Finite Group Databasebeta

← #30607267

Subgroups — #30607267

Order 15616.

614 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461656C212yesmaximal
2#21460917C212yesmaximal, complemented
3#21460916C212yesmaximal, complemented
4#21448409C211yesmaximal, characteristic
5C2×#14519838C2214yes—
6C2×#14519837—22no—
7#16840732—22no—
8C22×#11758224C2211yescharacteristic
9C2×#14519734C411yescharacteristic
10C2×C4⋊C4×D61C411yescharacteristic
11#16839668C2211yescharacteristic
12#16839667C2211yescharacteristic
13#16839665C411yescharacteristic
14#16839638—22no—
15#16839620—22no—
16C61×#390C411yescharacteristic
17C2×#11758217—24no—
18#14519838—28no—
19#14519837—44no—
20C22⋊#92420—44no—
21C2×#11758224—24no—
22C2×#11758224—42no—
23C2×#11758224—42no—
24C22×Dic122C2311yescharacteristic
25C22×C22⋊D61D412yes—
26C23×Dic61D412yes—
27C22×C4×D61—21no—
28C22×C4×D61C2×C411yescharacteristic
29#14519734—42no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C4⋊C4×D61—42no—
34C2×C22⋊Dic61—22no—
35C2×#11758198—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37#14519684—22no—
38#14519684—22no—
39C22×D4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C22⋊C4×C61—22no—
42C2×C42×C61C2×C411yescharacteristic
43C24×C61C22⋊C412yes—
44C23×D61C22⋊C411yescharacteristic
45C2×D4×C61—22no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22×C411yescharacteristic
51C2×C22⋊D61—24no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—42no—
54C22×Dic61—24no—
55C22×Dic61—24no—
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61—42no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×D412yes—
61#11758224—416no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—42no—
66C2×C4×D61—82no—
67C2×Dic122—41no—
68C2×Dic122—41no—
69C2×Dic122#4114yes—
70#11758217—44no—
71#11758217—44no—
72C2×#92420—44no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—82no—
75C42×C61—41no—
76C22⋊Dic61—82no—
77#11758198—42no—
78C4⋊Dic61—41no—
79#11758196—42no—
80#11758196—42no—
81C4×Dic61—41no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61—42no—
86C23×C61—42no—
87C23×C61C2×C22⋊C411yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—41no—
91C22×D61—41no—
92C22×D61#9912yes—
93D4×C61—44no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#11712yes—
102C22⋊D61—48no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—48no—
108C2×Dic61—41no—
109C2×Dic61—42no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61#9912yes—
114C2×Dic61#12314yes—
115C4×D61—28no—
116C4×D61—84no—
117Dic122—44no—
118#92420—84no—
119#12863—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—44no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—82no—
127C22×C61#38111yescharacteristic
128C22×C61C2×#9911yescharacteristic
129C22×C61C2×#9911yescharacteristic
130C2×D61—22no—
131C2×D61—42no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—42no—
135C4×C61—22no—
136C4×C61—81no—
137C4×C61—81no—
138Dic61—24no—
139Dic61—22no—
140Dic61—81no—
141Dic61—81no—
142#2311—611no—
143#1785—612no—
144#1394—612no—
145#1394—612no—
146C2×C61—21no—
147C2×C61—21no—
148C2×C61—82no—
149C2×C61#181911yescharacteristic
150C2×C61#213411yescharacteristic
151C2×C61#213511yescharacteristic
152D61—42no—
153C22×#41—611no—
154C2×#117—611no—
155C22×C4⋊C4—611no—
156C2×#101—614no—
157C2×#100—1222no—
158#407—1222no—
159#391—611no—
160#391—611no—
161#390—611no—
162#390#692311yescharacteristic
163#386—1222no—
164#380—1222no—
165C61#1286311yescharacteristic, complemented, Sylow
166C2×#41—1224no—
167C2×#41—2442no—
168C2×#41—2442no—
169C22×Q8—611no—
170C22×D4—612no—
171C22×D4C2×#692311yescharacteristic
172C23×C4—612no—
173C23×C4—611no—
174C23×C4—1221no—
175C2×M16—1224no—
176#117—2442no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—2442no—
181C2×C4⋊C4C2×#692311yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—1222no—
184C2×C22⋊C4—1221no—
185C2×C42—611no—
186C2×C42C2×#692311yescharacteristic
187#101—1228no—
188#100—2444no—
189C22⋊C8—2444no—
190#95—1222no—
191#95—1222no—
192C24—611no—
193C24C22⋊#692312yes—
194#41—24416no—
195C2×Q8—614no—
196C2×Q8—2441no—
197C2×Q8—2441no—
198C2×D4—22no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—1224no—
202C2×D4—1224no—
203C2×D4—2442no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—612no—
207C22×C4—611no—
208C22×C4—1222no—
209C22×C4—1222no—
210C22×C4—1224no—
211C22×C4—1224no—
212C22×C4—1222no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—4882no—
216C22×C4—2442no—
217C22×C4—2442no—
218C22×C4C22×#692311yescharacteristic
219M16—2444no—
220M16—2444no—
221C2×C8—2444no—
222C4⋊C4—41no—
223C4⋊C4—2441no—
224C4⋊C4—2442no—
225C4⋊C4—2442no—
226C22⋊C4—82no—
227C22⋊C4—4882no—
228C22⋊C4—2442no—
229C42—41no—
230C42—2441no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—42no—
235C23—42no—
236C23—612no—
237C23—1221no—
238C23—1221no—
239C23—2441no—
240C23—2441no—
241C23C2×C22⋊#692311yescharacteristic
242Q8—2444no—
243D4—44no—
244D4—2448no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—614no—
253C2×C4—612no—
254C2×C4—1228no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—4884no—
260C2×C4—2448no—
261C2×C4—2441no—
262C2×C4—2442no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4#1451985612yes—
267C8—4884no—
268C22—21no—
269C22—21no—
270C22—44no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—82no—
275C22—1222no—
276C22—2442no—
277C22—2442no—
278C22—2441no—
279C22—2441no—
280C22#1684070511yescharacteristic
281C22D61⋊#9911yescharacteristic
282C22D61⋊#9911yescharacteristic
283C4—22no—
284C4—81no—
285C4—81no—
286C4—1224no—
287C4—1222no—
288C4—4881no—
289C4—4881no—
290C2—21no—
291C2—21no—
292C2—82no—
293C2—2442no—
294C2#2146171511yescharacteristic
295C2#2146211911yescharacteristic
296C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×Dic122C23
hypercenter#390#6923
hypocenterC61#12863
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #21460917C2semidirect
3. #21460916C2semidirect
165. C61#12863semidirect

Maximal subgroups

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

subgroupindex
#214616562
#214609172
#214609162
#214484092
#1286361