Finite Group Databasebeta

← C2×#21447244 #29708834

Subgroups — C2×#21447244 #29708834

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×#14519711C211yesmaximal, characteristic, complemented
2C22×#14519689C211yesmaximal, characteristic
3C2×#16839619C212yesmaximal
4#21447244C218yesmaximal, direct product factor
5C2×#16839524C212yesmaximal, complemented
6C2×C61×#340C211yesmaximal, characteristic, complemented
7C23×C4×D61C2211yescharacteristic
8C23×#92418C2211yescharacteristic
9C22×C4⋊Dic61C2212yes—
10C22×#11758198—22no—
11C2×#14519711—24no—
12C2×#14519711C2214yescomplemented
13C2×#14519689—24no—
14C2×#14519689C2214yes—
15#16839619—24no—
16#16839619C2218yes—
17C2×#14519684—22no—
18#16839524C2218yescomplemented
19C23×C8×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2212yes—
21C61×#340C2214yescomplemented
22C24×D61D411yescharacteristic
23C23×Dic61—22no—
24C23×Dic61D411yescharacteristic
25C22×C4×D61—22no—
26C22×C4×D61—24no—
27C22×C4×D61—24no—
28C22×C4×D61—22no—
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#14519711—28no—
41#14519689—28no—
42#14519684—28no—
43C23×C4×C61—22no—
44C23×C4×C61C2311yescharacteristic
45C22×C8×C61—24no—
46C22×C8×C61D414yes—
47C22×C8×C61C2312yes—
48C2×C4⋊C4×C61—24no—
49C2×C4⋊C4×C61—24no—
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61C2314yes—
52C24×C61C2×D411yescharacteristic
53C23×D61—22no—
54C23×D61—24no—
55C23×D61—22no—
56C23×D61—24no—
57C23×D61D814yes—
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×D812yes—
101C23×C61#13512yes—
102C23×C61#13714yes—
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×D814yes—
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×#2075—611nomaximal, Sylow
141C22×C61#39714yes—
142C22×C61#46614yes—
143C22×C61#47014yes—
144C22×C61#48018yes—
145C22×C61#48518yes—
146C22×C61C2×#12111yescharacteristic
147C22×C61C2×#12312yes—
148C22×C61C22×D811yescharacteristic
149C22×C61C2×#13511yescharacteristic
150C22×C61C2×#13712yes—
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×#107—611no—
165C22×C22⋊C8—611no—
166C2×#380—612no—
167#2075—618no—
168C2×#340—612no—
169C2×#340D6111yescharacteristic, complemented
170C2×C61#207518yescomplemented
171C2×C61C2×#39711yescharacteristic
172C2×C61C2×#46611yescharacteristic
173C2×C61C2×#47011yescharacteristic
174C2×C61C2×#48012yes—
175C2×C61C2×#48512yes—
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—614no—
184C2×#107—1224no—
185C2×C22⋊C8—614no—
186C2×C22⋊C8—1224no—
187#380—618no—
188#380—1224no—
189C2×#95—1222no—
190#340—618no—
191#340C2×D6114yescomplemented
192C61C2×#207511yescharacteristic, complemented, Sylow
193C25—611no—
194C23×C4—22no—
195C23×C4—611no—
196C23×C4—612no—
197C23×C4—612no—
198C23×C4—1222no—
199C23×C4—1224no—
200C23×C4—1224no—
201C23×C4—1222no—
202C23×C4—1222no—
203C23×C4C22×D6111yescharacteristic
204C22×C8—24no—
205C22×C8—612no—
206C22×C8—1222no—
207C22×C8—1224no—
208C22×C8D24414yes—
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—1228no—
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—1224no—
239C22×C4—1224no—
240C22×C4—1222no—
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×C4C2×D24412yes—
251C22×C4#1175822214yes—
252C22×C4D4×D6111yescharacteristic
253C22×C4#1175822414yes—
254C22×C4#1175822612yes—
255C22×C4C23×D6111yescharacteristic
256C2×C8—24no—
257C2×C8—28no—
258C2×C8—1222no—
259C2×C8—1224no—
260C2×C8—2444no—
261C2×C8C2×D24414yes—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—44no—
265C4⋊C4—1224no—
266C4⋊C4—1224no—
267C4⋊C4—2444no—
268C22⋊C4—24416no—
269C23—614no—
270C23—1228no—
271C23—1222no—
272C23—1224no—
273C23—1222no—
274C23—1224no—
275C23—12216no—
276C23—2444no—
277C23—2444no—
278C23—2448no—
279C23#1451975212yes—
280C23#1451975914yes—
281C23D8×D6112yes—
282C23#1451980012yes—
283C23#1451980614yes—
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#1451975212yes—
301C2×C4#1451975914yes—
302C2×C4#1451976114yes—
303C2×C4#1451976514yes—
304C2×C4#1451977218yes—
305C2×C4C22×D24411yescharacteristic
306C2×C4C2×#1175822412yes—
307C2×C4C2×#1175822212yes—
308C2×C4C2×#1175822611yescharacteristic
309C8—24no—
310C8—2442no—
311C22—1224no—
312C22—1228no—
313C22—2442no—
314C22—24416no—
315C22—2442no—
316C22—2444no—
317C22#1683968914yes—
318C22#1683999914yes—
319C22#1684002114yes—
320C22#1684007418yes—
321C22#1684010218yes—
322C22C2×#1451975211yescharacteristic
323C22C2×#1451975912yes—
324C22C2×D8×D6111yescharacteristic
325C22C2×#1451980011yescharacteristic
326C22C2×#1451980612yes—
327C4—84no—
328C4—4884no—
329C4—2442no—
330C4#1683968914yes—
331C4C2×#1451976111yescharacteristic
332C4C2×#1451976511yescharacteristic
333C4C2×#1451977212yes—
334C2—2444no—
335C2#2144724418yesdirect product factor
336C2C2×#1683968911yescharacteristic
337C2C2×#1683999911yescharacteristic
338C2C2×#1684002111yescharacteristic
339C2C2×#1684007412yes—
340C2C2×#1684010212yes—
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC24×D61D4
hypercenterC2×#340D61
hypocenterC61C2×#2075
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#14519711C2semidirect
4. #21447244C2direct (N × H)
5. C2×#16839524C2semidirect
6. C2×C61×#340C2semidirect
12. C2×#14519711C22semidirect
18. #16839524C22semidirect
21. C61×#340C22semidirect
169. C2×#340D61semidirect
170. C2×C61#2075semidirect
191. #340C2×D61semidirect
192. C61C2×#2075semidirect
335. C2#21447244direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197112
C22×#145196892
C2×#168396192
#214472442
C2×#168395242
C2×C61×#3402
C2×#207561