Finite Group Databasebeta

← C2×#21461953 #30616234

Subgroups — C2×#21461953 #30616234

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×#14519841C214yesmaximal, complemented
3C2×C42×#6923C211yesmaximal, characteristic, complemented
4#21461953C218yesmaximal, direct product factor
5C2×#16840310C211yesmaximal, characteristic
6C22×#11758213C2212yes—
7C22×C4×#6923—22no—
8C22×C4×#6923C2212yes—
9#16840766—22no—
10#16840766C2214yescomplemented
11C2×C4⋊#92420—22no—
12C2×#14519841—216no—
13C2×#14519841C22116yescomplemented
14C42×#6923—22no—
15C42×#6923C2214yescomplemented
16C22×#11758224C2212yes—
17#16840310—22no—
18#16840310—22no—
19#16840310C414yescomplemented
20#16840310C2214yes—
21C2×#14519777C411yescharacteristic, complemented
22C2×#14519764C412yescomplemented
23C2×#14519748—22no—
24C2×D4×Dic61—22no—
25C2×C42×D61C2211yescharacteristic
26C2×#127×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#14519841—232no—
40C2×#11758224—28no—
41C2×#11758224—22no—
42C2×#11758224—22no—
43C2×#11758224—28no—
44C2×#11758224C2×C414yes—
45C2×#11758224C2314yes—
46C22×Dic122C2×C412yes—
47C22×C22⋊D61—22no—
48C23×Dic61—22no—
49C22×C4×D61D412yes—
50C22×C4×D61C2311yescharacteristic
51#14519777—22no—
52#14519777C2×C414yescomplemented
53#14519764—24no—
54#14519764C2×C418yescomplemented
55#14519748—28no—
56#14519748—28no—
57D4×Dic61—28no—
58D4×Dic61—28no—
59C2×C4⋊Dic61—22no—
60C2×C22⋊Dic61—24no—
61C2×C4×Dic61C2×C411yescharacteristic
62C2×C4×Dic61D412yes—
63C42×D61C2×C412yes—
64C42×D61D412yes—
65C42×D61D412yes—
66C42×D61C2312yes—
67C22×D4×C61—22no—
68C22×D4×C61C2×C412yes—
69#127×C61—22no—
70#127×C61C2×C414yescomplemented
71C2×C42×C61C2×C411yescharacteristic
72C24×C61—22no—
73C23×D61C2×D411yescharacteristic
74C22×#6923—216no—
75C22×#6923—28no—
76C22×#6923—24no—
77C2×D4×C61—22no—
78C2×D4×C61—28no—
79C2×D4×C61—28no—
80C2×D4×C61—48no—
81C2×D4×C61C22×C414yes—
82C22×C4×C61C22⋊C412yes—
83C22×C4×C61C22×C411yescharacteristic
84C2×C22⋊D61—24no—
85C2×C22⋊D61—24no—
86C2×C22⋊D61—48no—
87C22×Dic61—22no—
88C22×Dic61—24no—
89C22×Dic61—24no—
90C22×Dic61—44no—
91C22×Dic61—44no—
92C22×Dic61C22⋊C412yes—
93C22×Dic61C2×D411yescharacteristic
94#11758224—216no—
95#11758224—28no—
96#11758224—28no—
97#11758224—48no—
98#11758224—44no—
99#11758224—44no—
100C2×C4×D61—28no—
101C2×C4×D61C22⋊C414yes—
102C2×C4×D61C22×C411yescharacteristic
103C2×C4×D61C2×D414yes—
104C2×C4×D61C2×D414yes—
105C2×C4×D61C2×D411yescharacteristic
106C2×C4×D61C2×D411yescharacteristic
107C2×C4×D61#4114yes—
108C2×C4×D61C2411yescharacteristic
109C2×Dic122—28no—
110C2×Dic122—22no—
111C2×Dic122C22×C414yes—
112C2×#92420—24no—
113C2×#92420—44no—
114C4×#6923—232no—
115C4×#6923—28no—
116C4×#6923—24no—
117C4×#6923C2×D418yescomplemented
118#11758213—28no—
119#11758213—44no—
120C42×C61C22⋊C412yes—
121C42×C61C22×C412yes—
122C22⋊Dic61—216no—
123C4⋊Dic61—28no—
124C4×Dic61C22⋊C414yes—
125C4×Dic61C22⋊C412yes—
126C4×Dic61C22×C412yes—
127C4×Dic61C2×D414yes—
128C23×C61—24no—
129C23×C61—44no—
130C23×C61—48no—
131C23×C61C2×C22⋊C411yescharacteristic
132C22×D61—24no—
133C22×D61C2×C22⋊C411yescharacteristic
134C22×D61#12114yes—
135C22×D61C22×D411yescharacteristic
136C2×#6923—216no—
137C2×#6923—232no—
138C2×#6923—28no—
139D4×C61—28no—
140D4×C61—44no—
141D4×C61—416no—
142C2×C4×C61#10418yescomplemented
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61C2×C22⋊C414yes—
145C2×C4×C61C4×D414yes—
146C2×C4×C61C23×C411yescharacteristic
147C22⋊D61—48no—
148C22⋊D61—48no—
149C2×Dic61—24no—
150C2×Dic61—24no—
151C2×Dic61—44no—
152C2×Dic61—44no—
153C2×Dic61—44no—
154C2×Dic61—48no—
155C2×Dic61C2×C22⋊C414yes—
156C2×Dic61C2×C22⋊C411yescharacteristic
157C2×Dic61#12412yes—
158C2×Dic61#12712yes—
159C2×Dic61C22×D411yescharacteristic
160C4×D61—28no—
161C4×D61—28no—
162C4×D61C4×D414yes—
163C4×D61#12114yes—
164C4×D61#12412yes—
165C4×D61#12712yes—
166C4×D61C22×D412yes—
167C4×D61C2×#4112yes—
168Dic122—28no—
169Dic122—44no—
170#92420—44no—
171C2×#1962—611nomaximal, Sylow
172C22×C61—48no—
173C22×C61—44no—
174C22×C61—88no—
175C22×C61#39012yes—
176C22×C61C2×#10414yes—
177C22×C61C22×C22⋊C411yescharacteristic
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—28no—
181C2×D61#39012yes—
182C2×D61C2×#12112yes—
183#6923—216no—
184C4×C61#39012yes—
185C4×C61C2×#10418yescomplemented
186C4×C61C2×C4×D412yes—
187Dic61—24no—
188Dic61—44no—
189Dic61#39012yes—
190Dic61C2×#12411yescharacteristic
191Dic61C2×#12711yescharacteristic
192C2×#532—611no—
193C2×#423—611no—
194C22×#104—614no—
195C2×C43—611no—
196#1962—618no—
197C2×C61—84no—
198C2×C61#196214yescomplemented
199C2×C61C2×#39011yescharacteristic
200C2×C61C22×#10412yes—
201D61—22no—
202D61—22no—
203C22×#41—612no—
204C22×M16—612no—
205#532—614no—
206#532—614no—
207#532—1222no—
208#532—1222no—
209C2×C4⋊Q8—611no—
210C2×#127#692311yescharacteristic, complemented
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×Q8—612no—
232C22×D4—22no—
233C22×D4—1222no—
234C22×D4C2×#692312yes—
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—614no—
244C4⋊Q8—1222no—
245#127—22no—
246#127C2×#692314yescomplemented
247#124—618no—
248#124—1224no—
249#121—1228no—
250#121—1228no—
251C4×D4—1228no—
252C4×D4—1228no—
253C2×C4⋊C4—1222no—
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—22no—
271C24—611no—
272#41—1228no—
273#41—12216no—
274#41—1228no—
275#41—2448no—
276#41—2444no—
277#41—2444no—
278C2×Q8—614no—
279C2×Q8—1222no—
280C2×Q8—1228no—
281C2×D4—28no—
282C2×D4—22no—
283C2×D4—28no—
284C2×D4—48no—
285C2×D4—1224no—
286C2×D4—1224no—
287C2×D4—2448no—
288C2×D4C22×#692314yes—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—614no—
293C22×C4—614no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—612no—
297C22×C4—614no—
298C22×C4—614no—
299C22×C4—1224no—
300C22×C4—1224no—
301C22×C4—1224no—
302C22×C4—1228no—
303C22×C4—12216no—
304C22×C4—1228no—
305C22×C4—1222no—
306C22×C4—2444no—
307C22×C4—2444no—
308C22×C4C22⋊#692312yes—
309C22×C4C22×#692311yescharacteristic
310M16—1228no—
311M16—2444no—
312C2×C8—1224no—
313C2×C8—2444no—
314C4⋊C4—1228no—
315C22⋊C4—12216no—
316C42—614no—
317C42—614no—
318C42—612no—
319C42—612no—
320C42—618no—
321C42—1228no—
322C42—1224no—
323C42—12232no—
324C42C22⋊#692312yes—
325C42C22×#692312yes—
326C23—24no—
327C23—44no—
328C23—48no—
329C23—614no—
330C23—611no—
331C23—611no—
332C23—1224no—
333C23C2×C22⋊#692311yescharacteristic
334Q8—1228no—
335Q8—2444no—
336D4—28no—
337D4—44no—
338D4—416no—
339D4—2448no—
340D4—2448no—
341C2×C4—612no—
342C2×C4—612no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—614no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—614no—
349C2×C4—612no—
350C2×C4—612no—
351C2×C4—614no—
352C2×C4—1228no—
353C2×C4—12216no—
354C2×C4—12232no—
355C2×C4—1224no—
356C2×C4—1228no—
357C2×C4—1228no—
358C2×C4—1224no—
359C2×C4—2444no—
360C2×C4—2444no—
361C2×C4—2448no—
362C2×C4—2444no—
363C2×C4#1451984118yescomplemented
364C2×C4C2×C22⋊#692311yescharacteristic
365C2×C4C2×C22⋊#692314yes—
366C2×C4D4×#692314yes—
367C2×C4C23×#692311yescharacteristic
368C8—2444no—
369C22—44no—
370C22—48no—
371C22—88no—
372C22—612no—
373C22—612no—
374C22—1222no—
375C22—1222no—
376C22—1228no—
377C22#1684071412yes—
378C22C2×#1451984114yes—
379C22C22×C22⋊#692311yescharacteristic
380C4—611no—
381C4—611no—
382C4—612no—
383C4—12216no—
384C4—1224no—
385C4—2444no—
386C4#1684071412yes—
387C4C2×#1451984118yescomplemented
388C4C2×D4×#692312yes—
389C2—84no—
390C2—1222no—
391C2—1222no—
392C2#2146195314yesdirect product factor
393C2C2×#1684071411yescharacteristic
394C2C22×#1451984112yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#127×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840310C2
cosocleC2×C4×D61C24
hypercenterC2×#127#6923
hypocenterC61C2×#1962
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#16840766C2semidirect
2. C22×#14519841C2semidirect
3. C2×C42×#6923C2semidirect
4. #21461953C2direct (N × H)
10. #16840766C22semidirect
13. C2×#14519841C22semidirect
15. C42×#6923C22semidirect
19. #16840310C4semidirect
21. C2×#14519777C4semidirect
22. C2×#14519764C4semidirect
26. C2×#127×C61C4semidirect
36. C2×C4×#6923D4semidirect
52. #14519777C2×C4semidirect
54. #14519764C2×C4semidirect
70. #127×C61C2×C4semidirect
117. C4×#6923C2×D4semidirect
142. C2×C4×C61#104semidirect
185. C4×C61C2×#104semidirect
198. C2×C61#1962semidirect
210. C2×#127#6923semidirect
224. C61C2×#1962semidirect
246. #127C2×#6923semidirect
363. C2×C4#14519841semidirect
387. C4C2×#14519841semidirect
392. C2#21461953direct (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×#145198412
C2×C42×#69232
#214619532
C2×#168403102
C2×#196261