Finite Group Databasebeta

← C2×#21461952 #30616233

Subgroups — C2×#21461952 #30616233

Order 15616.

1878 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840766C211yesmaximal, characteristic, complemented
2C22×#14519842C214yesmaximal, complemented
3C2×C42×#6923C211yesmaximal, characteristic, complemented
4#21461952C218yesmaximal, direct product factor
5C2×#16840313C211yesmaximal, characteristic
6C22×#11758213C2212yes—
7C22×C4×#6923—22no—
8C22×C4×#6923C2212yes—
9#16840766—22no—
10#16840766C2214yescomplemented
11C2×C4⋊#92420—22no—
12C2×#14519842—216no—
13C2×#14519842C22116yescomplemented
14C42×#6923—22no—
15C42×#6923C2214yescomplemented
16C22×#11758226C2212yes—
17#16840313—22no—
18#16840313—22no—
19#16840313C414yescomplemented
20#16840313C2214yes—
21C2×#14519774C411yescharacteristic, complemented
22C2×#14519766C412yescomplemented
23C2×#14519752—22no—
24C2×#14519739—22no—
25C2×C42×D61C2211yescharacteristic
26C2×C4⋊Q8×C61C411yescharacteristic, complemented
27C23×#6923—22no—
28C2×#11758213—28no—
29C2×#11758213—22no—
30C2×#11758213C2314yes—
31C22×#92420—22no—
32C2×C4×#6923—216no—
33C2×C4×#6923—28no—
34C2×C4×#6923—22no—
35C2×C4×#6923—24no—
36C2×C4×#6923D418yescomplemented
37C2×C4×#6923C2314yes—
38C4⋊#92420—28no—
39#14519842—232no—
40C2×#11758226—22no—
41C2×#11758226—22no—
42C2×#11758226—28no—
43C2×#11758226—28no—
44C2×#11758226C2×C414yes—
45C2×#11758226C2314yes—
46C22×D244—22no—
47C22×D244—22no—
48C22×D244C2×C412yes—
49C22×C4×D61—22no—
50C22×C4×D61D412yes—
51C22×C4×D61C2311yescharacteristic
52#14519774—22no—
53#14519774C2×C414yescomplemented
54#14519766—24no—
55#14519766C2×C418yescomplemented
56#14519752—28no—
57#14519752—28no—
58#14519739—28no—
59#14519739—28no—
60C2×#11758198—24no—
61C2×C4×Dic61C2×C411yescharacteristic
62C2×C4×Dic61D412yes—
63C42×D61C2×C412yes—
64C42×D61D412yes—
65C42×D61D412yes—
66C42×D61C2312yes—
67C22×Q8×C61C2×C412yes—
68C4⋊Q8×C61—22no—
69C4⋊Q8×C61C2×C414yescomplemented
70C2×C4⋊C4×C61—22no—
71C2×C42×C61C2×C411yescharacteristic
72C23×D61—22no—
73C23×D61C2×D411yescharacteristic
74C22×#6923—216no—
75C22×#6923—28no—
76C22×#6923—24no—
77C2×Q8×C61—22no—
78C2×Q8×C61—28no—
79C2×Q8×C61C22×C414yes—
80C22×C4×C61—22no—
81C22×C4×C61C22⋊C412yes—
82C22×C4×C61C22×C411yescharacteristic
83C22×Dic61C22⋊C412yes—
84C22×Dic61C2×D411yescharacteristic
85#11758226—216no—
86#11758226—28no—
87#11758226—28no—
88#11758226—48no—
89#11758226—44no—
90#11758226—44no—
91C2×D244—28no—
92C2×D244—24no—
93C2×D244—24no—
94C2×D244—28no—
95C2×D244—22no—
96C2×D244—48no—
97C2×D244—48no—
98C2×D244C22×C414yes—
99C2×C4×D61—28no—
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—44no—
103C2×C4×D61—44no—
104C2×C4×D61C22⋊C414yes—
105C2×C4×D61C22×C411yescharacteristic
106C2×C4×D61C2×D414yes—
107C2×C4×D61C2×D414yes—
108C2×C4×D61C2×D411yescharacteristic
109C2×C4×D61C2×D411yescharacteristic
110C2×C4×D61#4114yes—
111C2×C4×D61C2411yescharacteristic
112C2×#92420—24no—
113C2×#92420—44no—
114C4×#6923—232no—
115C4×#6923—28no—
116C4×#6923—24no—
117C4×#6923C2×D418yescomplemented
118#11758213—28no—
119#11758213—44no—
120C4⋊C4×C61—28no—
121C42×C61C22⋊C412yes—
122C42×C61C22×C412yes—
123#11758198—216no—
124C4×Dic61C22⋊C414yes—
125C4×Dic61C22⋊C412yes—
126C4×Dic61C22×C412yes—
127C4×Dic61C2×D414yes—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—24no—
130C22×D61—24no—
131C22×D61—44no—
132C22×D61—48no—
133C22×D61C2×C22⋊C411yescharacteristic
134C22×D61#12114yes—
135C22×D61C22×D411yescharacteristic
136C2×#6923—216no—
137C2×#6923—232no—
138C2×#6923—28no—
139Q8×C61—28no—
140Q8×C61—44no—
141C2×C4×C61—24no—
142C2×C4×C61—44no—
143C2×C4×C61#10418yescomplemented
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61C2×C22⋊C414yes—
146C2×C4×C61C4×D414yes—
147C2×C4×C61C23×C411yescharacteristic
148C2×Dic61—24no—
149C2×Dic61C2×C22⋊C414yes—
150C2×Dic61C2×C22⋊C411yescharacteristic
151C2×Dic61#12412yes—
152C2×Dic61#12712yes—
153C2×Dic61C22×D411yescharacteristic
154D244—28no—
155D244—48no—
156D244—48no—
157D244—44no—
158D244—416no—
159C4×D61—28no—
160C4×D61—28no—
161C4×D61—44no—
162C4×D61—44no—
163C4×D61—48no—
164C4×D61C4×D414yes—
165C4×D61#12114yes—
166C4×D61#12412yes—
167C4×D61#12712yes—
168C4×D61C22×D412yes—
169C4×D61C2×#4112yes—
170#92420—44no—
171C2×#1962—611nomaximal, Sylow
172C22×C61#39012yes—
173C22×C61C2×#10414yes—
174C22×C61C22×C22⋊C411yescharacteristic
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—28no—
178C2×D61—48no—
179C2×D61—44no—
180C2×D61—88no—
181C2×D61#39012yes—
182C2×D61C2×#12112yes—
183#6923—216no—
184C4×C61—44no—
185C4×C61#39012yes—
186C4×C61C2×#10418yescomplemented
187C4×C61C2×C4×D412yes—
188Dic61—24no—
189Dic61#39012yes—
190Dic61C2×#12411yescharacteristic
191Dic61C2×#12711yescharacteristic
192C2×#532—611no—
193C2×#423—611no—
194C22×#104—614no—
195C2×C43—611no—
196#1962—618no—
197C2×C61#196214yescomplemented
198C2×C61C2×#39011yescharacteristic
199C2×C61C22×#10412yes—
200D61—22no—
201D61—22no—
202D61—84no—
203C22×#41—612no—
204C22×M16—612no—
205#532—614no—
206#532—614no—
207#532—1222no—
208#532—1222no—
209C2×C4⋊Q8#692311yescharacteristic, complemented
210C2×#127—611no—
211C2×#124—612no—
212C2×#121—1222no—
213C2×C4×D4—1222no—
214C22×C42—611no—
215C22×C42—612no—
216C22×C42—1222no—
217#423—614no—
218#423—1222no—
219C2×C4⋊C8—1222no—
220C2×#104—6116no—
221C2×#104—12216no—
222C43—614no—
223C43—1222no—
224C61C2×#196211yescharacteristic, complemented, Sylow
225C2×#41—614no—
226C2×#41—614no—
227C2×#41—1222no—
228C2×#41—1222no—
229C2×#41—1228no—
230C2×#41—1228no—
231C22×Q8C2×#692312yes—
232C22×D4—612no—
233C22×D4—1222no—
234C22×D4—1222no—
235C23×C4—611no—
236C23×C4—612no—
237C23×C4—1222no—
238C23×C4—1222no—
239C2×M16—614no—
240C2×M16—1222no—
241C2×M16—1228no—
242C22×C8—1222no—
243C4⋊Q8—22no—
244C4⋊Q8C2×#692314yescomplemented
245#127—614no—
246#127—1222no—
247#124—618no—
248#124—1224no—
249#121—1228no—
250#121—1228no—
251C4×D4—1228no—
252C4×D4—1228no—
253C2×C4⋊C4—22no—
254C2×C22⋊C4—1224no—
255C2×C42—612no—
256C2×C42—611no—
257C2×C42—612no—
258C2×C42—612no—
259C2×C42—612no—
260C2×C42—612no—
261C2×C42—618no—
262C2×C42—614no—
263C2×C42—1228no—
264C2×C42—1222no—
265C2×C42—1224no—
266C2×C42—12216no—
267C2×C42C2×#692311yescharacteristic
268C4⋊C8—1228no—
269#104—12232no—
270C24—611no—
271C24—1222no—
272#41—1228no—
273#41—12216no—
274#41—1228no—
275#41—2448no—
276#41—2444no—
277#41—2444no—
278C2×Q8—22no—
279C2×Q8—28no—
280C2×Q8C22×#692314yes—
281C2×D4—614no—
282C2×D4—1224no—
283C2×D4—1224no—
284C2×D4—1228no—
285C2×D4—1222no—
286C2×D4—1228no—
287C2×D4—2448no—
288C2×D4—2448no—
289C22×C4—22no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—614no—
294C22×C4—614no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—612no—
298C22×C4—614no—
299C22×C4—614no—
300C22×C4—1224no—
301C22×C4—1224no—
302C22×C4—1224no—
303C22×C4—1228no—
304C22×C4—12216no—
305C22×C4—1228no—
306C22×C4—2444no—
307C22×C4—2444no—
308C22×C4C22⋊#692312yes—
309C22×C4C22×#692311yescharacteristic
310M16—1228no—
311M16—2444no—
312C2×C8—1224no—
313C2×C8—2444no—
314C4⋊C4—28no—
315C22⋊C4—12216no—
316C42—614no—
317C42—614no—
318C42—612no—
319C42—612no—
320C42—618no—
321C42—1228no—
322C42—1224no—
323C42—12232no—
324C42C22⋊#692312yes—
325C42C22×#692312yes—
326C23—614no—
327C23—611no—
328C23—611no—
329C23—1224no—
330C23—1224no—
331C23—2444no—
332C23—2448no—
333C23C2×C22⋊#692311yescharacteristic
334Q8—28no—
335Q8—44no—
336D4—1228no—
337D4—2448no—
338D4—2448no—
339D4—2444no—
340D4—24416no—
341C2×C4—24no—
342C2×C4—44no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—614no—
348C2×C4—612no—
349C2×C4—612no—
350C2×C4—614no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—614no—
354C2×C4—1228no—
355C2×C4—12216no—
356C2×C4—12232no—
357C2×C4—1224no—
358C2×C4—1228no—
359C2×C4—1228no—
360C2×C4—2444no—
361C2×C4—2444no—
362C2×C4—2448no—
363C2×C4#1451984218yescomplemented
364C2×C4C2×C22⋊#692311yescharacteristic
365C2×C4C2×C22⋊#692314yes—
366C2×C4D4×#692314yes—
367C2×C4C23×#692311yescharacteristic
368C8—2444no—
369C22—612no—
370C22—612no—
371C22—1222no—
372C22—1222no—
373C22—1228no—
374C22—4888no—
375C22—2444no—
376C22—2448no—
377C22#1684071412yes—
378C22C2×#1451984214yes—
379C22C22×C22⋊#692311yescharacteristic
380C4—44no—
381C4—611no—
382C4—611no—
383C4—612no—
384C4—12216no—
385C4—1224no—
386C4#1684071412yes—
387C4C2×#1451984218yescomplemented
388C4C2×D4×#692312yes—
389C2—1222no—
390C2—1222no—
391C2—4884no—
392C2#2146195214yesdirect product factor
393C2C2×#1684071411yescharacteristic
394C2C22×#1451984212yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840313C2
cosocleC2×C4×D61C24
hypercenterC2×C4⋊Q8#6923
hypocenterC61C2×#1962
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
1. C2×#16840766C2semidirect
2. C22×#14519842C2semidirect
3. C2×C42×#6923C2semidirect
4. #21461952C2direct (N × H)
10. #16840766C22semidirect
13. C2×#14519842C22semidirect
15. C42×#6923C22semidirect
19. #16840313C4semidirect
21. C2×#14519774C4semidirect
22. C2×#14519766C4semidirect
26. C2×C4⋊Q8×C61C4semidirect
36. C2×C4×#6923D4semidirect
53. #14519774C2×C4semidirect
55. #14519766C2×C4semidirect
69. C4⋊Q8×C61C2×C4semidirect
117. C4×#6923C2×D4semidirect
143. C2×C4×C61#104semidirect
186. C4×C61C2×#104semidirect
197. C2×C61#1962semidirect
209. C2×C4⋊Q8#6923semidirect
224. C61C2×#1962semidirect
244. C4⋊Q8C2×#6923semidirect
363. C2×C4#14519842semidirect
387. C4C2×#14519842semidirect
392. C2#21461952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407662
C22×#145198422
C2×C42×#69232
#214619522
C2×#168403132
C2×#196261