Finite Group Databasebeta

← C2×#21461122 #30610390

Subgroups — C2×#21461122 #30610390

Order 15616.

1282 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840781C211yesmaximal, characteristic
2C2×#16840780C211yesmaximal, characteristic
3#21461122C218yesmaximal, direct product factor
4C2×#16840612C212yesmaximal, complemented
5C2×Q8⋊#92420C212yesmaximal, complemented
6C2×C4×Q8×D61C211yesmaximal, characteristic
7#16840781—22no—
8#16840781C2214yes—
9#16840780—22no—
10#16840780C2214yes—
11C2×#14519844—21no—
12C2×C4⋊#92420C2212yes—
13C2×#14519834—21no—
14C2×#14519834—21no—
15C2×C4×#92420—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
34C22×#92420—22no—
35C22×#92420—22no—
36#14519844—24no—
37C4⋊#92420—22no—
38C4⋊#92420C2314yes—
39#14519834—24no—
40#14519834—24no—
41C4×#92420—24no—
42C4×#92420—22no—
43C4×#92420C2314yes—
44C22×Dic122—21no—
45C22×Dic122C2×C411yescharacteristic
46C2×Q8×D61—22no—
47C2×Q8×D61—24no—
48C2×Q8×D61C818yescomplemented
49C2×Q8×D61C2×C414yes—
50C22×C4×D61—21no—
51C22×C4×D61—21no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55Q8×Dic61—21no—
56Q8×Dic61—21no—
57Q8×Dic61C2×C412yes—
58Q8×Dic61C2312yes—
59C4×Dic122—22no—
60C4×Dic122—24no—
61C4×Dic122—24no—
62C4×Dic122C2×C414yes—
63#14519742—24no—
64#14519742—21no—
65#14519742—21no—
66#14519742—24no—
67#14519742C2×C412yes—
68#14519742C2312yes—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2×C411yescharacteristic
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C4⋊C4×D61—24no—
75C4⋊C4×D61—22no—
76C4⋊C4×D61—24no—
77C4⋊C4×D61C2×C414yes—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61D411yescharacteristic
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C42×D61—24no—
85C42×D61—24no—
86C42×D61C2×C412yes—
87C42×D61D412yes—
88C42×D61D412yes—
89C42×D61C2312yes—
90C22×Q8×C61C2×C411yescharacteristic
91C4×Q8×C61—22no—
92C4×Q8×C61C2×C414yes—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61—21no—
96C2×C42×C61C2×C411yescharacteristic
97C23×D61C22⋊C411yescharacteristic
98C2×Q8×C61—21no—
99C2×Q8×C61—22no—
100C2×Q8×C61C2×C814yes—
101C2×Q8×C61C22×C412yes—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61C22⋊C411yescharacteristic
105C22×C4×C61C22⋊C411yescharacteristic
106C22×C4×C61C22×C411yescharacteristic
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61C22⋊C411yescharacteristic
110C22×Dic61C2×D411yescharacteristic
111C22×Dic61C2×D411yescharacteristic
112Q8×D61—216no—
113Q8×D61—28no—
114Q8×D61C2×C8116yescomplemented
115C2×C4×D61—28no—
116C2×C4×D61—24no—
117C2×C4×D61—24no—
118C2×C4×D61—24no—
119C2×C4×D61—42no—
120C2×C4×D61—44no—
121C2×C4×D61C22⋊C412yes—
122C2×C4×D61C22⋊C412yes—
123C2×C4×D61C22⋊C412yes—
124C2×C4×D61C2×C814yes—
125C2×C4×D61M1614yes—
126C2×C4×D61C22×C412yes—
127C2×C4×D61C2×D412yes—
128C2×C4×D61C2×D412yes—
129C2×Dic122—21no—
130C2×Dic122—22no—
131C2×Dic122—28no—
132C2×Dic122—24no—
133C2×Dic122C2×C814yes—
134C2×Dic122C22×C412yes—
135C2×#92420—24no—
136C2×#92420—24no—
137C2×#92420—44no—
138C2×#92420—44no—
139C4⋊C4×C61—24no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61C22×C412yes—
142C42×C61—24no—
143C42×C61C22⋊C412yes—
144C42×C61C22×C412yes—
145C4⋊Dic61—21no—
146C4⋊Dic61—22no—
147C4⋊Dic61—22no—
148C4⋊Dic61C22×C412yes—
149#11758196—24no—
150#11758196—22no—
151#11758196—24no—
152#11758196—22no—
153C4×Dic61—24no—
154C4×Dic61—22no—
155C4×Dic61—22no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C4×Dic61C22⋊C412yes—
159C4×Dic61C22⋊C412yes—
160C4×Dic61C22×C411yescharacteristic
161C4×Dic61C2×D411yescharacteristic
162C4×Dic61C2×D412yes—
163C4×Dic61C2×D411yescharacteristic
164C4×Dic61C2×D412yes—
165C4×Dic61C2411yescharacteristic
166C23×C61C2×C22⋊C411yescharacteristic
167C22×D61—22no—
168C22×D61—22no—
169C22×D61C22⋊C814yes—
170C22×D61C2×C22⋊C412yes—
171Q8×C61—22no—
172Q8×C61—24no—
173Q8×C61C22×C814yes—
174C2×C4×C61—22no—
175C2×C4×C61—24no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—42no—
180C2×C4×C61C2×C22⋊C412yes—
181C2×C4×C61C2×C22⋊C412yes—
182C2×C4×C61C2×C22⋊C411yescharacteristic
183C2×C4×C61C22×C812yes—
184C2×C4×C61C2×M1612yes—
185C2×C4×C61C23×C411yescharacteristic
186C2×Dic61—22no—
187C2×Dic61—24no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—42no—
191C2×Dic61C22⋊C814yes—
192C2×Dic61C2×C22⋊C411yescharacteristic
193C2×Dic61C2×C22⋊C412yes—
194C2×Dic61C2×C22⋊C411yescharacteristic
195C2×Dic61#13714yes—
196C2×Dic61C22×D411yescharacteristic
197C2×Dic61C22×D411yescharacteristic
198C4×D61—216no—
199C4×D61—24no—
200C4×D61—24no—
201C4×D61—42no—
202C4×D61—42no—
203C4×D61—48no—
204C4×D61C22⋊C818yes—
205C4×D61C22×C814yes—
206C4×D61C2×M1614yes—
207Dic122—22no—
208Dic122—24no—
209Dic122—216no—
210Dic122C22×C814yes—
211#92420—44no—
212#92420—44no—
213C2×#1479—611nomaximal, Sylow
214C22×C61C2×C22⋊C812yes—
215C22×C61#41912yes—
216C22×C61#42112yes—
217C22×C61C22×C22⋊C411yescharacteristic
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—28no—
221C2×D61C2×C22⋊C814yes—
222C4×C61—24no—
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—42no—
226C4×C61C2×C22⋊C812yes—
227C4×C61C23×C811yescharacteristic
228C4×C61C22×M1611yescharacteristic
229Dic61—24no—
230Dic61—21no—
231Dic61—21no—
232Dic61—42no—
233Dic61C2×C22⋊C814yes—
234Dic61#41912yes—
235Dic61C2×#13712yes—
236C22×C4×Q8—611no—
237C2×#431—611no—
238C2×#431—611no—
239#1479—618no—
240C2×Q8⋊C8—612no—
241C2×Q8⋊C8—612no—
242C2×C61#147914yescomplemented
243C2×C61C22×C22⋊C811yescharacteristic
244C2×C61C2×#41911yescharacteristic
245C2×C61C2×#42111yescharacteristic
246D61—24no—
247C23×Q8—611no—
248C2×C4×Q8—611no—
249C2×C4×Q8—614no—
250C2×C4×Q8—614no—
251C2×C4×Q8—611no—
252C2×C4×Q8—611no—
253C2×C4×Q8—1221no—
254C2×C4×Q8—1221no—
255C2×C4×Q8—1222no—
256C2×C4×Q8—1222no—
257C2×C4×Q8#692311yescharacteristic
258C22×C4⋊C4—611no—
259C22×C4⋊C4—1221no—
260C22×C42—611no—
261C22×C42—1221no—
262#431—614no—
263#431—614no—
264#431—1222no—
265#431—1222no—
266C2×C4⋊C8—612no—
267C2×C4⋊C8—1221no—
268C2×C22⋊C8—1221no—
269C2×C22⋊C8—1221no—
270C2×C4×C8—612no—
271C2×C4×C8—1221no—
272Q8⋊C8—618no—
273Q8⋊C8—618no—
274C61C2×#147911yescharacteristic, complemented, Sylow
275C22×Q8—618no—
276C22×Q8—614no—
277C22×Q8—611no—
278C22×Q8—1221no—
279C22×Q8—1222no—
280C22×Q8—1224no—
281C22×Q8C2×#692311yescharacteristic
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—1221no—
286C23×C4—1221no—
287C22×C8—1222no—
288C22×C8—1222no—
289C4×Q8—22no—
290C4×Q8—612no—
291C4×Q8—612no—
292C4×Q8—612no—
293C4×Q8—612no—
294C4×Q8—614no—
295C4×Q8—1224no—
296C4×Q8—1224no—
297C4×Q8—1224no—
298C4×Q8—1221no—
299C4×Q8—1221no—
300C4×Q8—1224no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×Q8—1222no—
304C4×Q8C2×#692314yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—614no—
308C2×C4⋊C4—1222no—
309C2×C4⋊C4—1224no—
310C2×C4⋊C4—1224no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4C2×#692311yescharacteristic
316C2×C42—21no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42—611no—
320C2×C42—612no—
321C2×C42—612no—
322C2×C42—612no—
323C2×C42—612no—
324C2×C42—1224no—
325C2×C42—1224no—
326C2×C42—1221no—
327C2×C42—1221no—
328C2×C42—1221no—
329C2×C42C2×#692311yescharacteristic
330C4⋊C8—614no—
331C4⋊C8—1222no—
332C4⋊C8—1224no—
333C22⋊C8—1224no—
334C22⋊C8—1224no—
335C4×C8—614no—
336C4×C8—1222no—
337C4×C8—1224no—
338C24—611no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—6116no—
342C2×Q8—614no—
343C2×Q8—612no—
344C2×Q8—1224no—
345C2×Q8—1228no—
346C2×Q8—12216no—
347C2×Q8—1228no—
348C2×Q8—1221no—
349C2×Q8—1222no—
350C2×Q8D61⋊C814yes—
351C2×Q8C22×#692312yes—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—612no—
357C22×C4—614no—
358C22×C4—614no—
359C22×C4—612no—
360C22×C4—611no—
361C22×C4—612no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—1224no—
366C22×C4—1224no—
367C22×C4—1228no—
368C22×C4—1224no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—2442no—
372C22×C4—2444no—
373C22×C4C22⋊#692311yescharacteristic
374C22×C4C22⋊#692311yescharacteristic
375C22×C4C22×#692311yescharacteristic
376C2×C8—1224no—
377C2×C8—1224no—
378C2×C8—2444no—
379C2×C8—2444no—
380C4⋊C4—24no—
381C4⋊C4—21no—
382C4⋊C4—612no—
383C4⋊C4—1224no—
384C4⋊C4—1222no—
385C4⋊C4—1222no—
386C4⋊C4—1222no—
387C4⋊C4—1222no—
388C4⋊C4—1221no—
389C4⋊C4—1224no—
390C4⋊C4C22×#692312yes—
391C42—24no—
392C42—611no—
393C42—612no—
394C42—612no—
395C42—611no—
396C42—612no—
397C42—612no—
398C42—611no—
399C42—611no—
400C42—1222no—
401C42—1222no—
402C42—1222no—
403C42—1222no—
404C42—1224no—
405C42C22⋊#692312yes—
406C42C22×#692312yes—
407C23—614no—
408C23—612no—
409C23—1222no—
410C23—1222no—
411C23C2×C22⋊#692311yescharacteristic
412Q8—24no—
413Q8—22no—
414Q8—614no—
415Q8—12216no—
416Q8—1224no—
417Q8—1222no—
418Q8C2×D61⋊C814yes—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—614no—
426C2×C4—614no—
427C2×C4—611no—
428C2×C4—612no—
429C2×C4—611no—
430C2×C4—618no—
431C2×C4—614no—
432C2×C4—614no—
433C2×C4—611no—
434C2×C4—611no—
435C2×C4—1224no—
436C2×C4—1224no—
437C2×C4—12216no—
438C2×C4—1224no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2448no—
445C2×C4—2442no—
446C2×C4C2×C22⋊#692312yes—
447C2×C4C2×C22⋊#692312yes—
448C2×C4C2×C22⋊#692311yescharacteristic
449C2×C4C2×D61⋊C812yes—
450C2×C4D61⋊M1612yes—
451C2×C4C23×#692311yescharacteristic
452C8—2444no—
453C8—2444no—
454C22—614no—
455C22—1228no—
456C22—1222no—
457C22—1222no—
458C22D61⋊(C22⋊C8)12yes—
459C22#1684075512yes—
460C22#1684075912yes—
461C22C22×C22⋊#692311yescharacteristic
462C4—24no—
463C4—22no—
464C4—22no—
465C4—42no—
466C4—614no—
467C4—612no—
468C4—612no—
469C4—1224no—
470C4—1221no—
471C4—1221no—
472C4—2442no—
473C4D61⋊(C22⋊C8)12yes—
474C4C22×D61⋊C811yescharacteristic
475C4C2×D61⋊M1611yescharacteristic
476C2—1224no—
477C2#2146112214yesdirect product factor
478C2C2×D61⋊(C22⋊C8)11yescharacteristic
479C2C2×#1684075511yescharacteristic
480C2C2×#1684075911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC4×C61C23×C8
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1479
LCSG ▷ 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. #21461122C2direct (N × H)
4. C2×#16840612C2semidirect
5. C2×Q8⋊#92420C2semidirect
17. #16840612C22semidirect
18. Q8⋊#92420C22semidirect
48. C2×Q8×D61C8semidirect
114. Q8×D61C2×C8semidirect
242. C2×C61#1479semidirect
274. C61C2×#1479semidirect
477. C2#21461122direct (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×#168407802
#214611222
C2×#168406122
C2×Q8⋊#924202
C2×C4×Q8×D612
C2×#147961