Finite Group Databasebeta

← #29573428

Subgroups — #29573428

Order 15616.

630 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 155 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#384×D61C211yesmaximal, characteristic
2#21445796C212yesmaximal
3#21443703C212yesmaximal, complemented
4#21443702C211yesmaximal, characteristic, complemented
5C61×#1296C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D61—22no—
7C2×C4⋊C4×D61C412yes—
8C2×C42×D61C2211yescharacteristic
9C2×C4⋊#92418C2212yes—
10C2×#14519689—22no—
11#16839632C2211yescharacteristic
12#16839631—22no—
13#16839631C412yes—
14#16839516—22no—
15C2×C4⋊C8×C61C2212yes—
16C61×#384C2211yescharacteristic
17C22×C4×D61—22no—
18C22×C4×D61C2×C411yescharacteristic
19C22×C4×D61D412yes—
20C22×#92418—22no—
21C2×C4⋊Dic61—22no—
22C2×C4⋊Dic61C2×C412yes—
23C2×#11758196—24no—
24C2×#11758196—22no—
25C4⋊C4×D61—44no—
26C4⋊C4×D61—44no—
27C4⋊C4×D61—44no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D412yes—
30C42×D61—22no—
31C42×D61—21no—
32C42×D61—21no—
33C4⋊#92418—22no—
34C4⋊#92418—22no—
35#14519689—44no—
36C22×C8×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61C2×C412yes—
39C2×C42×C61C2311yescharacteristic
40C4⋊C8×C61—22no—
41C4⋊C8×C61—22no—
42C23×D61C22⋊C411yescharacteristic
43C22×C4×C61—22no—
44C22×C4×C61C22×C411yescharacteristic
45C22×C4×C61C2×D412yes—
46C22×Dic61—22no—
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C22⋊C412yes—
49C2×C4×D61—22no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—22no—
53C2×C4×D61—22no—
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—44no—
58C2×C4×D61—48no—
59C2×C4×D61D814yes—
60C2×C4×D61SD1614yes—
61C2×C8×C61—42no—
62C2×C8×C61—42no—
63C2×C8×C61—42no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—42no—
67C42×C61#4112yes—
68C42×C61#4111yescharacteristic
69C42×C61#4111yescharacteristic
70C4⋊Dic61—42no—
71C4⋊Dic61—42no—
72C4⋊Dic61—42no—
73#11758196—44no—
74#11758196—48no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—22no—
78C4×Dic61—22no—
79C2×#92418—42no—
80C2×#92418—42no—
81C2×#92418—42no—
82C23×C61C2×C22⋊C411yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—22no—
86C22×D61#10012yes—
87C22×D61#10214yes—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—42no—
91C2×C4×C61—44no—
92C2×C4×C61#11711yescharacteristic
93C2×C4×C61#11711yescharacteristic
94C2×C4×C61#12312yes—
95C2×C4×C61#12312yes—
96C2×C4×C61C2×D812yes—
97C2×C4×C61C2×SD1612yes—
98C2×C4×C61#13712yes—
99C2×C4×C61#13712yes—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—42no—
105C2×Dic61—44no—
106C2×Dic61#10112yes—
107C2×Dic61#10214yes—
108C4×D61—24no—
109C4×D61—24no—
110C4×D61—24no—
111C4×D61—24no—
112C4×D61—24no—
113C4×D61—24no—
114C4×D61—88no—
115C8×C61—82no—
116#92418—82no—
117#8723—611nomaximal, Sylow
118C22×C61#38111yescharacteristic
119C22×C61C2×#10011yescharacteristic
120C22×C61C2×#10111yescharacteristic
121C22×C61C2×#10212yes—
122C22×C61#41912yes—
123C2×D61—24no—
124C2×D61—22no—
125C2×D61—22no—
126C2×D61—24no—
127C2×D61#33114yes—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—82no—
131C4×C61#48012yes—
132C4×C61#48012yes—
133C4×C61#48312yes—
134C4×C61#48312yes—
135Dic61—22no—
136Dic61—24no—
137Dic61—82no—
138C2×#384—611no—
139#1797—612no—
140#1296—612no—
141#1296—611no—
142#1296D6111yescharacteristic, complemented
143C2×C61C2×#33111yescharacteristic
144C2×C61#154612yes—
145C2×C61#155811yescharacteristic
146C2×C61#182111yescharacteristic
147C2×C61#182312yes—
148D61—24no—
149C22×C4⋊C4—612no—
150C22×C4⋊C4—1222no—
151C22×C42—611no—
152C2×C4⋊C8—612no—
153C2×C4⋊C8C2×D6112yes—
154C2×C22⋊C8—1222no—
155#384—612no—
156#384—611no—
157#384—1222no—
158#384C2×D6111yescharacteristic
159#336—1222no—
160C61#872311yescharacteristic, complemented, Sylow
161C23×C4—612no—
162C23×C4—611no—
163C23×C4—1222no—
164C22×C8—22no—
165C22×C8—1222no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—1222no—
169C2×C4⋊C4—1224no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4—2444no—
172C2×C4⋊C4—2444no—
173C2×C4⋊C4—2444no—
174C2×C4⋊C4C4×D6112yes—
175C2×C42—611no—
176C2×C42—612no—
177C2×C42—1222no—
178C2×C42—1221no—
179C2×C42—1221no—
180C2×C42C22×D6111yescharacteristic
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—1222no—
184C4⋊C8—1222no—
185C22⋊C8—2444no—
186C24—611no—
187C22×C4—22no—
188C22×C4—611no—
189C22×C4—612no—
190C22×C4—614no—
191C22×C4—614no—
192C22×C4—1222no—
193C22×C4—1222no—
194C22×C4—1222no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—1222no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4—1222no—
201C22×C4—2448no—
202C22×C4—2444no—
203C22×C4C2×C4×D6111yescharacteristic
204C22×C4D4×D6112yes—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—2442no—
209C2×C8—2442no—
210C2×C8—2442no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—2442no—
215C4⋊C4—2448no—
216C4⋊C4—2444no—
217C4⋊C4—2442no—
218C4⋊C4—2442no—
219C42—1221no—
220C42—1221no—
221C42—1222no—
222C42—1222no—
223C42#1175822212yes—
224C42#1175822411yescharacteristic
225C42#1175822611yescharacteristic
226C23—612no—
227C23—614no—
228C23—1221no—
229C23—1222no—
230C23—1221no—
231C23C22⋊C4×D6111yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—612no—
237C2×C4—614no—
238C2×C4—1224no—
239C2×C4—1224no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—1224no—
245C2×C4—1224no—
246C2×C4—1224no—
247C2×C4—1224no—
248C2×C4—4888no—
249C2×C4—2442no—
250C2×C4—2444no—
251C2×C4#1451973411yescharacteristic
252C2×C4#1451973511yescharacteristic
253C2×C4#1451975912yes—
254C2×C4#1451976212yes—
255C2×C4D8×D6112yes—
256C2×C4SD16×D6112yes—
257C2×C4#1451980612yes—
258C2×C4#1451980912yes—
259C8—82no—
260C8—4882no—
261C22—614no—
262C22—1222no—
263C22—1224no—
264C22—1224no—
265C22—1222no—
266C22#1683962411yescharacteristic
267C22#100×D6111yescharacteristic
268C22#101×D6111yescharacteristic
269C22#102×D6112yes—
270C22#1683976912yes—
271C4—21no—
272C4—21no—
273C4—82no—
274C4—1222no—
275C4—1224no—
276C4—4882no—
277C4#1684007412yes—
278C4#1684007712yes—
279C4#1684009112yes—
280C4#1684009412yes—
281C2—1224no—
282C2#331×D6111yescharacteristic
283C2#2144448912yes—
284C2#2144454311yescharacteristic
285C2#2144589811yescharacteristic
286C2#2144590412yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#8723
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #21443703C2semidirect
4. #21443702C2semidirect
5. C61×#1296C2semidirect
142. #1296D61semidirect
160. C61#8723semidirect

Maximal subgroups

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

subgroupindex
#384×D612
#214457962
#214437032
#214437022
C61×#12962
#872361