Finite Group Databasebeta

← C2×#21446174 #29681353

Subgroups — C2×#21446174 #29681353

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758201C211yesmaximal, characteristic
2C22×#14519701C211yesmaximal, characteristic, complemented
3C22×#14519697C211yesmaximal, characteristic
4C2×#16839664C211yesmaximal, characteristic
5#21446174C218yesmaximal, direct product factor
6C2×#16839524C211yesmaximal, characteristic, complemented
7C2×#16839517C211yesmaximal, characteristic, complemented
8C22×C4×Q8×C61C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C22×#11758201—24no—
11C22×#11758201—24no—
12C22×#11758201C418yescomplemented
13C22×#11758201C2214yes—
14C23×#92418C2211yescharacteristic
15C23×#92418C2211yescharacteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758198—21no—
18C22×#11758198—21no—
19C2×#14519701—24no—
20C2×#14519701C2214yescomplemented
21C2×#14519697—24no—
22C2×#14519697C2214yes—
23#16839664—22no—
24#16839664C2214yes—
25#16839524C2214yescomplemented
26#16839517C2214yescomplemented
27C23×Q8×C61C2211yescharacteristic
28C2×C4×Q8×C61—24no—
29C2×C4×Q8×C61—24no—
30C2×C4×Q8×C61—22no—
31C2×C4×Q8×C61C2214yescomplemented
32C22×C4⋊C4×C61—21no—
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C42×C61—21no—
35C22×C42×C61C2211yescharacteristic
36C24×D61—21no—
37C22×D244—22no—
38C22×D244—22no—
39C22×D244—22no—
40C22×D244—22no—
41C22×D244—21no—
42C22×D244—22no—
43C22×D244C2×C414yes—
44C22×D244C2312yes—
45C23×Dic61—21no—
46C2×#11758201—232no—
47C2×#11758201—28no—
48C2×#11758201—28no—
49C2×#11758201C2×C4116yescomplemented
50C22×#92418—22no—
51C22×#92418—22no—
52C22×#92418—22no—
53C22×#92418—22no—
54C22×#92418—22no—
55C22×#92418C2×C414yes—
56C22×#92418C2312yes—
57C22×#92418C2312yes—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61—22no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61C2312yes—
62C2×#11758198—24no—
63C2×#11758198—24no—
64C2×#11758198—44no—
65C2×#11758198—44no—
66#14519701—28no—
67#14519697—28no—
68C22×Q8×C61—22no—
69C22×Q8×C61—21no—
70C22×Q8×C61—22no—
71C22×Q8×C61—22no—
72C22×Q8×C61C2×C414yes—
73C22×Q8×C61D414yes—
74C22×Q8×C61D414yes—
75C22×Q8×C61C2312yes—
76C23×C4×C61—21no—
77C23×C4×C61—21no—
78C23×C4×C61D411yescharacteristic
79C23×C4×C61D411yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C4×Q8×C61—216no—
82C4×Q8×C61—28no—
83C4×Q8×C61—28no—
84C2×C4⋊C4×C61—28no—
85C2×C4⋊C4×C61—24no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61D414yes—
89C2×C4⋊C4×C61C2312yes—
90C2×C42×C61—28no—
91C2×C42×C61—24no—
92C2×C42×C61—22no—
93C2×C42×C61—22no—
94C2×C42×C61D412yes—
95C2×C42×C61C2312yes—
96C24×C61C2×D411yescharacteristic
97C23×D61—24no—
98C23×D61—22no—
99C23×D61—42no—
100C23×D61—42no—
101C23×D61—42no—
102C23×D61—42no—
103C23×D61—42no—
104C23×D61—42no—
105C2×Q8×C61—24no—
106C2×Q8×C61—28no—
107C2×Q8×C61—24no—
108C2×Q8×C61—24no—
109C2×Q8×C61—28no—
110C2×Q8×C61—28no—
111C2×Q8×C61—22no—
112C2×Q8×C61—22no—
113C2×Q8×C61—22no—
114C2×Q8×C61C22⋊C4116yescomplemented
115C2×Q8×C61C22×C414yes—
116C2×Q8×C61C2×D414yes—
117C2×Q8×C61C2×D414yes—
118C22×C4×C61—24no—
119C22×C4×C61—22no—
120C22×C4×C61—24no—
121C22×C4×C61—24no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—24no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61SD1614yescomplemented
132C22×C4×C61C22×C412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D412yes—
139C22×C4×C61#4112yes—
140C22×C4×C61#4112yes—
141C22×C4×C61C2411yescharacteristic
142C22×Dic61—22no—
143C22×Dic61—42no—
144C22×Dic61—42no—
145C22×Dic61—42no—
146C2×D244—28no—
147C2×D244—28no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—22no—
152C2×D244—24no—
153C2×D244—22no—
154C2×D244—42no—
155C2×D244—44no—
156C2×D244—42no—
157C2×D244—44no—
158C2×D244C22×C414yes—
159C4⋊C4×C61—216no—
160C4⋊C4×C61—24no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61C2×D414yes—
163C42×C61—216no—
164C42×C61—24no—
165C42×C61—22no—
166C42×C61—22no—
167#11758201—232no—
168#11758198—48no—
169#11758198—48no—
170C4⋊Dic61—22no—
171C4⋊Dic61—22no—
172C4⋊Dic61—42no—
173C2×#92418—28no—
174C2×#92418—22no—
175C2×#92418—22no—
176C2×#92418—22no—
177C2×#92418—22no—
178C2×#92418—22no—
179C2×#92418—44no—
180C2×#92418C22×C414yes—
181C23×C61C4×D412yes—
182C23×C61#12012yes—
183C23×C61#12112yes—
184C23×C61C2×SD1612yes—
185C23×C61#13512yes—
186C23×C61AGL(1,ℤ/8)12yes—
187C23×C61#13712yes—
188C23×C61C22×D411yescharacteristic
189C22×D61—24no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—48no—
197C22×D61—48no—
198C22×D61—48no—
199C22×D61—84no—
200C22×D61—84no—
201C22×D61—84no—
202C22×D61—84no—
203Q8×C61—24no—
204Q8×C61—24no—
205Q8×C61—24no—
206Q8×C61—216no—
207Q8×C61C2×C22⋊C418yescomplemented
208C2×C4×C61—24no—
209C2×C4×C61—22no—
210C2×C4×C61—24no—
211C2×C4×C61—24no—
212C2×C4×C61—22no—
213C2×C4×C61—216no—
214C2×C4×C61—28no—
215C2×C4×C61—22no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—44no—
222C2×C4×C61—48no—
223C2×C4×C61C2×C22⋊C414yes—
224C2×C4×C61C4×D414yes—
225C2×C4×C61C4×D412yes—
226C2×C4×C61#12012yes—
227C2×C4×C61#12114yes—
228C2×C4×C61#12112yes—
229C2×C4×C61#12314yes—
230C2×C4×C61C2×SD1614yescomplemented
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—84no—
241D244—24no—
242D244—24no—
243D244—42no—
244D244—42no—
245D244—48no—
246#92418—24no—
247#92418—42no—
248C2×#1880—611nomaximal, Sylow
249C22×C61#38614yes—
250C22×C61C4×SD1614yes—
251C22×C61#44014yes—
252C22×C61#44814yes—
253C22×C61#44914yes—
254C22×C61#46014yes—
255C22×C61#46414yes—
256C22×C61C2×C4×D411yescharacteristic
257C22×C61C2×#12011yescharacteristic
258C22×C61C2×#12111yescharacteristic
259C22×C61C22×SD1611yescharacteristic
260C22×C61C2×#13511yescharacteristic
261C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C61C2×#13711yescharacteristic
263C2×D61—44no—
264C2×D61—44no—
265C2×D61—44no—
266C2×D61—816no—
267C2×D61—82no—
268C2×D61—82no—
269C2×D61—82no—
270C2×D61—82no—
271C4×C61—24no—
272C4×C61—28no—
273C4×C61—42no—
274C4×C61—44no—
275C4×C61#38614yes—
276C4×C61C22×C22⋊C411yescharacteristic
277C4×C61C2×C4×D411yescharacteristic
278C4×C61C2×#12111yescharacteristic
279C4×C61C2×#12311yescharacteristic
280Dic61—82no—
281C23×SD16—611no—
282C22×C4×Q8D6111yescharacteristic, complemented
283C22×#103—611no—
284C22×#102—611no—
285C2×#390—611no—
286#1880—618no—
287C2×#340—611no—
288C2×#336—611no—
289C2×C61#188018yescomplemented
290C2×C61C2×#38611yescharacteristic
291C2×C61C2×C4×SD1611yescharacteristic
292C2×C61C2×#44011yescharacteristic
293C2×C61C2×#44811yescharacteristic
294C2×C61C2×#44911yescharacteristic
295C2×C61C2×#46011yescharacteristic
296C2×C61C2×#46411yescharacteristic
297D61—84no—
298C23×Q8C2×D6111yescharacteristic
299C23×D4—611no—
300C22×SD16—618no—
301C22×SD16—614no—
302C22×SD16—1224no—
303C22×SD16—1224no—
304C23×C8—611no—
305C23×C8—611no—
306C2×C4×Q8—24no—
307C2×C4×Q8—24no—
308C2×C4×Q8—22no—
309C2×C4×Q8C2×D6114yescomplemented
310C22×C4⋊C4—21no—
311C22×C4⋊C4—611no—
312C22×C4⋊C4C2×D6111yescharacteristic
313C22×C22⋊C4—1221no—
314C22×C22⋊C4—1221no—
315C22×C42—21no—
316C22×C42C2×D6111yescharacteristic
317C2×#103—614no—
318C2×#103—1224no—
319C2×#102—614no—
320C2×#102—1224no—
321#390—614no—
322#390—1222no—
323#340—614no—
324#336—614no—
325C61C2×#188011yescharacteristic, complemented, Sylow
326C25—1221no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8C4×D6114yes—
332C22×Q8D24414yes—
333C22×Q8C22⋊D6114yes—
334C22×Q8C22×D6112yes—
335C22×D4—614no—
336C22×D4—612no—
337C22×D4—1222no—
338C22×D4—1222no—
339C22×D4—1222no—
340C22×D4—1222no—
341C22×D4—1222no—
342C22×D4—1221no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—1221no—
346C23×C4C22⋊D6111yescharacteristic
347C23×C4C22⋊D6111yescharacteristic
348C23×C4C22×D6111yescharacteristic
349C2×SD16—6116no—
350C2×SD16—12232no—
351C2×SD16—1228no—
352C2×SD16—1228no—
353C22×C8—614no—
354C22×C8—612no—
355C22×C8—612no—
356C22×C8—1222no—
357C22×C8—1222no—
358C22×C8—1222no—
359C22×C8—1222no—
360C22×C8—1222no—
361C4×Q8—216no—
362C4×Q8—28no—
363C4×Q8—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—612no—
369C2×C4⋊C4—1222no—
370C2×C4⋊C4—1222no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4C22⋊D6114yes—
373C2×C4⋊C4C22×D6112yes—
374C2×C22⋊C4—1224no—
375C2×C22⋊C4—1224no—
376C2×C22⋊C4—2444no—
377C2×C22⋊C4—2444no—
378C2×C42—28no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42C22⋊D6112yes—
383C2×C42C22×D6112yes—
384#103—1228no—
385#102—1228no—
386C24—1222no—
387C24—1224no—
388C24—2442no—
389C24—2442no—
390C24—2442no—
391C24—2442no—
392C24—2442no—
393C24—2442no—
394C24C2×C22⋊D6111yescharacteristic
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—24no—
399C2×Q8—28no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—28no—
403C2×Q8—28no—
404C2×Q8#11758198116yescomplemented
405C2×Q8C2×C4×D6114yes—
406C2×Q8C2×D24414yes—
407C2×Q8C2×C22⋊D6114yes—
408C2×D4—614no—
409C2×D4—1222no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1228no—
415C2×D4—1228no—
416C2×D4—1224no—
417C2×D4—2442no—
418C2×D4—2444no—
419C2×D4—2442no—
420C2×D4—2444no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—1222no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4—2442no—
438C22×C4#1175820114yescomplemented
439C22×C4C2×C4×D6112yes—
440C22×C4C2×D24412yes—
441C22×C4#1175822212yes—
442C22×C4#1175822212yes—
443C22×C4C2×C22⋊D6112yes—
444C22×C4C2×C22⋊D6112yes—
445C22×C4C2×C22⋊D6112yes—
446C22×C4C2×C22⋊D6112yes—
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C23×D6111yescharacteristic
449SD16—12232no—
450C2×C8—614no—
451C2×C8—1222no—
452C2×C8—1222no—
453C2×C8—1228no—
454C2×C8—1222no—
455C2×C8—1222no—
456C2×C8—1222no—
457C2×C8—2444no—
458C4⋊C4—216no—
459C4⋊C4—22no—
460C4⋊C4—24no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—2442no—
464C4⋊C4C2×C22⋊D6114yes—
465C22⋊C4—2448no—
466C22⋊C4—2448no—
467C42—216no—
468C42—22no—
469C42—22no—
470C42—24no—
471C23—1224no—
472C23—4884no—
473C23—4884no—
474C23—4884no—
475C23—4884no—
476C23—2442no—
477C23—2442no—
478C23—2442no—
479C23—2442no—
480C23—2442no—
481C23—2442no—
482C23—2448no—
483C23—2448no—
484C23—2448no—
485C23C4×C22⋊D6112yes—
486C23#1451974612yes—
487C23#1451975112yes—
488C23C2×#1175820112yes—
489C23#1451979712yes—
490C23#1451980212yes—
491C23#1451980812yes—
492C23C22×C22⋊D6111yescharacteristic
493Q8—24no—
494Q8—24no—
495Q8—24no—
496Q8—216no—
497Q8C2×#1175819818yescomplemented
498D4—1224no—
499D4—1224no—
500D4—2442no—
501D4—2442no—
502D4—2448no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—216no—
509C2×C4—28no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—48no—
518C2×C4—4884no—
519C2×C4—2442no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4C2×#1175819814yes—
523C2×C4C4×C22⋊D6114yes—
524C2×C4C4×C22⋊D6112yes—
525C2×C4#1451974612yes—
526C2×C4#1451975114yes—
527C2×C4#1451975112yes—
528C2×C4#1451976014yes—
529C2×C4C2×#1175820114yescomplemented
530C2×C4C22×C4×D6111yescharacteristic
531C2×C4C22×C22⋊D6111yescharacteristic
532C2×C4C22×C22⋊D6111yescharacteristic
533C2×C4C22×D24411yescharacteristic
534C2×C4C2×#1175822211yescharacteristic
535C2×C4C2×#1175822211yescharacteristic
536C8—1224no—
537C8—2442no—
538C22—48816no—
539C22—4882no—
540C22—4882no—
541C22—4882no—
542C22—4882no—
543C22—2444no—
544C22—2444no—
545C22—2444no—
546C22#1683964114yes—
547C22C4×#1175820114yes—
548C22#1683986014yes—
549C22#1683990114yes—
550C22#1683990714yes—
551C22#1683996214yes—
552C22#1683998414yes—
553C22C2×C4×C22⋊D6111yescharacteristic
554C22C2×#1451974611yescharacteristic
555C22C2×#1451975111yescharacteristic
556C22C22×#1175820111yescharacteristic
557C22C2×#1451979711yescharacteristic
558C22C2×#1451980211yescharacteristic
559C22C2×#1451980811yescharacteristic
560C4—28no—
561C4—24no—
562C4—42no—
563C4—44no—
564C4—4882no—
565C4#1683964114yes—
566C4C22×#1175819811yescharacteristic
567C4C2×C4×C22⋊D6111yescharacteristic
568C4C2×#1451975111yescharacteristic
569C4C2×#1451976011yescharacteristic
570C2—4884no—
571C2#2144617418yesdirect product factor
572C2C2×#1683964111yescharacteristic
573C2C2×C4×#1175820111yescharacteristic
574C2C2×#1683986011yescharacteristic
575C2C2×#1683990111yescharacteristic
576C2C2×#1683990711yescharacteristic
577C2C2×#1683996211yescharacteristic
578C2C2×#1683998411yescharacteristic
subgroupG/H
centerC24C2×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×C4×Q8×C61C2
socleC24×C61C2×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenterC22×C4×Q8D61
hypocenterC61C2×#1880
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#14519701C2semidirect
5. #21446174C2direct (N × H)
6. C2×#16839524C2semidirect
7. C2×#16839517C2semidirect
8. C22×C4×Q8×C61C2semidirect
12. C22×#11758201C4semidirect
20. C2×#14519701C22semidirect
25. #16839524C22semidirect
26. #16839517C22semidirect
31. C2×C4×Q8×C61C22semidirect
49. C2×#11758201C2×C4semidirect
114. C2×Q8×C61C22⋊C4semidirect
131. C22×C4×C61SD16semidirect
207. Q8×C61C2×C22⋊C4semidirect
230. C2×C4×C61C2×SD16semidirect
282. C22×C4×Q8D61semidirect
289. C2×C61#1880semidirect
309. C2×C4×Q8C2×D61semidirect
325. C61C2×#1880semidirect
404. C2×Q8#11758198semidirect
438. C22×C4#11758201semidirect
497. Q8C2×#11758198semidirect
529. C2×C4C2×#11758201semidirect
571. C2#21446174direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117582012
C22×#145197012
C22×#145196972
C2×#168396642
#214461742
C2×#168395242
C2×#168395172
C22×C4×Q8×C612
C2×#188061