Finite Group Databasebeta

← C4×#16840639 #30602326

Subgroups — C4×#16840639 #30602326

Order 15616.

1482 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊#6923C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3C2×#16840639C214yesmaximal
4C4×C22⋊C4×D61C211yesmaximal, characteristic
5C22×C22⋊#6923C2212yes—
6C22×C22⋊#6923C2212yes—
7C22×C4×#6923—21no—
8C22×C4×#6923C412yescomplemented
9C4×C22⋊#6923—21no—
10C4×C22⋊#6923—21no—
11C4×C22⋊#6923—21no—
12C4×C22⋊#6923—21no—
13C4×C22⋊#6923—21no—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923C412yescomplemented
16C4×C22⋊#6923C412yescomplemented
17C2×(C2×#6923)⋊C4—21no—
18C2×(C2×#6923)⋊C4C412yescomplemented
19#16840639C4116yesdirect product factor
20C23×C4×D61C2211yescharacteristic
21C2×C22⋊C4×D61C2212yes—
22C2×C42×D61—21no—
23C22⋊C4×Dic61C412yescomplemented
24C4×#11758198—21no—
25C4×C22⋊Dic61C411yescharacteristic, complemented
26#16839609—21no—
27#95×D61—21no—
28C4×C22⋊C4×C61C411yescharacteristic, complemented
29C23×#6923—22no—
30C23×#6923C2×C414yes—
31C2×C22⋊#6923—22no—
32C2×C22⋊#6923—22no—
33C2×C22⋊#6923—22no—
34C2×C22⋊#6923—24no—
35C2×C22⋊#6923—24no—
36C2×C22⋊#6923C2×C418yes—
37C2×C22⋊#6923C2×C418yes—
38C2×C22⋊#6923C2×C414yes—
39C2×C4×#6923—22no—
40C2×C4×#6923—22no—
41C2×C4×#6923—22no—
42C2×C4×#6923—22no—
43C2×C4×#6923—44no—
44C2×C4×#6923—44no—
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—22no—
47(C2×#6923)⋊C4—22no—
48(C2×#6923)⋊C4—22no—
49C24×D61C2311yescharacteristic
50C23×Dic61C2×C411yescharacteristic
51C22×C4×D61—22no—
52C22×C4×D61—44no—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61Q811yescharacteristic
64C22×C4×D61Q811yescharacteristic
65C2×C22⋊Dic61C2×C412yes—
66C2×#11758198—22no—
67C22⋊C4×D61—24no—
68C22⋊C4×D61C2×C418yes—
69C2×C4×Dic61—21no—
70C2×C4×Dic61—22no—
71C42×D61—44no—
72#14519684—21no—
73#14519684—22no—
74C23×C4×C61C2×C411yescharacteristic
75C2×C22⋊C4×C61C2×C412yes—
76C2×C42×C61—21no—
77#95×C61—21no—
78C24×C61C22×C411yescharacteristic
79C23×D61—42no—
80C23×D61—42no—
81C23×D61C22×C411yescharacteristic
82C23×D61C22×C411yescharacteristic
83C23×D61C22×C414yes—
84C23×D61C2×D411yescharacteristic
85C23×D61C2×D411yescharacteristic
86C23×D61C2×D411yescharacteristic
87C23×D61C2×Q811yescharacteristic
88C23×D61#4114yes—
89C22×#6923—24no—
90C22×#6923—24no—
91C22×#6923—24no—
92C22×#6923—28no—
93C22×#6923—44no—
94C22×#6923—44no—
95C22×#6923—44no—
96C22×#6923—44no—
97C22×#6923C4218yescomplemented
98C22×C4×C61—22no—
99C22×C4×C61—42no—
100C22×C4×C61C4211yescharacteristic
101C22×C4×C61C4211yescharacteristic
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C4⋊C411yescharacteristic
105C22×C4×C61C4⋊C411yescharacteristic
106C22×Dic61—22no—
107C22×Dic61—42no—
108C22×Dic61C4211yescharacteristic
109C22×Dic61C4211yescharacteristic
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C4⋊C411yescharacteristic
113C22×Dic61C4⋊C411yescharacteristic
114C2×C4×D61—24no—
115C2×C4×D61—24no—
116C2×C4×D61—24no—
117C2×C4×D61—28no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61—42no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61—44no—
128C2×C4×D61—44no—
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C22⋊C411yescharacteristic
133C2×C4×D61C22⋊C411yescharacteristic
134C2×C4×D61C22⋊C411yescharacteristic
135C2×C4×D61C22⋊C411yescharacteristic
136C2×C4×D61C22⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138C2×C4×D61C4⋊C411yescharacteristic
139C2×C4×D61C4⋊C411yescharacteristic
140C2×C4×D61C4⋊C411yescharacteristic
141C2×C4×D61C4⋊C411yescharacteristic
142C2×C4×D61C4⋊C411yescharacteristic
143C2×C4×D61C4⋊C411yescharacteristic
144C2×C4×D61C4⋊C411yescharacteristic
145C22⋊#6923—24no—
146C22⋊#6923—28no—
147C22⋊#6923—28no—
148C22⋊#6923—28no—
149C22⋊#6923C4218yescomplemented
150C4×#6923—44no—
151C4×#6923—44no—
152C4×#6923—44no—
153C4×#6923—44no—
154C22⋊C4×C61—22no—
155C22⋊C4×C61C4214yescomplemented
156C42×C61—42no—
157C22⋊Dic61—22no—
158C22⋊Dic61C4214yescomplemented
159#11758198—28no—
160C4×Dic61—44no—
161C4×Dic61—42no—
162C23×C61—41no—
163C23×C61—41no—
164C23×C61C2×C4211yescharacteristic
165C23×C61C2×C4212yes—
166C23×C61C2×C22⋊C411yescharacteristic
167C23×C61C2×C4⋊C411yescharacteristic
168C23×C61#11712yes—
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—48no—
176C22×D61—48no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61C2×C4212yes—
184C22×D61C2×C4212yes—
185C22×D61C2×C22⋊C411yescharacteristic
186C22×D61C2×C22⋊C411yescharacteristic
187C22×D61C2×C4⋊C411yescharacteristic
188C22×D61C2×C4⋊C411yescharacteristic
189C22×D61#11712yes—
190C22×D61#11712yes—
191C22×D61C4×D414yes—
192C22×D61C4×D414yes—
193C22×D61C4×D414yes—
194C22×D61C4×Q814yes—
195C2×#6923—28no—
196C2×#6923—28no—
197C2×#6923—44no—
198C2×#6923—44no—
199C2×#6923—416no—
200C2×#6923—48no—
201C2×#6923—44no—
202C2×#6923—44no—
203C2×#6923—48no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—24no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61#9511yescharacteristic
214C2×C4×C61#9511yescharacteristic
215C2×C4×C61#9511yescharacteristic
216C2×C4×C61#9511yescharacteristic
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—24no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61#9511yescharacteristic
227C2×Dic61#9511yescharacteristic
228C2×Dic61#9511yescharacteristic
229C2×Dic61#9511yescharacteristic
230C4×D61—22no—
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—22no—
238C4×D61—22no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—416no—
246C4×D61#9914yes—
247C4×#342—611nomaximal, Sylow
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61C4311yescharacteristic
257C22×C61C2×#9511yescharacteristic
258C22×C61#37611yescharacteristic
259C22×C61C4×C22⋊C412yes—
260C22×C61C4×C4⋊C412yes—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—28no—
268C2×D61—24no—
269C2×D61—24no—
270C2×D61—28no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—44no—
274C2×D61—44no—
275C2×D61C4×C22⋊C412yes—
276C2×D61C4×C22⋊C412yes—
277C2×D61C4×C4⋊C412yes—
278C2×D61C4×C4⋊C412yes—
279C2×D61C2×#9912yes—
280C2×D61#41012yes—
281#6923—48no—
282#6923—48no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—44no—
287C4×C61#34212yescomplemented
288Dic61—21no—
289Dic61—21no—
290Dic61—21no—
291Dic61—44no—
292Dic61#34212yescomplemented
293C2×C4×C22⋊C4—611no—
294C2×C4×C22⋊C4—611no—
295C2×C4×C22⋊C4—611no—
296C2×#342—614no—
297C2×C61—22no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—22no—
301C2×C61C4×#9511yescharacteristic
302C2×C61C2×#34211yescharacteristic
303C2×C61#174011yescharacteristic
304D61—22no—
305D61—22no—
306D61—22no—
307D61C4×#9914yes—
308C24×C4—611no—
309C22×C22⋊C4—612no—
310C22×C22⋊C4—612no—
311C22×C22⋊C4—612no—
312C22×C42—612no—
313C22×C42—1221no—
314C22×C42—1221no—
315C4×C22⋊C4—612no—
316C4×C22⋊C4—612no—
317C4×C22⋊C4—611no—
318C4×C22⋊C4—612no—
319C4×C22⋊C4—1221no—
320C4×C22⋊C4—1221no—
321C4×C22⋊C4—1221no—
322C4×C22⋊C4—1221no—
323C4×C22⋊C4—1221no—
324C4×C22⋊C4—1221no—
325C4×C22⋊C4—1221no—
326C4×C22⋊C4—1221no—
327C4×C22⋊C4#692311yescharacteristic, complemented
328C2×#95—612no—
329C2×#95—1221no—
330C2×#95—1221no—
331#342—6116no—
332C61C4×#34211yescharacteristic, complemented, Sylow
333C25—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—614no—
348C23×C4—1222no—
349C23×C4—1222no—
350C23×C4—2444no—
351C23×C4C2×#692311yescharacteristic
352C2×C22⋊C4—618no—
353C2×C22⋊C4—614no—
354C2×C22⋊C4—612no—
355C2×C22⋊C4—618no—
356C2×C22⋊C4—618no—
357C2×C22⋊C4—1224no—
358C2×C22⋊C4—1222no—
359C2×C22⋊C4—1224no—
360C2×C22⋊C4—1224no—
361C2×C22⋊C4—1222no—
362C2×C22⋊C4—1222no—
363C2×C22⋊C4—1222no—
364C2×C22⋊C4C2×#692312yes—
365C2×C42—21no—
366C2×C42—1222no—
367C2×C42—1222no—
368C2×C42—1222no—
369C2×C42—1222no—
370C2×C42—1222no—
371C2×C42—1221no—
372C2×C42—2444no—
373C2×C42—2444no—
374C2×C42—2444no—
375#95—21no—
376#95—1222no—
377#95—1222no—
378#95—1222no—
379#95—1222no—
380#95—1222no—
381#95—1221no—
382C24—611no—
383C24—611no—
384C24—611no—
385C24—614no—
386C24—611no—
387C24—611no—
388C24—611no—
389C24—614no—
390C24—2442no—
391C24—2442no—
392C24C22×#692311yescharacteristic
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—618no—
418C22×C4—1224no—
419C22×C4—1224no—
420C22×C4—1224no—
421C22×C4—1228no—
422C22×C4—1224no—
423C22×C4—1224no—
424C22×C4—1228no—
425C22×C4—1224no—
426C22×C4—1222no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4—2442no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4—2442no—
434C22×C4—2442no—
435C22×C4—2442no—
436C22×C4—2444no—
437C22×C4—2444no—
438C22×C4—2442no—
439C22×C4—2444no—
440C22×C4—2444no—
441C22×C4—2444no—
442C22×C4—2444no—
443C22×C4C4×#692311yescharacteristic
444C22×C4C4×#692311yescharacteristic
445C22×C4C4⋊#692311yescharacteristic
446C22×C4C4⋊#692311yescharacteristic
447C22×C4C22⋊#692311yescharacteristic
448C22×C4C22⋊#692311yescharacteristic
449C22⋊C4—22no—
450C22⋊C4—618no—
451C22⋊C4—614no—
452C22⋊C4—1228no—
453C22⋊C4—1224no—
454C22⋊C4—1228no—
455C22⋊C4—1228no—
456C22⋊C4—1228no—
457C22⋊C4—1222no—
458C22⋊C4C4×#692314yescomplemented
459C42—42no—
460C42—2442no—
461C42—2444no—
462C42—2444no—
463C42—2444no—
464C42—2444no—
465C42—2444no—
466C23—41no—
467C23—41no—
468C23—611no—
469C23—612no—
470C23—611no—
471C23—611no—
472C23—611no—
473C23—612no—
474C23—614no—
475C23—614no—
476C23—612no—
477C23—612no—
478C23—614no—
479C23—614no—
480C23—1222no—
481C23—1222no—
482C23—1222no—
483C23—1222no—
484C23—1222no—
485C23—1222no—
486C23—2441no—
487C23—2441no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23—2441no—
492C23—2448no—
493C23—2448no—
494C23C2×C4×#692311yescharacteristic
495C23C2×C4×#692312yes—
496C23C2×C22⋊#692311yescharacteristic
497C23C2×C4⋊#692311yescharacteristic
498C23#1451985612yes—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—611no—
509C2×C4—614no—
510C2×C4—611no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—1222no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1228no—
526C2×C4—1228no—
527C2×C4—1224no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—24416no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2444no—
541C2×C4—2444no—
542C2×C4—2444no—
543C2×C4—2448no—
544C2×C4—24416no—
545C2×C4—2444no—
546C2×C4—2448no—
547C2×C4(C2×#6923)⋊C411yescharacteristic
548C2×C4(C2×#6923)⋊C411yescharacteristic
549C2×C4(C2×#6923)⋊C411yescharacteristic
550C2×C4(C2×#6923)⋊C411yescharacteristic
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—42no—
558C22—42no—
559C22—612no—
560C22—612no—
561C22—612no—
562C22—612no—
563C22—612no—
564C22—612no—
565C22—1228no—
566C22—1224no—
567C22—1224no—
568C22—1228no—
569C22—1221no—
570C22—1221no—
571C22—1221no—
572C22—1221no—
573C22—1221no—
574C22—1221no—
575C22—2444no—
576C22—2442no—
577C22—2442no—
578C22—2444no—
579C22C42×#692311yescharacteristic
580C22C2×(C2×#6923)⋊C411yescharacteristic
581C22#1684069811yescharacteristic
582C22C4×C22⋊#692312yes—
583C22C4×C4⋊#692312yes—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—44no—
588C4—612no—
589C4—1221no—
590C4—1221no—
591C4—1221no—
592C4—2444no—
593C4—2448no—
594C4—2448no—
595C4#1684063912yesdirect product factor
596C2—22no—
597C2—21no—
598C2—21no—
599C2—22no—
600C2—614no—
601C2—1222no—
602C2—1222no—
603C2—1222no—
604C2C4×(C2×#6923)⋊C411yescharacteristic
605C2C2×#1684063911yescharacteristic
606C2#2146151711yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC22×C61C43
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61C4×#342
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C22×C4×#6923C4semidirect
15. C4×C22⋊#6923C4semidirect
16. C4×C22⋊#6923C4semidirect
18. C2×(C2×#6923)⋊C4C4semidirect
19. #16840639C4direct (N × H)
23. C22⋊C4×Dic61C4semidirect
25. C4×C22⋊Dic61C4semidirect
28. C4×C22⋊C4×C61C4semidirect
97. C22×#6923C42semidirect
149. C22⋊#6923C42semidirect
155. C22⋊C4×C61C42semidirect
158. C22⋊Dic61C42semidirect
287. C4×C61#342semidirect
292. Dic61#342semidirect
327. C4×C22⋊C4#6923semidirect
332. C61C4×#342semidirect
458. C22⋊C4C4×#6923semidirect
595. C4#16840639direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊#69232
C2×#168406392
C4×C22⋊C4×D612
C4×#34261