Finite Group Databasebeta

← C2×#21461162 #30610436

Subgroups — C2×#21461162 #30610436

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840784C211yesmaximal, characteristic
2C2×C4×#11758213C211yesmaximal, characteristic
3#21461162C218yesmaximal, direct product factor
4C2×#16840612C212yesmaximal, complemented
5C2×Q8⋊#92420C212yesmaximal, complemented
6C2×C4×Q8×D61C211yesmaximal, characteristic
7C22×#11758213—21no—
8#16840784—22no—
9#16840784C2214yes—
10C2×C4⋊#92420C2212yes—
11C2×#14519834—21no—
12C4×#11758213—22no—
13C4×#11758213C2214yes—
14C2×#14519832—21no—
15C2×#14519832—21no—
16C2×C4×#92420C2212yes—
17#16840612C2218yescomplemented
18Q8⋊#92420C2218yescomplemented
19C22×Q8×D61C411yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×C4×Dic122—21no—
22C2×C4×Dic122C411yescharacteristic
23C2×#14519742—21no—
24C2×#14519742C2211yescharacteristic
25C4×Q8×D61—22no—
26C4×Q8×D61—22no—
27C4×Q8×D61C414yes—
28C4×Q8×D61C2214yes—
29C2×C4⋊C4×D61—21no—
30C2×C4⋊C4×D61C411yescharacteristic
31C2×C42×D61—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×Q8×C61C411yescharacteristic
34C2×#11758213—28no—
35C2×#11758213—24no—
36C22×#92420—22no—
37C22×#92420—22no—
38C4⋊#92420—22no—
39C4⋊#92420C2314yes—
40#14519834—24no—
41#14519832—24no—
42#14519832—24no—
43C4×#92420—22no—
44C4×#92420C2314yes—
45C22×Dic122—21no—
46C22×Dic122C2×C411yescharacteristic
47C2×Q8×D61—24no—
48C2×Q8×D61—22no—
49C2×Q8×D61—24no—
50C2×Q8×D61C2×C414yes—
51C22×C4×D61—21no—
52C22×C4×D61—21no—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56Q8×Dic61—21no—
57Q8×Dic61—21no—
58Q8×Dic61C2×C412yes—
59Q8×Dic61C2312yes—
60C4×Dic122—22no—
61C4×Dic122—24no—
62C4×Dic122—24no—
63C4×Dic122C2×C414yes—
64#14519742—24no—
65#14519742—21no—
66#14519742—21no—
67#14519742—24no—
68#14519742C2×C412yes—
69#14519742C2312yes—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C4⋊C4×D61—24no—
76C4⋊C4×D61—22no—
77C4⋊C4×D61—24no—
78C4⋊C4×D61C2×C414yes—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C42×D61—24no—
86C42×D61—24no—
87C42×D61C2×C412yes—
88C42×D61D412yes—
89C42×D61D412yes—
90C42×D61C2312yes—
91C22×Q8×C61C2×C411yescharacteristic
92C4×Q8×C61—22no—
93C4×Q8×C61C2×C414yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61C2×C411yescharacteristic
96C2×C42×C61—21no—
97C2×C42×C61C2×C411yescharacteristic
98C23×D61C22⋊C411yescharacteristic
99C2×Q8×C61—21no—
100C2×Q8×C61—22no—
101C2×Q8×C61M1614yescomplemented
102C2×Q8×C61C22×C412yes—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61C22⋊C411yescharacteristic
106C22×C4×C61C22⋊C411yescharacteristic
107C22×C4×C61C22×C411yescharacteristic
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C2×D411yescharacteristic
112C22×Dic61C2×D411yescharacteristic
113Q8×D61—216no—
114Q8×D61—28no—
115Q8×D61—28no—
116C2×C4×D61—28no—
117C2×C4×D61—24no—
118C2×C4×D61—24no—
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—24no—
122C2×C4×D61—24no—
123C2×C4×D61—44no—
124C2×C4×D61C22⋊C412yes—
125C2×C4×D61C22⋊C412yes—
126C2×C4×D61C22⋊C412yes—
127C2×C4×D61C22×C412yes—
128C2×C4×D61C2×D412yes—
129C2×C4×D61C2×D412yes—
130C2×Dic122—28no—
131C2×Dic122—21no—
132C2×Dic122—22no—
133C2×Dic122—24no—
134C2×Dic122M1614yescomplemented
135C2×Dic122C22×C412yes—
136C2×#92420—28no—
137C2×#92420—24no—
138C2×#92420—24no—
139C2×#92420—44no—
140#11758213—216no—
141C4⋊C4×C61—24no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61C22×C412yes—
144C42×C61—24no—
145C42×C61C22⋊C412yes—
146C42×C61C22×C412yes—
147C4⋊Dic61—21no—
148C4⋊Dic61—22no—
149C4⋊Dic61—22no—
150C4⋊Dic61C22×C412yes—
151#11758196—24no—
152#11758196—22no—
153#11758196—24no—
154#11758196—22no—
155C4×Dic61—24no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C4×Dic61—22no—
159C4×Dic61—22no—
160C4×Dic61C22⋊C412yes—
161C4×Dic61C22⋊C412yes—
162C4×Dic61C22×C411yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164C4×Dic61C2×D412yes—
165C4×Dic61C2×D412yes—
166C4×Dic61C2×D411yescharacteristic
167C4×Dic61C2411yescharacteristic
168C23×C61C2×C22⋊C411yescharacteristic
169C22×D61—22no—
170C22×D61—22no—
171C22×D61#10414yes—
172C22×D61C2×C22⋊C412yes—
173Q8×C61—22no—
174Q8×C61—24no—
175Q8×C61C2×M1614yescomplemented
176C2×C4×C61—22no—
177C2×C4×C61—24no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—42no—
182C2×C4×C61C2×C22⋊C412yes—
183C2×C4×C61C2×C22⋊C412yes—
184C2×C4×C61C2×C22⋊C411yescharacteristic
185C2×C4×C61C2×M1612yes—
186C2×C4×C61C2×M1612yes—
187C2×C4×C61C23×C411yescharacteristic
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—24no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—42no—
194C2×Dic61C2×C22⋊C411yescharacteristic
195C2×Dic61C2×C22⋊C412yes—
196C2×Dic61C2×C22⋊C411yescharacteristic
197C2×Dic61#13714yes—
198C2×Dic61C22×D411yescharacteristic
199C2×Dic61C22×D411yescharacteristic
200C4×D61—216no—
201C4×D61—24no—
202C4×D61—24no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—24no—
206C4×D61—24no—
207C4×D61—24no—
208C4×D61—48no—
209Dic122—216no—
210Dic122—22no—
211Dic122—24no—
212Dic122C2×M1614yescomplemented
213#92420—28no—
214#92420—44no—
215C2×#1491—611nomaximal, Sylow
216C22×C61#40712yes—
217C22×C61#41912yes—
218C22×C61C2×#10412yes—
219C22×C61C22×C22⋊C411yescharacteristic
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—28no—
223C2×D61C2×#10414yes—
224C4×C61—24no—
225C4×C61—22no—
226C4×C61—22no—
227C4×C61—42no—
228C4×C61#40712yes—
229C4×C61C22×M1611yescharacteristic
230C4×C61C22×M1611yescharacteristic
231Dic61—22no—
232Dic61—24no—
233Dic61—21no—
234Dic61—21no—
235Dic61—42no—
236Dic61#41912yes—
237Dic61C2×#13712yes—
238C22×C4×Q8—611no—
239C2×#432—611no—
240C2×C4×M16—611no—
241#1491—618no—
242C2×Q8⋊C8—612no—
243C2×Q8⋊C8—612no—
244C2×C61#149114yescomplemented
245C2×C61C2×#40711yescharacteristic
246C2×C61C2×#41911yescharacteristic
247C2×C61C22×#10411yescharacteristic
248D61—24no—
249C23×Q8—611no—
250C22×M16—1221no—
251C2×C4×Q8—611no—
252C2×C4×Q8—614no—
253C2×C4×Q8—614no—
254C2×C4×Q8—611no—
255C2×C4×Q8—611no—
256C2×C4×Q8—1221no—
257C2×C4×Q8—1221no—
258C2×C4×Q8—1222no—
259C2×C4×Q8—1222no—
260C2×C4×Q8#692311yescharacteristic
261C22×C4⋊C4—611no—
262C22×C4⋊C4—1221no—
263C22×C42—611no—
264C22×C42—1221no—
265#432—614no—
266#432—1222no—
267C2×C4⋊C8—612no—
268C2×C22⋊C8—1221no—
269C4×M16—614no—
270C4×M16—1222no—
271C2×#97—1221no—
272C2×#97—1221no—
273C2×C4×C8—612no—
274Q8⋊C8—618no—
275Q8⋊C8—618no—
276C61C2×#149111yescharacteristic, complemented, Sylow
277C22×Q8—614no—
278C22×Q8—611no—
279C22×Q8—1221no—
280C22×Q8—1222no—
281C22×Q8—1224no—
282C22×Q8—1224no—
283C22×Q8C2×#692311yescharacteristic
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—611no—
287C23×C4—1221no—
288C23×C4—1221no—
289C2×M16—1224no—
290C2×M16—1228no—
291C22×C8—1222no—
292C22×C8—1222no—
293C4×Q8—22no—
294C4×Q8—612no—
295C4×Q8—612no—
296C4×Q8—612no—
297C4×Q8—612no—
298C4×Q8—614no—
299C4×Q8—1224no—
300C4×Q8—1224no—
301C4×Q8—1221no—
302C4×Q8—1224no—
303C4×Q8—1221no—
304C4×Q8—1224no—
305C4×Q8—1221no—
306C4×Q8—1221no—
307C4×Q8—1222no—
308C4×Q8C2×#692314yes—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4—614no—
312C2×C4⋊C4—1222no—
313C2×C4⋊C4—1224no—
314C2×C4⋊C4—1224no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4C2×#692311yescharacteristic
320C2×C42—21no—
321C2×C42—611no—
322C2×C42—611no—
323C2×C42—611no—
324C2×C42—612no—
325C2×C42—612no—
326C2×C42—612no—
327C2×C42—612no—
328C2×C42—1224no—
329C2×C42—1224no—
330C2×C42—1221no—
331C2×C42—1221no—
332C2×C42—1221no—
333C2×C42C2×#692311yescharacteristic
334C4⋊C8—614no—
335C4⋊C8—1222no—
336C22⋊C8—1224no—
337#97—1224no—
338#97—1224no—
339C4×C8—614no—
340C4×C8—1222no—
341C24—611no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—614no—
345C2×Q8—612no—
346C2×Q8—1224no—
347C2×Q8—1228no—
348C2×Q8—1228no—
349C2×Q8—12216no—
350C2×Q8—1228no—
351C2×Q8—1221no—
352C2×Q8—1222no—
353C2×Q8#1175821314yescomplemented
354C2×Q8C22×#692312yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—1224no—
367C22×C4—1224no—
368C22×C4—1224no—
369C22×C4—1228no—
370C22×C4—1224no—
371C22×C4—1221no—
372C22×C4—1222no—
373C22×C4—1222no—
374C22×C4—1221no—
375C22×C4—2444no—
376C22×C4C22⋊#692311yescharacteristic
377C22×C4C22⋊#692311yescharacteristic
378C22×C4C22×#692311yescharacteristic
379M16—12216no—
380C2×C8—1224no—
381C2×C8—1228no—
382C2×C8—1224no—
383C2×C8—2444no—
384C4⋊C4—24no—
385C4⋊C4—21no—
386C4⋊C4—612no—
387C4⋊C4—1224no—
388C4⋊C4—1222no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4—1222no—
392C4⋊C4—1221no—
393C4⋊C4—1224no—
394C4⋊C4C22×#692312yes—
395C42—24no—
396C42—611no—
397C42—612no—
398C42—612no—
399C42—611no—
400C42—612no—
401C42—612no—
402C42—611no—
403C42—611no—
404C42—1222no—
405C42—1222no—
406C42—1222no—
407C42—1222no—
408C42—1224no—
409C42C22⋊#692312yes—
410C42C22×#692312yes—
411C23—614no—
412C23—612no—
413C23—1222no—
414C23—1222no—
415C23C2×C22⋊#692311yescharacteristic
416Q8—24no—
417Q8—22no—
418Q8—614no—
419Q8—12216no—
420Q8—1224no—
421Q8—1222no—
422Q8C2×#1175821314yescomplemented
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—614no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—611no—
433C2×C4—612no—
434C2×C4—611no—
435C2×C4—1224no—
436C2×C4—1224no—
437C2×C4—1224no—
438C2×C4—1224no—
439C2×C4—12216no—
440C2×C4—1222no—
441C2×C4—1224no—
442C2×C4—1222no—
443C2×C4—1222no—
444C2×C4—1224no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—2448no—
449C2×C4—2442no—
450C2×C4C2×C22⋊#692312yes—
451C2×C4C2×C22⋊#692312yes—
452C2×C4C2×C22⋊#692311yescharacteristic
453C2×C4D61⋊M1612yes—
454C2×C4C2×#1175821312yes—
455C2×C4C23×#692311yescharacteristic
456C8—1228no—
457C8—2444no—
458C22—614no—
459C22—1222no—
460C22—1222no—
461C22—1228no—
462C22#1684073312yes—
463C22#1684075512yes—
464C22D61⋊#10412yes—
465C22C22×C22⋊#692311yescharacteristic
466C4—24no—
467C4—22no—
468C4—22no—
469C4—42no—
470C4—612no—
471C4—612no—
472C4—1222no—
473C4—1224no—
474C4—1221no—
475C4—1221no—
476C4—2442no—
477C4#1684073312yes—
478C4C2×D61⋊M1611yescharacteristic
479C4C22×#1175821311yescharacteristic
480C2—1224no—
481C2#2146116214yesdirect product factor
482C2C2×#1684073311yescharacteristic
483C2C2×#1684075511yescharacteristic
484C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461162C2direct (N × H)
4. C2×#16840612C2semidirect
5. C2×Q8⋊#92420C2semidirect
17. #16840612C22semidirect
18. Q8⋊#92420C22semidirect
101. C2×Q8×C61M16semidirect
134. C2×Dic122M16semidirect
175. Q8×C61C2×M16semidirect
212. Dic122C2×M16semidirect
244. C2×C61#1491semidirect
276. C61C2×#1491semidirect
353. C2×Q8#11758213semidirect
422. Q8C2×#11758213semidirect
481. C2#21461162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407842
C2×C4×#117582132
#214611622
C2×#168406122
C2×Q8⋊#924202
C2×C4×Q8×D612
C2×#149161