Finite Group Databasebeta

← #30605657

Subgroups — #30605657

Order 15616.

382 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 84 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#21462181C211yesmaximal, characteristic
2#21461379C211yesmaximal, characteristic
3#21460834C214yesmaximal, complemented
4C2×#16840140C211yesmaximal, characteristic
5#16840783—21no—
6#16840683C2212yes—
7C22⋊#11758187—21no—
8#16840651—21no—
9#16840626C2212yes—
10#16840623—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×#11758187—22no—
21C4⋊#92420—22no—
22C22⋊#92420—41no—
23#14519832—41no—
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—
61C2×#92420—42no—
62Q16×C61—42no—
63Q16×C61—42no—
64C2×C8×C61—22no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22×C411yescharacteristic
67#11758202—44no—
68#11758202—44no—
69#11758196—42no—
70#11758196—42no—
71#11758196—42no—
72#11758196—42no—
73C4×Dic61C22⋊C411yescharacteristic
74C4×Dic61D811yescharacteristic
75C4×Dic61SD1611yescharacteristic
76C4×Dic61C2×D411yescharacteristic
77C2×#92418—22no—
78C2×#92418C22⋊C411yescharacteristic
79C2×#92418C2×D411yescharacteristic
80Dic244—42no—
81Dic244—42no—
82#11758187—42no—
83C23×C61#10211yescharacteristic
84Q8×C61—42no—
85Q8×C61—42no—
86Q8×C61—82no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61—82no—
91C2×C4×C61#10211yescharacteristic
92C2×C4×C61C2×C22⋊C411yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—42no—
96C2×Dic61—82no—
97C2×Dic61#10211yescharacteristic
98C2×Dic61#10211yescharacteristic
99C2×Dic61C2×D811yescharacteristic
100C2×Dic61C2×SD1611yescharacteristic
101Dic122—42no—
102Dic122—42no—
103Dic122—82no—
104#92420—82no—
105C8×C61—21no—
106C8×C61#10012yes—
107#92418—21no—
108#92418AGL(1,ℤ/8)12yes—
109#11965—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61#36212yes—
113C22×C61C2×#10211yescharacteristic
114C4×C61—21no—
115C4×C61—82no—
116C4×C61C2×#10011yescharacteristic
117C4×C61#41811yescharacteristic
118Dic61—21no—
119Dic61—21no—
120Dic61—21no—
121Dic61—82no—
122Dic61#51012yes—
123C2×#494—611no—
124#2163—611no—
125#1568—611no—
126#1362—614no—
127C2×C61—22no—
128C2×C61#154511yescharacteristic
129C2×C61#214111yescharacteristic
130C2×C61C2×#36211yescharacteristic
131C22×Q16—611no—
132C22×Q16—1221no—
133C22×Q16#692311yescharacteristic
134C2×C4⋊Q8—1221no—
135#494—612no—
136#494—612no—
137#494—1221no—
138#494—1221no—
139#432—1221no—
140C2×C4×C8—611no—
141C4⋊C16—612no—
142C22⋊C16—1221no—
143#346—1221no—
144#335—612no—
145#334—1221no—
146C61#1196511yescharacteristic, complemented, Sylow
147C22×Q8—21no—
148C22×Q8—1221no—
149C2×Q16—21no—
150C2×Q16—42no—
151C2×Q16—612no—
152C2×Q16—1222no—
153C2×Q16—1222no—
154C2×Q16—1221no—
155C2×Q16—2442no—
156C2×Q16—2444no—
157C2×Q16C2×#692312yes—
158C22×C8—611no—
159C22×C8C2×#692311yescharacteristic
160C4⋊Q8—1222no—
161C4⋊Q8—1222no—
162C4⋊Q8—2441no—
163C4⋊Q8—2441no—
164C2×C4⋊C4—2441no—
165C2×C4⋊C4—2441no—
166C2×C42—611no—
167C2×C16—1222no—
168C4⋊C8—1222no—
169C22⋊C8—2441no—
170#97—2441no—
171C4×C8—611no—
172C4×C8—611no—
173C4×C8—611no—
174C4×C8—611no—
175C2×Q8—22no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8—41no—
179C2×Q8—1222no—
180C2×Q8—2442no—
181C2×Q8—2442no—
182C2×Q8—2441no—
183C22×C4—41no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—2441no—
187C22×C4C22⋊#692311yescharacteristic
188Q16—42no—
189Q16—42no—
190Q16—2442no—
191Q16—2444no—
192Q16—2444no—
193Q16—2442no—
194C2×C8—22no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—1222no—
198C2×C8—2442no—
199C2×C8C22⋊#692311yescharacteristic
200C2×C8C22×#692311yescharacteristic
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C42—611no—
206C42—611no—
207C42—611no—
208C42—611no—
209C16—2442no—
210C23#1451983911yescharacteristic
211Q8—42no—
212Q8—42no—
213Q8—82no—
214Q8—4882no—
215Q8—2442no—
216Q8—2442no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—82no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—4882no—
228C2×C4—2442no—
229C2×C4#1451983911yescharacteristic
230C2×C4C2×C22⋊#692311yescharacteristic
231C8—21no—
232C8—612no—
233C8—1221no—
234C8—4882no—
235C8#1451983712yes—
236C22—21no—
237C22—21no—
238C22#1684068112yes—
239C22C2×#1451983911yescharacteristic
240C4—21no—
241C4—82no—
242C4—612no—
243C4—1221no—
244C4—1221no—
245C4—1221no—
246C4—4882no—
247C4C2×#1451983711yescharacteristic
248C4#1684075411yescharacteristic
249C2—22no—
250C2#2146132611yescharacteristic
251C2#2146212911yescharacteristic
252C2C2×#1684068111yescharacteristic
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#11965
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
146. C61#11965semidirect

Maximal subgroups

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

subgroupindex
#214621812
#214613792
#214608342
C2×#168401402
#1196561