Finite Group Databasebeta

← C2×#21462113 #30624006

Subgroups — C2×#21462113 #30624006

Order 15616.

1306 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×#16840749C212yesmaximal, complemented
2#21462113C218yesmaximal, direct product factor
3C2×#16840672C212yesmaximal, complemented
4C2×#16840671C212yesmaximal, complemented
5C2×#16840311C211yesmaximal, characteristic
6C22×#11758217—22no—
7#16840749—24no—
8#16840749C2218yescomplemented
9C2×#14519838C2214yes—
10C2×#14519837—22no—
11#16840672C2218yescomplemented
12#16840671C2218yescomplemented
13C22×#11758226C411yescharacteristic
14C22×#11758224C2211yescharacteristic
15#16840311—24no—
16#16840311C414yes—
17#16840311C2214yes—
18C2×#14519775C2211yescharacteristic
19C2×#14519773C411yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519750—22no—
22C2×#14519737—22no—
23C2×C42×D61C411yescharacteristic
24C2×#124×C61C411yescharacteristic
25C2×#11758217—24no—
26C2×#11758217—28no—
27C2×#11758217—42no—
28C2×#11758217—44no—
29C22×#92420—42no—
30#14519838—24no—
31#14519838C2318yes—
32#14519837—28no—
33C2×#11758226—22no—
34C2×#11758226—42no—
35C2×#11758226—41no—
36C2×#11758226—41no—
37C2×#11758226C2×C414yes—
38C2×#11758224—41no—
39C2×#11758224—41no—
40C2×#11758224—42no—
41C2×#11758224C2×C412yes—
42C2×#11758224D414yes—
43C2×#11758224C2312yes—
44C22×Dic122C2311yescharacteristic
45C22×D244—21no—
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—22no—
48C22×C22⋊D61D412yes—
49C23×Dic61D412yes—
50C22×C4×D61—21no—
51C22×C4×D61—21no—
52C22×C4×D61C2×C411yescharacteristic
53#14519775—22no—
54#14519775C2×C412yes—
55#14519775C2312yes—
56#14519773—22no—
57#14519773C2×C414yes—
58#14519765—22no—
59#14519765C2×C412yes—
60#14519765C2312yes—
61#14519750—28no—
62#14519750—28no—
63#14519737—28no—
64#14519737—28no—
65C2×#11758196—22no—
66C2×#11758198—22no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61C2×C411yescharacteristic
69C42×D61—22no—
70C42×D61C2×C414yes—
71C22×Q8×C61C2×C411yescharacteristic
72C22×D4×C61C2×C411yescharacteristic
73#124×C61—22no—
74#124×C61C2×C414yes—
75C2×C22⋊C4×C61—22no—
76C2×C42×C61C2×C411yescharacteristic
77C24×C61C22⋊C412yes—
78C23×D61—21no—
79C23×D61C22⋊C411yescharacteristic
80C2×Q8×C61—21no—
81C2×Q8×C61—41no—
82C2×Q8×C61—41no—
83C2×Q8×C61C22×C412yes—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61C22⋊C412yes—
87C2×D4×C61C22×C412yes—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C2×C22⋊D61—28no—
92C2×C22⋊D61—42no—
93C2×C22⋊D61—42no—
94C2×C22⋊D61—48no—
95C2×C22⋊D61C22⋊C414yes—
96C2×C22⋊D61C2×D414yes—
97C22×Dic61—21no—
98C22×Dic61—22no—
99C22×Dic61—22no—
100C22×Dic61—24no—
101C22×Dic61C22⋊C414yes—
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C2×D412yes—
104C22×Dic61C2×D414yes—
105#11758226—44no—
106#11758226—44no—
107#11758226—44no—
108#11758226—44no—
109#11758224—42no—
110#11758224—42no—
111#11758224—44no—
112#11758224—44no—
113#11758224—42no—
114#11758224—42no—
115C2×D244—24no—
116C2×D244—21no—
117C2×D244—41no—
118C2×D244—41no—
119C2×D244—42no—
120C2×D244—42no—
121C2×D244C22×C412yes—
122C2×C4×D61—22no—
123C2×C4×D61—21no—
124C2×C4×D61—21no—
125C2×C4×D61—24no—
126C2×C4×D61—24no—
127C2×C4×D61—44no—
128C2×C4×D61—42no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61C22⋊C412yes—
132C2×C4×D61C22×C412yes—
133C2×Dic122—41no—
134C2×Dic122—41no—
135C2×Dic122C22×C411yescharacteristic
136C2×Dic122C2×D412yes—
137C2×Dic122C2411yescharacteristic
138#11758217—28no—
139#11758217—44no—
140#11758217—48no—
141C2×#92420—44no—
142C2×#92420—48no—
143C22⋊C4×C61—28no—
144C42×C61—21no—
145C42×C61C22×C412yes—
146#11758198—24no—
147#11758198—24no—
148#11758196—24no—
149#11758196—24no—
150C4×Dic61—21no—
151C4×Dic61—24no—
152C4×Dic61C22×C412yes—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—44no—
156C23×C61C2×C22⋊C411yescharacteristic
157C23×C61C2×C22⋊C414yes—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—22no—
161C22×D61—42no—
162C22×D61—44no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61C2×C22⋊C412yes—
166Q8×C61—42no—
167Q8×C61—42no—
168D4×C61—42no—
169D4×C61—42no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—42no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61C2×C22⋊C411yescharacteristic
178C2×C4×C61C23×C411yescharacteristic
179C22⋊D61—44no—
180C22⋊D61—44no—
181C22⋊D61—416no—
182C2×Dic61—24no—
183C2×Dic61—22no—
184C2×Dic61—22no—
185C2×Dic61—22no—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—24no—
189C2×Dic61—24no—
190C2×Dic61#9912yes—
191C2×Dic61#9911yescharacteristic
192C2×Dic61#9911yescharacteristic
193C2×Dic61C2×C22⋊C412yes—
194C2×Dic61C2×C22⋊C412yes—
195C2×Dic61C22×D412yes—
196D244—42no—
197D244—42no—
198D244—48no—
199C4×D61—22no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—48no—
204C4×D61—44no—
205C4×D61—44no—
206Dic122—41no—
207Dic122—42no—
208Dic122—41no—
209#92420—48no—
210C2×#2132—611nomaximal, Sylow
211C22×C61—22no—
212C22×C61—24no—
213C22×C61—44no—
214C22×C61—44no—
215C22×C61—82no—
216C22×C61C2×#9911yescharacteristic
217C22×C61C2×#9911yescharacteristic
218C22×C61C22×C22⋊C411yescharacteristic
219C2×D61—22no—
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—42no—
223C2×D61—44no—
224C2×D61—42no—
225C2×D61—82no—
226C2×D61—82no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—42no—
230C4×C61—42no—
231Dic61—24no—
232Dic61—22no—
233Dic61—22no—
234Dic61C2×#9912yes—
235Dic61C2×#9912yes—
236C2×#532—611no—
237C2×#413—612no—
238#2132—618no—
239C2×#356—612no—
240C2×#355—612no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—44no—
244C2×C61#213212yescomplemented
245C2×C61C22×#9911yescharacteristic
246D61—42no—
247D61—82no—
248C22×#41—611no—
249C22×#41—611no—
250C22×M16—1222no—
251#532—614no—
252#532—614no—
253#532—1224no—
254C2×C4⋊Q8—611no—
255C2×#127—611no—
256C2×#124—611no—
257C2×#124#692311yescharacteristic
258C2×#121—1222no—
259C2×C4×D4—1222no—
260C22×C42—611no—
261#413—618no—
262#413—1224no—
263C2×#101—614no—
264C2×#100—1222no—
265#356—618no—
266#355—618no—
267C61C2×#213211yescharacteristic, complemented, Sylow
268C2×#41—614no—
269C2×#41—612no—
270C2×#41—612no—
271C2×#41—614no—
272C2×#41—1222no—
273C2×#41—2441no—
274C2×#41—2442no—
275C2×#41—2441no—
276C2×#41—2442no—
277C2×#41—2441no—
278C2×#41—2441no—
279C22×Q8—611no—
280C22×Q8C2×#692311yescharacteristic
281C22×D4—612no—
282C22×D4—611no—
283C22×D4—1221no—
284C22×D4—1222no—
285C22×D4C2×#692311yescharacteristic
286C23×C4—612no—
287C23×C4—611no—
288C23×C4—1221no—
289C23×C4—1221no—
290C2×M16—1224no—
291C2×M16—1228no—
292C2×M16—2444no—
293C2×M16—2442no—
294C22×C8—2442no—
295C4⋊Q8—612no—
296C4⋊Q8—612no—
297C4⋊Q8—1222no—
298#127—614no—
299#127—1222no—
300#124—22no—
301#124—612no—
302#124—612no—
303#124—1222no—
304#124C2×#692314yes—
305#121—1228no—
306#121—1228no—
307C4×D4—1228no—
308C4×D4—1228no—
309C2×C4⋊C4—1222no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—1222no—
312C2×C42—611no—
313C2×C42—614no—
314C2×C42—1222no—
315C2×C42—1221no—
316C2×C42C2×#692311yescharacteristic
317#101—618no—
318#101—1224no—
319#100—1228no—
320C24—611no—
321C24—1221no—
322C24C22⋊#692312yes—
323#41—2442no—
324#41—2444no—
325#41—2442no—
326#41—2444no—
327#41—2442no—
328#41—2442no—
329#41—2444no—
330#41—2444no—
331#41—2444no—
332#41—2444no—
333C2×Q8—21no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×Q8—612no—
337C2×Q8—611no—
338C2×Q8—611no—
339C2×Q8—2441no—
340C2×Q8—2441no—
341C2×Q8C22×#692312yes—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—614no—
345C2×D4—614no—
346C2×D4—612no—
347C2×D4—1224no—
348C2×D4—1228no—
349C2×D4—1221no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2442no—
353C2×D4—2442no—
354C2×D4—2442no—
355C2×D4—2442no—
356C2×D4—2448no—
357C2×D4C22⋊#692312yes—
358C2×D4C22×#692312yes—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—611no—
362C22×C4—614no—
363C22×C4—614no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—1222no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—1224no—
371C22×C4—1224no—
372C22×C4—1222no—
373C22×C4—1224no—
374C22×C4—1222no—
375C22×C4—1221no—
376C22×C4—2442no—
377C22×C4—2441no—
378C22×C4—2441no—
379C22×C4—2444no—
380C22×C4C22×#692311yescharacteristic
381M16—1228no—
382M16—2448no—
383M16—2444no—
384C2×C8—2448no—
385C2×C8—2444no—
386C4⋊C4—1224no—
387C4⋊C4—1224no—
388C22⋊C4—28no—
389C22⋊C4—1224no—
390C22⋊C4—1224no—
391C42—21no—
392C42—612no—
393C42—1224no—
394C42—1221no—
395C42C22×#692312yes—
396C23—22no—
397C23—22no—
398C23—44no—
399C23—612no—
400C23—1221no—
401C23—1221no—
402C23—1222no—
403C23—2444no—
404C23—2442no—
405C23—2441no—
406C23—2441no—
407C23C2×C22⋊#692314yes—
408C23C2×C22⋊#692311yescharacteristic
409Q8—42no—
410Q8—42no—
411Q8—2442no—
412Q8—2441no—
413Q8—2441no—
414D4—42no—
415D4—42no—
416D4—2442no—
417D4—2442no—
418D4—2448no—
419D4—2444no—
420D4—2444no—
421D4—24416no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—612no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—1222no—
436C2×C4—1222no—
437C2×C4—1222no—
438C2×C4—1222no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1224no—
442C2×C4—1224no—
443C2×C4—1224no—
444C2×C4—1222no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—2444no—
448C2×C4—2444no—
449C2×C4—2448no—
450C2×C4C2×C22⋊#692311yescharacteristic
451C2×C4C23×#692311yescharacteristic
452C8—2448no—
453C22—22no—
454C22—24no—
455C22—44no—
456C22—44no—
457C22—82no—
458C22—1222no—
459C22—4882no—
460C22—4882no—
461C22—2444no—
462C22—2442no—
463C22—2442no—
464C22—2442no—
465C22—2442no—
466C22D61⋊#9911yescharacteristic
467C22D61⋊#9911yescharacteristic
468C22C22×C22⋊#692311yescharacteristic
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—612no—
474C4—612no—
475C4—1224no—
476C4—1222no—
477C4—1222no—
478C2—21no—
479C2—21no—
480C2—44no—
481C2—4882no—
482C2—2442no—
483C2#2146211312yesdirect product factor
484C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840311C2
cosocleC2×Dic122C24
hypercenterC2×#124#6923
hypocenterC61C2×#2132
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16840749C2semidirect
2. #21462113C2direct (N × H)
3. C2×#16840672C2semidirect
4. C2×#16840671C2semidirect
8. #16840749C22semidirect
11. #16840672C22semidirect
12. #16840671C22semidirect
244. C2×C61#2132semidirect
267. C61C2×#2132semidirect
483. C2#21462113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407492
#214621132
C2×#168406722
C2×#168406712
C2×#168403112
C2×#213261