Finite Group Databasebeta

← C2×#21445003 #29655691

Subgroups — C2×#21445003 #29655691

Order 15616.

1042 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×#16840497C211yesmaximal, characteristic
2C2×#16840110C211yesmaximal, characteristic
3C2×#16840044C211yesmaximal, characteristic, complemented
4#21445003C218yesmaximal, direct product factor
5C2×#16839505C211yesmaximal, characteristic
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839492C211yesmaximal, characteristic, complemented
8C2×C61×#462C211yesmaximal, characteristic, complemented
9#16840497—22no—
10#16840497—22no—
11#16840497—22no—
12#16840497C2214yes—
13C2×#14519774C2211yescharacteristic
14C2×#14519766—21no—
15C2×#14519765—21no—
16C2×#14519762—22no—
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×D244—21no—
19C2×#14519739—21no—
20#16840110—22no—
21#16840110C2214yes—
22#16840044—22no—
23#16840044C2214yescomplemented
24C2×#14519708—21no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519700—21no—
27C2×#14519697—22no—
28C2×C4×#92418C2211yescharacteristic
29#16839505C2214yes—
30Q8⋊#92418C2214yescomplemented
31#16839492C2214yescomplemented
32C22×Q16×C61—21no—
33C2×C4⋊Q8×C61C2211yescharacteristic
34C2×C4×Q8×C61C2211yescharacteristic
35C61×#462—22no—
36C61×#462C2214yescomplemented
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#103×C61—21no—
39C22×Dic122D411yescharacteristic
40C22×D244—21no—
41C22×D244—21no—
42C22×D244D412yes—
43C22×C4×D61—22no—
44C22×#92418—21no—
45C22×#92418—21no—
46#14519774—21no—
47#14519774—21no—
48#14519774D412yes—
49#14519774C2312yes—
50#14519766—24no—
51#14519766—24no—
52#14519765—24no—
53#14519765—24no—
54#14519762—28no—
55#14519762—28no—
56C4×Dic122—21no—
57C4×Dic122—21no—
58C4×Dic122D412yes—
59C4×Dic122C2312yes—
60C4×D244—24no—
61C4×D244—24no—
62#14519739—24no—
63#14519739—24no—
64C2×C4⋊Dic61D411yescharacteristic
65C2×#11758196—21no—
66C2×#11758198—22no—
67C2×#11758198—22no—
68C2×#11758198—22no—
69C2×C4×Dic61—21no—
70#14519708—24no—
71C4⋊#92418—21no—
72C4⋊#92418C2312yes—
73#14519700—24no—
74#14519697—28no—
75C4×#92418—21no—
76C4×#92418C2312yes—
77C22×Q8×C61—21no—
78C22×Q8×C61D411yescharacteristic
79C2×Q16×C61—24no—
80C2×Q16×C61—44no—
81C22×C8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2312yes—
86C4×Q8×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61D412yes—
89C4×Q8×C61C2312yes—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98#103×C61—24no—
99C23×D61—22no—
100C2×Q8×C61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61—41no—
105C2×Q8×C61—42no—
106C2×Q8×C61—42no—
107C2×Q8×C61C2×D412yes—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—41no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×Dic61—21no—
115C22×Dic61—21no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—22no—
119C2×D244—22no—
120C2×D244—22no—
121C2×D244—42no—
122C2×D244—42no—
123C2×D244—42no—
124C2×D244—42no—
125C2×D244—44no—
126C2×D244C2×D414yes—
127C2×C4×D61—28no—
128C2×C4×D61—84no—
129C2×Dic122—22no—
130C2×Dic122—22no—
131C2×Dic122—21no—
132C2×Dic122C2×D412yes—
133Q16×C61—48no—
134C2×C8×C61—22no—
135C2×C8×C61—42no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61C2×D412yes—
144C42×C61—22no—
145C42×C61—22no—
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2411yescharacteristic
150#11758198—28no—
151#11758198—28no—
152#11758198—28no—
153C4⋊Dic61—21no—
154C4⋊Dic61C2×D412yes—
155#11758196—22no—
156#11758196—22no—
157C4×Dic61—22no—
158C4×Dic61—22no—
159C2×#92418—22no—
160C2×#92418—22no—
161C2×#92418—42no—
162C2×#92418—42no—
163C23×C61#12011yescharacteristic
164C22×D61—24no—
165C22×D61—44no—
166C22×D61—44no—
167C22×D61—44no—
168Q8×C61—22no—
169Q8×C61—22no—
170Q8×C61—42no—
171Q8×C61—42no—
172Q8×C61—42no—
173Q8×C61—82no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—82no—
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#13512yes—
185C2×C4×C61#13512yes—
186C2×C4×C61AGL(1,ℤ/8)12yes—
187C2×C4×C61#13712yes—
188C2×C4×C61C22×D411yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195D244—44no—
196D244—42no—
197D244—42no—
198D244—42no—
199D244—42no—
200D244—44no—
201D244—44no—
202D244—82no—
203C4×D61—88no—
204Dic122—22no—
205Dic122—22no—
206Dic122—42no—
207C8×C61—42no—
208#92418—42no—
209#92418—42no—
210C2×#1640—611nomaximal, Sylow
211C22×C61#44912yes—
212C22×C61#45212yes—
213C22×C61#45512yes—
214C22×C61C2×#12011yescharacteristic
215C2×D61—44no—
216C2×D61—44no—
217C2×D61—44no—
218C2×D61—88no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61—42no—
223C4×C61—82no—
224C4×C61#44912yes—
225C4×C61#45212yes—
226C4×C61C2×#13511yescharacteristic
227C4×C61C2×#13511yescharacteristic
228C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
229C4×C61C2×#13711yescharacteristic
230Dic61—42no—
231Dic61—42no—
232C2×#559—611no—
233C2×#486—611no—
234C2×#475—611no—
235C2×#462D6111yescharacteristic, complemented
236#1640—618no—
237C2×#331—611no—
238C2×Q8⋊C8—611no—
239C2×Q8⋊C8—611no—
240C2×C61#164014yescomplemented
241C2×C61C2×#44911yescharacteristic
242C2×C61C2×#45211yescharacteristic
243C2×C61C2×#45511yescharacteristic
244D61—84no—
245C22×Q16—21no—
246#559—614no—
247#559—1222no—
248#559—1222no—
249#559—1222no—
250C2×C4⋊Q8C2×D6111yescharacteristic
251C2×#127—611no—
252C2×#124—1221no—
253C2×#124—1221no—
254C2×#123—1222no—
255C2×C4×Q8—611no—
256C2×C4×Q8C2×D6111yescharacteristic
257C2×C4×D4—1221no—
258C2×C4×D4—1221no—
259#486—614no—
260#486—1222no—
261#475—614no—
262#475—1222no—
263#462—22no—
264#462C2×D6114yescomplemented
265C2×#106—1221no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8C2×D6111yescharacteristic
268C2×#103—21no—
269C2×#103—1221no—
270C2×#102—1222no—
271C2×C4×C8—611no—
272#331—614no—
273Q8⋊C8—614no—
274Q8⋊C8—614no—
275C61C2×#164011yescharacteristic, complemented, Sylow
276C22×Q8—21no—
277C22×Q8—611no—
278C22×Q8C22⋊D6111yescharacteristic
279C22×D4—612no—
280C22×D4—1221no—
281C22×D4—1221no—
282C23×C4—1222no—
283C2×Q16—24no—
284C2×Q16—44no—
285C22×C8—21no—
286C22×C8—1221no—
287C22×C8—1221no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8C22×D6112yes—
292#127—612no—
293#127—612no—
294#127—1221no—
295#127—1221no—
296#124—1224no—
297#124—1224no—
298#124—1224no—
299#124—1224no—
300#123—1228no—
301#123—1228no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—612no—
305C4×Q8—612no—
306C4×Q8—1221no—
307C4×Q8—1221no—
308C4×Q8C22⋊D6112yes—
309C4×Q8C22×D6112yes—
310C4×D4—1224no—
311C4×D4—1224no—
312C4×D4—1224no—
313C4×D4—1224no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4C22⋊D6111yescharacteristic
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1222no—
322C2×C22⋊C4—1222no—
323C2×C42—21no—
324C2×C42—1221no—
325C2×C42C22×D6111yescharacteristic
326#106—1224no—
327C4⋊C8—21no—
328C4⋊C8—612no—
329C4⋊C8—1221no—
330C4⋊C8C22×D6112yes—
331#103—24no—
332#103—1224no—
333#102—1228no—
334C4×C8—612no—
335C4×C8—1221no—
336C24—1222no—
337C2×Q8—21no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—41no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×Q8—612no—
345C2×Q8—1221no—
346C2×Q8—1222no—
347C2×Q8—1222no—
348C2×Q8C2×C22⋊D6112yes—
349C2×D4—614no—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—1222no—
354C2×D4—1222no—
355C2×D4—2444no—
356C2×D4—2442no—
357C2×D4—2442no—
358C2×D4—2442no—
359C2×D4—2442no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—1228no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—4884no—
367C22×C4D4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4C2×C22⋊D6111yescharacteristic
370Q16—48no—
371C2×C8—22no—
372C2×C8—42no—
373C2×C8—1222no—
374C2×C8—1222no—
375C2×C8—2442no—
376C2×C8—2442no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—612no—
385C4⋊C4—1222no—
386C4⋊C4—1221no—
387C4⋊C4—1222no—
388C4⋊C4C2×C22⋊D6112yes—
389C22⋊C4—1228no—
390C22⋊C4—1228no—
391C22⋊C4—1228no—
392C42—22no—
393C42—22no—
394C42—1222no—
395C42—1222no—
396C42D4×D6111yescharacteristic
397C42D4×D6111yescharacteristic
398C42C2×C22⋊D6111yescharacteristic
399C42C23×D6111yescharacteristic
400C23—1224no—
401C23—2444no—
402C23—2444no—
403C23—2444no—
404C23#1451974511yescharacteristic
405Q8—22no—
406Q8—22no—
407Q8—42no—
408Q8—42no—
409Q8—42no—
410Q8—82no—
411Q8—1222no—
412Q8—1222no—
413Q8—2442no—
414D4—4882no—
415D4—2444no—
416D4—2442no—
417D4—2442no—
418D4—2442no—
419D4—2442no—
420D4—2444no—
421D4—2444no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—82no—
429C2×C4—1222no—
430C2×C4—1222no—
431C2×C4—4888no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4#1451974511yescharacteristic
435C2×C4#1451974511yescharacteristic
436C2×C4#1451974511yescharacteristic
437C2×C4#1451979712yes—
438C2×C4#1451980012yes—
439C2×C4#1451980312yes—
440C2×C4#1451980912yes—
441C2×C4C2×D4×D6111yescharacteristic
442C2×C4C2×D4×D6111yescharacteristic
443C2×C4C22×C22⋊D6111yescharacteristic
444C8—42no—
445C8—2442no—
446C8—2442no—
447C22—4888no—
448C22—2444no—
449C22—2444no—
450C22—2444no—
451C22#1683990512yes—
452C22#1683992312yes—
453C22#1683993812yes—
454C22C2×#1451974511yescharacteristic
455C4—21no—
456C4—21no—
457C4—42no—
458C4—42no—
459C4—82no—
460C4—2442no—
461C4—2442no—
462C4#1683990512yes—
463C4#1683992312yes—
464C4C2×#1451979711yescharacteristic
465C4C2×#1451980011yescharacteristic
466C4C2×#1451980311yescharacteristic
467C4C2×#1451980911yescharacteristic
468C2—4884no—
469C2#2144500314yesdirect product factor
470C2C2×#1683990511yescharacteristic
471C2C2×#1683992311yescharacteristic
472C2C2×#1683993811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#462C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenterC2×#462D61
hypocenterC61C2×#1640
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. C2×#16840044C2semidirect
4. #21445003C2direct (N × H)
6. C2×Q8⋊#92418C2semidirect
7. C2×#16839492C2semidirect
8. C2×C61×#462C2semidirect
23. #16840044C22semidirect
30. Q8⋊#92418C22semidirect
31. #16839492C22semidirect
36. C61×#462C22semidirect
235. C2×#462D61semidirect
240. C2×C61#1640semidirect
264. #462C2×D61semidirect
275. C61C2×#1640semidirect
469. C2#21445003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
C2×#168401102
C2×#168400442
#214450032
C2×#168395052
C2×Q8⋊#924182
C2×#168394922
C2×C61×#4622
C2×#164061