Finite Group Databasebeta

← C2×#21461148 #30610417

Subgroups — C2×#21461148 #30610417

Order 15616.

1282 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840781C211yesmaximal, characteristic
2C2×#16840766C211yesmaximal, characteristic
3#21461148C218yesmaximal, direct product factor
4C2×#16840612C212yesmaximal, complemented
5C2×Q8⋊#92420C212yesmaximal, complemented
6C2×C4×Q8×D61C211yesmaximal, characteristic
7C22×#11758213—21no—
8#16840781—22no—
9#16840781C2214yes—
10#16840766—22no—
11#16840766C2214yes—
12C2×C4⋊#92420—21no—
13C2×C4⋊#92420—21no—
14C2×C4⋊#92420C2212yes—
15C2×#14519834—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—24no—
35C2×#11758213—44no—
36C22×#92420—22no—
37C22×#92420—22no—
38C4⋊#92420—24no—
39C4⋊#92420—24no—
40C4⋊#92420—22no—
41C4⋊#92420C2314yes—
42#14519834—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—22no—
119C2×C4×D61—22no—
120C2×C4×D61—24no—
121C2×C4×D61—42no—
122C2×C4×D61—44no—
123C2×C4×D61C22⋊C412yes—
124C2×C4×D61C22⋊C412yes—
125C2×C4×D61C22⋊C412yes—
126C2×C4×D61SD1614yes—
127C2×C4×D61Q1614yes—
128C2×C4×D61C22×C412yes—
129C2×C4×D61C2×D412yes—
130C2×C4×D61C2×D412yes—
131C2×Dic122—28no—
132C2×Dic122—21no—
133C2×Dic122—22no—
134C2×Dic122—24no—
135C2×Dic122M1614yescomplemented
136C2×Dic122C22×C412yes—
137C2×#92420—24no—
138C2×#92420—24no—
139C2×#92420—44no—
140C2×#92420—44no—
141#11758213—48no—
142C4⋊C4×C61—24no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61C22×C412yes—
145C42×C61—24no—
146C42×C61C22⋊C412yes—
147C42×C61C22×C412yes—
148C4⋊Dic61—21no—
149C4⋊Dic61—22no—
150C4⋊Dic61—22no—
151C4⋊Dic61C22×C412yes—
152#11758196—24no—
153#11758196—22no—
154#11758196—24no—
155#11758196—22no—
156C4×Dic61—24no—
157C4×Dic61—22no—
158C4×Dic61—22no—
159C4×Dic61—22no—
160C4×Dic61—22no—
161C4×Dic61C22⋊C412yes—
162C4×Dic61C22⋊C412yes—
163C4×Dic61C22×C411yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165C4×Dic61C2×D411yescharacteristic
166C4×Dic61C2×D412yes—
167C4×Dic61C2×D412yes—
168C4×Dic61C2411yescharacteristic
169C23×C61C2×C22⋊C411yescharacteristic
170C22×D61—22no—
171C22×D61—22no—
172C22×D61#10314yes—
173C22×D61C2×C22⋊C412yes—
174Q8×C61—22no—
175Q8×C61—24no—
176Q8×C61C2×M1614yescomplemented
177C2×C4×C61—22no—
178C2×C4×C61—24no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—42no—
182C2×C4×C61#10314yes—
183C2×C4×C61C2×C22⋊C412yes—
184C2×C4×C61C2×C22⋊C411yescharacteristic
185C2×C4×C61C2×C22⋊C412yes—
186C2×C4×C61C2×M1612yes—
187C2×C4×C61C2×M1612yes—
188C2×C4×C61C23×C411yescharacteristic
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—24no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—42no—
195C2×Dic61C2×C22⋊C411yescharacteristic
196C2×Dic61C2×C22⋊C412yes—
197C2×Dic61C2×C22⋊C411yescharacteristic
198C2×Dic61C2×SD1612yes—
199C2×Dic61C2×Q1612yes—
200C2×Dic61C22×D411yescharacteristic
201C2×Dic61C22×D411yescharacteristic
202C4×D61—216no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—24no—
206C4×D61—42no—
207C4×D61—42no—
208C4×D61—48no—
209C4×D61#10318yes—
210C4×D61C2×SD1614yes—
211C4×D61C2×Q1614yes—
212Dic122—216no—
213Dic122—22no—
214Dic122—24no—
215Dic122C2×M1614yescomplemented
216#92420—44no—
217#92420—44no—
218C2×#1487—611nomaximal, Sylow
219C22×C61#40712yes—
220C22×C61C2×#10312yes—
221C22×C61#42112yes—
222C22×C61C22×C22⋊C411yescharacteristic
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—28no—
226C2×D61C2×#10314yes—
227C4×C61—24no—
228C4×C61—22no—
229C4×C61—42no—
230C4×C61#40712yes—
231C4×C61C2×#10314yes—
232C4×C61C22×M1611yescharacteristic
233C4×C61C22×M1611yescharacteristic
234Dic61—22no—
235Dic61—24no—
236Dic61—21no—
237Dic61—21no—
238Dic61—42no—
239Dic61C2×#10312yes—
240Dic61C22×SD1611yescharacteristic
241Dic61C22×Q1611yescharacteristic
242C22×C4×Q8—611no—
243C2×#431—611no—
244C2×#423—611no—
245#1487—618no—
246C2×Q8⋊C8—612no—
247C2×Q8⋊C8—612no—
248C2×C61#148714yescomplemented
249C2×C61C2×#40711yescharacteristic
250C2×C61C22×#10311yescharacteristic
251C2×C61C2×#42111yescharacteristic
252D61—24no—
253C23×Q8—611no—
254C22×M16—1221no—
255C2×C4×Q8—611no—
256C2×C4×Q8—614no—
257C2×C4×Q8—614no—
258C2×C4×Q8—611no—
259C2×C4×Q8—611no—
260C2×C4×Q8—1221no—
261C2×C4×Q8—1221no—
262C2×C4×Q8—1222no—
263C2×C4×Q8—1222no—
264C2×C4×Q8#692311yescharacteristic
265C22×C4⋊C4—611no—
266C22×C4⋊C4—1221no—
267C22×C42—611no—
268C22×C42—1221no—
269#431—614no—
270#431—1222no—
271#423—614no—
272#423—1222no—
273C2×C4⋊C8—612no—
274C2×C4⋊C8—1221no—
275C2×C4⋊C8—1221no—
276C2×C22⋊C8—1221no—
277C2×C4×C8—612no—
278Q8⋊C8—618no—
279Q8⋊C8—618no—
280C61C2×#148711yescharacteristic, complemented, Sylow
281C22×Q8—614no—
282C22×Q8—611no—
283C22×Q8—1221no—
284C22×Q8—1222no—
285C22×Q8—1224no—
286C22×Q8—1224no—
287C22×Q8C2×#692311yescharacteristic
288C23×C4—611no—
289C23×C4—611no—
290C23×C4—611no—
291C23×C4—1221no—
292C23×C4—1221no—
293C2×M16—1224no—
294C2×M16—2444no—
295C22×C8—1222no—
296C22×C8—1222no—
297C4×Q8—22no—
298C4×Q8—612no—
299C4×Q8—612no—
300C4×Q8—612no—
301C4×Q8—612no—
302C4×Q8—614no—
303C4×Q8—1224no—
304C4×Q8—1224no—
305C4×Q8—1221no—
306C4×Q8—1224no—
307C4×Q8—1221no—
308C4×Q8—1224no—
309C4×Q8—1221no—
310C4×Q8—1221no—
311C4×Q8—1222no—
312C4×Q8C2×#692314yes—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—611no—
315C2×C4⋊C4—614no—
316C2×C4⋊C4—1222no—
317C2×C4⋊C4—1224no—
318C2×C4⋊C4—1224no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4C2×#692311yescharacteristic
324C2×C42—21no—
325C2×C42—611no—
326C2×C42—611no—
327C2×C42—611no—
328C2×C42—612no—
329C2×C42—612no—
330C2×C42—612no—
331C2×C42—612no—
332C2×C42—1224no—
333C2×C42—1224no—
334C2×C42—1221no—
335C2×C42—1221no—
336C2×C42—1221no—
337C2×C42C2×#692311yescharacteristic
338C4⋊C8—614no—
339C4⋊C8—1222no—
340C4⋊C8—1224no—
341C4⋊C8—1224no—
342C22⋊C8—1224no—
343C4×C8—614no—
344C4×C8—1222no—
345C24—611no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—614no—
349C2×Q8—612no—
350C2×Q8—1224no—
351C2×Q8—1228no—
352C2×Q8—1228no—
353C2×Q8—12216no—
354C2×Q8—1228no—
355C2×Q8—1221no—
356C2×Q8—1222no—
357C2×Q8#1175821314yescomplemented
358C2×Q8C22×#692312yes—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—611no—
362C22×C4—614no—
363C22×C4—614no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—612no—
369C22×C4—612no—
370C22×C4—612no—
371C22×C4—612no—
372C22×C4—1224no—
373C22×C4—1228no—
374C22×C4—1224no—
375C22×C4—1221no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1221no—
379C22×C4—2442no—
380C22×C4—2444no—
381C22×C4C22⋊#692311yescharacteristic
382C22×C4C22⋊#692311yescharacteristic
383C22×C4C22×#692311yescharacteristic
384M16—2448no—
385C2×C8—1224no—
386C2×C8—1224no—
387C2×C8—2444no—
388C2×C8—2444no—
389C4⋊C4—24no—
390C4⋊C4—21no—
391C4⋊C4—612no—
392C4⋊C4—1224no—
393C4⋊C4—1222no—
394C4⋊C4—1222no—
395C4⋊C4—1222no—
396C4⋊C4—1222no—
397C4⋊C4—1221no—
398C4⋊C4—1224no—
399C4⋊C4C22×#692312yes—
400C42—24no—
401C42—611no—
402C42—611no—
403C42—612no—
404C42—612no—
405C42—612no—
406C42—612no—
407C42—611no—
408C42—611no—
409C42—1222no—
410C42—1222no—
411C42—1222no—
412C42—1222no—
413C42—1224no—
414C42C22⋊#692312yes—
415C42C22×#692312yes—
416C23—614no—
417C23—612no—
418C23—1222no—
419C23—1222no—
420C23C2×C22⋊#692311yescharacteristic
421Q8—24no—
422Q8—22no—
423Q8—614no—
424Q8—12216no—
425Q8—1224no—
426Q8—1222no—
427Q8C2×#1175821314yescomplemented
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—42no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—611no—
436C2×C4—611no—
437C2×C4—618no—
438C2×C4—614no—
439C2×C4—614no—
440C2×C4—611no—
441C2×C4—612no—
442C2×C4—611no—
443C2×C4—12216no—
444C2×C4—1222no—
445C2×C4—1224no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1224no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2448no—
455C2×C4—2442no—
456C2×C4#1451984014yes—
457C2×C4C2×C22⋊#692312yes—
458C2×C4C2×C22⋊#692311yescharacteristic
459C2×C4C2×C22⋊#692312yes—
460C2×C4D61⋊M1612yes—
461C2×C4C2×#1175821312yes—
462C2×C4C23×#692311yescharacteristic
463C8—2444no—
464C8—2444no—
465C22—614no—
466C22—1222no—
467C22—1228no—
468C22—1222no—
469C22#1684073312yes—
470C22C2×#1451984012yes—
471C22#1684075912yes—
472C22C22×C22⋊#692311yescharacteristic
473C4—24no—
474C4—22no—
475C4—42no—
476C4—611no—
477C4—611no—
478C4—612no—
479C4—1222no—
480C4—1224no—
481C4—1221no—
482C4—1221no—
483C4—2442no—
484C4#1684073312yes—
485C4C2×#1451984014yes—
486C4C2×D61⋊M1611yescharacteristic
487C4C22×#1175821311yescharacteristic
488C2—1224no—
489C2#2146114814yesdirect product factor
490C2C2×#1684073311yescharacteristic
491C2C22×#1451984011yescharacteristic
492C2C2×#1684075911yescharacteristic
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×#1487
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. #21461148C2direct (N × H)
4. C2×#16840612C2semidirect
5. C2×Q8⋊#92420C2semidirect
17. #16840612C22semidirect
18. Q8⋊#92420C22semidirect
101. C2×Q8×C61M16semidirect
135. C2×Dic122M16semidirect
176. Q8×C61C2×M16semidirect
215. Dic122C2×M16semidirect
248. C2×C61#1487semidirect
280. C61C2×#1487semidirect
357. C2×Q8#11758213semidirect
427. Q8C2×#11758213semidirect
489. C2#21461148direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407812
C2×#168407662
#214611482
C2×#168406122
C2×Q8⋊#924202
C2×C4×Q8×D612
C2×#148761