Finite Group Databasebeta

← C4×#16839633 #29601178

Subgroups — C4×#16839633 #29601178

Order 15616.

2782 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D61C211yesmaximal, characteristic
2C2×#16839633C212yesmaximal
3C2×C4×#11758196C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic
5C2×C4×#11758198C211yesmaximal, characteristic
6#21444051C212yesmaximal, complemented
7#21444050C212yesmaximal, complemented
8#21444040C212yesmaximal
9C4×#14519684C211yesmaximal, characteristic, complemented
10C4×#14519684C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C4×D61C2212yes—
13C23×C4×D61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×#11758198C2212yes—
16C22×#11758198C2211yescharacteristic
17C22×#11758198C2211yescharacteristic
18C22×C4×Dic61C2212yes—
19C22×C4×Dic61C2211yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C2×C42×D61—24no—
23C2×C42×D61—24no—
24C2×C42×D61—24no—
25#16839633C4116yesdirect product factor
26C4×#11758196—24no—
27C4×#11758198—24no—
28C4×#11758198C418yescomplemented
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C22×C4⋊C4×C61C2212yes—
38C22×C42×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C4×C4⋊C4×C61—24no—
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2312yes—
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2312yes—
49C22×C4×D61—24no—
50C22×C4×D61—24no—
51C22×C4×D61—22no—
52C22×C4×D61—24no—
53C22×C4×D61—22no—
54C22×C4×D61—24no—
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—24no—
58C22×C4×D61—24no—
59C22×C4×D61C2×C418yes—
60C22×C4×D61C2×C414yes—
61C22×C4×D61D414yes—
62C22×C4×D61Q814yes—
63C2×#11758196—24no—
64C2×#11758196—24no—
65C2×#11758196C2×C418yescomplemented
66C2×#11758198—24no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198C2×C414yes—
70C2×#11758198C2×C418yes—
71C2×#11758198C2×C414yes—
72C2×#11758198C2×C418yes—
73C2×C4×Dic61—22no—
74C2×C4×Dic61—24no—
75C2×C4×Dic61—22no—
76C2×C4×Dic61—22no—
77C2×C4×Dic61—22no—
78C2×C4×Dic61—24no—
79C2×C4×Dic61—24no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61—22no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61C2×C414yescomplemented
84C2×C4×Dic61D414yes—
85C42×D61—232no—
86#14519684—24no—
87#14519684—24no—
88#14519684—24no—
89#14519684—24no—
90#14519684C2×C414yescomplemented
91#14519684C2×C414yescomplemented
92#14519684C2×C418yescomplemented
93#14519684C2×C418yescomplemented
94C23×C4×C61C2312yes—
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2312yes—
98C23×C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61—24no—
100C2×C4⋊C4×C61—24no—
101C2×C4⋊C4×C61C2×C418yescomplemented
102C2×C42×C61—22no—
103C2×C42×C61—22no—
104C2×C42×C61—22no—
105C2×C42×C61—22no—
106C2×C42×C61—22no—
107C2×C42×C61—22no—
108C2×C42×C61—22no—
109C2×C42×C61C2×C414yescomplemented
110C2×C42×C61D414yes—
111#95×C61—24no—
112C24×C61C2411yescharacteristic
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—21no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61C22×C412yes—
120C23×D61C22×C414yes—
121C23×D61C2×D412yes—
122C23×D61C2×Q812yes—
123C23×D61#4114yes—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61C22×C412yes—
142C22×C4×C61C22×C414yes—
143C22×C4×C61C22×C412yes—
144C22×C4×C61C22×C414yes—
145C22×C4×C61C22×C414yes—
146C22×C4×C61C22×C412yes—
147C22×C4×C61C2×D414yes—
148C22×C4×C61C2×D412yes—
149C22×C4×C61C2×D412yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×Q812yes—
152C22×C4×C61#4114yes—
153C22×C4×C61#4112yes—
154C22×C4×C61#4112yes—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61C22×C414yes—
177C22×Dic61C22×C412yes—
178C22×Dic61C22×C412yes—
179C22×Dic61C22×C414yes—
180C22×Dic61C22×C412yes—
181C22×Dic61C22×C414yes—
182C22×Dic61C2×D412yes—
183C22×Dic61C2×D414yes—
184C22×Dic61C2×Q812yes—
185C22×Dic61#4114yes—
186C2×C4×D61—216no—
187C2×C4×D61—216no—
188C2×C4×D61—216no—
189C2×C4×D61—216no—
190C2×C4×D61—216no—
191C2×C4×D61—216no—
192C2×C4×D61—28no—
193C2×C4×D61—28no—
194C2×C4×D61—28no—
195C2×C4×D61—28no—
196C2×C4×D61—28no—
197C2×C4×D61—28no—
198C2×C4×D61—216no—
199C2×C4×D61C4⋊C4116yescomplemented
200C4⋊C4×C61—216no—
201C42×C61—28no—
202C42×C61—28no—
203C42×C61—44no—
204#11758198—28no—
205#11758198—216no—
206#11758198C42116yescomplemented
207#11758196—216no—
208C4×Dic61—216no—
209C4×Dic61—28no—
210C4×Dic61—28no—
211C4×Dic61—44no—
212C23×C61C23×C411yescharacteristic
213C23×C61C23×C412yes—
214C23×C61C22×D411yescharacteristic
215C23×C61C22×D411yescharacteristic
216C23×C61C22×D411yescharacteristic
217C23×C61C22×Q811yescharacteristic
218C23×C61C2×#4112yes—
219C23×C61C2×#4111yescharacteristic
220C23×C61C2×#4111yescharacteristic
221C23×C61C2×#4112yes—
222C23×C61C2×#4112yes—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—24no—
226C22×D61—24no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—24no—
230C22×D61—24no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—24no—
236C22×D61—24no—
237C22×D61—24no—
238C22×D61—24no—
239C22×D61—24no—
240C22×D61—24no—
241C22×D61C2×C4214yes—
242C22×D61C2×C4⋊C414yes—
243C22×D61#11714yes—
244C22×D61C4×D418yes—
245C22×D61C4×Q818yes—
246C2×C4×C61—22no—
247C2×C4×C61—24no—
248C2×C4×C61—24no—
249C2×C4×C61—24no—
250C2×C4×C61—22no—
251C2×C4×C61—24no—
252C2×C4×C61—24no—
253C2×C4×C61—24no—
254C2×C4×C61—24no—
255C2×C4×C61—24no—
256C2×C4×C61—22no—
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—22no—
260C2×C4×C61—24no—
261C2×C4×C61—22no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61C2×C4214yescomplemented
269C2×C4×C61C2×C4⋊C414yes—
270C2×C4×C61C4×D418yes—
271C2×C4×C61C4×D414yes—
272C2×C4×C61C4×D414yes—
273C2×C4×C61#12014yes—
274C2×C4×C61C22⋊Q814yes—
275C2×C4×C61C22⋊Q814yes—
276C2×C4×C61#12314yes—
277C2×Dic61—22no—
278C2×Dic61—24no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—24no—
282C2×Dic61—24no—
283C2×Dic61—22no—
284C2×Dic61—24no—
285C2×Dic61—22no—
286C2×Dic61—24no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—24no—
291C2×Dic61—24no—
292C2×Dic61—24no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—24no—
296C2×Dic61—22no—
297C2×Dic61—24no—
298C2×Dic61—24no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61C2×C4214yescomplemented
306C2×Dic61C2×C4⋊C414yes—
307C2×Dic61C4×D418yes—
308C4×D61—264no—
309C4×D61—232no—
310C4×#385—611nomaximal, Sylow
311C22×C61C22×C4211yescharacteristic
312C22×C61C22×C4⋊C411yescharacteristic
313C22×C61C2×#11711yescharacteristic
314C22×C61C2×C4×D412yes—
315C22×C61C2×C4×D412yes—
316C22×C61C2×C4×D411yescharacteristic
317C22×C61C2×C4×D412yes—
318C22×C61C2×C4×D411yescharacteristic
319C22×C61C2×C4×Q812yes—
320C22×C61C4×#4111yescharacteristic
321C22×C61C4×#4111yescharacteristic
322C22×C61C4×#4112yes—
323C22×C61C4×#4112yes—
324C22×C61C2×#12011yescharacteristic
325C22×C61C2×C22⋊Q811yescharacteristic
326C22×C61C2×C22⋊Q811yescharacteristic
327C22×C61C2×#12311yescharacteristic
328C22×C61#52512yes—
329C22×C61#52512yes—
330C22×C61#52512yes—
331C22×C61#52912yes—
332C22×C61#52912yes—
333C22×C61#53312yes—
334C2×D61—24no—
335C2×D61—24no—
336C2×D61—24no—
337C2×D61—24no—
338C2×D61—24no—
339C2×D61—24no—
340C2×D61—28no—
341C2×D61—28no—
342C2×D61—28no—
343C2×D61—28no—
344C2×D61C4×C4⋊C418yescomplemented
345C4×C61—24no—
346C4×C61—28no—
347C4×C61—42no—
348C4×C61—44no—
349C4×C61#38518yescomplemented
350Dic61—24no—
351Dic61—24no—
352Dic61—28no—
353Dic61—42no—
354Dic61—44no—
355C23×C42—611no—
356C2×#385—612no—
357C2×C4×C4⋊C4—611no—
358C2×C4×C4⋊C4D6111yescharacteristic, complemented
359C2×C4×C22⋊C4—611no—
360C2×C4×C22⋊C4—611no—
361#1436—612no—
362#1436—612no—
363C22⋊#95—612no—
364C4×#95—611no—
365C4×#95—611no—
366C2×C61C2×C4×C4⋊C411yescharacteristic
367C2×C61C42×D411yescharacteristic
368C2×C61C42×D411yescharacteristic
369C2×C61C2×#38511yescharacteristic
370C2×C61#229011yescharacteristic
371C2×C61#229011yescharacteristic
372C2×C61#229611yescharacteristic
373C2×C61C4×#12012yes—
374C2×C61C4×#12312yes—
375C2×C61C4×C22⋊Q812yes—
376C2×C61C4×C22⋊Q812yes—
377D61—28no—
378C24×C4—611no—
379C24×C4—612no—
380C22×C4⋊C4—612no—
381C22×C4⋊C4C2×D6112yes—
382C22×C22⋊C4—611no—
383C22×C22⋊C4—611no—
384C22×C22⋊C4—612no—
385C22×C42—611no—
386C22×C42—611no—
387C22×C42—612no—
388C22×C42—611no—
389C22×C42—1224no—
390C22×C42—1224no—
391C22×C42—1224no—
392C22×C42C2×D6111yescharacteristic
393C22×C42C2×D6111yescharacteristic
394C22×C42C2×D6111yescharacteristic
395#385—6116no—
396C4×C4⋊C4—24no—
397C4×C4⋊C4—1224no—
398C4×C22⋊C4—618no—
399C4×C22⋊C4—1224no—
400C2×#95—612no—
401C2×#95—612no—
402C2×#95—611no—
403C2×#95—611no—
404C2×#95—612no—
405C2×#95—612no—
406C2×#95—612no—
407C2×#95—612no—
408C2×#95C2×D6112yes—
409C61C4×#38511yescharacteristic, complemented, Sylow
410C25—611no—
411C23×C4—611no—
412C23×C4—612no—
413C23×C4—611no—
414C23×C4—614no—
415C23×C4—614no—
416C23×C4—614no—
417C23×C4—612no—
418C23×C4—611no—
419C23×C4—618no—
420C23×C4—1224no—
421C23×C4—1224no—
422C23×C4—1224no—
423C23×C4—1224no—
424C23×C4—1224no—
425C23×C4—1222no—
426C23×C4—1222no—
427C23×C4—1222no—
428C23×C4—1224no—
429C23×C4—1222no—
430C23×C4C22×D6112yes—
431C23×C4C22×D6111yescharacteristic
432C23×C4C22×D6111yescharacteristic
433C23×C4C22×D6112yes—
434C23×C4C22×D6111yescharacteristic
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—618no—
438C2×C4⋊C4—1224no—
439C2×C4⋊C4—1224no—
440C2×C4⋊C4C4×D6118yescomplemented
441C2×C22⋊C4—614no—
442C2×C22⋊C4—618no—
443C2×C22⋊C4—614no—
444C2×C22⋊C4—618no—
445C2×C22⋊C4—1224no—
446C2×C22⋊C4—1224no—
447C2×C22⋊C4—1224no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—614no—
456C2×C42—614no—
457C2×C42—12232no—
458C2×C42—1224no—
459C2×C42—1224no—
460C2×C42—1222no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42—1224no—
464C2×C42—1222no—
465C2×C42—1222no—
466C2×C42—1222no—
467C2×C42—1222no—
468C2×C42C4×D6114yescomplemented
469C2×C42C22⋊D6114yes—
470#95—24no—
471#95—614no—
472#95—614no—
473#95—618no—
474#95—618no—
475#95—1224no—
476#95—1224no—
477#95—1224no—
478#95—1224no—
479C24—612no—
480C24—614no—
481C24—612no—
482C24—612no—
483C24—614no—
484C24—1221no—
485C24—1221no—
486C24—1222no—
487C24—1221no—
488C24—1222no—
489C24—1221no—
490C24C23×D6111yescharacteristic
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—612no—
509C22×C4—612no—
510C22×C4—614no—
511C22×C4—614no—
512C22×C4—612no—
513C22×C4—614no—
514C22×C4—612no—
515C22×C4—614no—
516C22×C4—6116no—
517C22×C4—614no—
518C22×C4—612no—
519C22×C4—12216no—
520C22×C4—12216no—
521C22×C4—12216no—
522C22×C4—12216no—
523C22×C4—12216no—
524C22×C4—12216no—
525C22×C4—1222no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1221no—
533C22×C4—1222no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—12216no—
537C22×C4—1228no—
538C22×C4—1228no—
539C22×C4—1228no—
540C22×C4—1228no—
541C22×C4—1228no—
542C22×C4—1228no—
543C22×C4—1221no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1221no—
552C22×C4—1222no—
553C22×C4C2×C4×D6112yes—
554C22×C4C2×C4×D6114yes—
555C22×C4C2×C4×D6112yes—
556C22×C4C2×C4×D6114yes—
557C22×C4C2×C4×D6114yes—
558C22×C4C2×C4×D6112yes—
559C22×C4#1175822214yes—
560C22×C4#1175822212yes—
561C22×C4D4×D6112yes—
562C22×C4D4×D6112yes—
563C22×C4Q8×D6112yes—
564C22×C4#1175822612yes—
565C22×C4C2×C22⋊D6114yes—
566C22×C4C2×C22⋊D6112yes—
567C4⋊C4—216no—
568C4⋊C4—12216no—
569C22⋊C4—6116no—
570C22⋊C4—1228no—
571C22⋊C4—12216no—
572C42—28no—
573C42—28no—
574C42—44no—
575C42—12216no—
576C42—1228no—
577C42—1228no—
578C42—2444no—
579C23—614no—
580C23—614no—
581C23—614no—
582C23—618no—
583C23—618no—
584C23—1224no—
585C23—1222no—
586C23—1224no—
587C23—1222no—
588C23—1222no—
589C23—1222no—
590C23—1224no—
591C23—1224no—
592C23—1222no—
593C23—1222no—
594C23—1222no—
595C23—1222no—
596C23—1224no—
597C23—1224no—
598C23—1224no—
599C23—1224no—
600C23—1224no—
601C23—1224no—
602C23C22×C4×D6111yescharacteristic
603C23C22×C4×D6112yes—
604C23C2×D4×D6111yescharacteristic
605C23C2×D4×D6111yescharacteristic
606C23C22×C22⋊D6111yescharacteristic
607C23C2×Q8×D6111yescharacteristic
608C23#41×D6112yes—
609C23#41×D6112yes—
610C23C2×#1175822211yescharacteristic
611C23C2×#1175822212yes—
612C23C2×#1175822611yescharacteristic
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—614no—
636C2×C4—614no—
637C2×C4—618no—
638C2×C4—12264no—
639C2×C4—1224no—
640C2×C4—1224no—
641C2×C4—1222no—
642C2×C4—1224no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1224no—
647C2×C4—1222no—
648C2×C4—1224no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1224no—
653C2×C4—1224no—
654C2×C4—1224no—
655C2×C4—12232no—
656C2×C4—1222no—
657C2×C4—1224no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1224no—
661C2×C4—1224no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4C42×D6114yescomplemented
669C2×C4C4⋊C4×D6114yes—
670C2×C4C4×C22⋊D6118yes—
671C2×C4C4×C22⋊D6114yes—
672C2×C4#1451973914yes—
673C2×C4#1451974514yes—
674C2×C4#1451975314yes—
675C2×C4#1451975514yes—
676C2×C4#1451976214yes—
677C22—618no—
678C22—1224no—
679C22—1224no—
680C22—1224no—
681C22—1224no—
682C22—1228no—
683C22—1228no—
684C22—1228no—
685C22—1228no—
686C22—1224no—
687C22—1224no—
688C22C2×C42×D6111yescharacteristic
689C22C2×C4⋊C4×D6111yescharacteristic
690C22#117×D6111yescharacteristic
691C22C4×D4×D6112yes—
692C22C4×D4×D6112yes—
693C22C2×C4×C22⋊D6111yescharacteristic
694C22C2×C4×C22⋊D6112yes—
695C22C2×#1451973911yescharacteristic
696C22C4×Q8×D6112yes—
697C22#1684023011yescharacteristic
698C22C4×#1175822211yescharacteristic
699C22C4×#1175822212yes—
700C22C4×#1175822612yes—
701C22C2×#1451974511yescharacteristic
702C22C2×#1451975311yescharacteristic
703C22C2×#1451975511yescharacteristic
704C22C2×#1451976211yescharacteristic
705C22#1684026912yes—
706C22#1684027112yes—
707C22#1684027112yes—
708C22#1684029012yes—
709C22#1684029912yes—
710C22#1684031612yes—
711C4—28no—
712C4—24no—
713C4—42no—
714C4—44no—
715C4—1224no—
716C4—1228no—
717C4—1224no—
718C4—2442no—
719C4—2444no—
720C4#1683963318yesdirect product factor
721C2—1228no—
722C2C4×C4⋊C4×D6111yescharacteristic
723C2C4×#1451973911yescharacteristic
724C2C42×C22⋊D6111yescharacteristic
725C2C2×#1683963311yescharacteristic
726C2#2144825611yescharacteristic
727C2#2144826011yescharacteristic
728C2#2144829911yescharacteristic
729C2C4×#1451974512yes—
730C2C4×#1451976212yes—
731C2C4×#1451975312yes—
732C2C4×#1451975512yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C22×C42
FrattiniC24C23×D61
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×C4×C4⋊C4D61
hypocenterC61C4×#385
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758196C2semidirect
6. #21444051C2semidirect
7. #21444050C2semidirect
9. C4×#14519684C2semidirect
10. C4×#14519684C2semidirect
11. C2×C4×C4⋊C4×C61C2semidirect
25. #16839633C4direct (N × H)
28. C4×#11758198C4semidirect
65. C2×#11758196C2×C4semidirect
83. C2×C4×Dic61C2×C4semidirect
90. #14519684C2×C4semidirect
91. #14519684C2×C4semidirect
92. #14519684C2×C4semidirect
93. #14519684C2×C4semidirect
101. C2×C4⋊C4×C61C2×C4semidirect
109. C2×C42×C61C2×C4semidirect
199. C2×C4×D61C4⋊C4semidirect
206. #11758198C42semidirect
268. C2×C4×C61C2×C42semidirect
305. C2×Dic61C2×C42semidirect
344. C2×D61C4×C4⋊C4semidirect
349. C4×C61#385semidirect
358. C2×C4×C4⋊C4D61semidirect
409. C61C4×#385semidirect
440. C2×C4⋊C4C4×D61semidirect
468. C2×C42C4×D61semidirect
668. C2×C4C42×D61semidirect
720. C4#16839633direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42×D612
C2×#168396332
C2×C4×#117581962
C2×C4×#117581982
#214440512
#214440502
#214440402
C4×#145196842
C2×C4×C4⋊C4×C612
C4×#38561