Finite Group Databasebeta

← C2×#21461212 #30610951

Subgroups — C2×#21461212 #30610951

Order 15616.

1130 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×#16840785C211yesmaximal, characteristic
2C2×#16840698C211yesmaximal, characteristic
3#21461212C218yesmaximal, direct product factor
4C2×#16840616C212yesmaximal
5C2×#16840615C212yesmaximal
6C2×#16840316C211yesmaximal, characteristic
7C22×C4×#6923—21no—
8#16840785—22no—
9#16840785C2214yes—
10C2×#14519844—21no—
11C2×#14519834C2212yes—
12C2×#14519832—21no—
13#16840698—22no—
14#16840698C2214yes—
15C2×(C2×#6923)⋊C4—21no—
16C2×(C2×#6923)⋊C4C2212yes—
17#16840616C2218yes—
18#16840615C2218yes—
19#16840316—22no—
20#16840316—22no—
21#16840316C414yescomplemented
22#16840316C2214yes—
23C2×#14519776C411yescharacteristic, complemented
24C2×#14519775C411yescharacteristic, complemented
25C2×#14519767—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519755—21no—
28C2×#14519753C2211yescharacteristic
29C2×C4×Dic122—21no—
30C2×C4×Dic122C411yescharacteristic, complemented
31C2×#14519734—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×Q8×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C22×#92420—22no—
36C2×C4×#6923—28no—
37C2×C4×#6923—24no—
38#14519844—24no—
39#14519834—22no—
40#14519834C2314yes—
41#14519832—24no—
42(C2×#6923)⋊C4—24no—
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4C2314yes—
45C22×Dic122—21no—
46C22×Dic122C2×C411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49C22×C4×D61C2311yescharacteristic
50#14519776—22no—
51#14519776C2×C414yescomplemented
52#14519775—22no—
53#14519775C2×C414yescomplemented
54#14519767—24no—
55#14519767—24no—
56#14519757—21no—
57#14519757—21no—
58#14519757C2×C412yes—
59#14519757C2312yes—
60#14519755—24no—
61#14519755—24no—
62#14519753—21no—
63#14519753—21no—
64#14519753C2×C412yes—
65#14519753C2312yes—
66C4×Dic122—22no—
67C4×Dic122—24no—
68C4×Dic122—24no—
69C4×Dic122C2×C414yescomplemented
70#14519734—24no—
71#14519734—24no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C42×D61C2×C412yes—
86C42×D61D412yes—
87C42×D61D412yes—
88C42×D61C2312yes—
89C22×Q8×C61C2×C411yescharacteristic
90C4×Q8×C61—22no—
91C4×Q8×C61C2×C414yescomplemented
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61C2×C411yescharacteristic
96C23×D61C2×D411yescharacteristic
97C22×#6923—28no—
98C22×#6923—24no—
99C22×#6923—44no—
100C22×#6923—44no—
101C2×Q8×C61—21no—
102C2×Q8×C61—42no—
103C2×Q8×C61C22×C412yes—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61C22⋊C411yescharacteristic
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C22×C411yescharacteristic
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C2×D411yescharacteristic
114C2×C4×D61—24no—
115C2×C4×D61—24no—
116C2×C4×D61—42no—
117C2×C4×D61C22⋊C412yes—
118C2×C4×D61C22⋊C412yes—
119C2×C4×D61C22×C411yescharacteristic
120C2×C4×D61C2×D412yes—
121C2×C4×D61C2×D412yes—
122C2×C4×D61C2×D411yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×C4×D61C2411yescharacteristic
125C2×Dic122—21no—
126C2×Dic122—24no—
127C2×Dic122—44no—
128C2×Dic122—42no—
129C2×Dic122C22×C412yes—
130C2×#92420—24no—
131C2×#92420—44no—
132C4×#6923—216no—
133C4⋊C4×C61—24no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61C22×C412yes—
136C42×C61—24no—
137C42×C61C22⋊C412yes—
138C42×C61C22×C412yes—
139#11758198—22no—
140#11758198—22no—
141#11758198—22no—
142#11758198—22no—
143C4⋊Dic61—21no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146C4⋊Dic61C22×C412yes—
147#11758196—24no—
148#11758196—24no—
149#11758196—24no—
150#11758196—22no—
151#11758196—24no—
152#11758196—22no—
153C4×Dic61—24no—
154C4×Dic61C22⋊C412yes—
155C4×Dic61C22⋊C412yes—
156C4×Dic61C22⋊C412yes—
157C4×Dic61C22×C412yes—
158C4×Dic61C2×D412yes—
159C4×Dic61C2×D412yes—
160C23×C61C2×C22⋊C411yescharacteristic
161C22×D61—22no—
162C22×D61—22no—
163C22×D61C2×C22⋊C411yescharacteristic
164C22×D61#13714yes—
165C22×D61C22×D411yescharacteristic
166C2×#6923—28no—
167C2×#6923—44no—
168C2×#6923—416no—
169C2×#6923—44no—
170Q8×C61—42no—
171Q8×C61—42no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61C2×C22⋊C412yes—
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61C2×C22⋊C412yes—
182C2×C4×C61C23×C411yescharacteristic
183C2×Dic61—22no—
184C2×Dic61—22no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61#10414yes—
190C2×Dic61C2×C22⋊C411yescharacteristic
191C2×Dic61C2×C22⋊C412yes—
192C2×Dic61C2×C22⋊C412yes—
193C2×Dic61C22×D411yescharacteristic
194C4×D61—24no—
195C4×D61—24no—
196C4×D61—24no—
197C4×D61—24no—
198C4×D61—41no—
199C4×D61—41no—
200C4×D61—41no—
201C4×D61—41no—
202Dic122—42no—
203Dic122—48no—
204Dic122—42no—
205#92420—44no—
206C2×#1506—611nomaximal, Sylow
207C22×C61#41012yes—
208C22×C61#41912yes—
209C22×C61C2×#10412yes—
210C22×C61C22×C22⋊C411yescharacteristic
211C2×D61—21no—
212C2×D61—21no—
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—28no—
216C2×D61#41912yes—
217C2×D61C2×#13712yes—
218#6923—48no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—22no—
222C4×C61—22no—
223C4×C61—42no—
224C4×C61—42no—
225Dic61—21no—
226Dic61—21no—
227Dic61—22no—
228Dic61—42no—
229Dic61—42no—
230Dic61C2×#10414yes—
231C2×#533—611no—
232C2×#432—611no—
233C2×#376—611no—
234#1506—618no—
235C2×#328—612no—
236C2×#328—612no—
237C2×C61#150614yescomplemented
238C2×C61C2×#41011yescharacteristic
239C2×C61C2×#41911yescharacteristic
240C2×C61C22×#10411yescharacteristic
241D61—22no—
242D61—22no—
243#533—614no—
244#533—614no—
245#533—1222no—
246#533—1222no—
247C2×C4⋊Q8—611no—
248C2×C4⋊Q8—611no—
249C2×#125—1221no—
250C2×C22⋊Q8—611no—
251C2×C22⋊Q8—611no—
252C2×C22⋊Q8—1221no—
253C2×C4×Q8—611no—
254C2×C4×Q8—1221no—
255C2×C4×Q8#692311yescharacteristic, complemented
256C2×#117—1221no—
257C22×C42—611no—
258C22×C42—1221no—
259#432—614no—
260#432—1222no—
261C2×C4⋊C8—1221no—
262C2×C22⋊C8—612no—
263C2×#97—1221no—
264#376—614no—
265#376—1222no—
266C2×#95—612no—
267C2×#95—1221no—
268#328—618no—
269#328—618no—
270C61C2×#150611yescharacteristic, complemented, Sylow
271C22×Q8—611no—
272C22×Q8—1221no—
273C22×Q8C2×#692311yescharacteristic
274C23×C4—611no—
275C23×C4—611no—
276C23×C4—611no—
277C23×C4—1222no—
278C22×C8—1222no—
279C4⋊Q8—614no—
280C4⋊Q8—614no—
281C4⋊Q8—1222no—
282C4⋊Q8—1222no—
283#125—1224no—
284#125—1224no—
285C22⋊Q8—612no—
286C22⋊Q8—612no—
287C22⋊Q8—612no—
288C22⋊Q8—612no—
289C22⋊Q8—1221no—
290C22⋊Q8—1221no—
291C22⋊Q8—1224no—
292C22⋊Q8—1224no—
293C22⋊Q8—1221no—
294C22⋊Q8—1221no—
295C4×Q8—22no—
296C4×Q8—614no—
297C4×Q8—1224no—
298C4×Q8—1224no—
299C4×Q8—1222no—
300C4×Q8C2×#692314yescomplemented
301#117—1224no—
302#117—1224no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—611no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4C2×#692311yescharacteristic
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C42—21no—
315C2×C42—611no—
316C2×C42—611no—
317C2×C42—611no—
318C2×C42—612no—
319C2×C42—612no—
320C2×C42—612no—
321C2×C42—612no—
322C2×C42—1224no—
323C2×C42—1228no—
324C2×C42—1221no—
325C2×C42C2×#692311yescharacteristic
326C4⋊C8—1224no—
327C22⋊C8—614no—
328C22⋊C8—1222no—
329#97—1224no—
330#95—614no—
331#95—1222no—
332#95—1224no—
333C24—611no—
334C2×Q8—21no—
335C2×Q8—42no—
336C2×Q8—612no—
337C2×Q8—1224no—
338C2×Q8—1221no—
339C2×Q8—2442no—
340C2×Q8—2444no—
341C2×Q8C22×#692312yes—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—612no—
348C22×C4—612no—
349C22×C4—612no—
350C22×C4—612no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—1224no—
356C22×C4—1224no—
357C22×C4—1224no—
358C22×C4—1228no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—2442no—
362C22×C4—2444no—
363C22×C4—2444no—
364C22×C4C22⋊#692311yescharacteristic
365C22×C4C22⋊#692311yescharacteristic
366C22×C4C22×#692311yescharacteristic
367C2×C8—1224no—
368C2×C8—2444no—
369C4⋊C4—24no—
370C4⋊C4—21no—
371C4⋊C4—612no—
372C4⋊C4—1224no—
373C4⋊C4—1224no—
374C4⋊C4—1222no—
375C4⋊C4—1222no—
376C4⋊C4—1224no—
377C4⋊C4—1222no—
378C4⋊C4—1222no—
379C4⋊C4—1221no—
380C4⋊C4—1224no—
381C4⋊C4C22×#692312yes—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—1222no—
385C22⋊C4—1222no—
386C42—24no—
387C42—612no—
388C42—612no—
389C42—612no—
390C42—612no—
391C42—612no—
392C42—612no—
393C42—12216no—
394C42—1224no—
395C42C22⋊#692312yes—
396C42C22×#692312yes—
397C23—614no—
398C23—611no—
399C23—611no—
400C23—1222no—
401C23—1222no—
402C23C2×C22⋊#692311yescharacteristic
403Q8—42no—
404Q8—42no—
405Q8—2442no—
406Q8—2442no—
407Q8—2448no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—614no—
416C2×C4—612no—
417C2×C4—611no—
418C2×C4—612no—
419C2×C4—611no—
420C2×C4—1224no—
421C2×C4—1224no—
422C2×C4—1224no—
423C2×C4—1224no—
424C2×C4—1222no—
425C2×C4—1222no—
426C2×C4—1228no—
427C2×C4—1222no—
428C2×C4—1222no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2444no—
434C2×C4—2444no—
435C2×C4—24416no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4C2×C22⋊#692312yes—
439C2×C4C2×C22⋊#692311yescharacteristic
440C2×C4C2×C22⋊#692312yes—
441C2×C4C23×#692311yescharacteristic
442C8—2444no—
443C22—612no—
444C22—612no—
445C22—1221no—
446C22—1221no—
447C22—1221no—
448C22—1221no—
449C22—1228no—
450C22#1684074112yes—
451C22#1684075512yes—
452C22D61⋊#10412yes—
453C22C22×C22⋊#692311yescharacteristic
454C4—21no—
455C4—21no—
456C4—22no—
457C4—22no—
458C4—42no—
459C4—42no—
460C4—614no—
461C4—1221no—
462C4—1221no—
463C4—1222no—
464C4—2448no—
465C4—2442no—
466C4—2442no—
467C2—1222no—
468C2—1222no—
469C2#2146121214yesdirect product factor
470C2C2×#1684074111yescharacteristic
471C2C2×#1684075511yescharacteristic
472C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1506
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461212C2direct (N × H)
21. #16840316C4semidirect
23. C2×#14519776C4semidirect
24. C2×#14519775C4semidirect
30. C2×C4×Dic122C4semidirect
33. C2×C4×Q8×C61C4semidirect
51. #14519776C2×C4semidirect
53. #14519775C2×C4semidirect
69. C4×Dic122C2×C4semidirect
91. C4×Q8×C61C2×C4semidirect
237. C2×C61#1506semidirect
255. C2×C4×Q8#6923semidirect
270. C61C2×#1506semidirect
300. C4×Q8C2×#6923semidirect
469. C2#21461212direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407852
C2×#168406982
#214612122
C2×#168406162
C2×#168406152
C2×#168403162
C2×#150661