Finite Group Databasebeta

← #29570663

Subgroups — #29570663

Order 15616.

562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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#21448283C211yesmaximal, characteristic
2#21445565C211yesmaximal, characteristic, complemented
3C2×#16839489C212yesmaximal
4#21443658C212yesmaximal, complemented
5C61×#1767C211yesmaximal, characteristic, complemented
6C2×C4×D244C2211yescharacteristic
7C2×#14519734—21no—
8C2×C4×#92418C2212yes—
9#16839664C412yes—
10#16839660C412yes—
11#16839653—22no—
12C4×C4⋊Dic61C2211yescharacteristic
13C4×#11758198—21no—
14#16839517—22no—
15#16839489C418yescomplemented
16C2×C4⋊C8×C61C2212yes—
17C2×#97×C61—21no—
18C43×C61C2211yescharacteristic
19C61×#336—21no—
20C22×D244C2×C411yescharacteristic
21C22×C4×D61—21no—
22C22×#92418—22no—
23C4×D244—22no—
24C4×D244C2×C414yes—
25#14519734—44no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—22no—
29C2×#11758198—21no—
30C2×#11758198—22no—
31C2×#11758198—22no—
32C2×C4×Dic61—21no—
33C4×#92418—22no—
34C4×#92418C2×C414yes—
35#14519684—22no—
36#14519684—21no—
37C22×C8×C61—22no—
38C2×C42×C61C2×C412yes—
39C2×C42×C61D412yes—
40C2×C42×C61D411yescharacteristic
41C2×C42×C61D411yescharacteristic
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—22no—
44C4⋊C8×C61C2×C414yes—
45#97×C61—42no—
46C23×D61—21no—
47C22×C4×C61C22⋊C412yes—
48C22×C4×C61C22⋊C412yes—
49C22×C4×C61C22×C411yescharacteristic
50C22×C4×C61C2×D411yescharacteristic
51C22×C4×C61C2×D411yescharacteristic
52C22×Dic61—21no—
53C22×Dic61—22no—
54C2×D244—24no—
55C2×D244—21no—
56C2×D244C4212yes—
57C2×C4×D61—24no—
58C2×C4×D61—41no—
59C2×C4×D61—42no—
60C2×C4×D61—41no—
61C2×C8×C61—24no—
62C2×C8×C61—42no—
63C2×C8×C61—42no—
64C42×C61—24no—
65C42×C61—21no—
66C42×C61—22no—
67C42×C61—21no—
68C42×C61—42no—
69C42×C61C22×C412yes—
70C42×C61#4112yes—
71#11758198—24no—
72#11758198—44no—
73#11758198—44no—
74C4⋊Dic61—21no—
75C4⋊Dic61—24no—
76C4⋊Dic61C4212yes—
77#11758196—44no—
78C4×Dic61—42no—
79C2×#92418—24no—
80C2×#92418—44no—
81C23×C61C2×C22⋊C411yescharacteristic
82C22×D61—22no—
83C22×D61—42no—
84C22×D61—41no—
85C22×D61—41no—
86C22×D61—42no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61C2×C4211yescharacteristic
95C2×C4×C61#11711yescharacteristic
96C2×C4×C61C4×D412yes—
97C2×C4×C61C4×D412yes—
98C2×C4×C61#13114yes—
99C2×C4×C61AGL(1,ℤ/8)12yes—
100C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
101C2×C4×C61#13711yescharacteristic
102C2×Dic61—22no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108D244—24no—
109D244—42no—
110C4×D61—44no—
111C4×D61—44no—
112C8×C61—44no—
113#92418—44no—
114#8179—611nomaximal, Sylow
115C22×C61C4×C22⋊C411yescharacteristic
116C22×C61#40812yes—
117C22×C61#41711yescharacteristic
118C22×C61#41811yescharacteristic
119C22×C61#42112yes—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—82no—
124C2×D61—82no—
125C4×C61—22no—
126C4×C61—42no—
127C4×C61—42no—
128C4×C61#40512yes—
129C4×C61#43312yes—
130C4×C61#44012yes—
131C4×C61#44212yes—
132Dic61—42no—
133Dic61—82no—
134#2293—611no—
135#1767D6111yescharacteristic, complemented
136#1744—611no—
137C2×D4⋊C8—612no—
138#1279—612no—
139C2×C61#149512yes—
140C2×C61#149612yes—
141C2×C61#175011yescharacteristic
142C2×C61#175911yescharacteristic
143C2×C61#176211yescharacteristic
144D61—82no—
145C2×C4×D4—611no—
146C2×#117—1221no—
147C2×C4⋊C8C2×D6112yes—
148C2×#97—21no—
149C2×C4×C8—612no—
150#390—612no—
151#389—612no—
152#388—1222no—
153C4×C4⋊C4—611no—
154C4×C22⋊C4—1221no—
155C43C2×D6111yescharacteristic
156#336—21no—
157#336—1222no—
158D4⋊C8—618no—
159C61#817911yescharacteristic, complemented, Sylow
160C22×D4—611no—
161C23×C4—1221no—
162C22×C8—22no—
163C22×C8—1222no—
164C4×D4—614no—
165C4×D4—1222no—
166#117—2444no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4—612no—
169C2×C4⋊C4—1222no—
170C2×C22⋊C4—1221no—
171C2×C22⋊C4—1222no—
172C2×C22⋊C4—1222no—
173C2×C42—1221no—
174C2×C42C4×D6112yes—
175C2×C42D24412yes—
176C2×C42C22⋊D6111yescharacteristic
177C2×C42C22⋊D6111yescharacteristic
178C2×C42C22×D6111yescharacteristic
179C4⋊C8—22no—
180C4⋊C8C4×D6114yes—
181#97—42no—
182C4×C8—614no—
183C4×C8—1222no—
184#95—1222no—
185#95—1221no—
186C24—1221no—
187C2×D4—612no—
188C2×D4—1221no—
189C2×D4—1224no—
190C22×C4—1221no—
191C22×C4—1224no—
192C22×C4—1222no—
193C22×C4—2441no—
194C22×C4—2442no—
195C22×C4—2441no—
196C22×C4#1175819812yes—
197C22×C4#1175819812yes—
198C22×C4C2×C4×D6111yescharacteristic
199C22×C4C2×D24411yescharacteristic
200C22×C4C2×C22⋊D6111yescharacteristic
201C2×C8—24no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—1224no—
205C2×C8—2444no—
206C4⋊C4—612no—
207C4⋊C4—1221no—
208C4⋊C4—1224no—
209C4⋊C4—2444no—
210C22⋊C4—1224no—
211C22⋊C4—2444no—
212C22⋊C4—2444no—
213C42—21no—
214C42—24no—
215C42—22no—
216C42—21no—
217C42—42no—
218C42—2442no—
219C42C2×C4×D6112yes—
220C42#1175822212yes—
221C23—1222no—
222C23—2442no—
223C23—2441no—
224C23—2441no—
225C23—2442no—
226C23C2×#1175819811yescharacteristic
227D4—1224no—
228D4—2442no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—1222no—
237C2×C4—2442no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2444no—
243C2×C4—2444no—
244C2×C4C42×D6111yescharacteristic
245C2×C4#1451973411yescharacteristic
246C2×C4C4×C22⋊D6112yes—
247C2×C4C4×D24412yes—
248C2×C4#1451978514yes—
249C2×C4#1451980212yes—
250C2×C4#1451980311yescharacteristic
251C2×C4#1451980811yescharacteristic
252C8—44no—
253C8—2444no—
254C22—4882no—
255C22—4882no—
256C22—2442no—
257C22—2442no—
258C22—2442no—
259C22C4×#1175819811yescharacteristic
260C22#1683973012yes—
261C22#1683976111yescharacteristic
262C22#1683976611yescharacteristic
263C22#1683977812yes—
264C4—22no—
265C4—42no—
266C4—42no—
267C4—4882no—
268C4—2442no—
269C4#1683971912yes—
270C4#1683982412yes—
271C4#1683986012yes—
272C4#1683987212yes—
273C2—4882no—
274C2#2144428212yes—
275C2#2144428712yes—
276C2#2144558811yescharacteristic
277C2#2144563211yescharacteristic
278C2#2144564711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC61×#1767C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1767D61
hypocenterC61#8179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. #21445565C2semidirect
4. #21443658C2semidirect
5. C61×#1767C2semidirect
15. #16839489C4semidirect
135. #1767D61semidirect
159. C61#8179semidirect

Maximal subgroups

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

subgroupindex
#214482832
#214455652
C2×#168394892
#214436582
C61×#17672
#817961