Finite Group Databasebeta

← C61×#12289 #29515722

Subgroups — C61×#12289 #29515722

Order 15616.

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

normal subgroups only

This group has 310 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×#3249C211yesmaximal, characteristic
2C61×#2235C212yesmaximal
3C61×#2086C211yesmaximal, characteristic
4C61×#1348C212yesmaximal
5C61×#1322C211yesmaximal, characteristic
6C61×#533—21no—
7C61×#477—22no—
8C61×#467—21no—
9C61×#467C2212yes—
10C61×#462—22no—
11C2×#107×C61C2211yescharacteristic
12C2×C4⋊C8×C61C2211yescharacteristic
13C61×#389—21no—
14C61×#367—22no—
15C61×#358—22no—
16C61×C22⋊C16C2212yes—
17C61×#340—21no—
18C61×#340C2211yescharacteristic
19C2×Q16×C61—21no—
20C2×Q16×C61D412yes—
21C22×C8×C61D411yescharacteristic
22C22×C8×C61C2311yescharacteristic
23C4⋊Q8×C61—21no—
24C4⋊Q8×C61—21no—
25#125×C61—41no—
26C22⋊Q8×C61—22no—
27C22⋊Q8×C61—41no—
28C4×Q8×C61—22no—
29C4×Q8×C61—41no—
30#117×C61—41no—
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—41no—
34C2×C42×C61D411yescharacteristic
35C2×C16×C61—22no—
36#107×C61—21no—
37#107×C61—22no—
38#107×C61D412yes—
39C4⋊C8×C61—22no—
40#103×C61—22no—
41#103×C61—22no—
42#95×C61—41no—
43C2×Q8×C61—22no—
44C2×Q8×C61—41no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61D811yescharacteristic
48C22×C4×C61D811yescharacteristic
49C22×C4×C61C2×D411yescharacteristic
50Q16×C61—42no—
51Q16×C61—81no—
52C2×C8×C61—21no—
53C2×C8×C61—41no—
54C2×C8×C61—41no—
55C2×C8×C61C2×D412yes—
56C4⋊C4×C61—22no—
57C4⋊C4×C61—22no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—82no—
67C22⋊C4×C61—42no—
68C42×C61—21no—
69C42×C61—21no—
70C42×C61—42no—
71C16×C61—42no—
72C23×C61C2×D811yescharacteristic
73Q8×C61—42no—
74Q8×C61—42no—
75Q8×C61—82no—
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—42no—
84C2×C4×C61—42no—
85C2×C4×C61—81no—
86C2×C4×C61—81no—
87C2×C4×C61—81no—
88C2×C4×C61—81no—
89C2×C4×C61—81no—
90C2×C4×C61SD3212yes—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
93C8×C61—22no—
94C8×C61—41no—
95#12289C6111yesmaximal, characteristic, direct product factor, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#44711yescharacteristic
99C22×C61C2×SD3211yescharacteristic
100C22×C61#51011yescharacteristic
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—41no—
104C4×C61—82no—
105C4×C61—82no—
106C4×C61—82no—
107C4×C61—161no—
108C4×C61#45611yescharacteristic
109C4×C61#45811yescharacteristic
110#3249C2×C6111yescharacteristic
111#2235C2×C6112yes—
112#2086C2×C6111yescharacteristic
113#1348C2×C6112yes—
114#1322C2×C6111yescharacteristic
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#161011yescharacteristic
118C2×C61#218511yescharacteristic
119C2×C61#219111yescharacteristic
120#533—21no—
121#477—22no—
122#467—21no—
123#467C22×C6112yes—
124#462—22no—
125C2×#107C22×C6111yescharacteristic
126C2×C4⋊C8C22×C6111yescharacteristic
127#389—21no—
128#367—22no—
129#358—22no—
130C22⋊C16C22×C6112yes—
131#340—21no—
132#340C22×C6111yescharacteristic
133C61#1228911yescharacteristic, direct product factor, Sylow
134C2×Q16—21no—
135C2×Q16D4×C6112yes—
136C22×C8D4×C6111yescharacteristic
137C22×C8C23×C6111yescharacteristic
138C4⋊Q8—21no—
139C4⋊Q8—21no—
140#125—41no—
141C22⋊Q8—22no—
142C22⋊Q8—41no—
143C4×Q8—22no—
144C4×Q8—41no—
145#117—41no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C42D4×C6111yescharacteristic
150C2×C16—22no—
151#107—21no—
152#107—22no—
153#107D4×C6112yes—
154C4⋊C8—22no—
155#103—22no—
156#103—22no—
157#95—41no—
158C2×Q8—22no—
159C2×Q8—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4D8×C6111yescharacteristic
163C22×C4D8×C6111yescharacteristic
164C22×C4C2×D4×C6111yescharacteristic
165Q16—42no—
166Q16—81no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8C2×D4×C6112yes—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—82no—
182C22⋊C4—42no—
183C42—21no—
184C42—21no—
185C42—42no—
186C16—42no—
187C23C2×D8×C6111yescharacteristic
188Q8—42no—
189Q8—42no—
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4SD32×C6112yes—
206C2×C4#120×C6111yescharacteristic
207C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22C61×#44711yescharacteristic
213C22C2×SD32×C6111yescharacteristic
214C22C61×#51011yescharacteristic
215C4—21no—
216C4—22no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—161no—
222C4C61×#45611yescharacteristic
223C4C61×#45811yescharacteristic
224C2—21no—
225C2—21no—
226C2C61×#161011yescharacteristic
227C2C61×#218511yescharacteristic
228C2C61×#219111yescharacteristic
subgroupG/H
center, socleC22×C61#447
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC23×C61C2×D8
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×C4⋊C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
95. #12289C61direct (N × H)
133. C61#12289direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32492
C61×#22352
C61×#20862
C61×#13482
C61×#13222
#1228961