Finite Group Databasebeta

← #30605437

Subgroups — #30605437

Order 15616.

412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 82 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
1#21462047C211yesmaximal, characteristic
2#21461695C211yesmaximal, characteristic
3#21460808C214yesmaximal, complemented
4C2×#16840004C211yesmaximal, characteristic
5C2×#14519852—21no—
6C2×#14519845—21no—
7#16840704—21no—
8#16840657C2212yes—
9C22⋊#11758187—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
20C2×C4⋊#6923—22no—
21C2×C22⋊#6923—41no—
22#14519852—42no—
23C2×#11758187—22no—
24#14519845—42no—
25(C2×#6923)⋊C4—41no—
26C22×Dic122—21no—
27C22×C4×D61D411yescharacteristic
28C2×Dic244—21no—
29C2×Dic244—42no—
30C2×Dic244C2×C412yes—
31C22×#92418D411yescharacteristic
32C2×C8×D61—42no—
33C2×C8×D61C2×C411yescharacteristic
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61C2311yescharacteristic
37#14519757—22no—
38#14519757—22no—
39#14519757—41no—
40#14519757—41no—
41C2×C4⋊Dic61—41no—
42C2×#11758198—41no—
43#14519700—22no—
44#14519700—22no—
45C22×C8×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61—21no—
47#107×C61—21no—
48#107×C61C2×C412yes—
49C23×D61D811yescharacteristic
50C22×#6923—42no—
51C22×C4×C61—41no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×Dic61—41no—
54C22×Dic61SD1611yescharacteristic
55C2×C4×D61—41no—
56C2×C4×D61—41no—
57C2×C4×D61C22⋊C411yescharacteristic
58C2×C4×D61D811yescharacteristic
59C2×C4×D61SD1611yescharacteristic
60C2×C4×D61C2×D411yescharacteristic
61C2×Dic122—22no—
62C2×Dic122—42no—
63C2×Dic122—42no—
64C2×Dic122—41no—
65C22⋊#6923—82no—
66C4⋊#6923—42no—
67C4⋊#6923—42no—
68C2×C8×C61—22no—
69C2×C8×C61C22⋊C411yescharacteristic
70C2×C8×C61C22×C411yescharacteristic
71C4⋊C4×C61—22no—
72C4⋊C4×C61—41no—
73#11758198—42no—
74#11758198—42no—
75C4⋊Dic61—42no—
76C4⋊Dic61—42no—
77C2×#92418—41no—
78C2×#92418C22⋊C411yescharacteristic
79C2×#92418C2×D411yescharacteristic
80Dic244—42no—
81Dic244—42no—
82C8×D61—22no—
83C8×D61—22no—
84C8×D61—41no—
85C8×D61—41no—
86#11758187—42no—
87C23×C61#10211yescharacteristic
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—41no—
91C22×D61#10211yescharacteristic
92C22×D61C2×D811yescharacteristic
93C2×#6923—82no—
94C2×#6923—82no—
95C2×#6923—82no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—42no—
99C2×C4×C61—82no—
100C2×C4×C61#10211yescharacteristic
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×Dic61—41no—
103C2×Dic61—42no—
104C2×Dic61—82no—
105C2×Dic61#10211yescharacteristic
106C2×Dic61C2×SD1611yescharacteristic
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—41no—
112C4×D61—41no—
113Dic122—42no—
114Dic122—42no—
115Dic122—82no—
116C8×C61—21no—
117C8×C61#9912yes—
118#92418—21no—
119#92418—21no—
120#11889—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#36012yes—
124C22×C61C2×#10211yescharacteristic
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—44no—
131C2×D61#51012yes—
132#6923—162no—
133C4×C61—21no—
134C4×C61—82no—
135C4×C61C2×#9911yescharacteristic
136C4×C61#42111yescharacteristic
137Dic61—21no—
138Dic61—21no—
139Dic61—82no—
140C2×#467—611no—
141#2112—611no—
142#1807—611no—
143#1348—614no—
144C2×C61—22no—
145C2×C61#151911yescharacteristic
146C2×C61#214111yescharacteristic
147C2×C61C2×#36011yescharacteristic
148D61—22no—
149D61—41no—
150C22×Q16—611no—
151C23×C8—611no—
152C2×C22⋊Q8—1221no—
153C2×M32—1221no—
154#467—612no—
155#467—612no—
156#467—1221no—
157#467—1221no—
158C2×#107#692311yescharacteristic, complemented
159C2×#106—1221no—
160C2×#103—1221no—
161#380—1221no—
162C22⋊C16—612no—
163C22⋊C16—1221no—
164#340—612no—
165C61#1188911yescharacteristic, complemented, Sylow
166C22×Q8—1221no—
167C23×C4—611no—
168C2×Q16—612no—
169C2×Q16—1221no—
170C2×Q16—2442no—
171C22×C8—611no—
172C22×C8—611no—
173C22×C8—611no—
174C22×C8—611no—
175C22×C8—611no—
176C22×C8—2442no—
177C22×C8C2×#692311yescharacteristic
178C22⋊Q8—1222no—
179C22⋊Q8—1222no—
180C22⋊Q8—2441no—
181C22⋊Q8—2441no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—1222no—
184C2×C4⋊C4—2441no—
185C2×C22⋊C4—2441no—
186C2×C22⋊C4—2441no—
187M32—2442no—
188C2×C16—1222no—
189#107—21no—
190#107C2×#692312yes—
191#106—2442no—
192#103—1222no—
193#103—1222no—
194#95—2441no—
195C24—611no—
196C2×Q8—1222no—
197C2×Q8—2442no—
198C2×Q8—2442no—
199C2×Q8—2441no—
200C22×C4—41no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—2441no—
207C22×C4—2441no—
208C22×C4—2442no—
209C22×C4—2441no—
210C22×C4C22⋊#692311yescharacteristic
211Q16—2442no—
212Q16—2442no—
213C2×C8—22no—
214C2×C8—611no—
215C2×C8—611no—
216C2×C8—1222no—
217C2×C8—1222no—
218C2×C8—2441no—
219C2×C8—2441no—
220C2×C8—2441no—
221C2×C8C22⋊#692311yescharacteristic
222C2×C8C22×#692311yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—2442no—
226C4⋊C4—2442no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C22⋊C4—4882no—
230C22⋊C4—2442no—
231C22⋊C4—2442no—
232C16—2442no—
233C23—611no—
234C23—611no—
235C23—1222no—
236C23—1222no—
237C23—2441no—
238C23#1451983911yescharacteristic
239Q8—4882no—
240Q8—2442no—
241Q8—2442no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—82no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—4882no—
253C2×C4—4882no—
254C2×C4—4882no—
255C2×C4—4882no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2442no—
260C2×C4#1451983911yescharacteristic
261C2×C4C2×C22⋊#692311yescharacteristic
262C8—21no—
263C8—1221no—
264C8—1221no—
265C8#1451983612yes—
266C22—21no—
267C22—21no—
268C22—612no—
269C22—1221no—
270C22—1221no—
271C22—1221no—
272C22—1221no—
273C22—1221no—
274C22—2444no—
275C22#1684067812yes—
276C22C2×#1451983911yescharacteristic
277C4—21no—
278C4—82no—
279C4—1221no—
280C4—1221no—
281C4—9762no—
282C4—4882no—
283C4C2×#1451983611yescharacteristic
284C4#1684076111yescharacteristic
285C2—22no—
286C2—1222no—
287C2—2441no—
288C2#2146125611yescharacteristic
289C2#2146212911yescharacteristic
290C2C2×#1684067811yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#107×C61C4
socleC22×C61C2×#102
prime radicalC23×D61D8
cosocleC2×C8×D61C23
hypercenterC2×#107#6923
hypocenterC61#11889
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #21460808C2semidirect
11. C22×Dic244C4semidirect
16. #16840004C4semidirect
19. C2×#107×C61C4semidirect
158. C2×#107#6923semidirect
165. C61#11889semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214616952
#214608082
C2×#168400042
#1188961