Finite Group Databasebeta

← #29573584

Subgroups — #29573584

Order 15616.

498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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#21445811C211yesmaximal, characteristic
2#21444140C211yesmaximal, characteristic
3#21443722C212yesmaximal, complemented
4#21443677C212yesmaximal, complemented
5C61×#2349C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839786C2212yes—
8C2×#14519694—21no—
9#16839531—21no—
10#16839486—22no—
11C2×C4×D4×C61—21no—
12C2×C4×D4×C61C2211yescharacteristic
13C61×#389—21no—
14C61×#385—22no—
15C61×#382C2211yescharacteristic
16C61×#380C412yes—
17C4×C4⋊C4×C61C2211yescharacteristic
18C2×#95×C61C412yes—
19C2×#11758194—22no—
20C4⋊#92418—22no—
21C4⋊#92418—22no—
22C4⋊#92418—22no—
23#14519694—42no—
24C22⋊#92418—22no—
25C4×#92418—22no—
26C22×D4×C61D411yescharacteristic
27C23×C4×C61—22no—
28C23×C4×C61C2×C412yes—
29C4×D4×C61—22no—
30C4×D4×C61—22no—
31C4×D4×C61—44no—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61D411yescharacteristic
36C2×C22⋊C4×C61—22no—
37C2×C22⋊C4×C61D412yes—
38C2×C42×C61—21no—
39C2×C42×C61C2311yescharacteristic
40#95×C61—22no—
41#95×C61—21no—
42#95×C61C2×C411yescharacteristic
43#95×C61C2×C412yes—
44#95×C61C2×C411yescharacteristic
45C24×C61C22⋊C412yes—
46C2×D4×C61—22no—
47C2×D4×C61—22no—
48C2×D4×C61SD1612yes—
49C2×D4×C61Q1612yes—
50C22×C4×C61—21no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—21no—
55C22×C4×C61—44no—
56C22×C4×C61—44no—
57C22×C4×C61—82no—
58C22×C4×C61—82no—
59C22×C4×C61C22⋊C412yes—
60C22×C4×C61C22×C411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C4⋊C4×C61—22no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—82no—
67C22⋊C4×C61—24no—
68C22⋊C4×C61—44no—
69C42×C61—42no—
70C42×C61#4112yes—
71C42×C61#4112yes—
72#11758194—42no—
73#11758194—42no—
74C2×#92418—42no—
75C2×#92418—42no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—42no—
79C23×C61—42no—
80C23×C61#10314yes—
81C23×C61C2×C22⋊C411yescharacteristic
82D4×C61—24no—
83D4×C61—24no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—82no—
98C2×C4×C61—82no—
99C2×C4×C61—88no—
100C2×C4×C61#11711yescharacteristic
101C2×C4×C61#11711yescharacteristic
102C2×C4×C61#12312yes—
103C2×C4×C61#12312yes—
104C2×C4×C61C2×SD1611yescharacteristic
105C2×C4×C61C2×Q1611yescharacteristic
106C2×C4×C61AGL(1,ℤ/8)12yes—
107#92418—82no—
108#92418—82no—
109#8765—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61—24no—
113C22×C61—44no—
114C22×C61—44no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61#38111yescharacteristic
118C22×C61C2×#10311yescharacteristic
119C22×C61#41811yescharacteristic
120C4×C61—22no—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—42no—
124C4×C61—42no—
125C4×C61—81no—
126C4×C61—82no—
127C4×C61#48112yes—
128C4×C61#48412yes—
129#2349D6111yescharacteristic
130#1800—611no—
131#1460—611no—
132#1303—612no—
133#1286—612no—
134C2×C61—21no—
135C2×C61—21no—
136C2×C61—44no—
137C2×C61#182411yescharacteristic
138C2×C61#182711yescharacteristic
139C2×C61#182911yescharacteristic
140C2×C4×D4—21no—
141C2×C4×D4C2×D6111yescharacteristic
142#431—612no—
143#423—612no—
144C2×#100—1221no—
145#389—21no—
146#385—22no—
147#382C2×D6111yescharacteristic
148#380Dic6112yes—
149C4×C4⋊C4C2×D6111yescharacteristic
150C2×#95Dic6112yes—
151#343—1221no—
152#323—1222no—
153C61#876511yescharacteristic, complemented, Sylow
154C22×D4C22⋊D6111yescharacteristic
155C23×C4—22no—
156C23×C4C2×Dic6112yes—
157C2×M16—1222no—
158C4×D4—22no—
159C4×D4—22no—
160C4×D4—44no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C22⋊D6111yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4C22⋊D6112yes—
167C2×C42—21no—
168C2×C42C22×D6111yescharacteristic
169C4⋊C8—1222no—
170C4⋊C8—1222no—
171C4⋊C8—1222no—
172#100—2442no—
173C22⋊C8—1222no—
174C4×C8—1222no—
175#95—22no—
176#95—21no—
177#95C2×Dic6111yescharacteristic
178#95C2×Dic6112yes—
179#95C2×Dic6111yescharacteristic
180C24C22⋊Dic6112yes—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4#1175820112yes—
184C2×D4#1175820212yes—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—44no—
191C22×C4—44no—
192C22×C4—82no—
193C22×C4—82no—
194C22×C4C22⋊Dic6112yes—
195C22×C4C22×Dic6111yescharacteristic
196C22×C4C2×C22⋊D6111yescharacteristic
197C22×C4C2×C22⋊D6111yescharacteristic
198M16—2442no—
199M16—2442no—
200C2×C8—2442no—
201C2×C8—2442no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—82no—
206C22⋊C4—24no—
207C22⋊C4—44no—
208C42—42no—
209C42#1175822212yes—
210C42#1175822212yes—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23#1451970114yes—
216C23C2×C22⋊Dic6111yescharacteristic
217D4—24no—
218D4—24no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4—88no—
235C2×C4#1451973611yescharacteristic
236C2×C4#1451973611yescharacteristic
237C2×C4#1451976012yes—
238C2×C4#1451976012yes—
239C2×C4C2×#1175820111yescharacteristic
240C2×C4C2×#1175820211yescharacteristic
241C2×C4#1451980312yes—
242C8—4882no—
243C8—4882no—
244C22—21no—
245C22—21no—
246C22—24no—
247C22—44no—
248C22—44no—
249C22—42no—
250C22—42no—
251C22#1683962511yescharacteristic
252C22C2×#1451970111yescharacteristic
253C22#1683976711yescharacteristic
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—81no—
260C4—82no—
261C4#1684008012yes—
262C4#1684009712yes—
263C2—21no—
264C2—21no—
265C2—44no—
266C2#2144590911yescharacteristic
267C2#2144592311yescharacteristic
268C2#2144593011yescharacteristic
subgroupG/H
centerC22#16839625
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2349C2
socleC22×C61#381
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#2349D61
hypocenterC61#8765
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #21443722C2semidirect
4. #21443677C2semidirect
153. C61#8765semidirect

Maximal subgroups

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

subgroupindex
#214458112
#214441402
#214437222
#214436772
C61×#23492
#876561