Finite Group Databasebeta

← C2×#21460806 #30604768

Subgroups — C2×#21460806 #30604768

Order 15616.

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

normal subgroups only

This group has 558 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, complemented
2C2×#16840636C211yesmaximal, characteristic, complemented
3#21460806C214yesmaximal, direct product factor
4C2×#16839999C211yesmaximal, characteristic
5C22×C4⋊#6923—21no—
6C22×#11758187—21no—
7#16840657—21no—
8#16840657C2212yescomplemented
9#16840636—21no—
10#16840636C2212yescomplemented
11C22×D488C411yescharacteristic, complemented
12C22×C8×D61C2211yescharacteristic
13C2×#14519752—21no—
14#16839999—21no—
15#16839999—21no—
16#16839999C412yescomplemented
17#16839999C2212yes—
18C2×#14519697—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×D244—21no—
28C22×D244—41no—
29C22×C4×D61D411yescharacteristic
30C2×D488—21no—
31C2×D488—42no—
32C2×D488C2×C412yescomplemented
33C22×#92418D411yescharacteristic
34C2×C8×D61—42no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61C2311yescharacteristic
39#14519752—22no—
40#14519752—22no—
41#14519752—41no—
42#14519752—41no—
43C2×#11758198—41no—
44#14519697—22no—
45#14519697—22no—
46C22×C8×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61—21no—
48#107×C61—21no—
49#107×C61C2×C412yescomplemented
50C23×D61—41no—
51C23×D61D811yescharacteristic
52C22×#6923—44no—
53C22×#6923—42no—
54C22×#6923—82no—
55C22×#6923—82no—
56C22×C4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×Dic61SD1611yescharacteristic
59C2×D244—22no—
60C2×D244—42no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244—42no—
64C2×D244—41no—
65C2×D244—82no—
66C2×D244—82no—
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×C4×D61C22⋊C411yescharacteristic
70C2×C4×D61D811yescharacteristic
71C2×C4×D61SD1611yescharacteristic
72C2×C4×D61C2×D411yescharacteristic
73C4⋊#6923—24no—
74C4⋊#6923—44no—
75C4⋊#6923—42no—
76C2×C8×C61—22no—
77C2×C8×C61C22⋊C411yescharacteristic
78C2×C8×C61C22×C411yescharacteristic
79C4⋊C4×C61—22no—
80C4⋊C4×C61—41no—
81#11758198—42no—
82#11758198—42no—
83C2×#92418—22no—
84C2×#92418C22⋊C411yescharacteristic
85C2×#92418C2×D411yescharacteristic
86D488—42no—
87D488—42no—
88C8×D61—41no—
89C8×D61—41no—
90C8×D61—41no—
91C8×D61—41no—
92#11758187—42no—
93C23×C61#10211yescharacteristic
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—42no—
97C22×D61—82no—
98C22×D61—82no—
99C22×D61—82no—
100C22×D61#10211yescharacteristic
101C22×D61D1612yes—
102C22×D61SD3212yes—
103C22×D61C2×D811yescharacteristic
104C2×#6923—44no—
105C2×#6923—88no—
106C2×#6923—82no—
107C2×#6923—82no—
108C2×C4×C61—42no—
109C2×C4×C61—82no—
110C2×C4×C61#9912yes—
111C2×C4×C61#10211yescharacteristic
112C2×C4×C61#10412yes—
113C2×C4×C61C2×C22⋊C411yescharacteristic
114C2×Dic61—22no—
115C2×Dic61#10211yescharacteristic
116C2×Dic61C2×SD1611yescharacteristic
117D244—42no—
118D244—42no—
119D244—84no—
120D244—82no—
121D244—82no—
122D244—82no—
123C4×D61—22no—
124C4×D61—22no—
125C4×D61—21no—
126C4×D61—21no—
127C4×D61—21no—
128C4×D61—21no—
129C8×C61—21no—
130C8×C61—21no—
131#92418—21no—
132#92418—21no—
133C2×#1347—611nomaximal, Sylow
134C22×C61#32712yes—
135C22×C61#35712yes—
136C22×C61#36012yes—
137C22×C61C2×#10211yescharacteristic
138C2×D61—24no—
139C2×D61—24no—
140C2×D61—21no—
141C2×D61—21no—
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—82no—
145C2×D61—82no—
146C2×D61—82no—
147C2×D61—164no—
148C2×D61#35712yes—
149C2×D61C2×D1611yescharacteristic
150C2×D61C2×SD3211yescharacteristic
151#6923—84no—
152C4×C61—82no—
153C4×C61#32712yes—
154C4×C61C2×#9911yescharacteristic
155C4×C61C2×#10411yescharacteristic
156Dic61—21no—
157Dic61—21no—
158C2×#466—611no—
159C2×C22⋊C16—611no—
160C2×#340—611no—
161#1347—614no—
162C2×C61#134714yescomplemented
163C2×C61C2×#32711yescharacteristic
164C2×C61C2×#35711yescharacteristic
165C2×C61C2×#36011yescharacteristic
166D61—21no—
167D61—22no—
168D61—21no—
169D61—162no—
170C22×D8—611no—
171C23×C8—611no—
172C2×#121—1221no—
173C22×C4⋊C4—1221no—
174C22×C16—1221no—
175#466—612no—
176#466—612no—
177#466—1221no—
178#466—1221no—
179C2×#107#692311yescharacteristic, complemented
180C2×#102—1221no—
181C22⋊C16—612no—
182C22⋊C16—1221no—
183#340—612no—
184#340—1221no—
185C61C2×#134711yescharacteristic, complemented, Sylow
186C22×D4—1221no—
187C22×D4—2441no—
188C23×C4—611no—
189C23×C4—2441no—
190C2×D8—612no—
191C2×D8—1221no—
192C2×D8—2442no—
193C22×C8—611no—
194C22×C8—611no—
195C22×C8—611no—
196C22×C8—611no—
197C22×C8—611no—
198C22×C8—2442no—
199C22×C8C2×#692311yescharacteristic
200#121—1222no—
201#121—1222no—
202#121—2441no—
203#121—2441no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—1222no—
206C2×C4⋊C4—1224no—
207C2×C4⋊C4—2441no—
208C2×C4⋊C4—2442no—
209C2×C22⋊C4—2441no—
210C2×C16—1222no—
211C2×C16—2442no—
212#107—21no—
213#107C2×#692312yescomplemented
214#102—1222no—
215#102—1222no—
216C24—611no—
217C24—2441no—
218C2×D4—1222no—
219C2×D4—4882no—
220C2×D4—4882no—
221C2×D4—2442no—
222C2×D4—2442no—
223C2×D4—2442no—
224C2×D4—2441no—
225C2×D4—2442no—
226C22×C4—41no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—4882no—
235C22×C4—4882no—
236C22×C4—2442no—
237C22×C4—2444no—
238C22×C4C22⋊#692311yescharacteristic
239D8—2442no—
240D8—2442no—
241C2×C8—22no—
242C2×C8—611no—
243C2×C8—611no—
244C2×C8—1222no—
245C2×C8—2441no—
246C2×C8—2441no—
247C2×C8—2441no—
248C2×C8—2441no—
249C2×C8C22⋊#692311yescharacteristic
250C2×C8C22×#692311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—1224no—
254C4⋊C4—2442no—
255C4⋊C4—2444no—
256C22⋊C4—2442no—
257C22⋊C4—2442no—
258C16—2442no—
259C23—611no—
260C23—611no—
261C23—612no—
262C23—612no—
263C23—1222no—
264C23—1222no—
265C23—4882no—
266C23—4882no—
267C23—4882no—
268C23—2442no—
269C23#1451983911yescharacteristic
270D4—4882no—
271D4—4884no—
272D4—4882no—
273D4—4882no—
274D4—2442no—
275D4—2442no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1222no—
286C2×C4—1222no—
287C2×C4—4882no—
288C2×C4—4888no—
289C2×C4—4882no—
290C2×C4—2444no—
291C2×C4#1451983612yes—
292C2×C4#1451983911yescharacteristic
293C2×C4#1451984212yes—
294C2×C4C2×C22⋊#692311yescharacteristic
295C8—21no—
296C8—21no—
297C8—1221no—
298C8—1221no—
299C22—611no—
300C22—612no—
301C22—611no—
302C22—1224no—
303C22—1224no—
304C22—1221no—
305C22—1221no—
306C22—1221no—
307C22—1221no—
308C22—9764no—
309C22—4882no—
310C22—4882no—
311C22—4882no—
312C22#1684061412yes—
313C22#1684067412yes—
314C22#1684067912yes—
315C22C2×#1451983911yescharacteristic
316C4—82no—
317C4—1221no—
318C4—1221no—
319C4—4884no—
320C4#1684061412yes—
321C4C2×#1451983611yescharacteristic
322C4C2×#1451984211yescharacteristic
323C2—1221no—
324C2—1222no—
325C2—1221no—
326C2—9762no—
327C2#2146080614yesdirect product factor
328C2C2×#1684061411yescharacteristic
329C2C2×#1684067411yescharacteristic
330C2C2×#1684067911yescharacteristic
subgroupG/H
centerC23#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#107×C61C4
socleC23×C61#102
prime radicalC2×#16839999C2
cosocleC2×C8×D61C23
hypercenterC2×#107#6923
hypocenterC61C2×#1347
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
1. C2×#16840657C2semidirect
2. C2×#16840636C2semidirect
3. #21460806C2direct (N × H)
8. #16840657C22semidirect
10. #16840636C22semidirect
11. C22×D488C4semidirect
16. #16839999C4semidirect
19. C2×#107×C61C4semidirect
32. C2×D488C2×C4semidirect
49. #107×C61C2×C4semidirect
162. C2×C61#1347semidirect
179. C2×#107#6923semidirect
185. C61C2×#1347semidirect
213. #107C2×#6923semidirect
327. C2#21460806direct (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
#214608062
C2×#168399992
C2×#134761