Finite Group Databasebeta

← C61×#11538 #29514971

Subgroups — C61×#11538 #29514971

Order 15616.

334 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2930C211yesmaximal, characteristic
2C61×#2166C212yesmaximal, complemented
3C61×#1321C212yesmaximal, complemented
4C61×#1320C212yesmaximal, complemented
5C2×#131×C61C411yescharacteristic
6C22×M16×C61C411yescharacteristic
7C61×#525C411yescharacteristic
8C61×#436—22no—
9C61×#435—22no—
10C61×#424C411yescharacteristic
11C61×#408C2211yescharacteristic
12C61×#407C2211yescharacteristic
13C61×#405C2211yescharacteristic
14C61×#364—22no—
15C61×#349C2214yes—
16C61×#347—22no—
17C2×#41×C61C2×C411yescharacteristic
18C23×C4×C61C2×C411yescharacteristic
19#131×C61—42no—
20C2×M16×C61—21no—
21C2×M16×C61—21no—
22C2×M16×C61—21no—
23C2×M16×C61—42no—
24C2×M16×C61C2×C411yescharacteristic
25C2×M16×C61C2311yescharacteristic
26C22×C8×C61—21no—
27C22×C8×C61C2×C411yescharacteristic
28C22×C8×C61C2×C411yescharacteristic
29#123×C61—21no—
30C22⋊Q8×C61—21no—
31#121×C61—21no—
32#120×C61—21no—
33C4×D4×C61—22no—
34#117×C61C2×C411yescharacteristic
35M32×C61—24no—
36C4⋊C8×C61—22no—
37C22⋊C8×C61—22no—
38C22⋊C8×C61—22no—
39#97×C61D412yes—
40C4×C8×C61D412yes—
41C24×C61M1611yescharacteristic
42#41×C61—41no—
43#41×C61—41no—
44C2×Q8×C61M1611yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61—22no—
47C2×D4×C61M1611yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61M1611yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55M16×C61—41no—
56M16×C61—42no—
57M16×C61—42no—
58M16×C61—42no—
59M16×C61—41no—
60C2×C8×C61—22no—
61C2×C8×C61—21no—
62C2×C8×C61—21no—
63C2×C8×C61—42no—
64C2×C8×C61—41no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C2×D412yes—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—21no—
70C22⋊C4×C61—22no—
71C22⋊C4×C61—22no—
72C22⋊C4×C61—21no—
73C42×C61C22⋊C412yes—
74C16×C61—44no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—41no—
78C23×C61—81no—
79C23×C61C2×M1611yescharacteristic
80Q8×C61—41no—
81D4×C61—41no—
82D4×C61—42no—
83D4×C61—82no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C2×M1611yescharacteristic
97C8×C61—22no—
98C8×C61—21no—
99C8×C61—41no—
100C8×C61—41no—
101C8×C61#10012yes—
102#11538C6111yesmaximal, characteristic, direct product factor, Sylow
103C22×C61—21no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—42no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61—82no—
111C22×C61#40711yescharacteristic
112C4×C61—21no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—41no—
116C4×C61#41011yescharacteristic
117C4×C61C2×#10011yescharacteristic
118#2930C2×C6111yescharacteristic
119#2166C2×C6112yescomplemented
120#1321C2×C6112yescomplemented
121#1320C2×C6112yescomplemented
122C2×C61—21no—
123C2×C61—41no—
124C2×C61—81no—
125C2×C61—81no—
126C2×C61#146611yescharacteristic
127C2×#131C4×C6111yescharacteristic
128C22×M16C4×C6111yescharacteristic
129#525C4×C6111yescharacteristic
130#436—22no—
131#435—22no—
132#424C4×C6111yescharacteristic
133#408C22×C6111yescharacteristic
134#407C22×C6111yescharacteristic
135#405C22×C6111yescharacteristic
136#364—22no—
137#349C22×C6114yes—
138#347—22no—
139C61#1153811yescharacteristic, direct product factor, Sylow
140C2×#41C2×C4×C6111yescharacteristic
141C23×C4C2×C4×C6111yescharacteristic
142#131—42no—
143C2×M16—21no—
144C2×M16—21no—
145C2×M16—21no—
146C2×M16—42no—
147C2×M16C2×C4×C6111yescharacteristic
148C2×M16C23×C6111yescharacteristic
149C22×C8—21no—
150C22×C8C2×C4×C6111yescharacteristic
151C22×C8C2×C4×C6111yescharacteristic
152#123—21no—
153C22⋊Q8—21no—
154#121—21no—
155#120—21no—
156C4×D4—22no—
157#117C2×C4×C6111yescharacteristic
158M32—24no—
159C4⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—22no—
162#97D4×C6112yes—
163C4×C8D4×C6112yes—
164C24M16×C6111yescharacteristic
165#41—41no—
166#41—41no—
167C2×Q8M16×C6111yescharacteristic
168C2×D4—21no—
169C2×D4—22no—
170C2×D4M16×C6111yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4M16×C6111yescharacteristic
177C22×C4C22×C4×C6111yescharacteristic
178M16—41no—
179M16—42no—
180M16—42no—
181M16—42no—
182M16—41no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8C22⋊C4×C6111yescharacteristic
189C2×C8C22⋊C4×C6111yescharacteristic
190C2×C8C2×D4×C6112yes—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—21no—
196C42C22⋊C4×C6112yes—
197C16—44no—
198C23—21no—
199C23—21no—
200C23—41no—
201C23—81no—
202C23C2×M16×C6111yescharacteristic
203Q8—41no—
204D4—41no—
205D4—42no—
206D4—82no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4C2×C22⋊C4×C6111yescharacteristic
219C2×C4C2×M16×C6111yescharacteristic
220C8—22no—
221C8—21no—
222C8—41no—
223C8—41no—
224C8#100×C6112yes—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—82no—
233C22C61×#40711yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4C61×#41011yescharacteristic
239C4C2×#100×C6111yescharacteristic
240C2—21no—
241C2—41no—
242C2—81no—
243C2—81no—
244C2C61×#146611yescharacteristic
subgroupG/H
centerC4×C61#410
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×M16C23×C61
socleC2×C61#1466
prime radicalC61×#525C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C2×C8×C61 ◁ C61×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2166C2semidirect
3. C61×#1321C2semidirect
4. C61×#1320C2semidirect
102. #11538C61direct (N × H)
119. #2166C2×C61semidirect
120. #1321C2×C61semidirect
121. #1320C2×C61semidirect
139. C61#11538direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#29302
C61×#21662
C61×#13212
C61×#13202
#1153861