Finite Group Databasebeta

← C2×#21460808 #30604771

Subgroups — C2×#21460808 #30604771

Order 15616.

506 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840657C211yesmaximal, characteristic
2C2×#16840636C211yesmaximal, characteristic
3#21460808C214yesmaximal, direct product factor
4C2×#16840004C211yesmaximal, characteristic
5C22×C4⋊#6923—21no—
6C22×#11758187—21no—
7#16840657—21no—
8#16840657C2212yes—
9#16840636—21no—
10#16840636C2212yes—
11C22×Dic244C411yescharacteristic, complemented
12C22×C8×D61C2211yescharacteristic
13C2×#14519757—21no—
14#16840004—21no—
15#16840004—21no—
16#16840004C412yescomplemented
17#16840004C2212yes—
18C2×#14519700—21no—
19C2×#107×C61C411yescharacteristic, complemented
20C23×#6923—41no—
21C2×C4⋊#6923—24no—
22C2×C4⋊#6923—22no—
23C2×C4⋊#6923—42no—
24C2×C4⋊#6923—41no—
25C2×#11758187—22no—
26C2×#11758187—42no—
27C22×Dic122—21no—
28C22×C4×D61D411yescharacteristic
29C2×Dic244—21no—
30C2×Dic244—42no—
31C2×Dic244C2×C412yescomplemented
32C22×#92418D411yescharacteristic
33C2×C8×D61—42no—
34C2×C8×D61C2×C411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61C2311yescharacteristic
38#14519757—22no—
39#14519757—22no—
40#14519757—41no—
41#14519757—41no—
42C2×C4⋊Dic61—41no—
43C2×#11758198—41no—
44#14519700—22no—
45#14519700—22no—
46C22×C8×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61—21no—
48#107×C61—21no—
49#107×C61C2×C412yescomplemented
50C23×D61D811yescharacteristic
51C22×#6923—44no—
52C22×#6923—42no—
53C22×#6923—82no—
54C22×#6923—82no—
55C22×C4×C61—41no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×Dic61—41no—
58C22×Dic61SD1611yescharacteristic
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×C4×D61D811yescharacteristic
63C2×C4×D61SD1611yescharacteristic
64C2×C4×D61C2×D411yescharacteristic
65C2×Dic122—22no—
66C2×Dic122—42no—
67C2×Dic122—42no—
68C2×Dic122—41no—
69C4⋊#6923—24no—
70C4⋊#6923—44no—
71C4⋊#6923—42no—
72C2×C8×C61—22no—
73C2×C8×C61C22⋊C411yescharacteristic
74C2×C8×C61C22×C411yescharacteristic
75C4⋊C4×C61—22no—
76C4⋊C4×C61—41no—
77#11758198—42no—
78#11758198—42no—
79C4⋊Dic61—42no—
80C4⋊Dic61—42no—
81C2×#92418—22no—
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84Dic244—42no—
85Dic244—42no—
86C8×D61—41no—
87C8×D61—41no—
88C8×D61—41no—
89C8×D61—41no—
90#11758187—42no—
91C23×C61#10211yescharacteristic
92C22×D61—22no—
93C22×D61—22no—
94C22×D61#10211yescharacteristic
95C22×D61SD3212yes—
96C22×D61Q3212yes—
97C22×D61C2×D811yescharacteristic
98C2×#6923—44no—
99C2×#6923—88no—
100C2×#6923—82no—
101C2×#6923—82no—
102C2×C4×C61—42no—
103C2×C4×C61—82no—
104C2×C4×C61#9912yes—
105C2×C4×C61#10211yescharacteristic
106C2×C4×C61#10412yes—
107C2×C4×C61C2×C22⋊C411yescharacteristic
108C2×Dic61—22no—
109C2×Dic61—42no—
110C2×Dic61—82no—
111C2×Dic61#10211yescharacteristic
112C2×Dic61C2×SD1611yescharacteristic
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119Dic122—42no—
120Dic122—42no—
121Dic122—82no—
122C8×C61—21no—
123C8×C61—21no—
124#92418—21no—
125#92418—21no—
126C2×#1348—611nomaximal, Sylow
127C22×C61#32712yes—
128C22×C61#35812yes—
129C22×C61#36012yes—
130C22×C61C2×#10211yescharacteristic
131C2×D61—24no—
132C2×D61—24no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—21no—
137C2×D61#35812yes—
138C2×D61C2×SD3211yescharacteristic
139C2×D61C2×Q3211yescharacteristic
140#6923—84no—
141C4×C61—82no—
142C4×C61#32712yes—
143C4×C61C2×#9911yescharacteristic
144C4×C61C2×#10411yescharacteristic
145Dic61—21no—
146Dic61—21no—
147Dic61—82no—
148C2×#467—611no—
149C2×C22⋊C16—611no—
150C2×#340—611no—
151#1348—614no—
152C2×C61#134814yescomplemented
153C2×C61C2×#32711yescharacteristic
154C2×C61C2×#35811yescharacteristic
155C2×C61C2×#36011yescharacteristic
156D61—21no—
157D61—22no—
158D61—21no—
159C22×Q16—611no—
160C23×C8—611no—
161C2×C22⋊Q8—1221no—
162C22×C4⋊C4—1221no—
163C22×C16—1221no—
164#467—612no—
165#467—612no—
166#467—1221no—
167#467—1221no—
168C2×#107#692311yescharacteristic, complemented
169C2×#103—1221no—
170C22⋊C16—612no—
171C22⋊C16—1221no—
172#340—612no—
173#340—1221no—
174C61C2×#134811yescharacteristic, complemented, Sylow
175C22×Q8—1221no—
176C23×C4—611no—
177C23×C4—2441no—
178C2×Q16—612no—
179C2×Q16—1221no—
180C2×Q16—2442no—
181C22×C8—611no—
182C22×C8—611no—
183C22×C8—611no—
184C22×C8—611no—
185C22×C8—611no—
186C22×C8—2442no—
187C22×C8C2×#692311yescharacteristic
188C22⋊Q8—1222no—
189C22⋊Q8—1222no—
190C22⋊Q8—2441no—
191C22⋊Q8—2441no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—1222no—
194C2×C4⋊C4—1224no—
195C2×C4⋊C4—2441no—
196C2×C4⋊C4—2441no—
197C2×C4⋊C4—2442no—
198C2×C22⋊C4—2441no—
199C2×C16—1222no—
200C2×C16—2442no—
201#107—21no—
202#107C2×#692312yescomplemented
203#103—1222no—
204#103—1222no—
205C24—611no—
206C2×Q8—1222no—
207C2×Q8—2442no—
208C2×Q8—2442no—
209C2×Q8—2441no—
210C22×C4—41no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1222no—
217C22×C4—1222no—
218C22×C4—4882no—
219C22×C4—4882no—
220C22×C4—2442no—
221C22×C4—2444no—
222C22×C4—2441no—
223C22×C4C22⋊#692311yescharacteristic
224Q16—2442no—
225Q16—2442no—
226C2×C8—22no—
227C2×C8—611no—
228C2×C8—611no—
229C2×C8—1222no—
230C2×C8—2441no—
231C2×C8—2441no—
232C2×C8—2441no—
233C2×C8—2441no—
234C2×C8C22⋊#692311yescharacteristic
235C2×C8C22×#692311yescharacteristic
236C4⋊C4—22no—
237C4⋊C4—41no—
238C4⋊C4—1224no—
239C4⋊C4—2442no—
240C4⋊C4—2442no—
241C4⋊C4—2442no—
242C4⋊C4—2444no—
243C22⋊C4—2442no—
244C22⋊C4—2442no—
245C16—2442no—
246C23—611no—
247C23—611no—
248C23—612no—
249C23—612no—
250C23—1222no—
251C23—1222no—
252C23#1451983911yescharacteristic
253Q8—4882no—
254Q8—2442no—
255Q8—2442no—
256C2×C4—42no—
257C2×C4—82no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—4882no—
268C2×C4—4888no—
269C2×C4—4882no—
270C2×C4—4882no—
271C2×C4—2444no—
272C2×C4—2442no—
273C2×C4#1451983612yes—
274C2×C4#1451983911yescharacteristic
275C2×C4#1451984212yes—
276C2×C4C2×C22⋊#692311yescharacteristic
277C8—21no—
278C8—21no—
279C8—1221no—
280C8—1221no—
281C22—611no—
282C22—612no—
283C22—611no—
284C22—1224no—
285C22—1224no—
286C22—1221no—
287C22—1221no—
288C22—1221no—
289C22—1221no—
290C22#1684061412yes—
291C22#1684067512yes—
292C22#1684067812yes—
293C22C2×#1451983911yescharacteristic
294C4—82no—
295C4—1221no—
296C4—1221no—
297C4—4884no—
298C4—4882no—
299C4#1684061412yes—
300C4C2×#1451983611yescharacteristic
301C4C2×#1451984211yescharacteristic
302C2—1221no—
303C2—1222no—
304C2—1221no—
305C2#2146080814yesdirect product factor
306C2C2×#1684061411yescharacteristic
307C2C2×#1684067511yescharacteristic
308C2C2×#1684067811yescharacteristic
subgroupG/H
centerC23#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#107×C61C4
socleC23×C61#102
prime radicalC23×D61D8
cosocleC2×C8×D61C23
hypercenterC2×#107#6923
hypocenterC61C2×#1348
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #21460808C2direct (N × H)
11. C22×Dic244C4semidirect
16. #16840004C4semidirect
19. C2×#107×C61C4semidirect
31. C2×Dic244C2×C4semidirect
49. #107×C61C2×C4semidirect
152. C2×C61#1348semidirect
168. C2×#107#6923semidirect
174. C61C2×#1348semidirect
202. #107C2×#6923semidirect
305. C2#21460808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406572
C2×#168406362
#214608082
C2×#168400042
C2×#134861