Finite Group Databasebeta

← #29596912

Subgroups — #29596912

Order 15616.

488 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 139 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#21454513C211yesmaximal, characteristic
2C2×#16839545C212yesmaximal, complemented
3#21447430C211yesmaximal, characteristic, complemented
4#21443907C212yesmaximal, complemented
5C22×M32×C61C211yesmaximal, characteristic, complemented
6C2×#14519783C2211yescharacteristic
7#16840273C411yescharacteristic
8C2×#14519717C2212yes—
9#16839833—22no—
10C8×C22⋊D61—22no—
11#16839788C411yescharacteristic
12#16839728C411yescharacteristic
13#16839726C411yescharacteristic
14#16839717C2211yescharacteristic
15#16839545—24no—
16C22⋊#11758185—22no—
17C23×C8×C61C2211yescharacteristic
18C2×M32×C61—22no—
19C2×M32×C61—24no—
20C22×C16×C61C2212yes—
21C2×#11758222C2×C411yescharacteristic
22#14519783—22no—
23#14519783—22no—
24C2×#11758194C2×C411yescharacteristic
25C2×#11758194C2×C411yescharacteristic
26C2×#11758189—21no—
27C2×C8×D61—21no—
28#14519760—21no—
29#14519756C812yes—
30#14519751C812yes—
31#14519746—21no—
32C4×C22⋊D61—22no—
33#14519736C2×C411yescharacteristic
34#14519717—22no—
35#14519717—22no—
36C2×#11758185—22no—
37#14519706—22no—
38C22⋊#92418—22no—
39#14519689—22no—
40#14519687—21no—
41C8×Dic61—21no—
42C23×C4×C61C2×C411yescharacteristic
43C22×C8×C61—22no—
44C22×C8×C61—22no—
45C22×C8×C61C2×C411yescharacteristic
46C22×C8×C61D412yes—
47C22×C8×C61D412yes—
48C22×C8×C61C2311yescharacteristic
49M32×C61—28no—
50C2×C16×C61—22no—
51C2×C16×C61—22no—
52C2×C16×C61D414yescomplemented
53C24×C61M1611yescharacteristic
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61C2×C812yes—
58C22×C4×C61M1611yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C2×C22⋊D61—22no—
61C2×C22⋊D61—21no—
62#11758222—22no—
63#11758222—22no—
64C2×D244C2×C811yescharacteristic
65C2×C4×D61—21no—
66C2×Dic122C2×C811yescharacteristic
67C2×C8×C61—22no—
68C2×C8×C61—22no—
69C2×C8×C61—24no—
70C2×C8×C61—22no—
71C2×C8×C61C22⋊C412yes—
72C2×C8×C61C2×D412yes—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61#4112yes—
76C22⋊Dic61—22no—
77C22⋊Dic61—21no—
78#11758198—22no—
79C4⋊Dic61C2×C812yes—
80#11758196—22no—
81C4×Dic61—21no—
82#11758194—22no—
83#11758194—22no—
84C2×#92418—21no—
85C2×#92418—21no—
86#11758189—41no—
87#11758189—41no—
88C8×D61—42no—
89C16×C61—24no—
90#11758185—42no—
91C23×C61—22no—
92C23×C61—42no—
93C23×C61C22⋊C812yes—
94C23×C61C2×M1611yescharacteristic
95C22×D61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—24no—
100C2×C4×C61C22⋊C812yes—
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61C4×D412yes—
103C2×C4×C61C22×C811yescharacteristic
104C2×C4×C61#13112yes—
105C22⋊D61—44no—
106C22⋊D61—42no—
107C2×Dic61—22no—
108C2×Dic61—21no—
109D244—22no—
110C4×D61—41no—
111C4×D61—41no—
112Dic122—22no—
113C8×C61—22no—
114C8×C61#12011yescharacteristic
115C8×C61#12112yes—
116C8×C61#12311yescharacteristic
117#92418—41no—
118#92418—41no—
119#12984—611nomaximal, Sylow
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—44no—
125C22×C61C2×C22⋊C811yescharacteristic
126C22×C61#43512yes—
127C2×D61—42no—
128C2×D61—41no—
129C4×C61—22no—
130C4×C61#38611yescharacteristic
131C4×C61#40811yescharacteristic
132C4×C61C8×D412yes—
133Dic61—42no—
134Dic61—41no—
135C22×M32D6111yescharacteristic, complemented
136#2929—611no—
137C2×#350—612no—
138#2112—611no—
139#1379—612no—
140C2×C61—22no—
141C2×C61—42no—
142C2×C61#186911yescharacteristic
143C2×C61#211712yes—
144D61—81no—
145C2×#131—611no—
146C23×C8C2×D6111yescharacteristic
147#525—611no—
148C2×M32—22no—
149C2×M32—24no—
150C2×M32—612no—
151C22×C16C2×D6112yes—
152#435—1222no—
153C8×D4—1222no—
154#424—611no—
155#408—611no—
156#407—611no—
157#405—611no—
158#350—1224no—
159C22⋊C16—1222no—
160C61#1298411yescharacteristic, complemented, Sylow
161C2×#41—611no—
162C23×C4C4×D6111yescharacteristic
163#131—1222no—
164#131—1222no—
165C2×M16—611no—
166C2×M16—611no—
167C2×M16—1221no—
168C22×C8—22no—
169C22×C8—22no—
170C22×C8—1221no—
171C22×C8C4×D6111yescharacteristic
172C22×C8D24412yes—
173C22×C8C22⋊D6112yes—
174C22×C8C22×D6111yescharacteristic
175#123—1221no—
176C22⋊Q8—612no—
177#121—612no—
178#120—1221no—
179C4×D4—1222no—
180#117—611no—
181M32—28no—
182M32—1222no—
183M32—1222no—
184C2×C16—22no—
185C2×C16—22no—
186C2×C16—1222no—
187C2×C16C22⋊D6114yescomplemented
188C4⋊C8—1222no—
189C22⋊C8—1222no—
190C22⋊C8—1222no—
191#97—1221no—
192C4×C8—1221no—
193C24#1175818911yescharacteristic
194#41—1222no—
195#41—1222no—
196C2×Q8—611no—
197C2×D4—611no—
198C2×D4—1222no—
199C2×D4—1221no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—1221no—
203C22×C4C8×D6112yes—
204C22×C4#1175818911yescharacteristic
205C22×C4#1175819812yes—
206C22×C4C2×C4×D6111yescharacteristic
207M16—1222no—
208M16—1222no—
209M16—2441no—
210M16—2441no—
211C2×C8—22no—
212C2×C8—22no—
213C2×C8—24no—
214C2×C8—22no—
215C2×C8—1221no—
216C2×C8—1221no—
217C2×C8—2442no—
218C2×C8#1175819812yes—
219C2×C8C2×D24411yescharacteristic
220C2×C8#1175822212yes—
221C2×C8C2×C22⋊D6112yes—
222C2×C8C2×C22⋊D6111yescharacteristic
223C4⋊C4—612no—
224C4⋊C4—1222no—
225C22⋊C4—1222no—
226C22⋊C4—1221no—
227C22⋊C4—1222no—
228C42—1221no—
229C16—24no—
230C16—2442no—
231C23—22no—
232C23—42no—
233C23—1221no—
234C23#1451968912yes—
235C23C2×#1175818911yescharacteristic
236Q8—1222no—
237D4—1222no—
238D4—2444no—
239D4—2442no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4#1451968912yes—
249C2×C4C2×#1175819811yescharacteristic
250C2×C4C4×C22⋊D6112yes—
251C2×C4C2×C8×D6111yescharacteristic
252C2×C4#1451978312yes—
253C8—22no—
254C8—2441no—
255C8—2441no—
256C8#1451974611yescharacteristic
257C8#1451975112yes—
258C8#1451976011yescharacteristic
259C22—22no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—44no—
264C22—2442no—
265C22—2441no—
266C22C2×#1451968911yescharacteristic
267C22#1683983312yes—
268C4—22no—
269C4—2442no—
270C4—2441no—
271C4#1683964111yescharacteristic
272C4#1683972811yescharacteristic
273C4C8×C22⋊D6112yes—
274C2—22no—
275C2—42no—
276C2—4881no—
277C2#2144611111yescharacteristic
278C2#2144744612yes—
subgroupG/H
centerC2×C8C2×D244
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC22×M32×C61C2
socleC22×C61C2×C22⋊C8
prime radical#16840273C4
cosocleC22×C8×C61C23
hypercenterC22×M32D61
hypocenterC61#12984
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×M32

Complements

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

NH ≅ G/Ntype
2. C2×#16839545C2semidirect
3. #21447430C2semidirect
4. #21443907C2semidirect
5. C22×M32×C61C2semidirect
52. C2×C16×C61D4semidirect
135. C22×M32D61semidirect
160. C61#12984semidirect
187. C2×C16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214545132
C2×#168395452
#214474302
#214439072
C22×M32×C612
#1298461