Finite Group Databasebeta

← C2×#21446962 #29707286

Subgroups — C2×#21446962 #29707286

Order 15616.

1518 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×#14519697C212yesmaximal
2C2×#16839664C211yesmaximal, characteristic
3#21446962C218yesmaximal, direct product factor
4C2×#16839524C212yesmaximal, complemented
5C2×#16839517C211yesmaximal, characteristic, complemented
6C22×#125×C61C211yesmaximal, characteristic, complemented
7C23×D244C2211yescharacteristic
8C23×#92418C2212yes—
9C22×C4⋊Dic61C2211yescharacteristic
10C22×#11758198—22no—
11C2×#14519697—28no—
12C2×#14519697C2218yes—
13#16839664—22no—
14#16839664C2214yes—
15#16839524C2218yescomplemented
16#16839517C2214yescomplemented
17C2×#125×C61—28no—
18C2×#125×C61—22no—
19C2×#125×C61C2214yescomplemented
20C22×C4⋊C4×C61—22no—
21C22×C4⋊C4×C61C2212yes—
22C22×C42×C61C2211yescharacteristic
23C24×D61—21no—
24C22×D244—24no—
25C22×D244—24no—
26C22×D244—21no—
27C22×D244—22no—
28C22×D244Q814yes—
29C22×D244C2312yes—
30C23×Dic61—21no—
31C22×#92418—24no—
32C22×#92418—24no—
33C22×#92418—24no—
34C22×#92418C2314yes—
35C2×C4⋊Dic61—24no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2312yes—
38C2×#11758198—28no—
39C2×#11758198—48no—
40#14519697—216no—
41C23×C4×C61—22no—
42C23×C4×C61D412yes—
43C23×C4×C61C2311yescharacteristic
44#125×C61—216no—
45#125×C61—216no—
46C2×C4⋊C4×C61—216no—
47C2×C4⋊C4×C61—28no—
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61—24no—
50C2×C4⋊C4×C61D418yes—
51C2×C4⋊C4×C61C2314yes—
52C2×C42×C61—24no—
53C2×C42×C61D412yes—
54C2×C42×C61C2312yes—
55C24×C61C2×D411yescharacteristic
56C23×D61—24no—
57C23×D61—22no—
58C23×D61—42no—
59C23×D61—42no—
60C23×D61—44no—
61C23×D61—44no—
62C22×C4×C61—24no—
63C22×C4×C61—28no—
64C22×C4×C61—24no—
65C22×C4×C61—24no—
66C22×C4×C61—24no—
67C22×C4×C61—44no—
68C22×C4×C61—44no—
69C22×C4×C61C2×D414yes—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D414yes—
72C22×C4×C61C2×Q812yes—
73C22×C4×C61#4114yes—
74C22×C4×C61#4112yes—
75C22×C4×C61C2411yescharacteristic
76C22×Dic61—22no—
77C22×Dic61—42no—
78C22×Dic61—44no—
79C2×D244—216no—
80C2×D244—24no—
81C2×D244—24no—
82C2×D244—24no—
83C2×D244—22no—
84C2×D244—42no—
85C2×D244—48no—
86C2×D244—42no—
87C2×D244C2×Q814yes—
88C4⋊C4×C61—232no—
89C4⋊C4×C61—28no—
90C4⋊C4×C61—24no—
91C4⋊C4×C61C2×D418yes—
92C42×C61—24no—
93C42×C61—24no—
94#11758198—416no—
95C4⋊Dic61—24no—
96C4⋊Dic61—42no—
97C2×#92418—24no—
98C2×#92418—24no—
99C2×#92418—24no—
100C2×#92418—48no—
101C23×C61#12012yes—
102C23×C61C22⋊Q812yes—
103C23×C61#12412yes—
104C23×C61#13514yes—
105C23×C61AGL(1,ℤ/8)14yes—
106C23×C61C22×D411yescharacteristic
107C22×D61—24no—
108C22×D61—42no—
109C22×D61—42no—
110C22×D61—44no—
111C22×D61—44no—
112C22×D61—48no—
113C22×D61—416no—
114C22×D61—88no—
115C22×D61—84no—
116C22×D61—84no—
117C2×C4×C61—24no—
118C2×C4×C61—28no—
119C2×C4×C61—24no—
120C2×C4×C61—24no—
121C2×C4×C61—44no—
122C2×C4×C61—44no—
123C2×C4×C61—48no—
124C2×C4×C61—416no—
125C2×C4×C61#12012yes—
126C2×C4×C61C22⋊Q818yes—
127C2×C4×C61C22⋊Q812yes—
128C2×C4×C61#12418yes—
129C2×C4×C61#12412yes—
130C2×C4×C61C22×D412yes—
131C2×C4×C61C22×Q811yescharacteristic
132C2×C4×C61C2×#4112yes—
133C2×C4×C61C2×#4111yescharacteristic
134C2×Dic61—42no—
135C2×Dic61—44no—
136C2×Dic61—84no—
137D244—28no—
138D244—44no—
139D244—48no—
140#92418—44no—
141C2×#2025—611nomaximal, Sylow
142C22×C61#39314yes—
143C22×C61#44918yes—
144C22×C61#47818yes—
145C22×C61#48814yes—
146C22×C61#49014yes—
147C22×C61C2×#12011yescharacteristic
148C22×C61C2×C22⋊Q811yescharacteristic
149C22×C61C2×#12411yescharacteristic
150C22×C61C2×#13512yes—
151C22×C61C2×AGL(1,ℤ/8)12yes—
152C2×D61—48no—
153C2×D61—44no—
154C2×D61—82no—
155C2×D61—82no—
156C2×D61—84no—
157C2×D61—816no—
158C4×C61—44no—
159C4×C61—48no—
160C4×C61#39314yes—
161C4×C61C2×C22⋊Q812yes—
162C4×C61C2×#12412yes—
163Dic61—82no—
164C22×#125D6111yescharacteristic, complemented
165C22×#102—612no—
166C2×#390—611no—
167#2025—618no—
168C2×#340—612no—
169C2×#336—611no—
170C2×C61#202518yescomplemented
171C2×C61C2×#39311yescharacteristic
172C2×C61C2×#44912yes—
173C2×C61C2×#47812yes—
174C2×C61C2×#48811yescharacteristic
175C2×C61C2×#49011yescharacteristic
176D61—84no—
177C23×D4—611no—
178C23×C8—612no—
179C2×#125—28no—
180C2×#125—22no—
181C2×#125C2×D6114yescomplemented
182C22×C4⋊C4—22no—
183C22×C4⋊C4—611no—
184C22×C4⋊C4C2×D6112yes—
185C22×C22⋊C4—1222no—
186C22×C42C2×D6111yescharacteristic
187C2×#102—618no—
188C2×#102—1228no—
189#390—614no—
190#390—1222no—
191#340—618no—
192#336—614no—
193C61C2×#202511yescharacteristic, complemented, Sylow
194C25—1221no—
195C22×D4—614no—
196C22×D4—612no—
197C22×D4—1224no—
198C22×D4—1222no—
199C22×D4—1224no—
200C22×D4—1221no—
201C23×C4—22no—
202C23×C4—1221no—
203C23×C4C22⋊D6112yes—
204C23×C4C22×D6111yescharacteristic
205C22×C8—614no—
206C22×C8—1224no—
207C22×C8—1224no—
208C22×C8—1224no—
209#125—216no—
210#125—216no—
211C2×C4⋊C4—216no—
212C2×C4⋊C4—28no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—612no—
216C2×C4⋊C4—1224no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4C22⋊D6118yes—
219C2×C4⋊C4C22×D6114yes—
220C2×C22⋊C4—1228no—
221C2×C22⋊C4—2448no—
222C2×C42—24no—
223C2×C42C22⋊D6112yes—
224C2×C42C22×D6112yes—
225#102—12216no—
226C24—1222no—
227C24—1224no—
228C24—2442no—
229C24—2442no—
230C24—2444no—
231C24—2444no—
232C24C2×C22⋊D6111yescharacteristic
233C2×D4—614no—
234C2×D4—1224no—
235C2×D4—1224no—
236C2×D4—1222no—
237C2×D4—12216no—
238C2×D4—1224no—
239C2×D4—2442no—
240C2×D4—2448no—
241C2×D4—2442no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—28no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—1222no—
250C22×C4—2442no—
251C22×C4—2444no—
252C22×C4Q8×D6112yes—
253C22×C4#1175822614yes—
254C22×C4#1175822612yes—
255C22×C4C2×C22⋊D6114yes—
256C22×C4C2×C22⋊D6114yes—
257C22×C4C2×C22⋊D6111yescharacteristic
258C22×C4C23×D6111yescharacteristic
259C2×C8—1224no—
260C2×C8—1224no—
261C2×C8—1224no—
262C2×C8—2448no—
263C4⋊C4—232no—
264C4⋊C4—24no—
265C4⋊C4—28no—
266C4⋊C4—1224no—
267C4⋊C4—2442no—
268C4⋊C4C2×C22⋊D6118yes—
269C22⋊C4—24416no—
270C42—24no—
271C42—24no—
272C23—1224no—
273C23—4884no—
274C23—4884no—
275C23—4888no—
276C23—2442no—
277C23—2442no—
278C23—2444no—
279C23—2444no—
280C23—24416no—
281C23—2448no—
282C23#1451974612yes—
283C23#1451975312yes—
284C23#1451976612yes—
285C23#1451979714yes—
286C23#1451980214yes—
287C23C22×C22⋊D6111yescharacteristic
288D4—1228no—
289D4—2444no—
290D4—2448no—
291C2×C4—24no—
292C2×C4—28no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—48no—
298C2×C4—416no—
299C2×C4—4884no—
300C2×C4—2442no—
301C2×C4—2444no—
302C2×C4#1451974612yes—
303C2×C4#1451975318yes—
304C2×C4#1451975312yes—
305C2×C4#1451976618yes—
306C2×C4#1451976612yes—
307C2×C4C22×C22⋊D6112yes—
308C2×C4C2×Q8×D6111yescharacteristic
309C2×C4C2×#1175822612yes—
310C2×C4C2×#1175822611yescharacteristic
311C8—2444no—
312C22—4882no—
313C22—4882no—
314C22—48816no—
315C22—4884no—
316C22—2444no—
317C22—2448no—
318C22#1683967314yes—
319C22#1683990718yes—
320C22#1684005918yes—
321C22#1684011914yes—
322C22#1684012814yes—
323C22C2×#1451974611yescharacteristic
324C22C2×#1451975311yescharacteristic
325C22C2×#1451976611yescharacteristic
326C22C2×#1451979712yes—
327C22C2×#1451980212yes—
328C4—44no—
329C4—48no—
330C4—4882no—
331C4#1683967314yes—
332C4C2×#1451975312yes—
333C4C2×#1451976612yes—
334C2—4884no—
335C2#2144696218yesdirect product factor
336C2C2×#1683967311yescharacteristic
337C2C2×#1683990712yes—
338C2C2×#1684005912yes—
339C2C2×#1684011911yescharacteristic
340C2C2×#1684012811yescharacteristic
subgroupG/H
centerC24C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#125×C61C2
socleC24×C61C2×D4
prime radicalC23×D244C22
hypercenterC22×#125D61
hypocenterC61C2×#2025
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
3. #21446962C2direct (N × H)
4. C2×#16839524C2semidirect
5. C2×#16839517C2semidirect
6. C22×#125×C61C2semidirect
15. #16839524C22semidirect
16. #16839517C22semidirect
19. C2×#125×C61C22semidirect
164. C22×#125D61semidirect
170. C2×C61#2025semidirect
181. C2×#125C2×D61semidirect
193. C61C2×#2025semidirect
335. C2#21446962direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145196972
C2×#168396642
#214469622
C2×#168395242
C2×#168395172
C22×#125×C612
C2×#202561