Finite Group Databasebeta

← C61×#12282 #29515715

Subgroups — C61×#12282 #29515715

Order 15616.

344 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C61×#3189C211yesmaximal, characteristic
2C61×#2236C212yesmaximal, complemented
3C61×#2076C211yesmaximal, characteristic
4C61×#1348C212yesmaximal, complemented
5C61×#1314C211yesmaximal, characteristic
6C2×C22⋊Q8×C61—21no—
7C61×#484—22no—
8C61×#467—21no—
9C61×#467C2212yes—
10C61×#451—22no—
11C2×#107×C61C2211yescharacteristic
12C2×C22⋊C8×C61C2211yescharacteristic
13C61×#380—21no—
14C61×#366—22no—
15C61×#358—22no—
16C61×C22⋊C16C2212yes—
17C61×#340—21no—
18C61×#340C2211yescharacteristic
19C22×Q8×C61—21no—
20C23×C4×C61D411yescharacteristic
21C2×Q16×C61—21no—
22C2×Q16×C61D412yes—
23C22×C8×C61D411yescharacteristic
24C22×C8×C61C2311yescharacteristic
25C22⋊Q8×C61—22no—
26C22⋊Q8×C61—22no—
27C22⋊Q8×C61—41no—
28C22⋊Q8×C61—41no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61—41no—
33C2×C22⋊C4×C61—41no—
34C2×C22⋊C4×C61—41no—
35C2×C16×C61—22no—
36#107×C61—21no—
37#107×C61—22no—
38#107×C61D412yes—
39#103×C61—22no—
40#103×C61—22no—
41C22⋊C8×C61—22no—
42#95×C61—41no—
43C24×C61D811yescharacteristic
44C2×Q8×C61—22no—
45C2×Q8×C61—41no—
46C2×Q8×C61—81no—
47C2×Q8×C61—81no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—41no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61D811yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58Q16×C61—42no—
59Q16×C61—81no—
60C2×C8×C61—21no—
61C2×C8×C61—41no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D412yes—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C22⋊C4×C61—42no—
73C22⋊C4×C61—42no—
74C22⋊C4×C61—82no—
75C16×C61—42no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61Q3212yes—
81C23×C61C2×D811yescharacteristic
82Q8×C61—42no—
83Q8×C61—42no—
84Q8×C61—82no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—81no—
94C2×C4×C61—82no—
95C2×C4×C61—82no—
96C2×C4×C61—81no—
97C2×C4×C61—81no—
98C2×C4×C61—81no—
99C2×C4×C61—81no—
100C2×C4×C61—81no—
101C2×C4×C61—81no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C8×C61—22no—
105C8×C61—41no—
106#12282C6111yesmaximal, characteristic, direct product factor, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—22no—
110C22×C61—42no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—81no—
114C22×C61#44711yescharacteristic
115C22×C61C2×Q3211yescharacteristic
116C22×C61#51011yescharacteristic
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—82no—
120C4×C61—82no—
121C4×C61—161no—
122C4×C61—161no—
123C4×C61#45511yescharacteristic
124C4×C61#45811yescharacteristic
125#3189C2×C6111yescharacteristic
126#2236C2×C6112yescomplemented
127#2076C2×C6111yescharacteristic
128#1348C2×C6112yescomplemented
129#1314C2×C6111yescharacteristic
130C2×C61—21no—
131C2×C61—21no—
132C2×C61—42no—
133C2×C61#160711yescharacteristic
134C2×C61#218811yescharacteristic
135C2×C61#219011yescharacteristic
136C2×C22⋊Q8—21no—
137#484—22no—
138#467—21no—
139#467C22×C6112yes—
140#451—22no—
141C2×#107C22×C6111yescharacteristic
142C2×C22⋊C8C22×C6111yescharacteristic
143#380—21no—
144#366—22no—
145#358—22no—
146C22⋊C16C22×C6112yes—
147#340—21no—
148#340C22×C6111yescharacteristic
149C61#1228211yescharacteristic, direct product factor, Sylow
150C22×Q8—21no—
151C23×C4D4×C6111yescharacteristic
152C2×Q16—21no—
153C2×Q16D4×C6112yes—
154C22×C8D4×C6111yescharacteristic
155C22×C8C23×C6111yescharacteristic
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158C22⋊Q8—41no—
159C22⋊Q8—41no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—41no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—41no—
166C2×C16—22no—
167#107—21no—
168#107—22no—
169#107D4×C6112yes—
170#103—22no—
171#103—22no—
172C22⋊C8—22no—
173#95—41no—
174C24D8×C6111yescharacteristic
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—81no—
178C2×Q8—81no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4D8×C6111yescharacteristic
188C22×C4C2×D4×C6111yescharacteristic
189Q16—42no—
190Q16—81no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8C2×D4×C6112yes—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—82no—
206C16—42no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23Q32×C6112yes—
212C23C2×D8×C6111yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—82no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—81no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4#120×C6111yescharacteristic
234C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22C61×#44711yescharacteristic
245C22C2×Q32×C6111yescharacteristic
246C22C61×#51011yescharacteristic
247C4—21no—
248C4—41no—
249C4—82no—
250C4—82no—
251C4—161no—
252C4—161no—
253C4C61×#45511yescharacteristic
254C4C61×#45811yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2C61×#160711yescharacteristic
259C2C61×#218811yescharacteristic
260C2C61×#219011yescharacteristic
subgroupG/H
center, socleC22×C61#447
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC24×C61D8
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×C22⋊C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2236C2semidirect
4. C61×#1348C2semidirect
106. #12282C61direct (N × H)
126. #2236C2×C61semidirect
128. #1348C2×C61semidirect
149. C61#12282direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31892
C61×#22362
C61×#20762
C61×#13482
C61×#13142
#1228261