Finite Group Databasebeta

← C2×#21444983 #29655732

Subgroups — C2×#21444983 #29655732

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×D4×Dic122C211yesmaximal, characteristic
2C2×#16840112C211yesmaximal, characteristic, complemented
3C2×#16840054C211yesmaximal, characteristic, complemented
4#21444983C218yesmaximal, direct product factor
5C2×#16839507C211yesmaximal, characteristic, complemented
6C2×#16839492C211yesmaximal, characteristic, complemented
7C2×D4⋊#92418C211yesmaximal, characteristic
8C2×C61×#476C211yesmaximal, characteristic
9C23×Dic122—21no—
10D4×Dic122—22no—
11D4×Dic122—22no—
12D4×Dic122—22no—
13D4×Dic122C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519776—21no—
16C2×#14519756—21no—
17C2×#14519754—22no—
18C2×C4×Dic122C2211yescharacteristic
19C2×D4×Dic61—21no—
20#16840112—22no—
21#16840112C2214yescomplemented
22#16840054—22no—
23#16840054C2214yescomplemented
24C2×#14519710—21no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701—22no—
27C2×#14519700—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839507C2214yescomplemented
30#16839492C2214yescomplemented
31D4⋊#92418C2214yes—
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C61×#476—22no—
35C61×#476C2214yes—
36C2×#106×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#102×C61—21no—
39C22×Dic122—22no—
40C22×Dic122—24no—
41C22×Dic122—21no—
42C22×Dic122—24no—
43C22×Dic122—44no—
44C22×Dic122—44no—
45C22×Dic122D411yescharacteristic
46C23×Dic61—22no—
47C22×#92418—21no—
48C22×#92418—21no—
49#14519777—21no—
50#14519777—21no—
51#14519777D412yes—
52#14519777C2312yes—
53#14519776—24no—
54#14519776—24no—
55#14519756—24no—
56#14519756—24no—
57#14519754—28no—
58#14519754—28no—
59C4×Dic122—21no—
60C4×Dic122—21no—
61C4×Dic122D412yes—
62C4×Dic122C2312yes—
63D4×Dic61—24no—
64D4×Dic61—24no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×C4⋊Dic61D412yes—
68C2×#11758196—22no—
69C2×#11758196—21no—
70C2×C22⋊Dic61—22no—
71C2×C4×Dic61—21no—
72#14519710—24no—
73C4⋊#92418—21no—
74C4⋊#92418C2312yes—
75#14519701—28no—
76#14519700—24no—
77C4×#92418—21no—
78C4×#92418C2312yes—
79C22×Q8×C61—21no—
80C22×D4×C61D411yescharacteristic
81C23×C4×C61—21no—
82C22×C8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61C2312yes—
87C4×D4×C61—21no—
88C4×D4×C61—21no—
89C4×D4×C61D412yes—
90C4×D4×C61C2312yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C22⋊C4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96#106×C61—24no—
97C4⋊C8×C61—21no—
98C4⋊C8×C61C2312yes—
99#102×C61—24no—
100C24×C61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—44no—
103C2×Q8×C61—41no—
104C2×D4×C61—21no—
105C2×D4×C61—22no—
106C2×D4×C61Q1614yes—
107C2×D4×C61C2×D412yes—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—42no—
112C22×C4×C61—42no—
113C22×C4×C61—41no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×Dic61—21no—
118C22×Dic61—28no—
119C22×Dic61—22no—
120C22×Dic61—21no—
121C22×Dic61—48no—
122C2×Dic122—21no—
123C2×Dic122—22no—
124C2×Dic122—28no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122—48no—
128C2×Dic122—416no—
129C2×Dic122—48no—
130C2×Dic122—42no—
131C2×Dic122—42no—
132C2×Dic122—48no—
133C2×Dic122SD1614yes—
134C2×Dic122C2×D412yes—
135C2×C8×C61—22no—
136C2×C8×C61—42no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61C2×D412yes—
143C22⋊C4×C61—22no—
144C22⋊C4×C61—22no—
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2411yescharacteristic
149C22⋊Dic61—28no—
150C4⋊Dic61—22no—
151C4⋊Dic61—21no—
152C4⋊Dic61—22no—
153C4⋊Dic61—22no—
154C4⋊Dic61C2×D414yes—
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—22no—
166C23×C61—24no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61#12011yescharacteristic
170Q8×C61—44no—
171Q8×C61—82no—
172D4×C61—22no—
173D4×C61—24no—
174D4×C61C2×Q1614yes—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—44no—
181C2×C4×C61—42no—
182C2×C4×C61—82no—
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61C2×SD1612yes—
187C2×C4×C61C2×Q1612yes—
188C2×C4×C61AGL(1,ℤ/8)12yes—
189C2×C4×C61#13712yes—
190C2×C4×C61C22×D411yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—24no—
195C2×Dic61—22no—
196C2×Dic61—24no—
197C2×Dic61—416no—
198C2×Dic61—44no—
199C2×Dic61—42no—
200Dic122—22no—
201Dic122—24no—
202Dic122—416no—
203Dic122—42no—
204Dic122—42no—
205Dic122—44no—
206Dic122C2×SD1614yes—
207C8×C61—42no—
208#92418—42no—
209#92418—42no—
210C2×#1637—611nomaximal, Sylow
211C22×C61—24no—
212C22×C61—48no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61#45012yes—
216C22×C61#45112yes—
217C22×C61#45412yes—
218C22×C61C2×#12011yescharacteristic
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
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—44no—
231Dic61—42no—
232C2×D4×Q8—611no—
233C2×#487—611no—
234C2×#477—611no—
235C2×#476D6111yescharacteristic
236#1637—618no—
237C2×#332—611no—
238C2×Q8⋊C8—611no—
239C2×D4⋊C8—611no—
240C2×C61—44no—
241C2×C61#163714yescomplemented
242C2×C61C2×#45011yescharacteristic
243C2×C61C2×#45111yescharacteristic
244C2×C61C2×#45411yescharacteristic
245C23×Q8—1221no—
246D4×Q8—614no—
247D4×Q8—1222no—
248D4×Q8—1222no—
249D4×Q8—1222no—
250C2×C4⋊Q8—611no—
251C2×C4⋊Q8—1221no—
252C2×C4⋊Q8C2×D6111yescharacteristic
253C2×C22⋊Q8—1222no—
254C2×C22⋊Q8—1221no—
255C2×C4×Q8—611no—
256C2×C4×D4—1221no—
257C2×C4×D4C2×D6111yescharacteristic
258#487—614no—
259#487—1222no—
260#477—614no—
261#477—1222no—
262#476—22no—
263#476C2×D6114yes—
264C2×#107—1221no—
265C2×#106—21no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8C2×D6111yescharacteristic
268C2×#103—1221no—
269C2×#103—1222no—
270C2×#102—21no—
271C2×C4×C8—611no—
272#332—614no—
273Q8⋊C8—614no—
274D4⋊C8—614no—
275C61C2×#163711yescharacteristic, complemented, Sylow
276C22×Q8—21no—
277C22×Q8—611no—
278C22×Q8—1224no—
279C22×Q8—1222no—
280C22×Q8—1224no—
281C22×Q8—1221no—
282C22×Q8—2444no—
283C22×Q8—2444no—
284C22×D4C22⋊D6111yescharacteristic
285C23×C4—21no—
286C23×C4—1222no—
287C22×C8—21no—
288C22×C8—1221no—
289C22×C8—1221no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—612no—
294C4⋊Q8—612no—
295C4⋊Q8—1224no—
296C4⋊Q8—1224no—
297C4⋊Q8—1221no—
298C4⋊Q8—1221no—
299C4⋊Q8C22×D6112yes—
300C22⋊Q8—1228no—
301C22⋊Q8—1228no—
302C22⋊Q8—1224no—
303C22⋊Q8—1224no—
304C4×Q8—612no—
305C4×Q8—612no—
306C4×Q8—1221no—
307C4×Q8—1221no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—1224no—
311C4×D4—1224no—
312C4×D4C22⋊D6112yes—
313C4×D4C22×D6112yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—612no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4C22⋊D6111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—1222no—
324C2×C42—1221no—
325C2×C42C22×D6111yescharacteristic
326#107—1224no—
327#106—24no—
328C4⋊C8—21no—
329C4⋊C8—612no—
330C4⋊C8—1221no—
331C4⋊C8C22×D6112yes—
332#103—1224no—
333#103—1228no—
334#102—24no—
335C4×C8—612no—
336C4×C8—1221no—
337C24—21no—
338C2×Q8—22no—
339C2×Q8—44no—
340C2×Q8—41no—
341C2×Q8—612no—
342C2×Q8—614no—
343C2×Q8—1228no—
344C2×Q8—1222no—
345C2×Q8—1221no—
346C2×Q8—1222no—
347C2×Q8—1222no—
348C2×Q8—2448no—
349C2×Q8—2448no—
350C2×Q8—2448no—
351C2×Q8—24416no—
352C2×Q8—2442no—
353C2×Q8—2442no—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4#1175820214yes—
357C2×D4C2×C22⋊D6112yes—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—41no—
364C22×C4—1221no—
365C22×C4—1228no—
366C22×C4—1221no—
367C22×C4—1222no—
368C22×C4—2448no—
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—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—614no—
384C4⋊C4—612no—
385C4⋊C4—1228no—
386C4⋊C4—1222no—
387C4⋊C4—1222no—
388C4⋊C4—1221no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4—1222no—
392C4⋊C4C2×C22⋊D6112yes—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—1228no—
396C42—1222no—
397C42—1222no—
398C42D4×D6111yescharacteristic
399C42D4×D6111yescharacteristic
400C42C2×C22⋊D6111yescharacteristic
401C42C23×D6111yescharacteristic
402C23—22no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23#1451974511yescharacteristic
407Q8—44no—
408Q8—82no—
409Q8—614no—
410Q8—1222no—
411Q8—1224no—
412Q8—24416no—
413Q8—2442no—
414Q8—2442no—
415Q8—2444no—
416D4—22no—
417D4—24no—
418D4C2×#1175820214yes—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—82no—
427C2×C4—1222no—
428C2×C4—1224no—
429C2×C4—1222no—
430C2×C4—1224no—
431C2×C4—24416no—
432C2×C4—2444no—
433C2×C4—2442no—
434C2×C4#1451974511yescharacteristic
435C2×C4#1451974511yescharacteristic
436C2×C4#1451974511yescharacteristic
437C2×C4SD16×D6112yes—
438C2×C4C2×#1175820212yes—
439C2×C4#1451980412yes—
440C2×C4#1451980712yes—
441C2×C4C2×D4×D6111yescharacteristic
442C2×C4C2×D4×D6111yescharacteristic
443C2×C4C22×C22⋊D6111yescharacteristic
444C8—42no—
445C8—2442no—
446C8—2442no—
447C22—24no—
448C22—42no—
449C22—48no—
450C22—42no—
451C22#1683991112yes—
452C22#1683991712yes—
453C22#1683993312yes—
454C22C2×#1451974511yescharacteristic
455C4—21no—
456C4—21no—
457C4—42no—
458C4—82no—
459C4—1224no—
460C4—2442no—
461C4—2444no—
462C4#1683991112yes—
463C4#1683991712yes—
464C4C2×SD16×D6111yescharacteristic
465C4C22×#1175820211yescharacteristic
466C4C2×#1451980411yescharacteristic
467C4C2×#1451980711yescharacteristic
468C2—44no—
469C2#2144498314yesdirect product factor
470C2C2×#1683991111yescharacteristic
471C2C2×#1683991711yescharacteristic
472C2C2×#1683993311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#476C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenterC2×#476D61
hypocenterC61C2×#1637
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#16840112C2semidirect
3. C2×#16840054C2semidirect
4. #21444983C2direct (N × H)
5. C2×#16839507C2semidirect
6. C2×#16839492C2semidirect
21. #16840112C22semidirect
23. #16840054C22semidirect
29. #16839507C22semidirect
30. #16839492C22semidirect
241. C2×C61#1637semidirect
275. C61C2×#1637semidirect
469. C2#21444983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic1222
C2×#168401122
C2×#168400542
#214449832
C2×#168395072
C2×#168394922
C2×D4⋊#924182
C2×C61×#4762
C2×#163761