Finite Group Databasebeta

← #29573414

Subgroups — #29573414

Order 15616.

554 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 111 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#382×D61C211yesmaximal, characteristic
2#21445582C212yesmaximal
3#21443701C212yesmaximal, complemented
4#21443700C211yesmaximal, characteristic, complemented
5C61×#1295C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D61C412yes—
7C2×C42×D61C2211yescharacteristic
8C2×#14519689—22no—
9C2×#14519688C2212yes—
10#16839628C2211yescharacteristic
11#16839627C412yes—
12#16839626—22no—
13#95×D61—22no—
14#16839516—22no—
15C2×#97×C61C2212yes—
16C61×#382C2211yescharacteristic
17C22×C4×D61—22no—
18C22×C4×D61C2×C411yescharacteristic
19C22×C4×D61D412yes—
20C22×#92418—22no—
21C2×C4⋊Dic61C2×C412yes—
22C2×#11758196—22no—
23C4⋊C4×D61—44no—
24C2×C4×Dic61C2×C411yescharacteristic
25C2×C4×Dic61D412yes—
26C42×D61—22no—
27C42×D61—21no—
28C42×D61—21no—
29#14519689—28no—
30#14519688—22no—
31#14519688—22no—
32#14519684—22no—
33#14519684—24no—
34C22×C8×C61—22no—
35C2×C4⋊C4×C61C2×C412yes—
36C2×C42×C61C2311yescharacteristic
37#97×C61—22no—
38#97×C61—22no—
39#95×C61—22no—
40C23×D61C22⋊C411yescharacteristic
41C22×C4×C61—22no—
42C22×C4×C61C22×C411yescharacteristic
43C22×C4×C61C2×D412yes—
44C22×Dic61—22no—
45C22×Dic61C22⋊C412yes—
46C22×Dic61C22⋊C411yescharacteristic
47C2×C4×D61—22no—
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—22no—
51C2×C4×D61—24no—
52C2×C4×D61—22no—
53C2×C4×D61—22no—
54C2×C4×D61—42no—
55C2×C4×D61—44no—
56C2×C4×D61—44no—
57C2×C4×D61—44no—
58C2×C8×C61—24no—
59C2×C8×C61—42no—
60C2×C8×C61—42no—
61C4⋊C4×C61—42no—
62C42×C61#4112yes—
63C42×C61#4111yescharacteristic
64C42×C61#4111yescharacteristic
65C4⋊Dic61—42no—
66#11758196—44no—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C2×#92418—24no—
72C2×#92418—42no—
73C2×#92418—42no—
74C23×C61C2×C22⋊C411yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—22no—
78C22×D61#10112yes—
79C22×D61#10414yes—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61#11711yescharacteristic
88C2×C4×C61#11711yescharacteristic
89C2×C4×C61#12312yes—
90C2×C4×C61#12312yes—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61#10012yes—
100C4×D61—24no—
101C4×D61—24no—
102C4×D61—44no—
103C4×D61—44no—
104C4×D61—88no—
105C8×C61—44no—
106#92418—44no—
107#8719—611nomaximal, Sylow
108C22×C61#38111yescharacteristic
109C22×C61C2×#10011yescharacteristic
110C22×C61C2×#10111yescharacteristic
111C22×C61C2×#10412yes—
112C22×C61#42112yes—
113C2×D61—22no—
114C2×D61—24no—
115C2×D61—24no—
116C2×D61—22no—
117C2×D61#33014yes—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—82no—
123Dic61—22no—
124Dic61—42no—
125Dic61—82no—
126C2×#382—611no—
127#1749—612no—
128#1295—612no—
129#1295—611no—
130#1295D6111yescharacteristic, complemented
131C2×C61C2×#33011yescharacteristic
132C2×C61#152712yes—
133C2×C61#153411yescharacteristic
134C2×C61#182111yescharacteristic
135C2×C61#182612yes—
136D61—24no—
137C22×C4⋊C4—612no—
138C22×C42—611no—
139C2×C22⋊C8—1222no—
140C2×#97—612no—
141C2×#97C2×D6112yes—
142#382—612no—
143#382—611no—
144#382—1222no—
145#382C2×D6111yescharacteristic
146C2×#95—1222no—
147#336—1222no—
148C61#871911yescharacteristic, complemented, Sylow
149C23×C4—611no—
150C23×C4—612no—
151C23×C4—1222no—
152C22×C8—22no—
153C22×C8—1222no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—2444no—
157C2×C4⋊C4C4×D6112yes—
158C2×C42—611no—
159C2×C42—612no—
160C2×C42—1222no—
161C2×C42—1221no—
162C2×C42—1221no—
163C2×C42C22×D6111yescharacteristic
164C22⋊C8—1228no—
165#97—22no—
166#97—22no—
167#97—1222no—
168#97—1222no—
169#95—22no—
170#95—1224no—
171#95—1222no—
172C24—611no—
173C22×C4—22no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—1222no—
177C22×C4—1222no—
178C22×C4—1224no—
179C22×C4—1221no—
180C22×C4—1221no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—1222no—
184C22×C4—2442no—
185C22×C4—2444no—
186C22×C4—2444no—
187C22×C4—2444no—
188C22×C4C2×C4×D6111yescharacteristic
189C22×C4D4×D6112yes—
190C2×C8—24no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—1224no—
194C2×C8—2442no—
195C2×C8—2442no—
196C4⋊C4—42no—
197C4⋊C4—2442no—
198C4⋊C4—2444no—
199C42—1221no—
200C42—1221no—
201C42—1222no—
202C42—1222no—
203C42#1175822212yes—
204C42#1175822411yescharacteristic
205C42#1175822611yescharacteristic
206C23—612no—
207C23—614no—
208C23—1221no—
209C23—1222no—
210C23—1221no—
211C23C22⋊C4×D6111yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—612no—
220C2×C4—1224no—
221C2×C4—1224no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—4888no—
228C2×C4—2444no—
229C2×C4—2444no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4#1451973411yescharacteristic
234C2×C4#1451973511yescharacteristic
235C2×C4#1451975912yes—
236C2×C4#1451976212yes—
237C8—44no—
238C8—2444no—
239C22—614no—
240C22—1222no—
241C22—1224no—
242C22—1224no—
243C22—1222no—
244C22#1683962411yescharacteristic
245C22#100×D6111yescharacteristic
246C22#101×D6111yescharacteristic
247C22#104×D6112yes—
248C22#1683977712yes—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—1222no—
255C4—4882no—
256C4—2442no—
257C2—1224no—
258C2#330×D6111yescharacteristic
259C2#2144441512yes—
260C2#2144444411yescharacteristic
261C2#2144589811yescharacteristic
262C2#2144591712yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#8719
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #21443701C2semidirect
4. #21443700C2semidirect
5. C61×#1295C2semidirect
130. #1295D61semidirect
148. C61#8719semidirect

Maximal subgroups

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

subgroupindex
#382×D612
#214455822
#214437012
#214437002
C61×#12952
#871961