Finite Group Databasebeta

← C2×#21460748 #30603832

Subgroups — C2×#21460748 #30603832

Order 15616.

834 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 120 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×#16840607C212yesmaximal, complemented
2#21460748C214yesmaximal, direct product factor
3C2×#16839664C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5#16840607—22no—
6#16840607C2214yescomplemented
7C23×D244C411yescharacteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C22×#11758198—22no—
10#16839664—22no—
11#16839664C412yes—
12#16839664C2212yes—
13C22×C42×C61C411yescharacteristic
14C22×#92420—42no—
15C22⋊#92420—24no—
16C22⋊#92420—42no—
17C24×D61—21no—
18C22×D244—21no—
19C22×D244—22no—
20C22×D244—41no—
21C22×D244—41no—
22C22×D244—42no—
23C22×D244C814yescomplemented
24C22×D244C2×C412yes—
25C23×Dic61D412yes—
26C2×C4⋊Dic61—41no—
27C2×C4⋊Dic61—41no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61D412yes—
30C2×C4⋊Dic61C2311yescharacteristic
31C2×#11758198—24no—
32C2×#11758198—24no—
33C2×#11758198—48no—
34C23×C4×C61—21no—
35C23×C4×C61C2×C411yescharacteristic
36C2×C42×C61—21no—
37C2×C42×C61—42no—
38C2×C42×C61C2×C412yes—
39C24×C61C22⋊C411yescharacteristic
40C23×D61—24no—
41C23×D61—22no—
42C23×D61—44no—
43C23×D61—44no—
44C23×D61—41no—
45C23×D61—41no—
46C23×D61—42no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—22no—
50C22×C4×C61—24no—
51C22×C4×C61—22no—
52C22×C4×C61—42no—
53C22×C4×C61—42no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C2×C812yes—
56C22×C4×C61M1612yes—
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C22×Dic61—44no—
61C22×Dic61C22⋊C412yes—
62C22×Dic61C2×D412yes—
63C2×D244—24no—
64C2×D244—22no—
65C2×D244—44no—
66C2×D244—44no—
67C2×D244—42no—
68C2×D244—42no—
69C2×D244—44no—
70C2×D244—44no—
71C2×D244—42no—
72C2×D244—42no—
73C2×D244C2×C814yescomplemented
74C2×#92420—44no—
75C2×#92420—84no—
76C42×C61—42no—
77C42×C61—42no—
78#11758198—48no—
79#11758198—48no—
80C4⋊Dic61—41no—
81C4⋊Dic61—42no—
82C4⋊Dic61—41no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61C22⋊C812yes—
86C23×C61#9911yescharacteristic
87C23×C61#9911yescharacteristic
88C23×C61#10012yes—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—24no—
91C22×D61—44no—
92C22×D61—416no—
93C22×D61—44no—
94C22×D61—44no—
95C22×D61—44no—
96C22×D61—42no—
97C22×D61—42no—
98C22×D61—88no—
99C22×D61—82no—
100C22×D61—82no—
101C22×D61—82no—
102C22×D61—82no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—22no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—24no—
112C2×C4×C61—48no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61C22⋊C812yes—
116C2×C4×C61C22×C811yescharacteristic
117C2×C4×C61C2×M1611yescharacteristic
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—44no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—82no—
124D244—44no—
125D244—48no—
126D244—44no—
127#92420—84no—
128C2×#1318—611nomaximal, Sylow
129C22×C61—24no—
130C22×C61—24no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#32312yes—
136C22×C61#32312yes—
137C22×C61#35312yes—
138C22×C61#35512yes—
139C22×C61C2×C22⋊C811yescharacteristic
140C22×C61C2×#9911yescharacteristic
141C22×C61C2×#10011yescharacteristic
142C2×D61—48no—
143C2×D61—44no—
144C2×D61—84no—
145C2×D61—88no—
146C2×D61—88no—
147C2×D61—82no—
148C2×D61—82no—
149C4×C61—22no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—44no—
153Dic61—42no—
154Dic61—42no—
155C2×#390—611no—
156C2×#324—612no—
157#1318—614no—
158C2×C61—21no—
159C2×C61—21no—
160C2×C61—22no—
161C2×C61#131814yescomplemented
162C2×C61C2×#32311yescharacteristic
163C2×C61C2×#35311yescharacteristic
164C2×C61C2×#35511yescharacteristic
165D61—84no—
166C23×D4—611no—
167C22×C4⋊C4—611no—
168C22×C22⋊C4—1222no—
169C22×C42#692311yescharacteristic
170C2×C22⋊C8—1222no—
171#390—612no—
172#390—612no—
173#390—1222no—
174#324—614no—
175#324—1222no—
176C61C2×#131811yescharacteristic, complemented, Sylow
177C25—1221no—
178C22×D4—614no—
179C22×D4—612no—
180C22×D4—1222no—
181C22×D4—1221no—
182C22×D4—2441no—
183C22×D4—2441no—
184C22×D4—2442no—
185C23×C4—21no—
186C23×C4—612no—
187C23×C4C2×#692311yescharacteristic
188C22×C8—2442no—
189C2×C4⋊C4—612no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—2441no—
193C2×C4⋊C4—2441no—
194C2×C22⋊C4—1224no—
195C2×C22⋊C4—1224no—
196C2×C22⋊C4—2448no—
197C2×C42—21no—
198C2×C42—42no—
199C2×C42C2×#692312yes—
200C22⋊C8—1224no—
201C22⋊C8—2442no—
202C24—1224no—
203C24—1222no—
204C24—2444no—
205C24—2444no—
206C24—2441no—
207C24—2441no—
208C24—2442no—
209C24C22⋊#692311yescharacteristic
210C2×D4—614no—
211C2×D4—1224no—
212C2×D4—1222no—
213C2×D4—2442no—
214C2×D4—2442no—
215C2×D4—2444no—
216C2×D4—2444no—
217C2×D4—2442no—
218C2×D4—2442no—
219C2×D4—2444no—
220C2×D4—2444no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—612no—
229C22×C4—612no—
230C22×C4—1222no—
231C22×C4—1222no—
232C22×C4—2444no—
233C22×C4D61⋊C812yes—
234C22×C4#1175821312yes—
235C22×C4C22⋊#692311yescharacteristic
236C22×C4C22×#692311yescharacteristic
237C2×C8—4884no—
238C2×C8—2444no—
239C4⋊C4—2442no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C22⋊C4—2448no—
243C22⋊C4—2448no—
244C42—42no—
245C42—42no—
246C23—22no—
247C23—22no—
248C23—1224no—
249C23—4888no—
250C23—4882no—
251C23—4882no—
252C23—4882no—
253C23—4882no—
254C23—2444no—
255C23—24416no—
256C23—2444no—
257C23—2442no—
258C23—2442no—
259C23—2444no—
260C23—2444no—
261C23#1451983412yes—
262C23#1451983611yescharacteristic
263C23#1451983611yescharacteristic
264C23#1451983712yes—
265C23C2×C22⋊#692311yescharacteristic
266D4—2444no—
267D4—2448no—
268D4—2444no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—24no—
278C2×C4—48no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—1222no—
282C2×C4—1222no—
283C2×C4—4882no—
284C2×C4—2444no—
285C2×C4—2442no—
286C2×C4—2442no—
287C2×C4#1451983412yes—
288C2×C4C2×D61⋊C811yescharacteristic
289C2×C4C2×#1175821311yescharacteristic
290C8—4884no—
291C22—24no—
292C22—24no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—4884no—
298C22—4888no—
299C22—4888no—
300C22—4882no—
301C22—4882no—
302C22—2448no—
303C22—2444no—
304C22#1684060612yes—
305C22#1684060612yes—
306C22#1684066712yes—
307C22#1684067112yes—
308C22C2×#1451983411yescharacteristic
309C22C2×#1451983611yescharacteristic
310C22C2×#1451983711yescharacteristic
311C4—22no—
312C4—21no—
313C4—21no—
314C4—44no—
315C4—2442no—
316C4—2442no—
317C2—21no—
318C2—22no—
319C2—21no—
320C2—4884no—
321C2#2146074814yesdirect product factor
322C2C2×#1684060611yescharacteristic
323C2C2×#1684066711yescharacteristic
324C2C2×#1684067111yescharacteristic
subgroupG/H
centerC23#14519836
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC23×C61#99
prime radicalC23×D244C4
cosocleC2×C4⋊Dic61C23
hypercenterC22×C42#6923
hypocenterC61C2×#1318
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#16840607C2semidirect
2. #21460748C2direct (N × H)
6. #16840607C22semidirect
23. C22×D244C8semidirect
73. C2×D244C2×C8semidirect
161. C2×C61#1318semidirect
176. C61C2×#1318semidirect
321. C2#21460748direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406072
#214607482
C2×#168396642
C2×#131861