Finite Group Databasebeta

← #29585023

Subgroups — #29585023

Order 15616.

354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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#21446652C211yesmaximal, characteristic
2#21445972C211yesmaximal, characteristic, complemented
3#21444590C211yesmaximal, characteristic, complemented
4#21444589C211yesmaximal, characteristic, complemented
5#21444218C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic, complemented
7C61×#1480C211yesmaximal, characteristic
8#16839815C2211yescharacteristic
9#16839786C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—22no—
12C2×#14519704—22no—
13#16839608C2211yescharacteristic
14#16839513—22no—
15#16839512—22no—
16D4⋊#92418—22no—
17C61×#532C2211yescharacteristic
18C61×#431C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C61×D4⋊C8—22no—
21C2×#11758194—21no—
22C22×#92418—21no—
23C2×C4×Dic61D412yes—
24C4⋊#92418—21no—
25C4⋊#92418—21no—
26C4⋊#92418—21no—
27C4⋊#92418—21no—
28C4⋊#92418—21no—
29#14519706—44no—
30#14519704—44no—
31C22⋊#92418—21no—
32C4×#92418D412yes—
33#14519684—21no—
34#14519684—21no—
35C2×#41×C61—21no—
36C22×C8×C61—21no—
37C4⋊Q8×C61Q811yescharacteristic
38#127×C61Q811yescharacteristic
39#124×C61—21no—
40#121×C61—21no—
41#121×C61—21no—
42C4×D4×C61—21no—
43C4×D4×C61—21no—
44C2×C42×C61C2311yescharacteristic
45C4⋊C8×C61—21no—
46C4⋊C8×C61—21no—
47C4⋊C8×C61—21no—
48C22⋊C8×C61—21no—
49C4×C8×C61D412yes—
50#41×C61—42no—
51#41×C61—42no—
52C2×Q8×C61—21no—
53C2×D4×C61—21no—
54C2×D4×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61#4111yescharacteristic
60C22×C4×C61#4111yescharacteristic
61C22×Dic61—22no—
62C2×C8×C61—22no—
63C2×C8×C61—41no—
64C2×C8×C61—42no—
65C4⋊C4×C61—21no—
66C4⋊C4×C61—21no—
67C22⋊C4×C61—41no—
68C22⋊C4×C61—41no—
69C42×C61C2×D411yescharacteristic
70C42×C61C2×D411yescharacteristic
71C42×C61C2×Q811yescharacteristic
72C42×C61#4111yescharacteristic
73C4×Dic61—22no—
74C4×Dic61SD1614yes—
75#11758194—42no—
76C2×#92418—22no—
77C2×#92418—41no—
78C2×#92418—41no—
79C2×#92418—42no—
80C23×C61—41no—
81C23×C61#12311yescharacteristic
82Q8×C61—42no—
83D4×C61—42no—
84D4×C61—42no—
85D4×C61—42no—
86D4×C61—82no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—81no—
91C2×C4×C61—81no—
92C2×C4×C61C22⋊Q811yescharacteristic
93C2×C4×C61C22⋊Q811yescharacteristic
94C2×C4×C61C22⋊Q811yescharacteristic
95C2×C4×C61#12311yescharacteristic
96C2×C4×C61#12311yescharacteristic
97C2×C4×C61#12711yescharacteristic
98C2×C4×C61C2×SD1612yes—
99C2×C4×C61AGL(1,ℤ/8)12yes—
100C2×Dic61—24no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C8×C61—42no—
104C8×C61—81no—
105#92418—42no—
106#92418—81no—
107#92418—81no—
108#10666—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61—81no—
114C22×C61#39911yescharacteristic
115C22×C61#48112yes—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—81no—
121C4×C61#47612yes—
122C4×C61#49211yescharacteristic
123C4×C61#49611yescharacteristic
124Dic61—44no—
125#1963—611no—
126#1843—611no—
127#1570—611no—
128#1570—611no—
129#1480—611no—
130#1480D6111yescharacteristic
131#1274—611no—
132C2×C61—22no—
133C2×C61—161no—
134C2×C61#209411yescharacteristic
135C2×C61#209811yescharacteristic
136C2×C61#209811yescharacteristic
137#532C2×D6111yescharacteristic
138#431—611no—
139#431C2×D6111yescharacteristic
140#423—611no—
141C2×C4⋊C8—611no—
142C2×C4⋊C8—1222no—
143C2×C4⋊C8C2×D6111yescharacteristic
144C2×#104—1222no—
145#376—611no—
146#334—1222no—
147#334—1222no—
148D4⋊C8—22no—
149D4⋊C8—1222no—
150C61#1066611yescharacteristic, complemented, Sylow
151C2×#41—21no—
152C2×M16—1221no—
153C22×C8—21no—
154C22×C8—1221no—
155C4⋊Q8Dic12211yescharacteristic
156#127Dic12211yescharacteristic
157#124—21no—
158#121—21no—
159#121—21no—
160C4×D4—21no—
161C4×D4—21no—
162C2×C42—612no—
163C2×C42C22×D6111yescharacteristic
164C4⋊C8—21no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—1221no—
168C4⋊C8—1221no—
169C4⋊C8—1221no—
170C4⋊C8—1221no—
171C4⋊C8—1221no—
172C4⋊C8—2444no—
173#104—2444no—
174C22⋊C8—21no—
175C22⋊C8—1221no—
176C4×C8—612no—
177C4×C8C22⋊D6112yes—
178#95—1221no—
179#95—1221no—
180#41—42no—
181#41—42no—
182C2×Q8—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—41no—
187C22×C4—41no—
188C22×C4—1222no—
189C22×C4#1175822211yescharacteristic
190C22×C4D4×D6111yescharacteristic
191C22×C4#1175822411yescharacteristic
192M16—2442no—
193C2×C8—22no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—1222no—
197C2×C8—2441no—
198C2×C8—2441no—
199C2×C8—2442no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C42—614no—
205C42—1222no—
206C42C2×Dic12211yescharacteristic
207C42D4×D6111yescharacteristic
208C42#1175822411yescharacteristic
209C42C2×C22⋊D6111yescharacteristic
210C23—41no—
211C23#1451975911yescharacteristic
212Q8—42no—
213D4—42no—
214D4—42no—
215D4—42no—
216D4—82no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—1224no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4#1451975411yescharacteristic
226C2×C4#1451975411yescharacteristic
227C2×C4#1451975611yescharacteristic
228C2×C4#1451975811yescharacteristic
229C2×C4#1451975911yescharacteristic
230C2×C4#1451977311yescharacteristic
231C2×C4SD16×D6112yes—
232C2×C4#1451980112yes—
233C8—42no—
234C8—81no—
235C8—4881no—
236C8—4881no—
237C8—2442no—
238C22—21no—
239C22—21no—
240C22—81no—
241C22—81no—
242C22—81no—
243C22#1683969811yescharacteristic
244C22#1684007912yes—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—81no—
250C4—2444no—
251C4#1684005012yes—
252C4#1684013311yescharacteristic
253C4#1684015011yescharacteristic
254C2—22no—
255C2—161no—
256C2#2144735011yescharacteristic
257C2#2144737211yescharacteristic
258C2#2144737411yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1480C2
socleC22×C61#399
prime radicalC61×#532C22
hypercenter#1480D61
hypocenterC61#10666
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #21445972C2semidirect
3. #21444590C2semidirect
4. #21444589C2semidirect
6. #21443647C2semidirect
150. C61#10666semidirect

Maximal subgroups

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

subgroupindex
#214466522
#214459722
#214445902
#214445892
#214442182
#214436472
C61×#14802
#1066661