Finite Group Databasebeta

← C4×#16839762 #29677806

Subgroups — C4×#16839762 #29677806

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic
2C2×#16839762C212yesmaximal
3C2×C4×#11758189C211yesmaximal, characteristic, complemented
4C4×C4⋊C4×D61C211yesmaximal, characteristic, complemented
5#21445651C212yesmaximal, complemented
6#21445643C212yesmaximal, complemented
7C4×#14519701C211yesmaximal, characteristic, complemented
8C4×#14519697C211yesmaximal, characteristic, complemented
9C4×#14519699C211yesmaximal, characteristic, complemented
10#21445537C212yesmaximal, complemented
11C4×#103×C61C211yesmaximal, characteristic, complemented
12C22×#11758226C2211yescharacteristic
13C22×#11758189C2212yes—
14C4×#11758226—24no—
15C4×#11758226C418yescomplemented
16C2×Q8×Dic61C2211yescharacteristic
17C2×C4×D244—21no—
18C2×C4×D244C2211yescharacteristic
19C2×#14519739—21no—
20C2×#14519739C2211yescharacteristic
21C2×#14519735—21no—
22C2×#14519735C2211yescharacteristic
23C2×C4⋊C4×D61C2212yes—
24C2×C42×D61—21no—
25C2×C42×D61—21no—
26C2×C42×D61C2211yescharacteristic
27#16839762C4116yesdirect product factor
28C2×#14519701C2212yes—
29C2×#14519699C2212yes—
30C2×#14519697C2212yes—
31C4×#11758189—24no—
32C2×#14519687C2212yes—
33C2×C4×#92418C2211yescharacteristic
34C4⋊C4×Dic61C2212yes—
35C4×#11758196—21no—
36C4×C4⋊Dic61C2211yescharacteristic
37#16839613—21no—
38#95×D61—21no—
39#16839525C2212yes—
40#16839524C2212yes—
41#16839524C2212yes—
42C2×C4×Q8×C61C2211yescharacteristic
43C2×#103×C61C2212yes—
44C2×C4×C8×C61C2211yescharacteristic
45C4×C4⋊C4×C61C2211yescharacteristic
46C61×#340C2212yes—
47C2×#11758226—22no—
48C2×#11758226—24no—
49C2×#11758226C2×C414yes—
50C2×#11758226C2×C418yes—
51C22×D244—21no—
52C22×D244C2311yescharacteristic
53C22×C4×D61—21no—
54C22×C4×D61—22no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758189—24no—
61C2×#11758189—24no—
62C2×#11758189C2×C418yescomplemented
63C22×#92418C2312yes—
64Q8×Dic61—22no—
65Q8×Dic61C2×C414yescomplemented
66C4×D244—28no—
67C4×D244—22no—
68C4×D244C2×C414yescomplemented
69#14519739—28no—
70#14519739—22no—
71#14519739C2×C414yescomplemented
72#14519735—22no—
73#14519735—28no—
74#14519735C2×C414yes—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61C2312yes—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—22no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61C2×C418yescomplemented
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C42×D61—28no—
92C42×D61—44no—
93C42×D61C2×C414yes—
94C42×D61D414yes—
95#14519701C2×C418yescomplemented
96#14519699C2×C418yescomplemented
97#14519697C2×C418yescomplemented
98#14519687—24no—
99C4×#92418—22no—
100#14519684—21no—
101#14519684—22no—
102C22×Q8×C61C2311yescharacteristic
103C22×C8×C61C2312yes—
104C4×Q8×C61—22no—
105C4×Q8×C61C2×C414yescomplemented
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61C2312yes—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C42×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112#103×C61C2×C418yescomplemented
113C4×C8×C61—22no—
114#95×C61—21no—
115C23×D61—21no—
116C23×D61C2×D411yescharacteristic
117C2×Q8×C61—21no—
118C2×Q8×C61—22no—
119C2×Q8×C61C22×C414yes—
120C2×Q8×C61C22×C412yes—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—21no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2411yescharacteristic
127C22×Dic61—22no—
128C22×Dic61—21no—
129C22×Dic61C2×D411yescharacteristic
130C22×Dic61C2×D411yescharacteristic
131C22×Dic61C2×D411yescharacteristic
132#11758226—28no—
133#11758226—216no—
134#11758226C42116yescomplemented
135C2×D244—24no—
136C2×D244—28no—
137C2×D244—21no—
138C2×D244—22no—
139C2×D244C22×C414yes—
140C2×D244C22×C412yes—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—24no—
144C2×C4×D61—28no—
145C2×C4×D61—28no—
146C2×C4×D61—24no—
147C2×C4×D61—24no—
148C2×C4×D61—42no—
149C2×C4×D61—44no—
150C2×C4×D61—44no—
151C2×C4×D61—44no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61C22⋊C414yes—
155C2×C4×D61C22⋊C414yes—
156C2×C4×D61C22×C412yes—
157C2×C4×D61C22×C414yes—
158C2×C4×D61C2×D412yes—
159C2×C4×D61#4114yes—
160C2×C8×C61—22no—
161C2×C8×C61—22no—
162C2×C8×C61C22×C414yes—
163C4⋊C4×C61—24no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61C22×C414yes—
167C4⋊C4×C61C22×C412yes—
168C42×C61—24no—
169C42×C61—42no—
170C42×C61C22×C412yes—
171C42×C61C2×D412yes—
172#11758198—24no—
173#11758198—24no—
174#11758198—24no—
175C4⋊Dic61—21no—
176C4⋊Dic61—22no—
177C4⋊Dic61—24no—
178C4⋊Dic61C22×C414yes—
179C4⋊Dic61C22×C412yes—
180#11758196—28no—
181C4×Dic61—24no—
182C4×Dic61—24no—
183C4×Dic61—44no—
184C4×Dic61—42no—
185C4×Dic61C22⋊C414yes—
186C4×Dic61C22⋊C414yes—
187C4×Dic61C22×C412yes—
188C4×Dic61C2×D412yes—
189C2×#92418—22no—
190C2×#92418—22no—
191C2×#92418C22×C414yes—
192#11758189—216no—
193C23×C61C22×D411yescharacteristic
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—22no—
197C22×D61—22no—
198C22×D61—24no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—42no—
202C22×D61C2×C22⋊C412yes—
203C22×D61C4×D414yes—
204Q8×C61—22no—
205Q8×C61—24no—
206Q8×C61C2×C4214yescomplemented
207C2×C4×C61—22no—
208C2×C4×C61—24no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—24no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61C2×C22⋊C412yes—
216C2×C4×C61C2×C22⋊C412yes—
217C2×C4×C61AGL(1,ℤ/8)12yes—
218C2×C4×C61#13712yes—
219C2×C4×C61C23×C411yescharacteristic
220C2×C4×C61C23×C412yes—
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C2×#4112yes—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—24no—
228C2×Dic61—42no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—42no—
232C2×Dic61C2×C22⋊C412yes—
233C2×Dic61C2×C22⋊C412yes—
234C2×Dic61C2×C22⋊C412yes—
235C2×Dic61C4×D414yes—
236D244—216no—
237D244—22no—
238D244—24no—
239D244C2×C4214yescomplemented
240C4×D61—28no—
241C4×D61—216no—
242C4×D61—44no—
243C4×D61—48no—
244C4×D61—416no—
245C4×D61—48no—
246C4×D61C2×C4214yes—
247C4×D61#11714yes—
248C4×D61C4×D418yes—
249C8×C61—24no—
250#92418—24no—
251C4×#417—611nomaximal, Sylow
252C22×C61C22×C22⋊C411yescharacteristic
253C22×C61C2×C4×D412yes—
254C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C61C2×#13711yescharacteristic
256C22×C61#57512yes—
257C2×D61—22no—
258C2×D61—22no—
259C2×D61—24no—
260C2×D61—24no—
261C2×D61—24no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—44no—
265C2×D61—44no—
266C2×D61C4×C22⋊C414yes—
267C4×C61—22no—
268C4×C61—24no—
269C4×C61—42no—
270C4×C61—44no—
271C4×C61#41714yescomplemented
272C4×C61C22×C4211yescharacteristic
273C4×C61C2×#11711yescharacteristic
274C4×C61C2×C4×D412yes—
275Dic61—22no—
276Dic61—22no—
277Dic61—42no—
278Dic61—44no—
279Dic61C4×C22⋊C414yes—
280C2×C4×#41—611no—
281C2×#417—612no—
282C2×C4×M16—611no—
283C2×C4×C4⋊C4—611no—
284#1763—612no—
285#1762—612no—
286C4×#103—611no—
287C4×#103D6111yescharacteristic, complemented
288C4×#102—611no—
289C4×#102—611no—
290#1736—612no—
291C2×C61C2×C4×C22⋊C411yescharacteristic
292C2×C61C2×#41711yescharacteristic
293C2×C61#289611yescharacteristic
294C2×C61C4×AGL(1,ℤ/8)12yes—
295C2×C61C4×#13712yes—
296D61—24no—
297D61—44no—
298C22×#41—611no—
299C22×M16—612no—
300C4×#41—618no—
301C4×#41—1224no—
302C2×C4×Q8—611no—
303C2×C4×Q8C2×D6111yescharacteristic
304C2×C4×D4—611no—
305C2×C4×D4—611no—
306C2×C4×D4—1221no—
307C2×C4×D4—1221no—
308C2×#117—611no—
309C2×#117—1221no—
310C22×C4⋊C4—612no—
311C22×C42—611no—
312C22×C42—1221no—
313C22×C42—1221no—
314#417—6116no—
315C2×#103—612no—
316C2×#103C2×D6112yes—
317C2×#102—612no—
318C2×#102—612no—
319C4×M16—1224no—
320C2×#97—612no—
321C2×C4×C8—611no—
322C2×C4×C8C2×D6111yescharacteristic
323C4×C4⋊C4—612no—
324C4×C4⋊C4—611no—
325C4×C4⋊C4—1221no—
326C4×C4⋊C4—1221no—
327C4×C4⋊C4C2×D6111yescharacteristic
328C2×#95—1221no—
329#340—612no—
330#340—612no—
331#340—612no—
332#340C2×D6112yes—
333C61C4×#41711yescharacteristic, complemented, Sylow
334C2×#41—614no—
335C2×#41—618no—
336C2×#41—1222no—
337C2×#41—1224no—
338C22×Q8C22×D6111yescharacteristic
339C22×D4—611no—
340C22×D4—1221no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—1221no—
345C23×C4—1221no—
346C23×C4—1222no—
347C23×C4—1221no—
348C2×M16—618no—
349C2×M16—1224no—
350C2×M16—1224no—
351C22×C8—612no—
352C22×C8C22×D6112yes—
353C4×Q8—22no—
354C4×Q8—614no—
355C4×Q8—1222no—
356C4×Q8C4×D6114yescomplemented
357C4×D4—614no—
358C4×D4—614no—
359C4×D4—1228no—
360C4×D4—1222no—
361C4×D4—1228no—
362C4×D4—1222no—
363#117—614no—
364#117—1228no—
365#117—1222no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—612no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—618no—
370C2×C4⋊C4—1224no—
371C2×C4⋊C4—1222no—
372C2×C4⋊C4—1221no—
373C2×C4⋊C4C22×D6112yes—
374C2×C4⋊C4C22×D6111yescharacteristic
375C2×C22⋊C4—1221no—
376C2×C22⋊C4—1221no—
377C2×C22⋊C4—1221no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—614no—
384C2×C42—614no—
385C2×C42—1228no—
386C2×C42—1221no—
387C2×C42—1221no—
388C2×C42—1222no—
389C2×C42—1221no—
390C2×C42—2444no—
391C2×C42C22×D6111yescharacteristic
392#103—618no—
393#103C4×D6118yescomplemented
394#102—618no—
395#102—618no—
396#97—1224no—
397C4×C8—22no—
398C4×C8—1222no—
399#95—21no—
400#95—1222no—
401#95—1221no—
402C24—611no—
403C24—1221no—
404#41—6116no—
405#41—1228no—
406#41—12216no—
407C2×Q8—21no—
408C2×Q8—22no—
409C2×Q8C2×C4×D6114yes—
410C2×Q8C2×C4×D6112yes—
411C2×D4—614no—
412C2×D4—612no—
413C2×D4—1224no—
414C2×D4—1228no—
415C2×D4—1221no—
416C2×D4—1222no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—611no—
421C22×C4—612no—
422C22×C4—614no—
423C22×C4—612no—
424C22×C4—614no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—614no—
428C22×C4—614no—
429C22×C4—1224no—
430C22×C4—1228no—
431C22×C4—1224no—
432C22×C4—1228no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1221no—
437C22×C4—1224no—
438C22×C4—2442no—
439C22×C4—2444no—
440C22×C4—2444no—
441C22×C4—2444no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4D4×D6111yescharacteristic
445C22×C4D4×D6111yescharacteristic
446C22×C4C23×D6111yescharacteristic
447M16—12216no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—614no—
451C2×C8—1222no—
452C2×C8—1222no—
453C2×C8C2×C4×D6114yes—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—24no—
457C4⋊C4—614no—
458C4⋊C4—612no—
459C4⋊C4—1228no—
460C4⋊C4—1224no—
461C4⋊C4—1221no—
462C4⋊C4—1222no—
463C4⋊C4C2×C4×D6114yes—
464C4⋊C4C2×C4×D6112yes—
465C22⋊C4—1224no—
466C22⋊C4—1224no—
467C22⋊C4—1224no—
468C42—24no—
469C42—42no—
470C42—612no—
471C42—612no—
472C42—614no—
473C42—614no—
474C42—1224no—
475C42—1224no—
476C42—2444no—
477C42—2442no—
478C42C2×C4×D6112yes—
479C42D4×D6112yes—
480C23—612no—
481C23—614no—
482C23—1221no—
483C23—1221no—
484C23—1222no—
485C23—1222no—
486C23—1224no—
487C23—2441no—
488C23—2441no—
489C23—2442no—
490C23C2×D4×D6111yescharacteristic
491Q8—22no—
492Q8—24no—
493Q8C42×D6114yescomplemented
494D4—614no—
495D4—12216no—
496D4—1222no—
497D4—1224no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—612no—
507C2×C4—614no—
508C2×C4—614no—
509C2×C4—614no—
510C2×C4—618no—
511C2×C4—612no—
512C2×C4—612no—
513C2×C4—12216no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1222no—
517C2×C4—1228no—
518C2×C4—1222no—
519C2×C4—1224no—
520C2×C4—2444no—
521C2×C4—2448no—
522C2×C4—24416no—
523C2×C4—2442no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2442no—
527C2×C4—2448no—
528C2×C4C22⋊C4×D6112yes—
529C2×C4C22⋊C4×D6112yes—
530C2×C4#1451980412yes—
531C2×C4#1451980912yes—
532C2×C4C22×C4×D6111yescharacteristic
533C2×C4C22×C4×D6112yes—
534C2×C4C2×D4×D6111yescharacteristic
535C2×C4#41×D6112yes—
536C8—24no—
537C8—1224no—
538C22—614no—
539C22—1224no—
540C22—1224no—
541C22—1222no—
542C22—1222no—
543C22—1224no—
544C22—2444no—
545C22—2444no—
546C22—2442no—
547C22—2442no—
548C22C2×C22⋊C4×D6111yescharacteristic
549C22C4×D4×D6112yes—
550C22C2×#1451980411yescharacteristic
551C22C2×#1451980911yescharacteristic
552C22#1684055912yes—
553C4—24no—
554C4—22no—
555C4—44no—
556C4—42no—
557C4—614no—
558C4—1222no—
559C4—1222no—
560C4—2444no—
561C4—2442no—
562C4#1683976214yesdirect product factor
563C4C2×C42×D6111yescharacteristic
564C4#117×D6111yescharacteristic
565C4C4×D4×D6112yes—
566C2—1224no—
567C2—2444no—
568C2C4×C22⋊C4×D6111yescharacteristic
569C2C2×#1683976211yescharacteristic
570C2#2145433411yescharacteristic
571C2C4×#1451980412yes—
572C2C4×#1451980912yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC4×#103×C61C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenterC4×#103D61
hypocenterC61C4×#417
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758189C2semidirect
4. C4×C4⋊C4×D61C2semidirect
5. #21445651C2semidirect
6. #21445643C2semidirect
7. C4×#14519701C2semidirect
8. C4×#14519697C2semidirect
9. C4×#14519699C2semidirect
10. #21445537C2semidirect
11. C4×#103×C61C2semidirect
15. C4×#11758226C4semidirect
27. #16839762C4direct (N × H)
62. C2×#11758189C2×C4semidirect
65. Q8×Dic61C2×C4semidirect
68. C4×D244C2×C4semidirect
71. #14519739C2×C4semidirect
80. C4⋊C4×D61C2×C4semidirect
95. #14519701C2×C4semidirect
96. #14519699C2×C4semidirect
97. #14519697C2×C4semidirect
105. C4×Q8×C61C2×C4semidirect
112. #103×C61C2×C4semidirect
134. #11758226C42semidirect
206. Q8×C61C2×C42semidirect
239. D244C2×C42semidirect
271. C4×C61#417semidirect
287. C4×#103D61semidirect
333. C61C4×#417semidirect
356. C4×Q8C4×D61semidirect
393. #103C4×D61semidirect
493. Q8C42×D61semidirect
562. C4#16839762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
C2×#168397622
C2×C4×#117581892
C4×C4⋊C4×D612
#214456512
#214456432
C4×#145197012
C4×#145196972
C4×#145196992
#214455372
C4×#103×C612
C4×#41761