Finite Group Databasebeta

← #28499341

Subgroups — #28499341

Order 15104.

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×#14273646C211yesmaximal, characteristic
2#21422440C211yesmaximal, characteristic
3#21422126C214yesmaximal
4C59×#2567C211yesmaximal, characteristic
5#16837459—21no—
6C2×#14273646—21no—
7C4×#11745664—21no—
8#16837171C2212yes—
9#16837128—21no—
10#16837128C2212yes—
11C2×C4⋊Q8×C59C411yescharacteristic
12C2×C4×Q8×C59C2211yescharacteristic
13C59×#395C412yes—
14C59×#395C2212yes—
15C59×#391—21no—
16C59×#389—21no—
17C59×#389—21no—
18C59×#384—21no—
19C4×C4⋊C4×C59C411yescharacteristic
20C2×#11745664—22no—
21C4⋊(C59⋊C8)—41no—
22#14273646—24no—
23C22⋊(C59⋊C8)—22no—
24#14273638—41no—
25#14273638—41no—
26C4×C59⋊C8—41no—
27C22×Q8×C59C2×C412yes—
28C22×Q8×C59D411yescharacteristic
29C4⋊Q8×C59—41no—
30C4⋊Q8×C59—41no—
31C4×Q8×C59—41no—
32C4×Q8×C59—41no—
33C2×C4⋊C4×C59—21no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59—21no—
36C2×C4⋊C4×C59—22no—
37C2×C4⋊C4×C59—22no—
38C2×C4⋊C4×C59C2×C411yescharacteristic
39C2×C4⋊C4×C59D411yescharacteristic
40C2×C4⋊C4×C59C2311yescharacteristic
41C2×C42×C59—21no—
42C2×C42×C59C2×C411yescharacteristic
43C2×C42×C59D411yescharacteristic
44C2×C42×C59D411yescharacteristic
45#95×C59—22no—
46#95×C59—22no—
47#95×C59C2×C412yes—
48C2×Q8×C59—22no—
49C2×Q8×C59—22no—
50C2×Q8×C59—41no—
51C2×Q8×C59—42no—
52C2×Q8×C59—82no—
53C22×C4×C59—22no—
54C22×C4×C59—22no—
55C22×C4×C59C22⋊C411yescharacteristic
56C22×C4×C59C22⋊C411yescharacteristic
57C22×C4×C59C22⋊C411yescharacteristic
58C22×C4×C59C22⋊C411yescharacteristic
59C22×C4×C59C22×C411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C4⋊C4×C59—24no—
63C4⋊C4×C59—41no—
64C4⋊C4×C59—41no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—42no—
67C4⋊C4×C59—41no—
68C4⋊C4×C59—41no—
69C4⋊C4×C59—82no—
70C4⋊C4×C59—82no—
71C42×C59—21no—
72C42×C59—21no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59—42no—
78#11745664—24no—
79#11745664—42no—
80C2×C59⋊C8—42no—
81C2×C59⋊C8—42no—
82C23×C59C2×C22⋊C411yescharacteristic
83Q8×C59—44no—
84Q8×C59—84no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—22no—
90C2×C4×C59—24no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—42no—
98C2×C4×C59—42no—
99C2×C4×C59—41no—
100C2×C4×C59—41no—
101C2×C4×C59—41no—
102C2×C4×C59—42no—
103C2×C4×C59—42no—
104C2×C4×C59—42no—
105C2×C4×C59#9911yescharacteristic
106C2×C4×C59#9911yescharacteristic
107C2×C4×C59#10412yes—
108C2×C4×C59#13712yes—
109C59⋊C8—44no—
110C59⋊C8—82no—
111#11795—591nomaximal, Sylow
112C22×C59—21no—
113C22×C59—21no—
114C22×C59C2×#9911yescharacteristic
115C22×C59#41911yescharacteristic
116C22×C59C2×#10411yescharacteristic
117C4×C59—21no—
118C4×C59—22no—
119C4×C59—22no—
120C4×C59—44no—
121C4×C59—41no—
122C4×C59—41no—
123C4×C59—41no—
124C4×C59—41no—
125C4×C59—82no—
126C4×C59#35612yes—
127#2567D5911yescharacteristic
128C4×#101—591no—
129#1467—591no—
130#1354—594no—
131C2×C59—21no—
132C2×C59—21no—
133C2×C59#150811yescharacteristic
134C2×C59#212211yescharacteristic
135C2×C59C2×#35611yescharacteristic
136C2×C4⋊Q8Dic5911yescharacteristic
137C2×C4×Q8C2×D5911yescharacteristic
138#432—1181no—
139C2×#101—1181no—
140C4×M16—1181no—
141#395Dic5912yes—
142#395C2×D5912yes—
143#391—21no—
144#389—21no—
145#389—21no—
146#384—21no—
147C4×C4⋊C4Dic5911yescharacteristic
148#343—592no—
149#324—592no—
150#324—1181no—
151C59#1179511yescharacteristic, complemented, Sylow
152C22×Q8C2×Dic5912yes—
153C22×Q8C22⋊D5911yescharacteristic
154C2×M16—1182no—
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×Dic5911yescharacteristic
165C2×C4⋊C4C22⋊D5911yescharacteristic
166C2×C4⋊C4C22×D5911yescharacteristic
167C2×C42—21no—
168C2×C42C2×Dic5911yescharacteristic
169C2×C42C22⋊D5911yescharacteristic
170C2×C42C22⋊D5911yescharacteristic
171C4⋊C8—2361no—
172#101—1184no—
173C22⋊C8—1182no—
174#97—2361no—
175#97—2361no—
176C4×C8—2361no—
177#95—22no—
178#95—22no—
179#95C2×Dic5912yes—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—42no—
184C2×Q8—82no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C22⋊Dic5911yescharacteristic
188C22×C4C22⋊Dic5911yescharacteristic
189C22×C4C22⋊Dic5911yescharacteristic
190C22×C4C22⋊Dic5911yescharacteristic
191C22×C4C22×Dic5911yescharacteristic
192C22×C4C2×C22⋊D5911yescharacteristic
193C22×C4C2×C22⋊D5911yescharacteristic
194M16—1184no—
195M16—2362no—
196C2×C8—2362no—
197C2×C8—2362no—
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⋊Dic5911yescharacteristic
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#1427364211yescharacteristic
238C2×C4#1427364211yescharacteristic
239C2×C4#1427365412yes—
240C2×C4#1427375812yes—
241C8—4722no—
242C8—2364no—
243C22—21no—
244C22—21no—
245C22C2×#1427364211yescharacteristic
246C22#1683741111yescharacteristic
247C22C2×#1427365411yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—44no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—82no—
257C4#1683720112yes—
258C2—21no—
259C2—21no—
260C2#2142261611yescharacteristic
261C2#2142574611yescharacteristic
262C2C2×#1683720111yescharacteristic
subgroupG/H
centerC22C2×#14273642
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#2567C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#2567D59
hypocenterC59#11795
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
151. C59#11795semidirect

Maximal subgroups

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

subgroupindex
C4×#142736462
#214224402
#214221262
C59×#25672
#1179559