Finite Group Databasebeta

← #29593275

Subgroups — #29593275

Order 15616.

354 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 67 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#21457129C211yesmaximal, characteristic
2#21447999C212yesmaximal, complemented
3#21443827C212yesmaximal, complemented
4#21443759C211yesmaximal, characteristic, complemented
5C61×#2086C211yesmaximal, characteristic, complemented
6#16840312—21no—
7#16840043—22no—
8#16839998—21no—
9#16839998C2212yes—
10#16839958—22no—
11#16839587—22no—
12#16839562—22no—
13C22⋊#11758185C2212yes—
14C2×#107×C61C2211yescharacteristic
15C2×C4⋊C8×C61C2211yescharacteristic
16C61×#389—21no—
17C61×#340—21no—
18C61×#340C2211yescharacteristic
19C2×#11758222—41no—
20C2×D488—21no—
21C2×D488D412yes—
22#14519777—21no—
23#14519774—21no—
24#14519765—41no—
25#14519751—22no—
26#14519751—41no—
27C4×D244—22no—
28C4×D244—41no—
29C2×#11758185—22no—
30#14519711—21no—
31#14519711D412yes—
32#14519699—22no—
33#14519699—22no—
34C22×C8×C61D411yescharacteristic
35C22×C8×C61C2311yescharacteristic
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—41no—
39C2×C42×C61D411yescharacteristic
40#107×C61—22no—
41C4⋊C8×C61—22no—
42#95×C61—41no—
43C22×C4×C61—41no—
44C22×C4×C61—41no—
45C22×C4×C61D811yescharacteristic
46C22×C4×C61D811yescharacteristic
47C22×C4×C61C2×D411yescharacteristic
48C2×C22⋊D61—42no—
49#11758222—82no—
50#11758222—82no—
51C2×D244—22no—
52C2×D244—41no—
53C2×D244—41no—
54C2×C4×D61—42no—
55C2×Dic122—41no—
56C2×C8×C61—21no—
57C2×C8×C61—41no—
58C2×C8×C61—41no—
59C2×C8×C61C2×D412yes—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—82no—
65C42×C61—21no—
66C42×C61—21no—
67#11758198—42no—
68#11758198—42no—
69C4⋊Dic61—22no—
70C4⋊Dic61—41no—
71D488—42no—
72D488—81no—
73#11758185—42no—
74C23×C61C2×D811yescharacteristic
75C22×D61—42no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—41no—
82C2×C4×C61—42no—
83C2×C4×C61—81no—
84C2×C4×C61—81no—
85C2×C4×C61—81no—
86C2×C4×C61—81no—
87C2×C4×C61—81no—
88C2×C4×C61D1612yes—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C22⋊D61—82no—
92C22⋊D61—82no—
93C2×Dic61—42no—
94D244—42no—
95D244—42no—
96D244—82no—
97D244—82no—
98C4×D61—84no—
99Dic122—82no—
100C8×C61—22no—
101C8×C61—41no—
102#12288—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—21no—
105C22×C61#44711yescharacteristic
106C22×C61C2×D1611yescharacteristic
107C22×C61#50911yescharacteristic
108C2×D61—82no—
109C2×D61—82no—
110C2×D61—82no—
111C4×C61—21no—
112C4×C61—22no—
113C4×C61—41no—
114C4×C61—82no—
115C4×C61—161no—
116C4×C61#45611yescharacteristic
117C4×C61#45811yescharacteristic
118Dic61—82no—
119#3245—611no—
120#2232—612no—
121#2086D6111yescharacteristic, complemented
122#1347—612no—
123#1322—611no—
124C2×C61—21no—
125C2×C61—21no—
126C2×C61#161011yescharacteristic
127C2×C61#218411yescharacteristic
128C2×C61#219111yescharacteristic
129D61—162no—
130#532—1221no—
131#474—1222no—
132#466—612no—
133#466—1221no—
134#459—1222no—
135C2×#107C2×D6111yescharacteristic
136C2×C4⋊C8C2×D6111yescharacteristic
137#389—21no—
138#366—1222no—
139#357—1222no—
140C22⋊C16—612no—
141#340—21no—
142#340C2×D6111yescharacteristic
143C61#1228811yescharacteristic, complemented, Sylow
144C2×#41—2441no—
145C2×D8—612no—
146C2×D8—1221no—
147C22×C8C22⋊D6111yescharacteristic
148C22×C8C22×D6111yescharacteristic
149C4⋊Q8—1221no—
150#127—1221no—
151#124—2441no—
152#121—1222no—
153#121—2441no—
154C4×D4—1222no—
155C4×D4—2441no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—41no—
159C2×C42C22⋊D6111yescharacteristic
160C2×C16—1222no—
161#107—22no—
162#107—612no—
163#107—1221no—
164C4⋊C8—22no—
165#102—1222no—
166#102—1222no—
167#95—41no—
168#41—4882no—
169#41—4882no—
170C2×Q8—2441no—
171C2×D4—1222no—
172C2×D4—2441no—
173C2×D4—2441no—
174C2×D4—2442no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—2442no—
178C22×C4#1175819911yescharacteristic
179C22×C4#1175819911yescharacteristic
180C22×C4C2×C22⋊D6111yescharacteristic
181D8—4881no—
182D8—2442no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8D4×D6112yes—
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—82no—
192C4⋊C4—1222no—
193C4⋊C4—2441no—
194C22⋊C4—2442no—
195C22⋊C4—2442no—
196C42—21no—
197C42—21no—
198C16—2442no—
199C23—2442no—
200C23C2×#1175819911yescharacteristic
201Q8—4882no—
202D4—4882no—
203D4—4882no—
204D4—4882no—
205D4—4882no—
206D4—2442no—
207D4—2442no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—4884no—
221C2×C4—2442no—
222C2×C4#1451971812yes—
223C2×C4#1451974511yescharacteristic
224C2×C4#1451980211yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—4882no—
230C22—4882no—
231C22—4882no—
232C22#1683989511yescharacteristic
233C22C2×#1451971811yescharacteristic
234C22#1684019711yescharacteristic
235C4—22no—
236C4—21no—
237C4—41no—
238C4—82no—
239C4—161no—
240C4—4882no—
241C4#1683994411yescharacteristic
242C4#1683995111yescharacteristic
243C2—21no—
244C2—21no—
245C2—9762no—
246C2#2144482111yescharacteristic
247C2#2144773011yescharacteristic
248C2#2144776911yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2086C2
socleC22×C61#447
prime radical#21457129C2
hypercenter#2086D61
hypocenterC61#12288
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2086

Complements

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

NH ≅ G/Ntype
2. #21447999C2semidirect
3. #21443827C2semidirect
4. #21443759C2semidirect
5. C61×#2086C2semidirect
121. #2086D61semidirect
143. C61#12288semidirect

Maximal subgroups

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

subgroupindex
#214571292
#214479992
#214438272
#214437592
C61×#20862
#1228861