Finite Group Databasebeta

← #30605651

Subgroups — #30605651

Order 15616.

394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462177C211yesmaximal, characteristic
2#21461376C211yesmaximal, characteristic
3#21460834C214yesmaximal, complemented
4C2×#16840140C211yesmaximal, characteristic
5#16840765—21no—
6#16840683C2212yes—
7C22⋊#11758187—21no—
8#16840648—21no—
9#16840626C2212yes—
10#16840625—21no—
11C22×Dic244C411yescharacteristic
12C22×#11758202—21no—
13C2×#14519775—21no—
14#16840140—21no—
15#16840140—21no—
16#16840140C412yes—
17#16840140C2212yes—
18C2×C8×Dic61C2211yescharacteristic
19C22×Q16×C61C411yescharacteristic
20C2×#11758217—41no—
21C2×#11758187—22no—
22#14519844—41no—
23C4⋊#92420—22no—
24C22×Dic122—21no—
25C2×Dic244—21no—
26C2×Dic244—42no—
27C2×Dic244C2×C412yes—
28C2×#11758202—22no—
29C2×#11758202—22no—
30C2×#11758202—44no—
31C22×#92418D411yescharacteristic
32#14519775—22no—
33#14519775—22no—
34#14519775—41no—
35#14519775—41no—
36C2×#11758196—41no—
37C2×#11758196—41no—
38C2×C4×Dic61D411yescharacteristic
39C8×Dic61C2×C411yescharacteristic
40C8×Dic61D411yescharacteristic
41C8×Dic61D411yescharacteristic
42C8×Dic61C2311yescharacteristic
43C22×Q8×C61—21no—
44C2×Q16×C61—21no—
45C2×Q16×C61—42no—
46C2×Q16×C61C2×C412yes—
47C22×C8×C61C2×C411yescharacteristic
48C2×Q8×C61—22no—
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C2×Q8×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×Dic61—41no—
55C22×Dic61D811yescharacteristic
56C22×Dic61SD1611yescharacteristic
57C2×Dic122—22no—
58C2×Dic122—42no—
59C2×Dic122—42no—
60C2×Dic122—41no—
61#11758217—82no—
62C2×#92420—42no—
63Q16×C61—42no—
64Q16×C61—42no—
65C2×C8×C61—22no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22×C411yescharacteristic
68#11758202—44no—
69#11758202—44no—
70#11758196—42no—
71#11758196—42no—
72#11758196—42no—
73#11758196—42no—
74C4×Dic61C22⋊C411yescharacteristic
75C4×Dic61D811yescharacteristic
76C4×Dic61SD1611yescharacteristic
77C4×Dic61C2×D411yescharacteristic
78C2×#92418—22no—
79C2×#92418C22⋊C411yescharacteristic
80C2×#92418C2×D411yescharacteristic
81Dic244—42no—
82Dic244—42no—
83#11758187—42no—
84C23×C61#10211yescharacteristic
85Q8×C61—42no—
86Q8×C61—42no—
87Q8×C61—82no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—42no—
91C2×C4×C61—82no—
92C2×C4×C61#10211yescharacteristic
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×Dic61—22no—
95C2×Dic61—42no—
96C2×Dic61—82no—
97C2×Dic61#10211yescharacteristic
98C2×Dic61#10211yescharacteristic
99C2×Dic61SD3212yes—
100C2×Dic61Q3212yes—
101C2×Dic61C2×D811yescharacteristic
102C2×Dic61C2×SD1611yescharacteristic
103Dic122—42no—
104Dic122—42no—
105Dic122—82no—
106#92420—82no—
107C8×C61—21no—
108C8×C61#10012yes—
109#92418—21no—
110#92418AGL(1,ℤ/8)12yes—
111#11962—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61#35812yes—
115C22×C61C2×#10211yescharacteristic
116C4×C61—21no—
117C4×C61—82no—
118C4×C61C2×#10011yescharacteristic
119C4×C61#41811yescharacteristic
120Dic61—21no—
121Dic61—82no—
122Dic61#35812yes—
123Dic61#36212yes—
124Dic61C2×SD3211yescharacteristic
125Dic61C2×Q3211yescharacteristic
126C2×#494—611no—
127#2162—611no—
128#1567—611no—
129#1362—614no—
130C2×C61—22no—
131C2×C61#154511yescharacteristic
132C2×C61C2×#35811yescharacteristic
133C2×C61C2×#36211yescharacteristic
134C22×Q16—611no—
135C22×Q16—1221no—
136C22×Q16#692311yescharacteristic
137C2×C4⋊Q8—1221no—
138#494—612no—
139#494—612no—
140#494—1221no—
141#494—1221no—
142#423—1221no—
143C2×C4×C8—611no—
144C4⋊C16—612no—
145C22⋊C16—1221no—
146C4×C16—1221no—
147#335—612no—
148#335—1221no—
149C61#1196211yescharacteristic, complemented, Sylow
150C22×Q8—21no—
151C22×Q8—1221no—
152C2×Q16—21no—
153C2×Q16—42no—
154C2×Q16—612no—
155C2×Q16—1222no—
156C2×Q16—1222no—
157C2×Q16—1221no—
158C2×Q16—2442no—
159C2×Q16—2444no—
160C2×Q16C2×#692312yes—
161C2×M16—2441no—
162C22×C8—611no—
163C22×C8C2×#692311yescharacteristic
164C4⋊Q8—1222no—
165C4⋊Q8—1222no—
166C4⋊Q8—2441no—
167C4⋊Q8—2441no—
168C2×C4⋊C4—2441no—
169C2×C4⋊C4—2441no—
170C2×C42—611no—
171C2×C16—1222no—
172C4⋊C8—1222no—
173C4⋊C8—2441no—
174C4×C8—611no—
175C4×C8—611no—
176C4×C8—611no—
177C4×C8—611no—
178C2×Q8—22no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—41no—
182C2×Q8—1222no—
183C2×Q8—2442no—
184C2×Q8—2442no—
185C2×Q8—2441no—
186C22×C4—41no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—2441no—
190C22×C4C22⋊#692311yescharacteristic
191Q16—42no—
192Q16—42no—
193Q16—2442no—
194Q16—2444no—
195Q16—2444no—
196Q16—2442no—
197M16—4882no—
198C2×C8—22no—
199C2×C8—611no—
200C2×C8—611no—
201C2×C8—1222no—
202C2×C8—2442no—
203C2×C8C22⋊#692311yescharacteristic
204C2×C8C22×#692311yescharacteristic
205C4⋊C4—2442no—
206C4⋊C4—2442no—
207C4⋊C4—2442no—
208C4⋊C4—2442no—
209C42—611no—
210C42—611no—
211C42—611no—
212C42—611no—
213C16—2442no—
214C23#1451983911yescharacteristic
215Q8—42no—
216Q8—42no—
217Q8—82no—
218Q8—4882no—
219Q8—2442no—
220Q8—2442no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—612no—
229C2×C4—612no—
230C2×C4—611no—
231C2×C4—1222no—
232C2×C4—4882no—
233C2×C4—2442no—
234C2×C4#1451983911yescharacteristic
235C2×C4C2×C22⋊#692311yescharacteristic
236C8—21no—
237C8—612no—
238C8—1221no—
239C8—4882no—
240C8#1451983712yes—
241C22—21no—
242C22—21no—
243C22#1684067512yes—
244C22C2×#1451983911yescharacteristic
245C4—21no—
246C4—82no—
247C4—612no—
248C4—611no—
249C4—611no—
250C4—612no—
251C4—1221no—
252C4—4882no—
253C4C2×#1451983711yescharacteristic
254C4#1684075411yescharacteristic
255C2—22no—
256C2#2146132611yescharacteristic
257C2C2×#1684067511yescharacteristic
258C2D61⋊#36211yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC22×Q16×C61C4
socleC22×C61C2×#102
prime radicalC23×C61#102
cosocleC8×Dic61C23
hypercenterC22×Q16#6923
hypocenterC61#11962
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
3. #21460834C2semidirect
149. C61#11962semidirect

Maximal subgroups

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

subgroupindex
#214621772
#214613762
#214608342
C2×#168401402
#1196261