Finite Group Databasebeta

← #29577870

Subgroups — #29577870

Order 15616.

518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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#21454860C211yesmaximal, characteristic
2#21451173C211yesmaximal, characteristic
3#21444247C212yesmaximal, complemented
4#21443679C212yesmaximal, complemented
5C61×#1800C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7#16839840—24no—
8#16839815C2212yes—
9#16839726—22no—
10#16839698C412yes—
11#16839674C412yes—
12#16839665—21no—
13#16839658—21no—
14#16839635—22no—
15#16839628C2211yescharacteristic
16#16839492—24no—
17C2×C4×D4×C61C2211yescharacteristic
18C61×#423C2212yes—
19C2×#100×C61—21no—
20C61×#343—21no—
21C22×Dic122C2×C411yescharacteristic
22C2×#11758194—24no—
23C4×Dic122—22no—
24C4×Dic122—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—21no—
28C2×#11758196—22no—
29C2×C22⋊Dic61—22no—
30C2×C22⋊Dic61—22no—
31C2×C4×Dic61—21no—
32C4⋊#92418—22no—
33C22⋊#92418—24no—
34C22⋊#92418—22no—
35C4×#92418D414yes—
36#14519684—22no—
37#14519684—21no—
38#14519684C2×C412yes—
39C22×D4×C61D411yescharacteristic
40C23×C4×C61D412yes—
41C2×M16×C61—22no—
42C4×D4×C61—22no—
43C4×D4×C61—22no—
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61C2×C412yes—
46C2×C42×C61C2311yescharacteristic
47C4⋊C8×C61—22no—
48C4⋊C8×C61—22no—
49#100×C61—42no—
50C24×C61C22⋊C412yes—
51C2×D4×C61—22no—
52C2×D4×C61—21no—
53C2×D4×C61—22no—
54C2×D4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—82no—
58C22×C4×C61C22⋊C412yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—22no—
64C22×Dic61—21no—
65C2×Dic122—22no—
66C2×Dic122—42no—
67M16×C61—42no—
68M16×C61—42no—
69C2×C8×C61—42no—
70C4⋊C4×C61—22no—
71C22⋊C4×C61—24no—
72C42×C61C2×D412yes—
73C42×C61#4112yes—
74C22⋊Dic61—44no—
75C22⋊Dic61—82no—
76C4⋊Dic61—22no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—41no—
80#11758196—41no—
81#11758196—82no—
82C4×Dic61—42no—
83#11758194—84no—
84C2×#92418—24no—
85C23×C61—22no—
86C23×C61—22no—
87C23×C61—22no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61C2×C22⋊C411yescharacteristic
91D4×C61—42no—
92D4×C61—42no—
93C2×C4×C61—22no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—44no—
97C2×C4×C61—42no—
98C2×C4×C61—82no—
99C2×C4×C61C4×D412yes—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61#12112yes—
102C2×C4×C61#12311yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×C4×C61#13712yes—
105C2×C4×C61#13711yescharacteristic
106C2×Dic61—22no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115Dic122—24no—
116Dic122—42no—
117C8×C61—82no—
118#92418—44no—
119#9487—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#38611yescharacteristic
128C22×C61#41711yescharacteristic
129C22×C61#41911yescharacteristic
130C4×C61—22no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—42no—
134C4×C61#46812yes—
135C4×C61#47012yes—
136Dic61—42no—
137Dic61—82no—
138Dic61—81no—
139#2975—611no—
140#2580—611no—
141#1800D6111yescharacteristic
142#1487—612no—
143#1286—612no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61—82no—
147C2×C61#189111yescharacteristic
148C2×C61#189411yescharacteristic
149C2×C61#191111yescharacteristic
150C2×C4×Q8—611no—
151C2×C4×D4C2×D6111yescharacteristic
152#436—1224no—
153#431—612no—
154#423C2×D6112yes—
155C2×#100—21no—
156#407—1222no—
157#399—612no—
158#393—612no—
159#390—1221no—
160#389—1221no—
161#385—1222no—
162#382—611no—
163#343—21no—
164Q8⋊C8—1224no—
165C61#948711yescharacteristic, complemented, Sylow
166C22×Q8—611no—
167C22×D4C22⋊D6111yescharacteristic
168C23×C4D24412yes—
169C2×M16—22no—
170C2×M16—1224no—
171C4×Q8—1222no—
172C4×Q8—1222no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—1222no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4C22⋊D6111yescharacteristic
180C2×C22⋊C4—1222no—
181C2×C22⋊C4—1222no—
182C2×C22⋊C4C4×D6112yes—
183C2×C42—1221no—
184C2×C42C22×D6111yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—1222no—
188#100—42no—
189C22⋊C8—1224no—
190C22⋊C8—1222no—
191C4×C8—614no—
192#95—612no—
193#95—1222no—
194#95—1221no—
195C24#1175819812yes—
196C2×Q8—1222no—
197C2×Q8—2442no—
198C2×D4—21no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—82no—
205C22×C4—1221no—
206C22×C4—1222no—
207C22×C4—1221no—
208C22×C4#1175819812yes—
209C22×C4C2×C4×D6111yescharacteristic
210C22×C4C2×D24411yescharacteristic
211C22×C4C2×C22⋊D6111yescharacteristic
212M16—42no—
213M16—42no—
214M16—4884no—
215C2×C8—42no—
216C2×C8—1224no—
217C4⋊C4—22no—
218C4⋊C4—1222no—
219C4⋊C4—4882no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C22⋊C4—24no—
225C22⋊C4—4882no—
226C22⋊C4—2444no—
227C42—2442no—
228C42D4×D6112yes—
229C42#1175822412yes—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—42no—
235C23C2×#1175819811yescharacteristic
236Q8—1224no—
237Q8—2442no—
238D4—42no—
239D4—42no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—82no—
246C2×C4—1222no—
247C2×C4—2441no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4—2441no—
251C2×C4—2442no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4#1451973712yes—
256C2×C4#1451974711yescharacteristic
257C2×C4#1451974912yes—
258C2×C4#1451976111yescharacteristic
259C2×C4#1451980311yescharacteristic
260C2×C4#1451980712yes—
261C2×C4#1451980811yescharacteristic
262C8—82no—
263C8—2444no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—82no—
271C22#1683963911yescharacteristic
272C22#1683976111yescharacteristic
273C22#1683977011yescharacteristic
274C4—22no—
275C4—21no—
276C4—21no—
277C4—42no—
278C4—4882no—
279C4—4881no—
280C4—2442no—
281C4#1684000612yes—
282C4#1684001812yes—
283C2—21no—
284C2—21no—
285C2—82no—
286C2#2144623511yescharacteristic
287C2#2144625011yescharacteristic
288C2#2144634911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1800C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#1800D61
hypocenterC61#9487
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #21444247C2semidirect
4. #21443679C2semidirect
165. C61#9487semidirect

Maximal subgroups

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

subgroupindex
#214548602
#214511732
#214442472
#214436792
C61×#18002
#948761