—28no—
230C2×C4×D61—28no—
231C2×C4×D61—28no—
232C2×C4×D61—28no—
233C2×C4×D61—216no—
234C2×C4×D61C22⋊C4116yescomplemented
235C22⋊C4×C61—216no—
236C42×C61—28no—
237C42×C61—44no—
238C22⋊Dic61—28no—
239C22⋊Dic61—216no—
240#11758198—28no—
241#11758198—216no—
242#11758196—28no—
243C4×Dic61—216no—
244C4×Dic61—28no—
245C4×Dic61—28no—
246C4×Dic61—44no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—24no—
250C23×C61—24no—
251C23×C61—24no—
252C23×C61—24no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—24no—
258C23×C61—24no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—42no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61—42no—
269C23×C61C2×C4214yescomplemented
270C23×C61C23×C411yescharacteristic
271C23×C61C23×C412yes—
272C23×C61C22×D411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C23×C61C22×D411yescharacteristic
275C23×C61C22×D411yescharacteristic
276C23×C61C2×#4112yes—
277C23×C61C2×#4111yescharacteristic
278C23×C61C2×#4111yescharacteristic
279C23×C61C2×#4112yes—
280C23×C61C2×#4112yes—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—24no—
284C22×D61—24no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—24no—
288C22×D61—24no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—24no—
294C22×D61—24no—
295C22×D61—24no—
296C22×D61—24no—
297C22×D61—24no—
298C22×D61—24no—
299C22×D61C2×C4214yes—
300C22×D61C2×C22⋊C414yes—
301C22×D61#11714yes—
302C22×D61C4×D418yes—
303C22×D61C4×D418yes—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—24no—
307C2×C4×C61—24no—
308C2×C4×C61—24no—
309C2×C4×C61—24no—
310C2×C4×C61—22no—
311C2×C4×C61—24no—
312C2×C4×C61—24no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—41no—
317C2×C4×C61—42no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—416no—
325C2×C4×C61C2×C22⋊C414yes—
326C2×C4×C61C4×D414yes—
327C2×C4×C61C4×D414yes—
328C2×C4×C61C4×D418yescomplemented
329C2×C4×C61#12014yes—
330C2×C4×C61#12114yes—
331C2×C4×C61#12114yes—
332C2×C4×C61#12314yes—
333C22⋊D61—232no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—24no—
339C2×Dic61—24no—
340C2×Dic61—24no—
341C2×Dic61—24no—
342C2×Dic61—22no—
343C2×Dic61—24no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—24no—
348C2×Dic61—24no—
349C2×Dic61—24no—
350C2×Dic61—22no—
351C2×Dic61—24no—
352C2×Dic61—24no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—24no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61—42no—
362C2×Dic61C2×C4214yescomplemented
363C2×Dic61C2×C22⋊C414yes—
364C2×Dic61C4×D418yescomplemented
365C4×D61—264no—
366C4×D61—232no—
367C4×#386—611nomaximal, Sylow
368C22×C61—24no—
369C22×C61—24no—
370C22×C61—24no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—44no—
376C22×C61—44no—
377C22×C61—44no—
378C22×C61—44no—
379C22×C61C22×C4211yescharacteristic
380C22×C61C22×C22⋊C411yescharacteristic
381C22×C61C2×#11711yescharacteristic
382C22×C61C2×C4×D412yes—
383C22×C61C2×C4×D412yes—
384C22×C61C2×C4×D412yes—
385C22×C61C2×C4×D411yescharacteristic
386C22×C61C2×C4×D411yescharacteristic
387C22×C61C2×C4×D412yes—
388C22×C61C4×#4112yes—
389C22×C61C4×#4111yescharacteristic
390C22×C61C4×#4111yescharacteristic
391C22×C61C4×#4112yes—
392C22×C61C2×#12011yescharacteristic
393C22×C61C2×#12111yescharacteristic
394C22×C61C2×#12111yescharacteristic
395C22×C61C2×#12311yescharacteristic
396C22×C61#52512yes—
397C22×C61#52512yes—
398C22×C61#52512yes—
399C22×C61#52912yes—
400C22×C61#52912yes—
401C22×C61#53212yes—
402C2×D61—24no—
403C2×D61—24no—
404C2×D61—24no—
405C2×D61—24no—
406C2×D61—24no—
407C2×D61—24no—
408C2×D61—28no—
409C2×D61—28no—
410C2×D61—28no—
411C2×D61—28no—
412C2×D61C4×C22⋊C418yescomplemented
413C4×C61—28no—
414C4×C61—42no—
415C4×C61—44no—
416C4×C61#38618yescomplemented
417Dic61—24no—
418Dic61—24no—
419Dic61—28no—
420Dic61—42no—
421Dic61—44no—
422C22×C4×D4—611no—
423C23×C42—611no—
424C2×#386—612no—
425C2×C4×C22⋊C4—611no—
426C2×C4×C22⋊C4—611no—
427C2×C4×C22⋊C4D6111yescharacteristic, complemented
428#1437—612no—
429#1436—612no—
430C22⋊#95—612no—
431C4×#95—611no—
432C4×#95—611no—
433C2×C61—44no—
434C2×C61C2×C4×C22⋊C411yescharacteristic
435C2×C61C42×D411yescharacteristic
436C2×C61C42×D411yescharacteristic
437C2×C61C2×#38611yescharacteristic
438C2×C61#229011yescharacteristic
439C2×C61#229011yescharacteristic
440C2×C61#229711yescharacteristic
441C2×C61C4×#12012yes—
442C2×C61C4×#12112yes—
443C2×C61C4×#12112yes—
444C2×C61C4×#12312yes—
445D61—28no—
446C23×D4—611no—
447C24×C4—611no—
448C24×C4—612no—
449C24×C4C2×D6111yescharacteristic
450C2×C4×D4—618no—
451C2×C4×D4—1224no—
452C2×C4×D4—1224no—
453C22×C4⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—612no—
456C22×C22⋊C4—611no—
457C22×C22⋊C4—612no—
458C22×C22⋊C4C2×D6112yes—
459C22×C42—611no—
460C22×C42—611no—
461C22×C42—612no—
462C22×C42—611no—
463C22×C42—1224no—
464C22×C42—1224no—
465C22×C42—1224no—
466C22×C42C2×D6111yescharacteristic
467C22×C42C2×D6111yescharacteristic
468#386—6116no—
469C4×C22⋊C4—24no—
470C4×C22⋊C4—1224no—
471C4×C22⋊C4—1224no—
472C2×#95—612no—
473C2×#95—612no—
474C2×#95—612no—
475C2×#95—612no—
476C2×#95—612no—
477C2×#95—612no—
478C2×#95C2×D6112yes—
479C61C4×#38611yescharacteristic, complemented, Sylow
480C25—611no—
481C25C22×D6111yescharacteristic
482C22×D4—614no—
483C22×D4—618no—
484C22×D4—1222no—
485C22×D4—1222no—
486C22×D4—1224no—
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—611no—
494C23×C4—612no—
495C23×C4—611no—
496C23×C4—614no—
497C23×C4—614no—
498C23×C4—614no—
499C23×C4—612no—
500C23×C4—611no—
501C23×C4—618no—
502C23×C4—1224no—
503C23×C4—1224no—
504C23×C4—1224no—
505C23×C4—1224no—
506C23×C4—1224no—
507C23×C4—1222no—
508C23×C4—1222no—
509C23×C4—1222no—
510C23×C4—1224no—
511C23×C4—1222no—
512C23×C4C4×D6114yescomplemented
513C23×C4C22×D6112yes—
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6112yes—
516C23×C4C22×D6111yescharacteristic
517C4×D4—12232no—
518C2×C4⋊C4—614no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1222no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—614no—
524C2×C22⋊C4—618no—
525C2×C22⋊C4—614no—
526C2×C22⋊C4—618no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—1224no—
531C2×C22⋊C4—1222no—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4C4×D6118yescomplemented
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—614no—
542C2×C42—614no—
543C2×C42—12232no—
544C2×C42—1224no—
545C2×C42—1224no—
546C2×C42—1222no—
547C2×C42—1222no—
548C2×C42—1222no—
549C2×C42—1224no—
550C2×C42—1222no—
551C2×C42—1222no—
552C2×C42—1222no—
553C2×C42—1222no—
554C2×C42C22⋊D6114yescomplemented
555#95—24no—
556#95—618no—
557#95—618no—
558#95—1224no—
559#95—1224no—
560#95—1224no—
561#95—1224no—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—22no—
567C24—22no—
568C24—21no—
569C24—22no—
570C24—21no—
571C24—612no—
572C24—614no—
573C24—612no—
574C24—612no—
575C24—614no—
576C24—1221no—
577C24—1221no—
578C24—1222no—
579C24—1221no—
580C24—1221no—
581C24—1222no—
582C24C2×C4×D6114yes—
583C24C2×C4×D6112yes—
584C24C23×D6111yescharacteristic
585C2×D4—6116no—
586C2×D4—1228no—
587C2×D4—1228no—
588C2×D4—12216no—
589C2×D4—12216no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—614no—
619C22×C4—612no—
620C22×C4—614no—
621C22×C4—6116no—
622C22×C4—614no—
623C22×C4—612no—
624C22×C4—12216no—
625C22×C4—12216no—
626C22×C4—12216no—
627C22×C4—12216no—
628C22×C4—12216no—
629C22×C4—12216no—
630C22×C4—1222no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1222no—
641C22×C4—1228no—
642C22×C4—1228no—
643C22×C4—12216no—
644C22×C4—1228no—
645C22×C4—1228no—
646C22×C4—1228no—
647C22×C4—1228no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4C2×C4×D6114yes—
659C22×C4C2×C4×D6112yes—
660C22×C4C2×C4×D6114yes—
661C22×C4C2×C4×D6112yes—
662C22×C4#1175822214yes—
663C22×C4#1175822212yes—
664C22×C4D4×D6112yes—
665C22×C4D4×D6112yes—
666C22×C4D4×D6112yes—
667C22×C4#1175822412yes—
668C22×C4C2×C22⋊D6114yes—
669C22×C4C2×C22⋊D6112yes—
670C4⋊C4—1228no—
671C22⋊C4—216no—
672C22⋊C4—1228no—
673C22⋊C4—12216no—
674C22⋊C4—1228no—
675C22⋊C4—12216no—
676C42—28no—
677C42—44no—
678C42—12216no—
679C42—1228no—
680C42—1228no—
681C42—2444no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—22no—
688C23—24no—
689C23—22no—
690C23—24no—
691C23—22no—
692C23—22no—
693C23—24no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—614no—
705C23—614no—
706C23—614no—
707C23—618no—
708C23—618no—
709C23—1224no—
710C23—1222no—
711C23—1222no—
712C23—1224no—
713C23—1224no—
714C23—1222no—
715C23—1222no—
716C23—1224no—
717C23—1222no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23—1224no—
722C23—1224no—
723C23—1224no—
724C23—1224no—
725C23—1224no—
726C23—1224no—
727C23C42×D6114yescomplemented
728C23C22×C4×D6111yescharacteristic
729C23C22×C4×D6112yes—
730C23C2×D4×D6111yescharacteristic
731C23C2×D4×D6111yescharacteristic
732C23C2×D4×D6111yescharacteristic
733C23C22×C22⋊D6111yescharacteristic
734C23#41×D6112yes—
735C23#41×D6112yes—
736C23C2×#1175822411yescharacteristic
737C23C2×#1175822211yescharacteristic
738C23C2×#1175822212yes—
739D4—12232no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—416no—
761C2×C4—614no—
762C2×C4—614no—
763C2×C4—618no—
764C2×C4—12264no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1224no—
768C2×C4—1224no—
769C2×C4—1224no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1224no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1224no—
779C2×C4—1224no—
780C2×C4—1224no—
781C2×C4—12232no—
782C2×C4—1222no—
783C2×C4—1224no—
784C2×C4—1224no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1224no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4C22⋊C4×D6114yes—
795C2×C4#1451973714yes—
796C2×C4C4×C22⋊D6114yes—
797C2×C4C4×C22⋊D6118yescomplemented
798C2×C4#1451974514yes—
799C2×C4#1451974814yes—
800C2×C4#1451975014yes—
801C2×C4#1451975914yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—618no—
814C22—1224no—
815C22—1224no—
816C22—1224no—
817C22—1224no—
818C22—1228no—
819C22—1228no—
820C22—1228no—
821C22—1228no—
822C22—1224no—
823C22—1224no—
824C22C2×C42×D6111yescharacteristic
825C22C2×C22⋊C4×D6111yescharacteristic
826C22#117×D6111yescharacteristic
827C22C4×D4×D6112yes—
828C22C4×D4×D6112yes—
829C22C4×D4×D6112yes—
830C22C2×#1451973711yescharacteristic
831C22C2×C4×C22⋊D6111yescharacteristic
832C22C2×C4×C22⋊D6112yes—
833C22C4×#1175822412yes—
834C22#1684023011yescharacteristic
835C22C4×#1175822211yescharacteristic
836C22C4×#1175822212yes—
837C22C2×#1451974511yescharacteristic
838C22C2×#1451974811yescharacteristic
839C22C2×#1451975011yescharacteristic
840C22C2×#1451975911yescharacteristic
841C22#1684026912yes—
842C22#1684027112yes—
843C22#1684027112yes—
844C22#1684029012yes—
845C22#1684029412yes—
846C22#1684030912yes—
847C4—28no—
848C4—42no—
849C4—44no—
850C4—1224no—
851C4—1228no—
852C4—1224no—
853C4—2442no—
854C4—2444no—
855C4#1683963818yesdirect product factor
856C2—44no—
857C2—1228no—
858C2C4×C22⋊C4×D6111yescharacteristic
859C2C4×#1451973711yescharacteristic
860C2C42×C22⋊D6111yescharacteristic
861C2C2×#1683963811yescharacteristic
862C2#2144825611yescharacteristic
863C2#2144826511yescharacteristic
864C2#2144830511yescharacteristic
865C2C4×#1451974512yes—
866C2C4×#1451974812yes—
867C2C4×#1451975012yes—
868C2C4×#1451975912yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C22×C42
FrattiniC24C23×D61
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C4×#386
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C42×D61C2semidirect
4. C2×C4×#11758198C2semidirect
5. C2×C4×C22⋊Dic61C2semidirect
6. #21444056C2semidirect
7. #21444050C2semidirect
8. #21444040C2semidirect
9. C4×#14519684C2semidirect
10. C4×#14519684C2semidirect
11. C2×C4×C22⋊C4×C61C2semidirect
17. C2×C4×C22⋊D61C4semidirect
30. #16839638C4direct (N × H)
67. C22×C4×D61C2×C4semidirect
73. C2×#11758196C2×C4semidirect
78. C2×C22⋊Dic61C2×C4semidirect
79. C2×C22⋊Dic61C2×C4semidirect
85. C2×#11758198C2×C4semidirect
96. C2×C4×Dic61C2×C4semidirect
97. C2×C4×Dic61D4semidirect
103. #14519684C2×C4semidirect
104. #14519684C2×C4semidirect
112. C23×C4×C61C2×C4semidirect
119. C2×C22⋊C4×C61C2×C4semidirect
125. C2×C42×C61D4semidirect
189. C2×C22⋊D61C42semidirect
234. C2×C4×D61C22⋊C4semidirect
269. C23×C61C2×C42semidirect
328. C2×C4×C61C4×D4semidirect
362. C2×Dic61C2×C42semidirect
364. C2×Dic61C4×D4semidirect
412. C2×D61C4×C22⋊C4semidirect
416. C4×C61#386semidirect
427. C2×C4×C22⋊C4D61semidirect
479. C61C4×#386semidirect
512. C23×C4C4×D61semidirect
535. C2×C22⋊C4C4×D61semidirect
554. C2×C42C22⋊D61semidirect
727. C23C42×D61semidirect
797. C2×C4C4×C22⋊D61semidirect
855. C4#16839638direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C22×C42×D612
C2×#168396382
C2×C4×#117581982
C2×C4×C22⋊Dic612
#214440562
#214440502
#214440402
C4×#145196842
C2×C4×C22⋊C4×C612
C4×#38661