Finite Group Databasebeta

← #29589294

Subgroups — #29589294

Order 15616.

428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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#21448386C211yesmaximal, characteristic
2#21444141C212yesmaximal
3#21443765C211yesmaximal, characteristic
4#21443752C212yesmaximal
5C61×#1325C211yesmaximal, characteristic
6C2×#14519777C411yescharacteristic
7C2×#14519742C411yescharacteristic
8C2×#14519742C2211yescharacteristic
9#16839812—22no—
10#16839667C411yescharacteristic
11#16839667C2211yescharacteristic
12#16839658—22no—
13C4⋊C4×Dic61—22no—
14C42×Dic61C411yescharacteristic
15#16839488C2212yes—
16#16839487—22no—
17C61×#384C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×Dic122C2×C411yescharacteristic
21#14519777—22no—
22#14519777C814yescomplemented
23#14519742—41no—
24#14519742—41no—
25#14519742—41no—
26#14519742—41no—
27C2×C4⋊Dic61—22no—
28C2×#11758196—21no—
29C2×#11758196D412yes—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D412yes—
36#14519706—42no—
37C22⋊#92418—22no—
38C8×Dic61—42no—
39#14519684—22no—
40#14519684—22no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2311yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C22⋊C8×C61—22no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C22×C411yescharacteristic
49C22×C4×C61C2×D412yes—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61C22⋊C412yes—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C22⋊C411yescharacteristic
55C2×Dic122—21no—
56C2×Dic122—41no—
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×Dic122C2×C812yes—
61C2×Dic122C2×C812yes—
62C2×Dic122M1612yes—
63C2×C8×C61—42no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—44no—
66C4⋊C4×C61—41no—
67C42×C61—21no—
68C42×C61C2×C812yes—
69C4⋊Dic61—28no—
70#11758196—42no—
71#11758196—42no—
72C4×Dic61—24no—
73C4×Dic61—22no—
74C4×Dic61—22no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—42no—
78C4×Dic61—41no—
79C4×Dic61—41no—
80C4×Dic61—41no—
81C2×#92418—42no—
82C23×C61C2×C22⋊C411yescharacteristic
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61C22×C811yescharacteristic
93C2×C4×C61C2×M1611yescharacteristic
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61C22⋊C814yes—
106C2×Dic61#9911yescharacteristic
107C2×Dic61#9911yescharacteristic
108Dic122—42no—
109Dic122—42no—
110Dic122—42no—
111Dic122—42no—
112C8×C61—82no—
113#92418—82no—
114#11478—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C2×C22⋊C811yescharacteristic
118C22×C61C2×#9911yescharacteristic
119C22×C61#41311yescharacteristic
120C4×C61—24no—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—42no—
124C4×C61—81no—
125Dic61—21no—
126Dic61—24no—
127Dic61—42no—
128Dic61—41no—
129Dic61—42no—
130Dic61#35612yes—
131C4×C4⋊Q8—611no—
132#1461—612no—
133#1325—611no—
134#1325D6111yescharacteristic
135#1319—612no—
136C2×C61—21no—
137C2×C61—21no—
138C2×C61#145911yescharacteristic
139C2×C61#212611yescharacteristic
140C2×C61C2×#35611yescharacteristic
141C2×C4⋊Q8—611no—
142C2×C4×Q8—611no—
143C2×C4×Q8—611no—
144#431—1222no—
145#391—611no—
146#391—611no—
147#389—1222no—
148#384C2×D6111yescharacteristic
149C4×C4⋊C4—1222no—
150C43—611no—
151#324—612no—
152#324—1222no—
153#324C2×D6112yes—
154C61#1147811yescharacteristic, complemented, Sylow
155C22×Q8—611no—
156C22×Q8—611no—
157C4⋊Q8—614no—
158C4⋊Q8—1222no—
159C4×Q8—2441no—
160C4×Q8—2441no—
161C4×Q8—2441no—
162C4×Q8—2441no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4C4×D6111yescharacteristic
168C2×C4⋊C4C22×D6111yescharacteristic
169C2×C42—611no—
170C2×C42—612no—
171C2×C42—611no—
172C2×C42—1221no—
173C2×C42—1221no—
174C2×C42—1221no—
175C2×C42C4×D6111yescharacteristic
176C4⋊C8—2442no—
177C22⋊C8—22no—
178C22⋊C8—1222no—
179C4×C8—2442no—
180#95—1222no—
181#95—1222no—
182C2×Q8—612no—
183C2×Q8—612no—
184C2×Q8—612no—
185C2×Q8—1221no—
186C2×Q8—2441no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×Q8—2441no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—612no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4C2×C4×D6111yescharacteristic
198C22×C4D4×D6112yes—
199C2×C8—42no—
200C2×C8—2442no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—44no—
204C4⋊C4—1228no—
205C4⋊C4—2442no—
206C4⋊C4—2442no—
207C42—21no—
208C42—1222no—
209C42—1222no—
210C42—1221no—
211C42—1221no—
212C42—1224no—
213C42—2441no—
214C42—2442no—
215C42—2441no—
216C42—2441no—
217C42C8×D6112yes—
218C23C22⋊C4×D6111yescharacteristic
219Q8—2442no—
220Q8—2442no—
221Q8—2442no—
222Q8—2442no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—611no—
233C2×C4—614no—
234C2×C4—611no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1221no—
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—
252C22C22⋊C8×D6111yescharacteristic
253C22#99×D6111yescharacteristic
254C22#1683974511yescharacteristic
255C4—24no—
256C4—21no—
257C4—21no—
258C4—42no—
259C4—81no—
260C4—612no—
261C4—1224no—
262C4—1221no—
263C4—2442no—
264C4—2442no—
265C4—2441no—
266C2—21no—
267C2—21no—
268C2#2144413611yescharacteristic
269C2#2144748111yescharacteristic
270C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1325D61
hypocenterC61#11478
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
22. #14519777C8semidirect
154. C61#11478semidirect

Maximal subgroups

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

subgroupindex
#214483862
#214441412
#214437652
#214437522
C61×#13252
#1147861