Finite Group Databasebeta

← #29577418

Subgroups — #29577418

Order 15616.

534 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 119 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#21450811C211yesmaximal, characteristic
2#21445811C211yesmaximal, characteristic
3#21444490C212yesmaximal, complemented
4#21443721C212yesmaximal, complemented
5C61×#2975C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519764—21no—
8#16839786C2212yes—
9C2×#14519694—21no—
10#16839687C414yes—
11#16839667—21no—
12#16839622—22no—
13C4×C4⋊Dic61C2211yescharacteristic
14#16839531—21no—
15#16839507—24no—
16C2×C4×D4×C61C2211yescharacteristic
17C61×#436—24no—
18C61×#431C2212yes—
19C61×#407—22no—
20C22×Dic122—21no—
21C2×#11758194—22no—
22#14519777—22no—
23#14519777—22no—
24#14519764—44no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C412yes—
28C2×C22⋊Dic61—24no—
29C2×C4×Dic61—21no—
30C4⋊#92418—22no—
31C4⋊#92418—22no—
32#14519694—42no—
33#14519684—24no—
34#14519684C2×C412yes—
35C22×D4×C61D411yescharacteristic
36C23×C4×C61D412yes—
37C2×M16×C61—24no—
38C4×D4×C61—22no—
39C4×D4×C61—22no—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61C2×C412yes—
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61D414yes—
44C22⋊C8×C61—24no—
45C22⋊C8×C61—22no—
46C4×C8×C61—22no—
47C24×C61C22⋊C412yes—
48C2×D4×C61—22no—
49C2×D4×C61—21no—
50C2×D4×C61—22no—
51C2×D4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—44no—
55C22×C4×C61C22⋊C412yes—
56C22×C4×C61C22×C411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×Dic61—22no—
60C22×Dic61—22no—
61C2×Dic122—42no—
62C2×Dic122—41no—
63C2×Dic122—42no—
64C2×Dic122—41no—
65M16×C61—84no—
66C2×C8×C61—24no—
67C4⋊C4×C61—22no—
68C22⋊C4×C61—24no—
69C42×C61C2×D412yes—
70C42×C61#4112yes—
71C22⋊Dic61—48no—
72C4⋊Dic61—24no—
73C4⋊Dic61—42no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76C4×Dic61—42no—
77#11758194—42no—
78#11758194—42no—
79C2×#92418—42no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—42no—
84C23×C61—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86D4×C61—42no—
87D4×C61—42no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61—44no—
92C2×C4×C61—42no—
93C2×C4×C61—82no—
94C2×C4×C61C4×D412yes—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61#12112yes—
97C2×C4×C61#12311yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)12yes—
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C61#13711yescharacteristic
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107Dic122—82no—
108Dic122—82no—
109C8×C61—44no—
110#92418—82no—
111#9401—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61—44no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—82no—
119C22×C61#38611yescharacteristic
120C22×C61#41711yescharacteristic
121C22×C61#41811yescharacteristic
122C4×C61—21no—
123C4×C61—22no—
124C4×C61—42no—
125C4×C61#45512yes—
126C4×C61#46812yes—
127C4×C61#46912yes—
128Dic61—82no—
129Dic61—82no—
130#2975D6111yescharacteristic
131#2547—611no—
132#1800—611no—
133#1546—612no—
134#1303—612no—
135C2×C61—21no—
136C2×C61—21no—
137C2×C61—82no—
138C2×C61#188511yescharacteristic
139C2×C61#189511yescharacteristic
140C2×C61#191511yescharacteristic
141C2×C4⋊Q8—611no—
142C2×#124—1221no—
143C2×C4×D4C2×D6111yescharacteristic
144#436—24no—
145#431C2×D6112yes—
146#423—612no—
147C2×#100—1221no—
148#407—22no—
149#397—614no—
150#391—1221no—
151#380—1222no—
152C4×C4⋊C4—611no—
153#343—1221no—
154#332—1224no—
155C61#940111yescharacteristic, complemented, Sylow
156C22×Q8—1221no—
157C22×D4D24411yescharacteristic
158C23×C4C22⋊D6112yes—
159C2×M16—24no—
160C2×M16—1222no—
161C4⋊Q8—1222no—
162C4⋊Q8—1222no—
163#124—2444no—
164C4×D4—22no—
165C4×D4—22no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4D24411yescharacteristic
170C2×C22⋊C4—1224no—
171C2×C22⋊C4C4×D6112yes—
172C2×C42—1221no—
173C2×C42C22×D6111yescharacteristic
174C4⋊C8—1222no—
175C4⋊C8—1222no—
176C4⋊C8C22⋊D6114yes—
177#100—2442no—
178C22⋊C8—24no—
179C22⋊C8—22no—
180C4×C8—22no—
181#95—612no—
182#95—1224no—
183C24#1175819812yes—
184C2×Q8—2441no—
185C2×Q8—2442no—
186C2×Q8—2442no—
187C2×Q8—2441no—
188C2×D4—21no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—1222no—
196C22×C4—1222no—
197C22×C4#1175819812yes—
198C22×C4C2×C4×D6111yescharacteristic
199C22×C4C2×D24411yescharacteristic
200C22×C4C2×C22⋊D6111yescharacteristic
201M16—84no—
202M16—2442no—
203M16—2442no—
204C2×C8—24no—
205C2×C8—2442no—
206C4⋊C4—22no—
207C4⋊C4—1224no—
208C4⋊C4—2442no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C22⋊C4—24no—
212C22⋊C4—2448no—
213C42—2442no—
214C42#1175822212yes—
215C42C2×C22⋊D6112yes—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23C2×#1175819811yescharacteristic
222Q8—4882no—
223Q8—4882no—
224D4—42no—
225D4—42no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4C4×C22⋊D6112yes—
239C2×C4#1451974611yescharacteristic
240C2×C4#1451975112yes—
241C2×C4#1451976011yescharacteristic
242C2×C4#1451980512yes—
243C2×C4#1451980511yescharacteristic
244C2×C4#1451981011yescharacteristic
245C8—44no—
246C8—4882no—
247C22—21no—
248C22—21no—
249C22—44no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—82no—
254C22#1683964111yescharacteristic
255C22#1683976411yescharacteristic
256C22#1683976811yescharacteristic
257C4—21no—
258C4—22no—
259C4—42no—
260C4—4882no—
261C4—4882no—
262C4#1683994012yes—
263C4#1684000812yes—
264C4#1684001512yes—
265C2—21no—
266C2—21no—
267C2—82no—
268C2#2144620711yescharacteristic
269C2#2144625711yescharacteristic
270C2#2144637111yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2975C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#2975D61
hypocenterC61#9401
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
3. #21444490C2semidirect
4. #21443721C2semidirect
155. C61#9401semidirect

Maximal subgroups

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

subgroupindex
#214508112
#214458112
#214444902
#214437212
C61×#29752
#940161