Finite Group Databasebeta

← C2×#21444981 #29655731

Subgroups — C2×#21444981 #29655731

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840427C211yesmaximal, characteristic
2C2×#16840054C211yesmaximal, characteristic, complemented
3C2×#16840049C211yesmaximal, characteristic
4#21444981C218yesmaximal, direct product factor
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×#16839494C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic
8C2×C61×#487C211yesmaximal, characteristic, complemented
9C22×Q8×D61—21no—
10#16840427—22no—
11#16840427—22no—
12#16840427—22no—
13#16840427C2214yes—
14C2×#14519776—21no—
15C2×#14519755—22no—
16C2×#14519753—21no—
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739—21no—
20#16840054—22no—
21#16840054C2214yescomplemented
22#16840049—22no—
23#16840049C2214yes—
24C2×#14519710—21no—
25C2×#14519708—21no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519700—21no—
29C2×#14519697—21no—
30#16839508C2214yescomplemented
31#16839494C2214yescomplemented
32#16839491C2214yes—
33C2×C4⋊Q8×C61C2211yescharacteristic
34C2×C4⋊Q8×C61C2211yescharacteristic
35C61×#487—22no—
36C61×#487C2214yescomplemented
37C2×#103×C61—22no—
38C2×C4×C8×C61C2211yescharacteristic
39C22×Dic122—22no—
40C22×Dic122D411yescharacteristic
41C2×Q8×D61—24no—
42C2×Q8×D61—24no—
43C2×Q8×D61—44no—
44C2×Q8×D61—44no—
45C22×D244D411yescharacteristic
46C22×C4×D61—22no—
47C22×C4×D61—21no—
48C22×#92418—21no—
49C22×#92418—21no—
50#14519776—24no—
51#14519776—24no—
52#14519755—28no—
53#14519755—28no—
54#14519753—24no—
55#14519753—24no—
56C4×Dic122—21no—
57C4×Dic122—21no—
58C4×Dic122D412yes—
59C4×Dic122C2312yes—
60C4×D244—21no—
61C4×D244—21no—
62C4×D244D412yes—
63C4×D244C2312yes—
64#14519739—24no—
65#14519739—24no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×C4⋊Dic61D411yescharacteristic
68C2×#11758196—22no—
69C2×#11758196—21no—
70C2×#11758198—22no—
71C2×#11758198—21no—
72C2×C4×Dic61—21no—
73#14519710—24no—
74#14519708—24no—
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418C2312yes—
78C4⋊#92418C2312yes—
79#14519700—24no—
80#14519697—24no—
81C22×Q8×C61—21no—
82C22×Q8×C61—21no—
83C22×C8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61D412yes—
90C4⋊Q8×C61C2312yes—
91C4⋊Q8×C61C2312yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61D412yes—
96C2×C42×C61C2311yescharacteristic
97#103×C61—28no—
98C4×C8×C61—21no—
99C4×C8×C61C2312yes—
100C23×D61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61—44no—
105C2×Q8×C61—41no—
106C2×Q8×C61—42no—
107C2×Q8×C61—42no—
108C22×C4×C61—22no—
109C22×C4×C61—41no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116Q8×D61—48no—
117Q8×D61—416no—
118Q8×D61—48no—
119C2×D244—21no—
120C2×D244—22no—
121C2×D244Q1614yes—
122C2×D244C2×D412yes—
123C2×C4×D61—28no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—48no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×Dic122—21no—
130C2×Dic122—22no—
131C2×Dic122—28no—
132C2×Dic122—48no—
133C2×Dic122SD1614yes—
134C2×Dic122C2×D412yes—
135C2×C8×C61—22no—
136C2×C8×C61—42no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61C2×D414yes—
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2411yescharacteristic
149#11758198—28no—
150#11758198—22no—
151#11758198—22no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61C2×D412yes—
155C4⋊Dic61C2×D412yes—
156#11758196—28no—
157#11758196—22no—
158#11758196—22no—
159C4×Dic61—22no—
160C4×Dic61—22no—
161C2×#92418—22no—
162C2×#92418—22no—
163C2×#92418—42no—
164C2×#92418—42no—
165C23×C61#12011yescharacteristic
166C22×D61—22no—
167C22×D61—24no—
168C22×D61—42no—
169C22×D61—42no—
170Q8×C61—44no—
171Q8×C61—42no—
172Q8×C61—42no—
173Q8×C61—44no—
174Q8×C61—82no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—44no—
178C2×C4×C61—42no—
179C2×C4×C61—82no—
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61C2×SD1612yes—
184C2×C4×C61C2×Q1612yes—
185C2×C4×C61AGL(1,ℤ/8)12yes—
186C2×C4×C61#13712yes—
187C2×C4×C61C22×D411yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×Dic61—22no—
191C2×Dic61—24no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196D244—22no—
197D244—24no—
198D244C2×Q1614yes—
199C4×D61—416no—
200C4×D61—42no—
201C4×D61—42no—
202C4×D61—44no—
203Dic122—22no—
204Dic122—24no—
205Dic122—416no—
206Dic122C2×SD1614yes—
207C8×C61—42no—
208#92418—42no—
209#92418—42no—
210C2×#1637—611nomaximal, Sylow
211C22×C61#45012yes—
212C22×C61#45112yes—
213C22×C61#45412yes—
214C22×C61C2×#12011yescharacteristic
215C2×D61—24no—
216C2×D61—48no—
217C2×D61—42no—
218C2×D61—42no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—44no—
222C4×C61—82no—
223C4×C61#45012yes—
224C4×C61#45112yes—
225C4×C61C22×SD1611yescharacteristic
226C4×C61C22×Q1611yescharacteristic
227C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C61C2×#13711yescharacteristic
229Dic61—24no—
230Dic61—42no—
231Dic61—42no—
232C2×D4×Q8—611no—
233C2×#487D6111yescharacteristic, complemented
234C2×#477—611no—
235C2×#476—611no—
236#1637—618no—
237C2×#332—611no—
238C2×Q8⋊C8—611no—
239C2×D4⋊C8—611no—
240C2×C61#163714yescomplemented
241C2×C61C2×#45011yescharacteristic
242C2×C61C2×#45111yescharacteristic
243C2×C61C2×#45411yescharacteristic
244D61—44no—
245C23×Q8—1221no—
246D4×Q8—614no—
247D4×Q8—1222no—
248D4×Q8—1222no—
249D4×Q8—1222no—
250C2×C4⋊Q8—1221no—
251C2×C4⋊Q8C2×D6111yescharacteristic
252C2×C4⋊Q8C2×D6111yescharacteristic
253C2×C22⋊Q8—1221no—
254C2×C22⋊Q8—1222no—
255C2×C4×Q8—611no—
256C2×C4×D4—611no—
257C2×C4×D4—1221no—
258#487—22no—
259#487C2×D6114yescomplemented
260#477—614no—
261#477—1222no—
262#476—614no—
263#476—1222no—
264C2×#107—1221no—
265C2×#106—1221no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8—611no—
268C2×#103—22no—
269C2×#103—1221no—
270C2×#102—1221no—
271C2×C4×C8C2×D6111yescharacteristic
272#332—614no—
273Q8⋊C8—614no—
274D4⋊C8—614no—
275C61C2×#163711yescharacteristic, complemented, Sylow
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—611no—
279C22×Q8—1222no—
280C22×Q8—1224no—
281C22×Q8—1224no—
282C22×Q8—2444no—
283C22×Q8—2444no—
284C22×D4—611no—
285C23×C4—1222no—
286C23×C4—1221no—
287C22×C8—21no—
288C22×C8—1221no—
289C22×C8—1221no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—1224no—
296C4⋊Q8—1224no—
297C4⋊Q8C22⋊D6112yes—
298C4⋊Q8C22×D6112yes—
299C4⋊Q8C22×D6112yes—
300C22⋊Q8—1228no—
301C22⋊Q8—1224no—
302C22⋊Q8—1224no—
303C22⋊Q8—1228no—
304C4×Q8—612no—
305C4×Q8—612no—
306C4×Q8—1221no—
307C4×Q8—1221no—
308C4×D4—612no—
309C4×D4—612no—
310C4×D4—1224no—
311C4×D4—1224no—
312C4×D4—1221no—
313C4×D4—1221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—611no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4C22⋊D6112yes—
322C2×C22⋊C4—1222no—
323C2×C22⋊C4—1221no—
324C2×C42—1221no—
325C2×C42C22×D6111yescharacteristic
326#107—1224no—
327#106—1224no—
328C4⋊C8—612no—
329C4⋊C8—612no—
330C4⋊C8—1221no—
331C4⋊C8—1221no—
332#103—28no—
333#103—1224no—
334#102—1224no—
335C4×C8—21no—
336C4×C8C22×D6112yes—
337C24—1221no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—44no—
342C2×Q8—41no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8—612no—
346C2×Q8—614no—
347C2×Q8—1228no—
348C2×Q8—1221no—
349C2×Q8—1222no—
350C2×Q8—2448no—
351C2×Q8—2448no—
352C2×Q8—2448no—
353C2×Q8—24416no—
354C2×D4—612no—
355C2×D4—614no—
356C2×D4—1222no—
357C2×D4—1221no—
358C22×C4—22no—
359C22×C4—41no—
360C22×C4—1228no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—2448no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4D4×D6111yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C22×C4C2×C22⋊D6111yescharacteristic
372C2×C8—22no—
373C2×C8—42no—
374C2×C8—1222no—
375C2×C8—1222no—
376C2×C8—2442no—
377C2×C8—2442no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—612no—
386C4⋊C4—612no—
387C4⋊C4—1228no—
388C4⋊C4—1222no—
389C4⋊C4—1221no—
390C4⋊C4—1221no—
391C4⋊C4—1222no—
392C4⋊C4C2×C22⋊D6114yes—
393C22⋊C4—1228no—
394C22⋊C4—1222no—
395C22⋊C4—1222no—
396C42—1222no—
397C42—1222no—
398C42D4×D6111yescharacteristic
399C42D4×D6111yescharacteristic
400C42C2×C22⋊D6111yescharacteristic
401C42C23×D6111yescharacteristic
402C23—1222no—
403C23—1224no—
404C23—2442no—
405C23—2442no—
406C23#1451974511yescharacteristic
407Q8—44no—
408Q8—42no—
409Q8—42no—
410Q8—44no—
411Q8—82no—
412Q8—614no—
413Q8—1222no—
414Q8—1224no—
415Q8—24416no—
416D4—614no—
417D4—1222no—
418D4—1224no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4—1222no—
425C2×C4—1224no—
426C2×C4—1222no—
427C2×C4—1222no—
428C2×C4—24416no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2444no—
434C2×C4#1451974511yescharacteristic
435C2×C4#1451974511yescharacteristic
436C2×C4#1451974511yescharacteristic
437C2×C4SD16×D6112yes—
438C2×C4Q16×D6112yes—
439C2×C4#1451980412yes—
440C2×C4#1451980912yes—
441C2×C4C2×D4×D6111yescharacteristic
442C2×C4C2×D4×D6111yescharacteristic
443C2×C4C22×C22⋊D6111yescharacteristic
444C8—42no—
445C8—2442no—
446C8—2442no—
447C22—1224no—
448C22—2442no—
449C22—2448no—
450C22—2442no—
451C22#1683991112yes—
452C22#1683991612yes—
453C22#1683993412yes—
454C22C2×#1451974511yescharacteristic
455C4—21no—
456C4—21no—
457C4—44no—
458C4—82no—
459C4—1224no—
460C4—2442no—
461C4—2442no—
462C4#1683991112yes—
463C4#1683991612yes—
464C4C2×SD16×D6111yescharacteristic
465C4C2×Q16×D6111yescharacteristic
466C4C2×#1451980411yescharacteristic
467C4C2×#1451980911yescharacteristic
468C2—2444no—
469C2#2144498114yesdirect product factor
470C2C2×#1683991111yescharacteristic
471C2C2×#1683991611yescharacteristic
472C2C2×#1683993411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#487C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×#487D61
hypocenterC61C2×#1637
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
2. C2×#16840054C2semidirect
4. #21444981C2direct (N × H)
5. C2×#16839508C2semidirect
6. C2×#16839494C2semidirect
8. C2×C61×#487C2semidirect
21. #16840054C22semidirect
30. #16839508C22semidirect
31. #16839494C22semidirect
36. C61×#487C22semidirect
233. C2×#487D61semidirect
240. C2×C61#1637semidirect
259. #487C2×D61semidirect
275. C61C2×#1637semidirect
469. C2#21444981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404272
C2×#168400542
C2×#168400492
#214449812
C2×#168395082
C2×#168394942
C2×#168394912
C2×C61×#4872
C2×#163761