Finite Group Databasebeta

← #30594753

Subgroups — #30594753

Order 15616.

328 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 54 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#21461796C211yesmaximal, characteristic
2#21461075C211yesmaximal, characteristic
3#21445809C211yesmaximal, characteristic
4C22×#11758217C411yescharacteristic
5#16840732—21no—
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420C411yescharacteristic
8#16840628—21no—
9#16840607—21no—
10#16840605C412yes—
11C2×D4×Dic61C2211yescharacteristic
12#16839785—21no—
13C2×#14519694C411yescharacteristic
14#16839530—21no—
15C2×#100×C61C411yescharacteristic
16C2×#11758217—42no—
17C2×#11758217—41no—
18C2×#11758217—41no—
19C22×#92420—21no—
20C22×#92420—21no—
21C22⋊#92420—22no—
22C22⋊#92420—42no—
23C22⋊#92420—41no—
24C22⋊#92420—41no—
25C23×Dic61C2×C411yescharacteristic
26C23×Dic61D411yescharacteristic
27C2×#11758194—21no—
28D4×Dic61—41no—
29D4×Dic61—41no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C22⋊Dic61C2×C411yescharacteristic
32C2×C22⋊Dic61Q811yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34#14519706—41no—
35#14519706—41no—
36#14519694—41no—
37C22×D4×C61C2×C411yescharacteristic
38C2×M16×C61—21no—
39#100×C61—41no—
40C24×C61C4211yescharacteristic
41C24×C61C4⋊C411yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61—41no—
45C2×D4×C61—41no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61—41no—
52C22×Dic61—41no—
53C22×Dic61—41no—
54C22×Dic61—41no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C4⋊C411yescharacteristic
58C22×Dic61C4⋊C411yescharacteristic
59#11758217—42no—
60#11758217—42no—
61#11758217—81no—
62#11758217—81no—
63C2×#92420—22no—
64C2×#92420—41no—
65C2×#92420—41no—
66C2×#92420—42no—
67C2×#92420—41no—
68C2×#92420—41no—
69C2×#92420—41no—
70M16×C61—41no—
71M16×C61—41no—
72C2×C8×C61—41no—
73C22⋊Dic61—41no—
74C22⋊Dic61—41no—
75C4⋊Dic61—41no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78#11758194—41no—
79#11758194—41no—
80C2×#92418—41no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—41no—
88C23×C61—41no—
89C23×C61—41no—
90C23×C61—41no—
91C23×C61#9511yescharacteristic
92D4×C61—42no—
93D4×C61—42no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61#10011yescharacteristic
97C2×C4×C61#10111yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—42no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—81no—
112C2×Dic61#9911yescharacteristic
113C2×Dic61#9911yescharacteristic
114#92420—42no—
115#92420—81no—
116#92420—82no—
117C8×C61—81no—
118#92418—81no—
119#7321—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—42no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61—81no—
132C22×C61#34211yescharacteristic
133C22×C61#34311yescharacteristic
134C22×C61#34411yescharacteristic
135C4×C61—21no—
136C4×C61—21no—
137Dic61—21no—
138Dic61—41no—
139Dic61—41no—
140Dic61—41no—
141Dic61AΣL(1,𝔽16)11yescharacteristic
142Dic61#35211yescharacteristic
143#1870—611no—
144#1800—611no—
145#1465—611no—
146C2×C61—21no—
147C2×C61—21no—
148C2×C61—81no—
149C2×C61—81no—
150C2×C61#130511yescharacteristic
151C2×C61#139011yescharacteristic
152C2×C61#139211yescharacteristic
153C22×M16—611no—
154C2×C4×D4—611no—
155#423—1221no—
156C2×#100—611no—
157C2×#100#692311yescharacteristic
158#407—1221no—
159C2×C22⋊C8—611no—
160C2×C22⋊C8—1221no—
161#343—1221no—
162#336—1221no—
163#324—1221no—
164#323—612no—
165C61#732111yescharacteristic, complemented, Sylow
166C22×D4C2×#692311yescharacteristic
167C23×C4—611no—
168C23×C4—611no—
169C2×M16—21no—
170C2×M16—1221no—
171C2×M16—2442no—
172C2×M16—2441no—
173C2×M16—2441no—
174C22×C8—1221no—
175C22×C8—1221no—
176C4×D4—2441no—
177C4×D4—2441no—
178C2×C4⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—611no—
181C2×C42—611no—
182C4⋊C8—2441no—
183C4⋊C8—2441no—
184#100—41no—
185#100—2441no—
186C22⋊C8—1222no—
187C22⋊C8—2442no—
188C22⋊C8—2441no—
189C22⋊C8—2441no—
190C24C4×#692311yescharacteristic
191C24C4⋊#692311yescharacteristic
192C2×D4—21no—
193C2×D4—21no—
194C2×D4—41no—
195C2×D4—41no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1221no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—2441no—
205C22×C4—2441no—
206C22×C4—2441no—
207C22×C4—2441no—
208C22×C4C22⋊#692311yescharacteristic
209M16—41no—
210M16—41no—
211M16—4881no—
212M16—4881no—
213M16—2441no—
214M16—2441no—
215M16—2442no—
216M16—2442no—
217C2×C8—41no—
218C2×C8—1222no—
219C2×C8—2441no—
220C2×C8—2441no—
221C2×C8—2442no—
222C2×C8—2441no—
223C2×C8—2441no—
224C2×C8—2441no—
225C2×C8—2441no—
226C4⋊C4—2441no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C42—1221no—
230C42—1221no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23(C2×#6923)⋊C411yescharacteristic
242D4—42no—
243D4—42no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—4881no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4—2442no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4#1451983711yescharacteristic
263C2×C4#1451983811yescharacteristic
264C8—81no—
265C8—4881no—
266C8—4881no—
267C8—4882no—
268C8—2442no—
269C22—21no—
270C22—21no—
271C22—42no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22#1684063911yescharacteristic
282C22#1684064211yescharacteristic
283C22#1684064311yescharacteristic
284C4—21no—
285C4—21no—
286C4—611no—
287C4—611no—
288C4—1221no—
289C4—2441no—
290C4—2441no—
291C4—2441no—
292C2—21no—
293C2—21no—
294C2—81no—
295C2—81no—
296C2#2146072011yescharacteristic
297C2#2146090511yescharacteristic
298C2#2146090911yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC24×C61C42
FrattiniC22×D4C2×#6923
FittingC2×#100×C61C4
socleC22×C61#342
prime radicalC22×D4×C61C2×C4
cosocleC2×D4×Dic61C22
hypercenterC2×#100#6923
hypocenterC61#7321
LCSG ▷ C24×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
165. C61#7321semidirect

Maximal subgroups

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

subgroupindex
#214617962
#214610752
#214458092
#732161