Finite Group Databasebeta

← C61×#10037 #29513470

Subgroups — C61×#10037 #29513470

Order 15616.

476 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3162C211yesmaximal, characteristic
2C61×#3104C212yesmaximal
3C61×#1985C211yesmaximal, characteristic
4C61×#1481C212yesmaximal
5C61×#1275C211yesmaximal, characteristic
6C61×#533C2212yes—
7C2×C4×Q8×C61C2211yescharacteristic
8C61×#501—22no—
9C61×#501—22no—
10C61×#484—22no—
11C61×#477—22no—
12C61×#462—22no—
13C61×#451—22no—
14C4×Q16×C61—24no—
15C61×#431C2212yes—
16C61×#427—22no—
17C2×C4⋊C8×C61C2211yescharacteristic
18C2×#97×C61C2211yescharacteristic
19C61×#336—22no—
20C61×Q8⋊C8—24no—
21C22×Q8×C61D411yescharacteristic
22C2×Q16×C61—24no—
23C22×C8×C61—21no—
24C22×C8×C61D412yes—
25C4⋊Q8×C61D412yes—
26C4⋊Q8×C61D412yes—
27#125×C61—22no—
28C22⋊Q8×C61—22no—
29C22⋊Q8×C61—22no—
30C4×Q8×C61—22no—
31C4×Q8×C61—22no—
32C4×Q8×C61—22no—
33C4×Q8×C61—22no—
34#117×C61—22no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61D411yescharacteristic
37C2×C42×C61—21no—
38C2×C42×C61C2311yescharacteristic
39#107×C61—22no—
40#107×C61—22no—
41#107×C61—24no—
42#106×C61—24no—
43C4⋊C8×C61—22no—
44C4⋊C8×C61—22no—
45#103×C61—24no—
46#103×C61—24no—
47C22⋊C8×C61—22no—
48#97×C61—22no—
49C4×C8×C61D414yes—
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61—42no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61#4111yescharacteristic
59Q16×C61—48no—
60C2×C8×C61—22no—
61C2×C8×C61—22no—
62C2×C8×C61—24no—
63C2×C8×C61—41no—
64C2×C8×C61—42no—
65C2×C8×C61Q1614yescomplemented
66C4⋊C4×C61—22no—
67C4⋊C4×C61—22no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—42no—
74C22⋊C4×C61—42no—
75C42×C61—41no—
76C42×C61—41no—
77C42×C61—42no—
78C42×C61C2×D412yes—
79C42×C61C2×D412yes—
80C23×C61#12111yescharacteristic
81Q8×C61—24no—
82Q8×C61—42no—
83Q8×C61—44no—
84Q8×C61—44no—
85C2×C4×C61—22no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61#12012yes—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61#12112yes—
97C2×C4×C61#12711yescharacteristic
98C2×C4×C61C2×Q1612yes—
99C2×C4×C61#13712yes—
100C8×C61—24no—
101C8×C61—44no—
102C8×C61—81no—
103#10037C6111yesmaximal, characteristic, direct product factor, Sylow
104C22×C61—21no—
105C22×C61—21no—
106C22×C61#39211yescharacteristic
107C22×C61#46212yes—
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—42no—
111C4×C61—82no—
112C4×C61—81no—
113C4×C61—82no—
114C4×C61#45112yes—
115C4×C61#49411yescharacteristic
116C4×C61#49711yescharacteristic
117#3162C2×C6111yescharacteristic
118#3104C2×C6112yes—
119#1985C2×C6111yescharacteristic
120#1481C2×C6112yes—
121#1275C2×C6111yescharacteristic
122C2×C61—22no—
123C2×C61#201011yescharacteristic
124C2×C61#201611yescharacteristic
125C2×C61#201711yescharacteristic
126#533C22×C6112yes—
127C2×C4×Q8C22×C6111yescharacteristic
128#501—22no—
129#501—22no—
130#484—22no—
131#477—22no—
132#462—22no—
133#451—22no—
134C4×Q16—24no—
135#431C22×C6112yes—
136#427—22no—
137C2×C4⋊C8C22×C6111yescharacteristic
138C2×#97C22×C6111yescharacteristic
139#336—22no—
140Q8⋊C8—24no—
141C61#1003711yescharacteristic, direct product factor, Sylow
142C22×Q8D4×C6111yescharacteristic
143C2×Q16—24no—
144C22×C8—21no—
145C22×C8D4×C6112yes—
146C4⋊Q8D4×C6112yes—
147C4⋊Q8D4×C6112yes—
148#125—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155#117—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D4×C6111yescharacteristic
158C2×C42—21no—
159C2×C42C23×C6111yescharacteristic
160#107—22no—
161#107—22no—
162#107—24no—
163#106—24no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166#103—24no—
167#103—24no—
168C22⋊C8—22no—
169#97—22no—
170C4×C8D4×C6114yes—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—42no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D4×C6111yescharacteristic
178C22×C4C2×D4×C6111yescharacteristic
179C22×C4#41×C6111yescharacteristic
180Q16—48no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—24no—
184C2×C8—41no—
185C2×C8—42no—
186C2×C8Q16×C6114yescomplemented
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C22⋊C4—42no—
196C42—41no—
197C42—41no—
198C42—42no—
199C42C2×D4×C6112yes—
200C42C2×D4×C6112yes—
201C23#121×C6111yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—44no—
205Q8—44no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4#120×C6112yes—
216C2×C4#120×C6111yescharacteristic
217C2×C4#121×C6112yes—
218C2×C4#127×C6111yescharacteristic
219C2×C4C2×Q16×C6112yes—
220C2×C4#137×C6112yes—
221C8—24no—
222C8—44no—
223C8—81no—
224C22—21no—
225C22—21no—
226C22C61×#39211yescharacteristic
227C22C61×#46212yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—82no—
232C4—81no—
233C4—82no—
234C4C61×#45112yes—
235C4C61×#49411yescharacteristic
236C4C61×#49711yescharacteristic
237C2—22no—
238C2C61×#201011yescharacteristic
239C2C61×#201611yescharacteristic
240C2C61×#201711yescharacteristic
subgroupG/H
centerC2×C4×C61#127
commutator, Frattini, cosocleC2×C42C23×C61
socleC22×C61#392
prime radicalC23×C61#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
65. C2×C8×C61Q16semidirect
103. #10037C61direct (N × H)
141. C61#10037direct (N × H)
186. C2×C8Q16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31622
C61×#31042
C61×#19852
C61×#14812
C61×#12752
#1003761