Finite Group Databasebeta

← C2×#21461067 #30609939

Subgroups — C2×#21461067 #30609939

Order 15616.

1718 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840732C212yesmaximal
2#21461067C218yesmaximal, direct product factor
3C2×#16840607C214yesmaximal, complemented
4C23×C4⋊Dic61C211yesmaximal, characteristic
5C22×#11758217—22no—
6#16840732—24no—
7#16840732C2218yes—
8C2×C22⋊#92420—22no—
9C2×C22⋊#92420C2214yes—
10#16840607C22116yescomplemented
11C24×Dic61C411yescharacteristic
12C24×Dic61C2211yescharacteristic
13C22×C4⋊Dic61—22no—
14C22×C4⋊Dic61—22no—
15C22×C4⋊Dic61—24no—
16C22×C4⋊Dic61C414yes—
17C22×C4⋊Dic61C412yes—
18C22×C4⋊Dic61C2212yes—
19C22×C4⋊Dic61C2214yes—
20C24×C4×C61C411yescharacteristic
21C2×#11758217—28no—
22C2×#11758217—48no—
23C22×#92420—24no—
24C22⋊#92420—28no—
25C22⋊#92420—24no—
26C22⋊#92420C2318yes—
27C23×Dic61—22no—
28C23×Dic61—21no—
29C23×Dic61—21no—
30C23×Dic61—44no—
31C23×Dic61—44no—
32C23×Dic61C2×C414yes—
33C23×Dic61C2×C412yes—
34C23×Dic61C2×C412yes—
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61D412yes—
37C23×Dic61D412yes—
38C23×Dic61D414yes—
39C23×Dic61C2311yescharacteristic
40C23×Dic61C2312yes—
41C2×C4⋊Dic61—28no—
42C2×C4⋊Dic61—24no—
43C2×C4⋊Dic61—24no—
44C2×C4⋊Dic61—28no—
45C2×C4⋊Dic61—24no—
46C2×C4⋊Dic61—28no—
47C2×C4⋊Dic61—24no—
48C2×C4⋊Dic61—28no—
49C2×C4⋊Dic61C2×C414yes—
50C2×C4⋊Dic61C2×C418yes—
51C2×C4⋊Dic61C2314yes—
52C25×C61C2×C411yescharacteristic
53C23×C4×C61—22no—
54C23×C4×C61—21no—
55C23×C4×C61—21no—
56C23×C4×C61—28no—
57C23×C4×C61C2×C414yes—
58C23×C4×C61C2×C412yes—
59C24×C61—24no—
60C24×C61—24no—
61C24×C61—24no—
62C24×C61C22⋊C412yes—
63C24×C61C22⋊C411yescharacteristic
64C24×C61C22⋊C411yescharacteristic
65C24×C61C22×C412yes—
66C24×C61C22×C411yescharacteristic
67C22×C4×C61—216no—
68C22×C4×C61—28no—
69C22×C4×C61—28no—
70C22×C4×C61—24no—
71C22×C4×C61—24no—
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—24no—
75C22×C4×C61—216no—
76C22×C4×C61M1618yescomplemented
77C22×C4×C61C22×C414yes—
78C22×Dic61—28no—
79C22×Dic61—22no—
80C22×Dic61—24no—
81C22×Dic61—24no—
82C22×Dic61—22no—
83C22×Dic61—44no—
84C22×Dic61—42no—
85C22×Dic61—44no—
86C22×Dic61—48no—
87C22×Dic61—42no—
88C22×Dic61—44no—
89C22×Dic61—48no—
90C22×Dic61—44no—
91C22×Dic61—44no—
92C22×Dic61—48no—
93C22×Dic61—44no—
94C22×Dic61C22⋊C414yes—
95C22×Dic61C22⋊C412yes—
96C22×Dic61C22⋊C412yes—
97C22×Dic61C22⋊C414yes—
98C22×Dic61C22×C414yes—
99C22×Dic61C22×C411yescharacteristic
100C22×Dic61C22×C412yes—
101C22×Dic61C2×D412yes—
102C22×Dic61C2×D414yes—
103C22×Dic61C2×D412yes—
104C22×Dic61C2×D414yes—
105C22×Dic61C2411yescharacteristic
106#11758217—416no—
107C2×#92420—28no—
108C2×#92420—48no—
109C4⋊Dic61—28no—
110C4⋊Dic61—216no—
111C4⋊Dic61—28no—
112C23×C61—232no—
113C23×C61—24no—
114C23×C61—24no—
115C23×C61—22no—
116C23×C61—22no—
117C23×C61—24no—
118C23×C61—22no—
119C23×C61—24no—
120C23×C61—22no—
121C23×C61—24no—
122C23×C61—22no—
123C23×C61—24no—
124C23×C61—22no—
125C23×C61#9914yes—
126C23×C61#10114yes—
127C23×C61C2×C22⋊C411yescharacteristic
128C23×C61C2×C22⋊C412yes—
129C23×C61C2×C22⋊C412yes—
130C23×C61C2×C22⋊C411yescharacteristic
131C23×C61C2×M1614yes—
132C23×C61C23×C411yescharacteristic
133C2×C4×C61—216no—
134C2×C4×C61—216no—
135C2×C4×C61—24no—
136C2×C4×C61—24no—
137C2×C4×C61—28no—
138C2×C4×C61—28no—
139C2×C4×C61C2×M1618yescomplemented
140C2×Dic61—24no—
141C2×Dic61—28no—
142C2×Dic61—28no—
143C2×Dic61—24no—
144C2×Dic61—24no—
145C2×Dic61—44no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—44no—
151C2×Dic61—41no—
152C2×Dic61—44no—
153C2×Dic61—48no—
154C2×Dic61—48no—
155C2×Dic61—44no—
156C2×Dic61—44no—
157C2×Dic61C2×C22⋊C412yes—
158C2×Dic61C2×C22⋊C414yes—
159C2×Dic61C22×D412yes—
160#92420—48no—
161C2×#1463—611nomaximal, Sylow
162C22×C61—216no—
163C22×C61—216no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—21no—
167C22×C61—22no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—22no—
171C22×C61—21no—
172C22×C61—28no—
173C22×C61—28no—
174C22×C61—28no—
175C22×C61#40712yes—
176C22×C61#40712yes—
177C22×C61C2×#9914yes—
178C22×C61C2×#9912yes—
179C22×C61C2×#10114yes—
180C22×C61C2×#10112yes—
181C22×C61C22×C22⋊C411yescharacteristic
182C22×C61C22×M1612yes—
183C4×C61—28no—
184Dic61—22no—
185Dic61—22no—
186Dic61—24no—
187Dic61—44no—
188C23×C4⋊C4—611no—
189C2×#407—612no—
190#1463—618no—
191C2×#324—614no—
192C2×C61—22no—
193C2×C61—22no—
194C2×C61—24no—
195C2×C61—24no—
196C2×C61#146314yescomplemented
197C2×C61C2×#40711yescharacteristic
198C2×C61C22×#9911yescharacteristic
199C2×C61C22×#10111yescharacteristic
200C24×C4—611no—
201C24×C4—611no—
202C24×C4#692311yescharacteristic
203C22×M16—1222no—
204C22×C4⋊C4—614no—
205C22×C4⋊C4—612no—
206C22×C4⋊C4—612no—
207C22×C4⋊C4—614no—
208C22×C4⋊C4—1222no—
209C22×C4⋊C4—1222no—
210C22×C4⋊C4—1224no—
211#407—618no—
212#407—1224no—
213C2×C22⋊C8—614no—
214C2×C22⋊C8—1222no—
215#324—6116no—
216C61C2×#146311yescharacteristic, complemented, Sylow
217C25C2×#692311yescharacteristic
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—28no—
222C23×C4—612no—
223C23×C4—612no—
224C23×C4—614no—
225C23×C4—612no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—612no—
229C23×C4—614no—
230C23×C4—612no—
231C23×C4—1222no—
232C23×C4—1221no—
233C23×C4—1221no—
234C23×C4—2444no—
235C23×C4—2444no—
236C23×C4C2×#692314yes—
237C23×C4C2×#692312yes—
238C2×M16—1228no—
239C2×M16—2448no—
240C22×C8—1224no—
241C2×C4⋊C4—614no—
242C2×C4⋊C4—614no—
243C2×C4⋊C4—618no—
244C2×C4⋊C4—1228no—
245C2×C4⋊C4—1228no—
246C2×C4⋊C4—1224no—
247C2×C4⋊C4—1228no—
248C2×C4⋊C4—1228no—
249C2×C4⋊C4—1224no—
250C2×C4⋊C4—1224no—
251C2×C4⋊C4—1224no—
252C22⋊C8—618no—
253C22⋊C8—1224no—
254C22⋊C8—1228no—
255C24—24no—
256C24—24no—
257C24—24no—
258C24C22⋊#692312yes—
259C24C22⋊#692311yescharacteristic
260C24C22⋊#692311yescharacteristic
261C24C22×#692312yes—
262C24C22×#692311yescharacteristic
263C22×C4—216no—
264C22×C4—28no—
265C22×C4—28no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—24no—
271C22×C4—216no—
272C22×C4—614no—
273C22×C4—614no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—614no—
278C22×C4—612no—
279C22×C4—614no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—612no—
283C22×C4—614no—
284C22×C4—1228no—
285C22×C4—1222no—
286C22×C4—1224no—
287C22×C4—1224no—
288C22×C4—1222no—
289C22×C4—2442no—
290C22×C4—2444no—
291C22×C4—2444no—
292C22×C4—2448no—
293C22×C4—2444no—
294C22×C4—2442no—
295C22×C4—2448no—
296C22×C4—2444no—
297C22×C4—2444no—
298C22×C4—2448no—
299C22×C4—2444no—
300C22×C4#1175821718yescomplemented
301C22×C4C22×#692314yes—
302M16—24416no—
303C2×C8—1228no—
304C2×C8—2448no—
305C4⋊C4—12216no—
306C4⋊C4—1228no—
307C4⋊C4—1228no—
308C23—232no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—24no—
313C23—22no—
314C23—24no—
315C23—22no—
316C23—24no—
317C23—22no—
318C23—24no—
319C23—22no—
320C23—24no—
321C23#1451983614yes—
322C23#1451983814yes—
323C23C2×C22⋊#692311yescharacteristic
324C23C2×C22⋊#692312yes—
325C23C2×C22⋊#692312yes—
326C23C2×C22⋊#692311yescharacteristic
327C23C2×#1175821714yes—
328C23C23×#692311yescharacteristic
329C2×C4—216no—
330C2×C4—216no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—614no—
336C2×C4—612no—
337C2×C4—612no—
338C2×C4—1224no—
339C2×C4—1228no—
340C2×C4—1228no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—2441no—
344C2×C4—2442no—
345C2×C4—2444no—
346C2×C4—2444no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2442no—
350C2×C4—2444no—
351C2×C4—2448no—
352C2×C4—2448no—
353C2×C4—2444no—
354C2×C4—2444no—
355C2×C4C2×#1175821718yescomplemented
356C8—2448no—
357C22—216no—
358C22—216no—
359C22—28no—
360C22—28no—
361C22—28no—
362C22—22no—
363C22—22no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—21no—
370C22#1684073212yes—
371C22#1684073212yes—
372C22C2×#1451983614yes—
373C22C2×#1451983612yes—
374C22C2×#1451983814yes—
375C22C2×#1451983812yes—
376C22C22×C22⋊#692311yescharacteristic
377C22C22×#1175821712yes—
378C4—28no—
379C4—1222no—
380C4—1222no—
381C4—1224no—
382C4—2444no—
383C2—22no—
384C2—24no—
385C2—24no—
386C2—22no—
387C2#2146106714yesdirect product factor
388C2C2×#1684073211yescharacteristic
389C2C22×#1451983611yescharacteristic
390C2C22×#1451983811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC24×C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×Dic61C24
hypercenterC24×C4#6923
hypocenterC61C2×#1463
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. #21461067C2direct (N × H)
3. C2×#16840607C2semidirect
10. #16840607C22semidirect
76. C22×C4×C61M16semidirect
139. C2×C4×C61C2×M16semidirect
196. C2×C61#1463semidirect
216. C61C2×#1463semidirect
300. C22×C4#11758217semidirect
355. C2×C4C2×#11758217semidirect
387. C2#21461067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407322
#214610672
C2×#168406072
C23×C4⋊Dic612
C2×#146361