Finite Group Databasebeta

← C2×#21462110 #30624002

Subgroups — C2×#21462110 #30624002

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×#16840748C212yesmaximal, complemented
2#21462110C218yesmaximal, direct product factor
3C2×#16840672C212yesmaximal, complemented
4C2×#16840670C212yesmaximal, complemented
5C2×#16840308C211yesmaximal, characteristic
6C2×D61⋊M16—22no—
7#16840748—24no—
8#16840748C2218yescomplemented
9C2×#14519838C2214yes—
10C2×#14519837—22no—
11#16840672C2218yescomplemented
12#16840670C2218yescomplemented
13C22×#11758222C2211yescharacteristic
14#16840308—24no—
15#16840308C414yes—
16#16840308C2214yes—
17C2×#14519775C2211yescharacteristic
18C2×#14519773C411yescharacteristic
19C2×#14519766C411yescharacteristic
20C2×#14519764C2211yescharacteristic
21C2×#14519749—22no—
22C2×C4×C22⋊D61—22no—
23C22×C4×Dic61C411yescharacteristic
24C22×#41×C61C411yescharacteristic
25C2×#11758213—42no—
26D61⋊M16—28no—
27D61⋊M16—44no—
28C2×#11758217—24no—
29C2×D61⋊C8—42no—
30#14519838—24no—
31#14519838C2318yes—
32#14519837—28no—
33C2×#11758222—41no—
34C2×#11758222—42no—
35C2×#11758222—41no—
36C2×#11758222C2×C412yes—
37C2×#11758222D414yes—
38C2×#11758222C2312yes—
39C22×Dic122C2311yescharacteristic
40C22×D244C2×C411yescharacteristic
41C22×C22⋊D61—22no—
42C22×C22⋊D61D412yes—
43C23×Dic61—21no—
44C22×C4×D61D412yes—
45#14519775—22no—
46#14519775C2×C412yes—
47#14519775C2312yes—
48#14519773—22no—
49#14519773C2×C414yes—
50#14519766—22no—
51#14519766C2×C414yes—
52#14519764—22no—
53#14519764C2×C412yes—
54#14519764C2312yes—
55#14519749—28no—
56#14519749—28no—
57C4×C22⋊D61—28no—
58C4×C22⋊D61—28no—
59C2×#11758196—22no—
60C2×C22⋊Dic61—22no—
61C2×#11758198—22no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—22no—
64C2×C4×Dic61C2×C411yescharacteristic
65C2×C4×Dic61C2×C411yescharacteristic
66C2×C4×Dic61C2×C414yes—
67C2×#41×C61—22no—
68C2×#41×C61—42no—
69C2×#41×C61—41no—
70C2×#41×C61—41no—
71C2×#41×C61C2×C414yes—
72C22×Q8×C61C2×C411yescharacteristic
73C22×D4×C61—21no—
74C22×D4×C61C2×C411yescharacteristic
75C23×C4×C61—21no—
76C23×C4×C61C2×C411yescharacteristic
77C24×C61—21no—
78C24×C61C22⋊C411yescharacteristic
79C23×D61C22⋊C412yes—
80#41×C61—44no—
81#41×C61—44no—
82#41×C61—44no—
83#41×C61—44no—
84C2×Q8×C61—21no—
85C2×Q8×C61—41no—
86C2×Q8×C61—41no—
87C2×Q8×C61C22×C412yes—
88C2×D4×C61—24no—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—42no—
93C2×D4×C61—42no—
94C2×D4×C61C22×C412yes—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—24no—
100C22×C4×C61—42no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61C22⋊C412yes—
104C22×C4×C61C22⋊C411yescharacteristic
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C22×C412yes—
107C2×C22⋊D61—28no—
108C2×C22⋊D61—42no—
109C2×C22⋊D61—42no—
110C2×C22⋊D61—48no—
111C2×C22⋊D61C22⋊C414yes—
112C2×C22⋊D61C2×D414yes—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—24no—
116C22×Dic61—44no—
117C22×Dic61C2×D412yes—
118#11758222—42no—
119#11758222—42no—
120#11758222—44no—
121#11758222—44no—
122#11758222—42no—
123#11758222—42no—
124C2×D244—41no—
125C2×D244—41no—
126C2×D244C22⋊C412yes—
127C2×D244C22×C412yes—
128C2×C4×D61—22no—
129C2×C4×D61—24no—
130C2×C4×D61—22no—
131C2×C4×D61C22⋊C414yes—
132C2×C4×D61C2×D414yes—
133C2×Dic122—41no—
134C2×Dic122—41no—
135C2×Dic122C22×C411yescharacteristic
136C2×Dic122C2×D412yes—
137C2×Dic122C2411yescharacteristic
138#11758217—28no—
139#11758217—44no—
140C2×#92420—44no—
141#11758213—48no—
142D61⋊C8—48no—
143C22⋊Dic61—24no—
144C22⋊Dic61—24no—
145#11758198—28no—
146#11758196—24no—
147#11758196—24no—
148C4×Dic61—24no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61C22×C412yes—
152C4×Dic61C22×C412yes—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—22no—
156C23×C61—42no—
157C23×C61—44no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61C2×C22⋊C411yescharacteristic
161C23×C61C2×C22⋊C412yes—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—44no—
165C22×D61C2×C22⋊C414yes—
166Q8×C61—42no—
167Q8×C61—42no—
168D4×C61—42no—
169D4×C61—42no—
170D4×C61—48no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—44no—
181C2×C4×C61—44no—
182C2×C4×C61#9912yes—
183C2×C4×C61#9911yescharacteristic
184C2×C4×C61#9911yescharacteristic
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×C4×C61C2×C22⋊C412yes—
187C2×C4×C61C23×C411yescharacteristic
188C22⋊D61—44no—
189C22⋊D61—44no—
190C22⋊D61—416no—
191C2×Dic61—24no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—48no—
197C2×Dic61—42no—
198C2×Dic61C2×C22⋊C412yes—
199C2×Dic61C22×D412yes—
200D244—42no—
201D244—42no—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—24no—
205C4×D61—24no—
206Dic122—41no—
207Dic122—42no—
208Dic122—41no—
209#92420—48no—
210C2×#2132—611nomaximal, Sylow
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—44no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—82no—
219C22×C61—82no—
220C22×C61C2×#9911yescharacteristic
221C22×C61C2×#9911yescharacteristic
222C22×C61C22×C22⋊C411yescharacteristic
223C2×D61—24no—
224C2×D61—44no—
225C2×D61—44no—
226C2×D61—82no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—42no—
230C4×C61C2×#9912yes—
231C4×C61C2×#9912yes—
232Dic61—24no—
233Dic61—22no—
234Dic61—22no—
235Dic61—42no—
236C2×#532—611no—
237C2×#413—612no—
238#2132—618no—
239C2×#356—612no—
240C2×#355—612no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—42no—
244C2×C61—82no—
245C2×C61#213212yescomplemented
246C2×C61C22×#9911yescharacteristic
247D61—44no—
248C22×#41—611no—
249C22×#41#692311yescharacteristic
250C22×M16—1222no—
251#532—614no—
252#532—614no—
253#532—1224no—
254C2×C4⋊Q8—611no—
255C2×#127—611no—
256C2×#124—611no—
257C2×#124—611no—
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—22no—
269C2×#41—42no—
270C2×#41—41no—
271C2×#41—41no—
272C2×#41—614no—
273C2×#41—612no—
274C2×#41—612no—
275C2×#41—2441no—
276C2×#41—2442no—
277C2×#41—2441no—
278C2×#41C2×#692314yes—
279C22×Q8—611no—
280C22×Q8C2×#692311yescharacteristic
281C22×D4—21no—
282C22×D4—612no—
283C22×D4—611no—
284C22×D4—1222no—
285C22×D4C2×#692311yescharacteristic
286C23×C4—21no—
287C23×C4—612no—
288C23×C4—1221no—
289C23×C4C2×#692311yescharacteristic
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—614no—
301#124—612no—
302#124—612no—
303#124—1222no—
304#124—1222no—
305#121—1228no—
306#121—1228no—
307C4×D4—1228no—
308C4×D4—1228no—
309C2×C4⋊C4—1222no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C42—611no—
313C2×C42—611no—
314C2×C42—614no—
315C2×C42—1222no—
316C2×C42—1221no—
317#101—618no—
318#101—1224no—
319#100—1228no—
320C24—21no—
321C24—612no—
322C24C22⋊#692311yescharacteristic
323#41—44no—
324#41—44no—
325#41—44no—
326#41—44no—
327#41—2444no—
328#41—2444no—
329#41—2442no—
330#41—2442no—
331#41—2442no—
332#41—2442no—
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—24no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—614no—
349C2×D4—614no—
350C2×D4—612no—
351C2×D4—612no—
352C2×D4—1228no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2442no—
356C2×D4—2442no—
357C2×D4—2448no—
358C2×D4C22×#692312yes—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—24no—
364C22×C4—42no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—612no—
368C22×C4—614no—
369C22×C4—614no—
370C22×C4—1221no—
371C22×C4—1222no—
372C22×C4—1224no—
373C22×C4—1222no—
374C22×C4—1221no—
375C22×C4—1224no—
376C22×C4—2444no—
377C22×C4C22⋊#692312yes—
378C22×C4C22⋊#692311yescharacteristic
379C22×C4C22×#692311yescharacteristic
380C22×C4C22×#692312yes—
381M16—1228no—
382M16—2448no—
383M16—2444no—
384C2×C8—2448no—
385C2×C8—2444no—
386C4⋊C4—1224no—
387C4⋊C4—1224no—
388C22⋊C4—1228no—
389C22⋊C4—1224no—
390C22⋊C4—1224no—
391C42—612no—
392C42—612no—
393C42—1224no—
394C42—1221no—
395C42—1221no—
396C23—21no—
397C23—21no—
398C23—22no—
399C23—42no—
400C23—44no—
401C23—41no—
402C23—41no—
403C23—614no—
404C23—1222no—
405C23—1222no—
406C23—2444no—
407C23C2×C22⋊#692311yescharacteristic
408C23C2×C22⋊#692312yes—
409Q8—42no—
410Q8—42no—
411Q8—2442no—
412Q8—2441no—
413Q8—2441no—
414D4—42no—
415D4—42no—
416D4—48no—
417D4—2442no—
418D4—2442no—
419D4—2444no—
420D4—2444no—
421D4—24416no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—1224no—
436C2×C4—1222no—
437C2×C4—1222no—
438C2×C4—1222no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1224no—
442C2×C4—1224no—
443C2×C4—1222no—
444C2×C4—2448no—
445C2×C4—2442no—
446C2×C4#1451983511yescharacteristic
447C2×C4#1451983512yes—
448C2×C4#1451983511yescharacteristic
449C2×C4C2×C22⋊#692311yescharacteristic
450C2×C4C2×C22⋊#692312yes—
451C2×C4C23×#692311yescharacteristic
452C8—2448no—
453C22—22no—
454C22—22no—
455C22—42no—
456C22—42no—
457C22—44no—
458C22—42no—
459C22—42no—
460C22—82no—
461C22—82no—
462C22—1224no—
463C22—4882no—
464C22—2444no—
465C22—2444no—
466C22C2×#1451983511yescharacteristic
467C22C2×#1451983511yescharacteristic
468C22C22×C22⋊#692311yescharacteristic
469C4—21no—
470C4—21no—
471C4—42no—
472C4—1224no—
473C4—1222no—
474C4—1222no—
475C4—2442no—
476C4C2×#1451983512yes—
477C4C2×#1451983512yes—
478C2—21no—
479C2—21no—
480C2—42no—
481C2—82no—
482C2—2444no—
483C2#2146211012yesdirect product factor
484C2C22×#1451983511yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×#41×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840308C2
cosocleC2×Dic122C24
hypercenterC22×#41#6923
hypocenterC61C2×#2132
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16840748C2semidirect
2. #21462110C2direct (N × H)
3. C2×#16840672C2semidirect
4. C2×#16840670C2semidirect
8. #16840748C22semidirect
11. #16840672C22semidirect
12. #16840670C22semidirect
245. C2×C61#2132semidirect
267. C61C2×#2132semidirect
483. C2#21462110direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407482
#214621102
C2×#168406722
C2×#168406702
C2×#168403082
C2×#213261