Finite Group Databasebeta

← #29589513

Subgroups — #29589513

Order 15616.

348 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 91 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#21447635C212yesmaximal, complemented
2#21443757C212yesmaximal, complemented
3#21443755C212yesmaximal, complemented
4C61×#2929C211yesmaximal, characteristic
5#16839583—22no—
6#16839544C2214yes—
7#16839540—22no—
8C2×#131×C61C411yescharacteristic
9C23×C8×C61C411yescharacteristic
10C61×#525C411yescharacteristic
11C61×#435—22no—
12C8×D4×C61—22no—
13C61×#424C411yescharacteristic
14C61×#408C2211yescharacteristic
15C61×#407C2211yescharacteristic
16C61×#405C2211yescharacteristic
17#14519717—24no—
18C2×#41×C61C2×C411yescharacteristic
19C23×C4×C61C2×C411yescharacteristic
20#131×C61—42no—
21C2×M16×C61—21no—
22C2×M16×C61C2×C411yescharacteristic
23C2×M16×C61C2311yescharacteristic
24C22×C8×C61—21no—
25C22×C8×C61—21no—
26C22×C8×C61—21no—
27C22×C8×C61—42no—
28C22×C8×C61C2×C411yescharacteristic
29C22×C8×C61C2×C411yescharacteristic
30#123×C61—21no—
31C22⋊Q8×C61—21no—
32#121×C61—21no—
33#120×C61—21no—
34C4×D4×C61—22no—
35#117×C61C2×C411yescharacteristic
36C4⋊C8×C61—22no—
37C22⋊C8×C61—22no—
38C22⋊C8×C61—22no—
39#97×C61D412yes—
40C4×C8×C61D412yes—
41C24×C61M1611yescharacteristic
42#41×C61—41no—
43#41×C61—41no—
44C2×Q8×C61M1611yescharacteristic
45C2×D4×C61—22no—
46C2×D4×C61—21no—
47C2×D4×C61M1611yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61M1611yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55M16×C61—41no—
56M16×C61—42no—
57M16×C61—41no—
58C2×C8×C61—22no—
59C2×C8×C61—21no—
60C2×C8×C61—21no—
61C2×C8×C61—42no—
62C2×C8×C61—42no—
63C2×C8×C61—42no—
64C2×C8×C61—41no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C2×D412yes—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—21no—
70C22⋊C4×C61—22no—
71C22⋊C4×C61—22no—
72C22⋊C4×C61—21no—
73C42×C61C22⋊C412yes—
74#11758185—44no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—41no—
78C23×C61—42no—
79C23×C61C2×M1611yescharacteristic
80Q8×C61—41no—
81D4×C61—41no—
82D4×C61—44no—
83D4×C61—42no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C2×M1611yescharacteristic
97C8×C61—22no—
98C8×C61—21no—
99C8×C61—41no—
100C8×C61—41no—
101C8×C61#10012yes—
102#11537—611nomaximal, Sylow
103C22×C61—22no—
104C22×C61—21no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61#40711yescharacteristic
113C4×C61—21no—
114C4×C61—42no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C61#41011yescharacteristic
118C4×C61C2×#10011yescharacteristic
119#2929D6111yescharacteristic
120#2166—612no—
121#1321—612no—
122#1320—612no—
123C2×C61—21no—
124C2×C61—42no—
125C2×C61—41no—
126C2×C61—81no—
127C2×C61#146611yescharacteristic
128C2×#131Dic6111yescharacteristic
129C23×C8Dic6111yescharacteristic
130#525Dic6111yescharacteristic
131#435—22no—
132C8×D4—22no—
133#424Dic6111yescharacteristic
134#408C2×D6111yescharacteristic
135#407C2×D6111yescharacteristic
136#405C2×D6111yescharacteristic
137#364—1222no—
138#349—614no—
139#347—1222no—
140C61#1153711yescharacteristic, complemented, Sylow
141C2×#41C2×Dic6111yescharacteristic
142C23×C4C2×Dic6111yescharacteristic
143#131—42no—
144C2×M16—21no—
145C2×M16C2×Dic6111yescharacteristic
146C2×M16C22×D6111yescharacteristic
147C22×C8—21no—
148C22×C8—21no—
149C22×C8—21no—
150C22×C8—42no—
151C22×C8C2×Dic6111yescharacteristic
152C22×C8C2×Dic6111yescharacteristic
153#123—21no—
154C22⋊Q8—21no—
155#121—21no—
156#120—21no—
157C4×D4—22no—
158#117C2×Dic6111yescharacteristic
159M32—1224no—
160C4⋊C8—22no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163#97C22⋊D6112yes—
164C4×C8C22⋊D6112yes—
165C24#1175819411yescharacteristic
166#41—41no—
167#41—41no—
168C2×Q8#1175819411yescharacteristic
169C2×D4—22no—
170C2×D4—21no—
171C2×D4#1175819411yescharacteristic
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4#1175819411yescharacteristic
178C22×C4C22×Dic6111yescharacteristic
179M16—41no—
180M16—42no—
181M16—41no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—41no—
189C2×C8C22⋊Dic6111yescharacteristic
190C2×C8C22⋊Dic6111yescharacteristic
191C2×C8C2×C22⋊D6112yes—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—21no—
197C42C22⋊Dic6112yes—
198C16—2444no—
199C23—21no—
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#1175819411yescharacteristic
204Q8—41no—
205D4—41no—
206D4—44no—
207D4—42no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4C2×C22⋊Dic6111yescharacteristic
220C2×C4C2×#1175819411yescharacteristic
221C8—22no—
222C8—21no—
223C8—41no—
224C8—41no—
225C8#1451969412yes—
226C22—22no—
227C22—21no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22#1683972611yescharacteristic
236C4—21no—
237C4—42no—
238C4—41no—
239C4—41no—
240C4#1683973611yescharacteristic
241C4C2×#1451969411yescharacteristic
242C2—21no—
243C2—42no—
244C2—41no—
245C2—81no—
246C2#2144416011yescharacteristic
subgroupG/H
centerC4#16839736
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#2929C2
socleC2×C61#1466
prime radicalC61×#525C4
cosocleC2×M16×C61C23
hypercenter#2929D61
hypocenterC61#11537
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ #405 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #21447635C2semidirect
2. #21443757C2semidirect
3. #21443755C2semidirect
140. C61#11537semidirect

Maximal subgroups

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

subgroupindex
#214476352
#214437572
#214437552
C61×#29292
#1153761