Finite Group Databasebeta

← C61×#10217 #29513650

Subgroups — C61×#10217 #29513650

Order 15616.

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3255C211yesmaximal, characteristic
2C61×#3237C212yesmaximal
3C61×#1995C211yesmaximal, characteristic
4C61×#1506C212yesmaximal
5C61×#1307C211yesmaximal, characteristic
6C61×#533C2212yes—
7C61×#533C2211yescharacteristic
8C61×#501—22no—
9C61×#491—22no—
10C61×#485—24no—
11C61×#477—22no—
12C61×#475—22no—
13C61×#475—22no—
14C61×#470—22no—
15C61×#462—22no—
16C61×#432C2212yes—
17C61×#423C2211yescharacteristic
18C61×#376C2211yescharacteristic
19C61×#339—22no—
20C61×#328—24no—
21C2×Q16×C61—22no—
22C2×M16×C61D412yes—
23C4⋊Q8×C61D412yes—
24C4⋊Q8×C61D412yes—
25C4⋊Q8×C61D412yes—
26#125×C61—22no—
27#125×C61—21no—
28C22⋊Q8×C61—22no—
29C22⋊Q8×C61—22no—
30C22⋊Q8×C61—22no—
31C4×Q8×C61—22no—
32C4×Q8×C61—22no—
33C4×Q8×C61—22no—
34#117×C61—21no—
35#117×C61—22no—
36C2×C42×C61—21no—
37C2×C42×C61C2311yescharacteristic
38#107×C61—24no—
39#106×C61—22no—
40#106×C61—24no—
41C4⋊C8×C61—22no—
42C4⋊C8×C61—22no—
43#103×C61—24no—
44#103×C61—24no—
45#103×C61—24no—
46C22⋊C8×C61D414yes—
47#97×C61—22no—
48#95×C61—22no—
49C2×Q8×C61—22no—
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C22×C4×C61—41no—
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61C2×D412yes—
55Q16×C61—82no—
56M16×C61—42no—
57C2×C8×C61—24no—
58C2×C8×C61—22no—
59C4⋊C4×C61—22no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—22no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—42no—
68C22⋊C4×C61—41no—
69C22⋊C4×C61—42no—
70C42×C61—22no—
71C42×C61—41no—
72C42×C61—41no—
73C42×C61—42no—
74C42×C61C2×D411yescharacteristic
75C42×C61C2×D412yes—
76C42×C61#4111yescharacteristic
77C23×C61#12711yescharacteristic
78Q8×C61—44no—
79Q8×C61—42no—
80Q8×C61—42no—
81Q8×C61—82no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61—82no—
90C2×C4×C61#12012yes—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61#12112yes—
93C2×C4×C61#12111yescharacteristic
94C8×C61—44no—
95C8×C61—42no—
96#10217C6111yesmaximal, characteristic, direct product factor, Sylow
97C22×C61—21no—
98C22×C61—22no—
99C22×C61#39211yescharacteristic
100C4×C61—21no—
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—82no—
104C4×C61—82no—
105C4×C61—82no—
106C4×C61—82no—
107C4×C61#45511yescharacteristic
108C4×C61#45611yescharacteristic
109#3255C2×C6111yescharacteristic
110#3237C2×C6112yes—
111#1995C2×C6111yescharacteristic
112#1506C2×C6112yes—
113#1307C2×C6111yescharacteristic
114C2×C61—41no—
115C2×C61#200711yescharacteristic
116C2×C61#200912yes—
117#533C22×C6111yescharacteristic
118#533C22×C6112yes—
119#501—22no—
120#491—22no—
121#485—24no—
122#477—22no—
123#475—22no—
124#475—22no—
125#470—22no—
126#462—22no—
127#432C22×C6112yes—
128#423C22×C6111yescharacteristic
129#376C22×C6111yescharacteristic
130#339—22no—
131#328—24no—
132C61#1021711yescharacteristic, direct product factor, Sylow
133C2×Q16—22no—
134C2×M16D4×C6112yes—
135C4⋊Q8D4×C6112yes—
136C4⋊Q8D4×C6112yes—
137C4⋊Q8D4×C6112yes—
138#125—22no—
139#125—21no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146#117—21no—
147#117—22no—
148C2×C42—21no—
149C2×C42C23×C6111yescharacteristic
150#107—24no—
151#106—22no—
152#106—24no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155#103—24no—
156#103—24no—
157#103—24no—
158C22⋊C8D4×C6114yes—
159#97—22no—
160#95—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—22no—
164C22×C4—41no—
165C22×C4C2×D4×C6111yescharacteristic
166C22×C4C2×D4×C6112yes—
167Q16—82no—
168M16—42no—
169C2×C8—24no—
170C2×C8—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—42no—
182C42—22no—
183C42—41no—
184C42—41no—
185C42—42no—
186C42C2×D4×C6111yescharacteristic
187C42C2×D4×C6112yes—
188C42#41×C6111yescharacteristic
189C23#127×C6111yescharacteristic
190Q8—44no—
191Q8—42no—
192Q8—42no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—82no—
202C2×C4#120×C6112yes—
203C2×C4#120×C6111yescharacteristic
204C2×C4#121×C6112yes—
205C2×C4#121×C6111yescharacteristic
206C8—44no—
207C8—42no—
208C22—21no—
209C22—22no—
210C22C61×#39211yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—82no—
217C4—82no—
218C4C61×#45511yescharacteristic
219C4C61×#45611yescharacteristic
220C2—41no—
221C2C61×#200711yescharacteristic
222C2C61×#200912yes—
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC23×C61#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
96. #10217C61direct (N × H)
132. C61#10217direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32552
C61×#32372
C61×#19952
C61×#15062
C61×#13072
#1021761