Finite Group Databasebeta

← #29590665

Subgroups — #29590665

Order 15616.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#14519696C211yesmaximal, characteristic
2#21444163C211yesmaximal, characteristic
3#21443849C214yesmaximal
4C61×#2567C211yesmaximal, characteristic
5#16839819—21no—
6C2×#14519696—21no—
7C4×#11758194—21no—
8#16839531C2212yes—
9#16839488—21no—
10#16839488C2212yes—
11C2×C4⋊Q8×C61C411yescharacteristic
12C2×C4×Q8×C61C2211yescharacteristic
13C61×#395C412yes—
14C61×#395C2212yes—
15C61×#391—21no—
16C61×#389—21no—
17C61×#389—21no—
18C61×#384—21no—
19C4×C4⋊C4×C61C411yescharacteristic
20C2×#11758194—22no—
21C4⋊#92418—41no—
22#14519696—24no—
23C22⋊#92418—22no—
24#14519688—41no—
25#14519688—41no—
26C4×#92418—41no—
27C22×Q8×C61C2×C412yes—
28C22×Q8×C61D411yescharacteristic
29C4⋊Q8×C61—41no—
30C4⋊Q8×C61—41no—
31C4×Q8×C61—41no—
32C4×Q8×C61—41no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—21no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C42×C61—21no—
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45#95×C61—22no—
46#95×C61—22no—
47#95×C61C2×C412yes—
48C2×Q8×C61—22no—
49C2×Q8×C61—22no—
50C2×Q8×C61—41no—
51C2×Q8×C61—42no—
52C2×Q8×C61—82no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C4⋊C4×C61—24no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—82no—
70C4⋊C4×C61—82no—
71C42×C61—21no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—21no—
77C42×C61—42no—
78#11758194—24no—
79#11758194—42no—
80C2×#92418—42no—
81C2×#92418—42no—
82C23×C61C2×C22⋊C411yescharacteristic
83Q8×C61—44no—
84Q8×C61—84no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—24no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61#9911yescharacteristic
106C2×C4×C61#9911yescharacteristic
107C2×C4×C61#10412yes—
108C2×C4×C61#13712yes—
109#92418—44no—
110#92418—82no—
111#11795—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61C2×#9911yescharacteristic
115C22×C61#41911yescharacteristic
116C22×C61C2×#10411yescharacteristic
117C4×C61—21no—
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—44no—
121C4×C61—41no—
122C4×C61—41no—
123C4×C61—41no—
124C4×C61—41no—
125C4×C61—82no—
126C4×C61#35612yes—
127#2567D6111yescharacteristic
128C4×#101—611no—
129#1467—611no—
130#1354—614no—
131C2×C61—21no—
132C2×C61—21no—
133C2×C61#150811yescharacteristic
134C2×C61#212211yescharacteristic
135C2×C61C2×#35611yescharacteristic
136C2×C4⋊Q8Dic6111yescharacteristic
137C2×C4×Q8C2×D6111yescharacteristic
138#432—1221no—
139C2×#101—1221no—
140C4×M16—1221no—
141#395Dic6112yes—
142#395C2×D6112yes—
143#391—21no—
144#389—21no—
145#389—21no—
146#384—21no—
147C4×C4⋊C4Dic6111yescharacteristic
148#343—612no—
149#324—612no—
150#324—1221no—
151C61#1179511yescharacteristic, complemented, Sylow
152C22×Q8C2×Dic6112yes—
153C22×Q8C22⋊D6111yescharacteristic
154C2×M16—1222no—
155C4⋊Q8—41no—
156C4⋊Q8—41no—
157C4×Q8—41no—
158C4×Q8—41no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C2×Dic6111yescharacteristic
165C2×C4⋊C4C22⋊D6111yescharacteristic
166C2×C4⋊C4C22×D6111yescharacteristic
167C2×C42—21no—
168C2×C42C2×Dic6111yescharacteristic
169C2×C42C22⋊D6111yescharacteristic
170C2×C42C22⋊D6111yescharacteristic
171C4⋊C8—2441no—
172#101—1224no—
173C22⋊C8—1222no—
174#97—2441no—
175#97—2441no—
176C4×C8—2441no—
177#95—22no—
178#95—22no—
179#95C2×Dic6112yes—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—42no—
184C2×Q8—82no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C22⋊Dic6111yescharacteristic
188C22×C4C22⋊Dic6111yescharacteristic
189C22×C4C22⋊Dic6111yescharacteristic
190C22×C4C22⋊Dic6111yescharacteristic
191C22×C4C22×Dic6111yescharacteristic
192C22×C4C2×C22⋊D6111yescharacteristic
193C22×C4C2×C22⋊D6111yescharacteristic
194M16—1224no—
195M16—2442no—
196C2×C8—2442no—
197C2×C8—2442no—
198C4⋊C4—24no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—82no—
206C4⋊C4—82no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—42no—
214C23C2×C22⋊Dic6111yescharacteristic
215Q8—44no—
216Q8—84no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4#1451969211yescharacteristic
238C2×C4#1451969211yescharacteristic
239C2×C4#1451970412yes—
240C2×C4#1451980812yes—
241C8—4882no—
242C8—2444no—
243C22—21no—
244C22—21no—
245C22C2×#1451969211yescharacteristic
246C22#1683977111yescharacteristic
247C22C2×#1451970411yescharacteristic
248C4—21no—
249C4—22no—
250C4—22no—
251C4—44no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—82no—
257C4#1683956112yes—
258C2—21no—
259C2—21no—
260C2#2144433911yescharacteristic
261C2#2144746911yescharacteristic
262C2C2×#1683956111yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2567C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2567D61
hypocenterC61#11795
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
151. C61#11795semidirect

Maximal subgroups

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

subgroupindex
C4×#145196962
#214441632
#214438492
C61×#25672
#1179561