Finite Group Databasebeta

← #29589302

Subgroups — #29589302

Order 15616.

440 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448527C211yesmaximal, characteristic
2#21444141C212yesmaximal, complemented
3#21443765C211yesmaximal, characteristic, complemented
4#21443750C212yesmaximal
5C61×#1325C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic
7C2×#14519742C2211yescharacteristic
8C2×#14519739C411yescharacteristic
9#16839812—22no—
10#16839667C411yescharacteristic
11#16839663C2211yescharacteristic
12#16839652—22no—
13#16839633—22no—
14#16839608C411yescharacteristic
15#16839488C2212yes—
16#16839487—22no—
17C61×#384C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×D244C2×C411yescharacteristic
21C22×C4×D61—21no—
22#14519765—22no—
23#14519765C814yescomplemented
24#14519742—42no—
25#14519739—42no—
26C2×#11758196D412yes—
27C2×#11758198—22no—
28C2×#11758198—21no—
29C2×#11758198—22no—
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61D412yes—
33#14519706—42no—
34C22⋊#92418—22no—
35C8×Dic61—42no—
36#14519684—21no—
37#14519684—21no—
38#14519684—22no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61C2311yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C22⋊C8×C61—22no—
44C23×D61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C22×C411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—21no—
50C22×Dic61C22⋊C412yes—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C411yescharacteristic
53C2×D244—21no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244C2×C812yes—
57C2×C4×D61—42no—
58C2×C4×D61—82no—
59C2×Dic122—41no—
60C2×Dic122—41no—
61C2×Dic122C2×C812yes—
62C2×Dic122M1612yes—
63C2×C8×C61—42no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—82no—
67C42×C61—21no—
68C42×C61C2×C812yes—
69#11758198—28no—
70#11758198—42no—
71#11758198—82no—
72#11758196—42no—
73C4×Dic61—22no—
74C4×Dic61—22no—
75C4×Dic61—22no—
76C4×Dic61—41no—
77C2×#92418—42no—
78C23×C61C2×C22⋊C411yescharacteristic
79C22×D61—22no—
80C22×D61—42no—
81C22×D61—42no—
82C22×D61—41no—
83C22×D61—41no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—41no—
93C2×C4×C61C22×C811yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61C22⋊C814yes—
104C2×Dic61#9912yes—
105D244—42no—
106D244—42no—
107C4×D61—84no—
108Dic122—42no—
109Dic122—42no—
110C8×C61—82no—
111#92418—82no—
112#11480—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61C2×C22⋊C811yescharacteristic
116C22×C61C2×#9911yescharacteristic
117C22×C61#41311yescharacteristic
118C2×D61—44no—
119C2×D61—42no—
120C2×D61—82no—
121C2×D61—81no—
122C2×D61—81no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61—42no—
126C4×C61—42no—
127C4×C61—81no—
128Dic61—22no—
129Dic61—24no—
130Dic61—41no—
131Dic61—81no—
132#2326—611no—
133#1461—612no—
134#1325—611no—
135#1325D6111yescharacteristic, complemented
136#1318—612no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61#145911yescharacteristic
140C2×C61#212811yescharacteristic
141C2×C61#213311yescharacteristic
142D61—82no—
143C2×#124—611no—
144C2×C4×Q8—611no—
145C2×C4×D4—611no—
146#431—1222no—
147#391—611no—
148#390—611no—
149#388—1222no—
150#385—1222no—
151#384C2×D6111yescharacteristic
152#376—611no—
153#324—612no—
154#324—1222no—
155#324C2×D6112yes—
156C61#1148011yescharacteristic, complemented, Sylow
157C22×Q8—611no—
158C22×D4—611no—
159C23×C4—1221no—
160#124—614no—
161#124—1222no—
162C4×Q8—2442no—
163C4×D4—2442no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—612no—
166C2×C4⋊C4C4×D6111yescharacteristic
167C2×C4⋊C4C22×D6111yescharacteristic
168C2×C22⋊C4—1222no—
169C2×C22⋊C4—1222no—
170C2×C22⋊C4—1221no—
171C2×C42—611no—
172C2×C42—612no—
173C2×C42—611no—
174C2×C42C4×D6111yescharacteristic
175C4⋊C8—2442no—
176C22⋊C8—22no—
177C22⋊C8—1222no—
178C4×C8—2442no—
179#95—1221no—
180#95—1221no—
181#95—1222no—
182C24—1221no—
183C2×Q8—612no—
184C2×Q8—612no—
185C2×Q8—2441no—
186C2×Q8—2441no—
187C2×D4—612no—
188C2×D4—1221no—
189C2×D4—2441no—
190C2×D4—2441no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—612no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—1221no—
197C22×C4—4882no—
198C22×C4—2442no—
199C22×C4C2×C4×D6111yescharacteristic
200C22×C4D4×D6112yes—
201C2×C8—42no—
202C2×C8—2442no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—82no—
206C4⋊C4—2442no—
207C22⋊C4—1228no—
208C22⋊C4—4882no—
209C22⋊C4—2442no—
210C42—21no—
211C42—1222no—
212C42—1222no—
213C42—1222no—
214C42—2441no—
215C42C8×D6112yes—
216C23—1222no—
217C23—2442no—
218C23—2442no—
219C23—2441no—
220C23—2441no—
221C23C22⋊C4×D6111yescharacteristic
222Q8—2442no—
223Q8—2442no—
224D4—2442no—
225D4—2442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—614no—
236C2×C4—612no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—4884no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4C2×C8×D6111yescharacteristic
247C2×C4M16×D6111yescharacteristic
248C8—82no—
249C8—4882no—
250C22—21no—
251C22—21no—
252C22—4882no—
253C22—4881no—
254C22—4881no—
255C22—2444no—
256C22—2442no—
257C22C22⋊C8×D6111yescharacteristic
258C22#99×D6111yescharacteristic
259C22#1683974511yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—42no—
264C4—81no—
265C4—1224no—
266C4—1222no—
267C4—4881no—
268C4—2441no—
269C2—21no—
270C2—21no—
271C2—4882no—
272C2#2144413611yescharacteristic
273C2#2144748911yescharacteristic
274C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1325D61
hypocenterC61#11480
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #21444141C2semidirect
3. #21443765C2semidirect
5. C61×#1325C2semidirect
23. #14519765C8semidirect
135. #1325D61semidirect
156. C61#11480semidirect

Maximal subgroups

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

subgroupindex
#214485272
#214441412
#214437652
#214437502
C61×#13252
#1148061