Finite Group Databasebeta

← C2×#21447248 #29708847

Subgroups — C2×#21447248 #29708847

Order 15616.

1270 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519689C211yesmaximal, characteristic
2C2×#16839619C212yesmaximal
3#21447248C218yesmaximal, direct product factor
4C2×#16839525C211yesmaximal, characteristic, complemented
5C2×#16839524C212yesmaximal, complemented
6C22×#107×C61C211yesmaximal, characteristic, complemented
7C23×C4×D61C2211yescharacteristic
8C23×#92418C2211yescharacteristic
9C22×C4⋊Dic61C2212yes—
10C22×#11758198—22no—
11C2×#14519689—24no—
12C2×#14519689C2214yes—
13#16839619—24no—
14#16839619C2218yes—
15C2×#14519684—22no—
16#16839525C2214yescomplemented
17#16839524C2218yescomplemented
18C23×C8×C61C2211yescharacteristic
19C22×C4⋊C4×C61C2212yes—
20C2×#107×C61—24no—
21C2×#107×C61C2214yescomplemented
22C24×D61D411yescharacteristic
23C23×Dic61—22no—
24C23×Dic61D411yescharacteristic
25C22×C4×D61—22no—
26C22×C4×D61—24no—
27C22×C4×D61—22no—
28C22×C4×D61—24no—
29C22×C4×D61D412yes—
30C22×C4×D61C2312yes—
31C22×#92418—22no—
32C22×#92418—24no—
33C22×#92418C2312yes—
34C2×C4⋊Dic61—24no—
35C2×C4⋊Dic61—24no—
36C2×C4⋊Dic61—22no—
37C2×C4⋊Dic61C2314yes—
38C2×#11758198—28no—
39C2×#11758198—48no—
40#14519689—28no—
41#14519684—28no—
42C23×C4×C61—22no—
43C23×C4×C61C2311yescharacteristic
44C22×C8×C61—24no—
45C22×C8×C61D414yes—
46C22×C8×C61C2312yes—
47C2×C4⋊C4×C61—24no—
48C2×C4⋊C4×C61—24no—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61C2314yes—
51#107×C61—28no—
52C24×C61C2×D411yescharacteristic
53C23×D61—22no—
54C23×D61—24no—
55C23×D61—22no—
56C23×D61—24no—
57C23×D61Q1614yes—
58C23×D61C2×D412yes—
59C22×C4×C61—24no—
60C22×C4×C61—44no—
61C22×C4×C61—44no—
62C22×C4×C61—44no—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D412yes—
65C22×C4×C61#4112yes—
66C22×C4×C61#4114yes—
67C22×C4×C61#4114yes—
68C22×C4×C61C2411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—24no—
71C22×Dic61—24no—
72C22×Dic61—44no—
73C22×Dic61—44no—
74C22×Dic61—44no—
75C22×Dic61C2×D412yes—
76C2×C4×D61—24no—
77C2×C4×D61—28no—
78C2×C4×D61—22no—
79C2×C4×D61—24no—
80C2×C4×D61—24no—
81C2×C4×D61—22no—
82C2×C4×D61—44no—
83C2×C4×D61—44no—
84C2×C4×D61—48no—
85C2×C8×C61—28no—
86C2×C8×C61—24no—
87C2×C8×C61C2×D414yes—
88C4⋊C4×C61—24no—
89C4⋊C4×C61—24no—
90C4⋊C4×C61—44no—
91#11758198—416no—
92C4⋊Dic61—24no—
93C4⋊Dic61—24no—
94C4⋊Dic61—44no—
95C2×#92418—22no—
96C2×#92418—24no—
97C2×#92418—44no—
98C23×C61#12112yes—
99C23×C61#12314yes—
100C23×C61C2×Q1612yes—
101C23×C61#13512yes—
102C23×C61AGL(1,ℤ/8)14yes—
103C23×C61C22×D411yescharacteristic
104C22×D61—22no—
105C22×D61—24no—
106C22×D61—22no—
107C22×D61—24no—
108C22×D61—28no—
109C22×D61—216no—
110C22×D61—44no—
111C22×D61—44no—
112C22×D61—48no—
113C22×D61C2×Q1614yes—
114C2×C4×C61—44no—
115C2×C4×C61—44no—
116C2×C4×C61—44no—
117C2×C4×C61—88no—
118C2×C4×C61#12112yes—
119C2×C4×C61#12314yes—
120C2×C4×C61#12314yes—
121C2×C4×C61#12414yes—
122C2×C4×C61#12618yes—
123C2×C4×C61C22×D411yescharacteristic
124C2×C4×C61C2×#4112yes—
125C2×C4×C61C2×#4112yes—
126C2×C4×C61C2×#4111yescharacteristic
127C2×Dic61—22no—
128C2×Dic61—24no—
129C2×Dic61—44no—
130C2×Dic61—44no—
131C2×Dic61—44no—
132C2×Dic61—44no—
133C2×Dic61—88no—
134C4×D61—42no—
135C4×D61—42no—
136C4×D61—44no—
137C4×D61—48no—
138C8×C61—24no—
139#92418—42no—
140C2×#2076—611nomaximal, Sylow
141C22×C61#39714yes—
142C22×C61#46714yes—
143C22×C61#46914yes—
144C22×C61#48218yes—
145C22×C61#48418yes—
146C22×C61C2×#12111yescharacteristic
147C22×C61C2×#12312yes—
148C22×C61C22×Q1611yescharacteristic
149C22×C61C2×#13511yescharacteristic
150C22×C61C2×AGL(1,ℤ/8)12yes—
151C2×D61—28no—
152C2×D61—24no—
153C2×D61—44no—
154C2×D61—416no—
155C2×D61—42no—
156C2×D61—42no—
157C4×C61—84no—
158C4×C61#39714yes—
159C4×C61C2×#12311yescharacteristic
160C4×C61C2×#12411yescharacteristic
161C4×C61C2×#12612yes—
162Dic61—42no—
163Dic61—84no—
164C22×#107D6111yescharacteristic, complemented
165C22×C22⋊C8—611no—
166C2×#380—612no—
167#2076—618no—
168C2×#340—611no—
169C2×#340—612no—
170C2×C61#207618yescomplemented
171C2×C61C2×#39711yescharacteristic
172C2×C61C2×#46711yescharacteristic
173C2×C61C2×#46911yescharacteristic
174C2×C61C2×#48212yes—
175C2×C61C2×#48412yes—
176D61—44no—
177C24×C4—611no—
178C23×C8—611no—
179C23×C8C2×D6111yescharacteristic
180C22×C4⋊C4—612no—
181C22×C4⋊C4C2×D6112yes—
182C22×C22⋊C4—1222no—
183C2×#107—24no—
184C2×#107C2×D6114yescomplemented
185C2×C22⋊C8—614no—
186C2×C22⋊C8—1224no—
187#380—618no—
188#380—1224no—
189C2×#95—1222no—
190#340—614no—
191#340—618no—
192C61C2×#207611yescharacteristic, complemented, Sylow
193C25—611no—
194C23×C4—22no—
195C23×C4—611no—
196C23×C4—612no—
197C23×C4—612no—
198C23×C4—1224no—
199C23×C4—1222no—
200C23×C4—1224no—
201C23×C4—1222no—
202C23×C4—1222no—
203C23×C4C22×D6111yescharacteristic
204C22×C8—24no—
205C22×C8—612no—
206C22×C8—1224no—
207C22×C8—1222no—
208C22×C8C22⋊D6114yes—
209C22×C8C22×D6112yes—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—614no—
214C2×C4⋊C4—1224no—
215C2×C4⋊C4—1224no—
216C2×C4⋊C4—1222no—
217C2×C4⋊C4C22×D6114yes—
218C2×C22⋊C4—1228no—
219C2×C22⋊C4—2448no—
220#107—28no—
221C22⋊C8—1228no—
222#95—1228no—
223C24—612no—
224C24—614no—
225C24—1222no—
226C24—1224no—
227C24—1222no—
228C24—1224no—
229C24D4×D6111yescharacteristic
230C22×C4—24no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4—612no—
235C22×C4—1222no—
236C22×C4—1224no—
237C22×C4—1222no—
238C22×C4—1222no—
239C22×C4—1224no—
240C22×C4—1224no—
241C22×C4—1224no—
242C22×C4—1228no—
243C22×C4—1224no—
244C22×C4—2444no—
245C22×C4—2444no—
246C22×C4—2444no—
247C22×C4—2444no—
248C22×C4—2444no—
249C22×C4—2448no—
250C22×C4#1175822214yes—
251C22×C4D4×D6111yescharacteristic
252C22×C4#1175822412yes—
253C22×C4#1175822614yes—
254C22×C4C2×C22⋊D6112yes—
255C22×C4C23×D6111yescharacteristic
256C2×C8—24no—
257C2×C8—28no—
258C2×C8—1222no—
259C2×C8—1224no—
260C2×C8—2444no—
261C2×C8C2×C22⋊D6114yes—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—44no—
265C4⋊C4—1224no—
266C4⋊C4—1224no—
267C4⋊C4—2444no—
268C22⋊C4—24416no—
269C23—614no—
270C23—1222no—
271C23—1228no—
272C23—1224no—
273C23—1222no—
274C23—1224no—
275C23—12216no—
276C23—2444no—
277C23—2444no—
278C23—2448no—
279C23#1451974812yes—
280C23#1451976214yes—
281C23Q16×D6112yes—
282C23#1451980012yes—
283C23#1451980114yes—
284C23C2×D4×D6111yescharacteristic
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—88no—
289C2×C4—1222no—
290C2×C4—1224no—
291C2×C4—4888no—
292C2×C4—2444no—
293C2×C4—2444no—
294C2×C4—2444no—
295C2×C4—2444no—
296C2×C4—2448no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4—2444no—
300C2×C4#1451974812yes—
301C2×C4#1451976014yes—
302C2×C4#1451976214yes—
303C2×C4#1451976614yes—
304C2×C4#1451977218yes—
305C2×C4C22×C22⋊D6111yescharacteristic
306C2×C4C2×#1175822411yescharacteristic
307C2×C4C2×#1175822212yes—
308C2×C4C2×#1175822612yes—
309C8—24no—
310C8—2442no—
311C22—1224no—
312C22—1228no—
313C22—2442no—
314C22—24416no—
315C22—2442no—
316C22—2444no—
317C22#1683968814yes—
318C22#1684000014yes—
319C22#1684001214yes—
320C22#1684008918yes—
321C22#1684009918yes—
322C22C2×#1451974811yescharacteristic
323C22C2×#1451976212yes—
324C22C2×Q16×D6111yescharacteristic
325C22C2×#1451980011yescharacteristic
326C22C2×#1451980112yes—
327C4—84no—
328C4—4884no—
329C4—2442no—
330C4#1683968814yes—
331C4C2×#1451976011yescharacteristic
332C4C2×#1451976611yescharacteristic
333C4C2×#1451977212yes—
334C2—2444no—
335C2#2144724818yesdirect product factor
336C2C2×#1683968811yescharacteristic
337C2C2×#1684000011yescharacteristic
338C2C2×#1684001211yescharacteristic
339C2C2×#1684008912yes—
340C2C2×#1684009912yes—
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#107×C61C2
socleC24×C61C2×D4
prime radicalC24×D61D4
hypercenterC22×#107D61
hypocenterC61C2×#2076
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
3. #21447248C2direct (N × H)
4. C2×#16839525C2semidirect
5. C2×#16839524C2semidirect
6. C22×#107×C61C2semidirect
16. #16839525C22semidirect
17. #16839524C22semidirect
21. C2×#107×C61C22semidirect
164. C22×#107D61semidirect
170. C2×C61#2076semidirect
184. C2×#107C2×D61semidirect
192. C61C2×#2076semidirect
335. C2#21447248direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145196892
C2×#168396192
#214472482
C2×#168395252
C2×#168395242
C22×#107×C612
C2×#207661