Finite Group Databasebeta

← C2×#21458457 #30559573

Subgroups — C2×#21458457 #30559573

Order 15616.

2058 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D244C211yesmaximal, characteristic
2#21458457C2116yesmaximal, direct product factor
3C2×#16840112C213yesmaximal, complemented
4C2×#16840047C213yesmaximal, complemented
5C2×#16839964C213yesmaximal
6C2×Q8×#92418C211yesmaximal, characteristic, complemented
7C2×C4×#11758201C213yesmaximal
8C2×C61×#557C211yesmaximal, characteristic, complemented
9C22×Q8×D61—21no—
10C22×#11758201C2213yes—
11Q8×D244—24no—
12Q8×D244C2218yes—
13C2×#14519777C2213yes—
14C2×#14519757—23no—
15C2×C4×D244C2213yes—
16#16840112C22124yescomplemented
17#16840047C22124yescomplemented
18#16839964C22124yes—
19Q8×#92418C2218yescomplemented
20C4×#11758201C22124yes—
21C2×#14519708C2213yes—
22C2×C4⋊#92418C2213yes—
23C2×#14519701C2213yes—
24C2×#14519701C2216yes—
25C2×#14519697C2211yescharacteristic
26C2×C4×#92418C2213yes—
27C61×#557—24no—
28C61×#557C2218yescomplemented
29C2×C4⋊Q8×C61C2213yes—
30C2×#125×C61—23no—
31C2×C4×Q8×C61—21no—
32C2×C4×Q8×C61C2213yes—
33C2×C4×Q8×C61C2211yescharacteristic
34C22×Dic122—23no—
35C2×Q8×D61—28no—
36C2×Q8×D61—48no—
37C22×D244C2311yescharacteristic
38C22×C4×D61—23no—
39C2×#11758201—212no—
40C2×#11758201C23112yes—
41C22×#92418C2311yescharacteristic
42C22×#92418C2313yes—
43#14519777—26no—
44#14519777C23112yes—
45#14519757—224no—
46C4×D244—26no—
47C4×D244C23112yes—
48C2×C4⋊Dic61—23no—
49C2×C4⋊Dic61C2313yes—
50C2×#11758198—23no—
51#14519708C23112yes—
52C4⋊#92418C23112yes—
53#14519701C23124yes—
54#14519701C23112yes—
55#14519697C2314yes—
56C4×#92418C23112yes—
57C22×Q8×C61D411yescharacteristic
58C22×Q8×C61C2313yes—
59C4⋊Q8×C61—26no—
60C4⋊Q8×C61C23112yes—
61#125×C61—224no—
62C4×Q8×C61—28no—
63C4×Q8×C61—26no—
64C4×Q8×C61D414yes—
65C4×Q8×C61C23112yes—
66C4×Q8×C61C2314yes—
67C2×C4⋊C4×C61—23no—
68C2×C4⋊C4×C61—23no—
69C2×C4⋊C4×C61—23no—
70C2×C4⋊C4×C61D413yes—
71C2×C4⋊C4×C61C2311yescharacteristic
72C2×C42×C61—23no—
73C2×C42×C61C2313yes—
74C23×D61—21no—
75C2×Q8×C61—23no—
76C2×Q8×C61—26no—
77C2×Q8×C61—26no—
78C2×Q8×C61SD1618yescomplemented
79C2×Q8×C61C2×D414yes—
80C2×Q8×C61C2416yes—
81C22×C4×C61—21no—
82C22×C4×C61—23no—
83C22×C4×C61C2×D413yes—
84C22×C4×C61C2×D413yes—
85C22×C4×C61C2411yescharacteristic
86C22×Dic61—23no—
87Q8×D61—432no—
88C2×D244—21no—
89C2×D244—22no—
90C2×D244#4114yes—
91C2×D244C2412yes—
92C2×C4×D61—212no—
93C2×C4×D61—412no—
94C2×Dic122—212no—
95C2×Dic122—412no—
96C4⋊C4×C61—212no—
97C4⋊C4×C61—212no—
98C4⋊C4×C61—212no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61C2×D4112yes—
101C4⋊C4×C61C2412yes—
102C42×C61—212no—
103C42×C61C2×D416yes—
104C42×C61C2416yes—
105#11758201—224no—
106#11758198—212no—
107C4⋊Dic61—212no—
108C4⋊Dic61—23no—
109C4⋊Dic61C2416yes—
110C2×#92418—26no—
111C2×#92418—22no—
112C2×#92418C2412yes—
113C2×#92418C2416yes—
114C23×C61C22×D411yescharacteristic
115C22×D61—24no—
116C22×D61—22no—
117C22×D61—42no—
118C22×D61—42no—
119Q8×C61—26no—
120Q8×C61—26no—
121Q8×C61—46no—
122Q8×C61C2×SD16116yescomplemented
123C2×C4×C61—26no—
124C2×C4×C61—22no—
125C2×C4×C61—26no—
126C2×C4×C61—46no—
127C2×C4×C61—42no—
128C2×C4×C61C2×SD16112yes—
129C2×C4×C61C22×D416yes—
130C2×C4×C61C22×D411yescharacteristic
131C2×C4×C61C22×D416yes—
132C2×C4×C61C2×#4112yes—
133C2×C4×C612−1+412yes—
134C2×C4×C61C2511yescharacteristic
135C2×Dic61—26no—
136C2×Dic61—46no—
137D244—24no—
138D244—22no—
139D244C2×#4114yes—
140C4×D61—424no—
141Dic122—424no—
142#92418—26no—
143#92418—22no—
144C2×#3359—611nomaximal, Sylow
145C22×C61#54812yes—
146C22×C61C22×SD1612yes—
147C22×C61#57812yes—
148C22×C61C23×D411yescharacteristic
149C2×D61—24no—
150C2×D61—48no—
151C2×D61—42no—
152C2×D61—42no—
153C4×C61—26no—
154C4×C61—46no—
155C4×C61—42no—
156C4×C61#54812yes—
157C4×C61C22×SD16112yes—
158C4×C61C22×#4111yescharacteristic
159C4×C61C2×2−1+411yescharacteristic
160Dic61—46no—
161C2×#557D6111yescharacteristic, complemented
162C2×D4×Q8—611no—
163#3359—6116no—
164C2×#487—613no—
165C2×#475—613no—
166C2×#461—613no—
167C2×C8×Q8—611no—
168C2×C4×SD16—613no—
169C2×C61#335914yescomplemented
170C2×C61C2×#54811yescharacteristic
171C2×C61C23×SD1611yescharacteristic
172C2×C61C2×#57811yescharacteristic
173D61—44no—
174C23×Q8—1221no—
175C22×SD16—613no—
176#557—24no—
177#557C2×D6118yescomplemented
178D4×Q8—618no—
179D4×Q8—1224no—
180C2×C4⋊Q8—613no—
181C2×C4⋊Q8C2×D6113yes—
182C2×#125—23no—
183C2×C22⋊Q8—1223no—
184C2×C4×Q8—21no—
185C2×C4×Q8C2×D6113yes—
186C2×C4×Q8C2×D6111yescharacteristic
187C2×C4×D4—613no—
188#487—6124no—
189#475—6124no—
190#461—6124no—
191C8×Q8—618no—
192C4×SD16—6124no—
193C2×#106—613no—
194C2×C4⋊C8—613no—
195C2×#103—616no—
196C2×#103—613no—
197C2×#102—611no—
198C2×C4×C8—613no—
199C61C2×#335911yescharacteristic, complemented, Sylow
200C22×Q8—1228no—
201C22×Q8—1223no—
202C22×Q8—2448no—
203C22×Q8C22⋊D6111yescharacteristic
204C22×Q8C22×D6113yes—
205C22×D4—611no—
206C23×C4—1223no—
207C2×SD16—6112no—
208C2×SD16—12212no—
209C22×C8—613no—
210C22×C8—611no—
211C4⋊Q8—26no—
212C4⋊Q8—6112no—
213C4⋊Q8—1226no—
214C4⋊Q8C22×D61112yes—
215#125—224no—
216C22⋊Q8—12224no—
217C4×Q8—28no—
218C4×Q8—26no—
219C4×Q8C22⋊D6114yes—
220C4×Q8C22×D61112yes—
221C4×Q8C22×D6114yes—
222C4×D4—6112no—
223C4×D4—1226no—
224C2×C4⋊C4—23no—
225C2×C4⋊C4—23no—
226C2×C4⋊C4—23no—
227C2×C4⋊C4—613no—
228C2×C4⋊C4—1223no—
229C2×C4⋊C4C22⋊D6113yes—
230C2×C4⋊C4C22×D6111yescharacteristic
231C2×C22⋊C4—1223no—
232C2×C42—23no—
233C2×C42C22×D6113yes—
234#106—6112no—
235C4⋊C8—6112no—
236#103—6112no—
237#103—6124no—
238#102—614no—
239C4×C8—6112no—
240C24—1221no—
241C2×Q8—23no—
242C2×Q8—26no—
243C2×Q8—26no—
244C2×Q8—12212no—
245C2×Q8—24432no—
246C2×Q8—24412no—
247C2×Q8#1175820118yescomplemented
248C2×Q8C2×C22⋊D6114yes—
249C2×Q8C23×D6116yes—
250C2×D4—614no—
251C2×D4—612no—
252C2×D4—1221no—
253C2×D4—1222no—
254C22×C4—21no—
255C22×C4—23no—
256C22×C4—1223no—
257C22×C4—12212no—
258C22×C4—24412no—
259C22×C4C2×C22⋊D6113yes—
260C22×C4C2×C22⋊D6113yes—
261C22×C4C23×D6111yescharacteristic
262SD16—12224no—
263C2×C8—612no—
264C2×C8—616no—
265C2×C8—1226no—
266C2×C8—1222no—
267C4⋊C4—212no—
268C4⋊C4—212no—
269C4⋊C4—212no—
270C4⋊C4—21no—
271C4⋊C4—616no—
272C4⋊C4—1223no—
273C4⋊C4—12212no—
274C4⋊C4C2×C22⋊D61112yes—
275C4⋊C4C23×D6112yes—
276C22⋊C4—12212no—
277C42—212no—
278C42C2×C22⋊D6116yes—
279C42C23×D6116yes—
280C23—1222no—
281C23—1224no—
282C23—2442no—
283C23—2442no—
284C23C22×C22⋊D6111yescharacteristic
285Q8—26no—
286Q8—26no—
287Q8—46no—
288Q8—24424no—
289Q8C2×#11758201116yescomplemented
290D4—614no—
291D4—1222no—
292D4—1224no—
293C2×C4—26no—
294C2×C4—22no—
295C2×C4—26no—
296C2×C4—42no—
297C2×C4—46no—
298C2×C4—1226no—
299C2×C4—2446no—
300C2×C4—24424no—
301C2×C4C2×#11758201112yes—
302C2×C4C22×C22⋊D6116yes—
303C2×C4C22×C22⋊D6116yes—
304C2×C4C22×C22⋊D6111yescharacteristic
305C2×C4#41×D6112yes—
306C2×C4#1451982412yes—
307C2×C4C24×D6111yescharacteristic
308C8—1226no—
309C8—1222no—
310C22—1224no—
311C22—2448no—
312C22—2442no—
313C22—2442no—
314C22#1684041912yes—
315C22C22×#1175820112yes—
316C22#1684057712yes—
317C22C23×C22⋊D6111yescharacteristic
318C4—26no—
319C4—46no—
320C4—42no—
321C4—2446no—
322C4#1684041912yes—
323C4C22×#11758201112yes—
324C4C2×#41×D6111yescharacteristic
325C4C2×#1451982411yescharacteristic
326C2—2444no—
327C2#2145845714yesdirect product factor
328C2C2×#1684041911yescharacteristic
329C2C23×#1175820111yescharacteristic
330C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#557C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#557D61
hypocenterC61C2×#3359
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #21458457C2direct (N × H)
3. C2×#16840112C2semidirect
4. C2×#16840047C2semidirect
6. C2×Q8×#92418C2semidirect
8. C2×C61×#557C2semidirect
16. #16840112C22semidirect
17. #16840047C22semidirect
19. Q8×#92418C22semidirect
28. C61×#557C22semidirect
78. C2×Q8×C61SD16semidirect
122. Q8×C61C2×SD16semidirect
161. C2×#557D61semidirect
169. C2×C61#3359semidirect
177. #557C2×D61semidirect
199. C61C2×#3359semidirect
247. C2×Q8#11758201semidirect
289. Q8C2×#11758201semidirect
327. C2#21458457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D2442
#214584572
C2×#168401122
C2×#168400472
C2×#168399642
C2×Q8×#924182
C2×C4×#117582012
C2×C61×#5572
C2×#335961