Finite Group Databasebeta

← C61×#13368 #29516801

Subgroups — C61×#13368 #29516801

Order 15616.

370 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2141C212yesmaximal
3C61×#1971C211yesmaximal, characteristic
4C61×#1386C212yesmaximal
5C61×#1377C211yesmaximal, characteristic
6C22×Q16×C61C2211yescharacteristic
7C61×#533—21no—
8C2×M32×C61C2212yes—
9C61×#501—24no—
10C61×#427—21no—
11C61×#427C2212yes—
12C2×#106×C61C2211yescharacteristic
13C2×#103×C61—21no—
14C2×#97×C61C2211yescharacteristic
15C61×#391—21no—
16C61×#358—24no—
17C22×Q8×C61—21no—
18C2×Q16×C61—22no—
19C2×Q16×C61—22no—
20C2×Q16×C61—21no—
21C2×Q16×C61Q812yescomplemented
22C22×C8×C61D411yescharacteristic
23C22×C8×C61C2311yescharacteristic
24C4⋊Q8×C61—22no—
25#125×C61—22no—
26C22⋊Q8×C61—42no—
27C4×Q8×C61—42no—
28#117×C61—22no—
29C2×C4⋊C4×C61—21no—
30C2×C42×C61D411yescharacteristic
31M32×C61—22no—
32M32×C61—22no—
33C2×C16×C61—22no—
34#107×C61—22no—
35#107×C61D414yes—
36#106×C61—22no—
37#106×C61—22no—
38#106×C61—22no—
39#103×C61—42no—
40#97×C61—22no—
41#95×C61—42no—
42C2×Q8×C61—22no—
43C2×Q8×C61—42no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C22×C4×C61—41no—
50C22×C4×C61—41no—
51C22×C4×C61D812yes—
52C22×C4×C61C2×D411yescharacteristic
53Q16×C61—24no—
54Q16×C61—42no—
55C2×C8×C61—21no—
56C2×C8×C61—21no—
57C2×C8×C61SD1612yes—
58C2×C8×C61C2×D412yes—
59C2×C8×C61C2×Q811yescharacteristic
60C2×C8×C61#4112yes—
61C2×C8×C61#4111yescharacteristic
62C4⋊C4×C61—24no—
63C4⋊C4×C61—44no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
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—84no—
76Q8×C61—81no—
77Q8×C61—81no—
78C2×C4×C61—22no—
79C2×C4×C61—42no—
80C2×C4×C61—44no—
81C2×C4×C61—42no—
82C2×C4×C61—81no—
83C2×C4×C61—81no—
84C2×C4×C61—82no—
85C2×C4×C61—81no—
86C2×C4×C61#12011yescharacteristic
87C2×C4×C61C22⋊Q811yescharacteristic
88C2×C4×C61#12411yescharacteristic
89C2×C4×C61C2×SD1611yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C61#13711yescharacteristic
92C8×C61—22no—
93C8×C61C22⋊Q812yes—
94C8×C61#12412yes—
95#13368C6111yesmaximal, characteristic, direct product factor, Sylow
96C22×C61—22no—
97C22×C61#44711yescharacteristic
98C22×C61#47411yescharacteristic
99C22×C61#48611yescharacteristic
100C4×C61—42no—
101C4×C61—84no—
102C4×C61—82no—
103C4×C61—161no—
104C4×C61#39311yescharacteristic
105C4×C61#44811yescharacteristic
106C4×C61#47611yescharacteristic
107C4×C61#48911yescharacteristic
108#3162C2×C6111yescharacteristic
109#2141C2×C6112yes—
110#1971C2×C6111yescharacteristic
111#1386C2×C6112yes—
112#1377C2×C6111yescharacteristic
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#202311yescharacteristic
116C2×C61#219112yes—
117C22×Q16C22×C6111yescharacteristic
118#533—21no—
119C2×M32C22×C6112yes—
120#501—24no—
121#427—21no—
122#427C22×C6112yes—
123C2×#106C22×C6111yescharacteristic
124C2×#103—21no—
125C2×#97C22×C6111yescharacteristic
126#391—21no—
127#358—24no—
128C61#1336811yescharacteristic, direct product factor, Sylow
129C22×Q8—21no—
130C2×Q16—22no—
131C2×Q16—22no—
132C2×Q16—21no—
133C2×Q16Q8×C6112yescomplemented
134C22×C8D4×C6111yescharacteristic
135C22×C8C23×C6111yescharacteristic
136C4⋊Q8—22no—
137#125—22no—
138C22⋊Q8—42no—
139C4×Q8—42no—
140#117—22no—
141C2×C4⋊C4—21no—
142C2×C42D4×C6111yescharacteristic
143M32—22no—
144M32—22no—
145C2×C16—22no—
146#107—22no—
147#107D4×C6114yes—
148#106—22no—
149#106—22no—
150#106—22no—
151#103—42no—
152#97—22no—
153#95—42no—
154C2×Q8—22no—
155C2×Q8—42no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4D8×C6112yes—
164C22×C4C2×D4×C6111yescharacteristic
165Q16—24no—
166Q16—42no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8SD16×C6112yes—
170C2×C8C2×D4×C6112yes—
171C2×C8C2×Q8×C6111yescharacteristic
172C2×C8#41×C6112yes—
173C2×C8#41×C6111yescharacteristic
174C4⋊C4—24no—
175C4⋊C4—44no—
176C4⋊C4—42no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C22⋊C4—42no—
180C42—21no—
181C42—21no—
182C42—42no—
183C16—42no—
184C23C2×D8×C6111yescharacteristic
185Q8—42no—
186Q8—42no—
187Q8—84no—
188Q8—81no—
189Q8—81no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—44no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4—81no—
198C2×C4#120×C6111yescharacteristic
199C2×C4C22⋊Q8×C6111yescharacteristic
200C2×C4#124×C6111yescharacteristic
201C2×C4C2×SD16×C6111yescharacteristic
202C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
203C2×C4#137×C6111yescharacteristic
204C8—22no—
205C8C22⋊Q8×C6112yes—
206C8#124×C6112yes—
207C22—22no—
208C22C61×#44711yescharacteristic
209C22C61×#47411yescharacteristic
210C22C61×#48611yescharacteristic
211C4—42no—
212C4—82no—
213C4—84no—
214C4—161no—
215C4C61×#39311yescharacteristic
216C4C61×#44811yescharacteristic
217C4C61×#47611yescharacteristic
218C4C61×#48911yescharacteristic
219C2—21no—
220C2—21no—
221C2C61×#202311yescharacteristic
222C2C61×#219112yes—
subgroupG/H
center, socleC22×C61#447
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC23×C61C2×D8
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#97×C61 ◁ G

Complements

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

NH ≅ G/Ntype
21. C2×Q16×C61Q8semidirect
95. #13368C61direct (N × H)
128. C61#13368direct (N × H)
133. C2×Q16Q8×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31622
C61×#21412
C61×#19712
C61×#13862
C61×#13772
#1336861